1...... ············ ~o jjr?Y - Unsworks.unsw.edu.au.

Surname or Family name: Turner

First name: Alexander

THE UNIVERSITY OF NEW SOUTH WALES Thesis/Project Report Sheet

Other name/s: William Lyttleton

Abbreviation for degree as given in the University calendar: PhD

School: Mechanical and Manufacturing Engineering Faculty: Engineering

Title: A Theoretical and Experimental Investigation of Stress Distribution and Remodelling of a Femur Implanted with a Femoral Prosthesis

Abstract 350 words maximum: Bone loss around uncemented hip replacement stems is associated with stress shielding, with bone resorption occurring in accordance with "Wolff's Law". Extensive bone loss may cause implant or bone failure, and complicate revision procedures. This thesis was concerned with developing a mathematical formulation of "Wolff's Law", which was combined with finite element modelling to simulate time-dependent adaptive bone remodelling.

Experimental and finite element investigations were undertaken to determine the alteration in strain distribution of a femur caused by reconstruction with a cobalt-chrome hip prosthesis (Margron). A site-specific, strain-adaptive bone remodelling theory was developed to predict changes in apparent density due to these changes in strain, based on an equivalent strain stimulus. Time-dependent density changes were compared with radiographic clinical data at the 7 Gruen zones. Remodelling was simulated for 2 additional femora implanted with titanium alloy (Stability) and composite (Epoch) stems. The influences of implant-bone contact conditions, femoral head position, dead zone width, postoperative activity level and prosthesis stiffness on periprosthetic bone remodelling were investigated.

Severe proximal stress shielding medially and laterally was evident for the Margron implant. This was also the case for the Stability and Epoch Stems, although to a lesser extent distally. The finite element model was validated by comparison with experimental strains. Mesh refinement led to adoption of a 5 mm element size, with variable material properties applied to the integration points.

Bone density changes in the Gruen zones were correlated with the radiographic clinical data at 1, 2 and 3 year time points for the Margron model, and at 2 years for the Stability and Epoch models. All correlations were significant (ff > 0.67, p < 0.02), with average errors of less than 5.4% at 2 years. This is the first report of bone density changes measured in Gruen zones correlating with radiographic measurements. Previous studies have overestimated proximal bone loss in the calcar region.

A strain-adaptive bone remodeling theory was developed, which simulated bone density changes in accordance with those seen clinically. This tool could be employed for pre-clinical testing of new implants, investigation of design modifications, and patient-specific implant selection.

Declaration relating to disposition of project report/thesis

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I also authorise th publication by University Microfilms of a 350 word abstract in Dissertation Abstracts International (applicable

~ ' '" .# /"'-; 7 _,.., j

to doctoral s o -. . 1. i s;g;~rr;;;;····················· . ~~1...... ············ ~o jjr?Y ........ .

The niversity recognises that there may be exceptional circumstances requiring restrictions on copying or conditions on use. Requests for restriction for a period of up to 2 years must be made in writing to the Registrar. Requests for a longer period of restriction may be considered in exceptional circumstances if accompanied by a letter of support from the Supervisor or Head of School. Such requests must be submitted with the thesis/project report.

FOR OFFICE USE ONLY Date of completion of requirements for Award:

/c~tr

A THEORETICAL AND EXPERIMENTAL INVESTIGATION OF STRESS DISTRIBUTION AND

RElVIODELLING OF A FEMUR IMPLANTED WITH A FEMORAL PROSTHESIS

A THESIS SUBMITTED IN FULFILMENT

OF THE REQUIREMENTS FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

Alexander W. L. Turner

School of Mechanical and Manufacturing Engineering,

The University of New South Wales.

November 2003

I hereby declare that this submission is my own work and to

the best of my knowledge it contains no materials previously

published or written by another person, nor material which to

a substantial extent has been accepted for the award of any

other degree or diploma at UNSW or any other educational

institution, except where due acknowledgement is made in

the thesis. Any contribution made to the research by others,

with whom I have worked at UNSW or elsewhere, is explicitly

acknowledged in the thesis.

I also declare that the intellectual content of this thesis is the

product of my own work, except to the extent that assistance

from others in the project's design and conception or in style,

presentation and linguistic expression is acknowledged.

""' A. W. L. Turner

z8503529

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"By seeking and blundering we learn."

Johann Wolfgang Von Goethe

ii

Executive Summary

Abstract

Bone loss around uncemented hip replacement stems is associated with stress shield

ing, with bone resorption occurring in accordance with "Wolff's Law". Extensive

bone loss may cause implant or bone failure, and complicate revision procedures.

This thesis was concerned with development of a mathematical formulation of

"\:Volff's Law", which was combined with finite element modelling to simulate time

dependent adaptive bone remodelling changes.

Experimental and finite element investigations were undertaken to determine the

alteration in strain distribution of a femur caused by reconstruction with a cobalt

chrome hip prosthesis (Margron). A site-specific, strain-adaptive bone remodelling

theory was developed to predict changes in apparent density due to these changes in

strain, based on an equivalent strain stimulus equal to the magnitude of the strain

tensor. Time-dependent density changes were compared with radiographic clinical

measurements from the 7 Gruen zones. Remodelling was simulated for 2 additional

femora implanted with titanium alloy (Stability) and composite (Epoch) stems.

The influences of implant-bone contact conditions, femoral head position, dead

zone width, postoperative activity level and prosthesis stiffness on periprosthetic

bone remodelling were investigated.

Severe proximal stress shielding medially and laterally was evident for the Mar

gron implant. This was also the case for the Stability and Epoch stems, although

to a lesser extent distally. The finite element model was validated by comparison

iii

with experimental strains. Mesh refinement led to adoption of a 5 mm element size,

with variable material properties applied to the integration points.

Bone density changes in the Gruen zones correlated with the radiographic find

ings at 1, 2 and 3 year time points for the JVIargron model (R2 > 0.67, p < 0.02),

with an average error of 5.4% at 2 years. Density changes with the Stability and

Epoch models were correlated with radiographic clinical data at 2 years, with good

agreement again (R2 > 0.76, p < 0.02), and with average errors of 3.4% and 3.9%

respectively. This is the first report of bone density changes measured in Gruen

zones correlating with radiographic clinical measurements. Previous studies have

overestimated proximal bone loss in the calcar region.

A strain-adaptive bone remodelling theory was developed, which simulated bone

density changes in accordance with those seen clinically. This tool could be em

ployed for pre-clinical testing of new implants, investigation of design modifications,

and patient-specific implant selection.

Aims

The objective of this study was to evaluate the strain distribution in a femur im

planted with a cobalt-chrome femoral prosthesis, and to simulate bone remodelling

in this femur, consistent with radiographic clinical outcomes. The scope of the

research was to:

• experimentally determine the cortical strain distribution of a femur, before

and after implantation with the Margron hip prosthesis;

• create an anatomical finite element model of a femur;

• validate the finite element model and undertake mesh refinement;

• develop a strain-adaptive remodelling theory, to be coupled with the finite

element model, to predict periprosthetic bone apparent density changes con

sistent with radiographic clinical data;

• investigate the effects of various parameters on remodelling results;

iv

• discuss the limitations of the modelling; and

• suggest further theoretical research.

Recommendations

The results of this study suggest that the proposed computational bone remodelling

theory may be appropriate for determining subject-specific, time-dependent bone

density adaptation around femoral prostheses. The theory could also be applied to

pre-clinical testing of new implant designs, and modifications to existing products.

Further work is proposed to further verify the theory and improve, and the

influence of additional parameters could be investigated. Consideration should be

given to:

• verification of the dead zone width and time-dependence;

• the influence of postoperative rehabilitation and altered musculoskeletal load

ing on remodelling; and

• incorporation of other factors that modulate bone remodelling into the theory.

v

Acknowledgements

By far the greatest thanks must go to my supervisors Bill Walsh, Richard Frost and

Khosrhow Zarrabi for their guidance, support and facilities.

Thanks also to my colleagues at the Orthopaedic Research Laboratories, especially

Mark Gillies, Adam Butler, Richard Harris and Gina O'Reilly, for providing assis

tance, motivation and stress relief.

I would also like to acknowledge Dr. Ron Sekel (St. George Hospital) and A/Prof

Nicholas Pocock (St. Vincent's Hospital) for providing radiographic data, Bill Taylor

for initial modelling help, the medical imaging staff at the Prince of Wales Hospital

for use of their equipment, and my father for his clinical input and proof-reading

skills.

Alex Turner, November 28, 2003.

Vl

Contents

Chapter 1 Introduction

1.1 Objectives . . .

1.2 Thesis Outline .

Chapter 2 Anatomy and Biomechanics of the Hip

2.1 Anatomy of the Hip Joint .....

2.1.1 Proximal Articular Surface .

2.1.2 Distal Articular Surface ..

2.1.3 Joint Capsule and Ligaments

2.1.4 Muscles ....... .

2.2 Biomechanics of the Hip Joint

2.2.1 Stance

2.2.2 Gait .

2.2.3 Stair Climbing

2.2.4 Joint and Muscle Forces

Chapter 3 Hip Arthroplasty

3.1 Indications . . . . . . . . . . . . . . .

3.2 Evolution of Total Hip Arthroplasty .

3.3 Biomaterials .

3.3.1 Metals

3.3.2 Polymers .

3.3.3 Ceramics .

Vll

1

3

4

5

5

5

7

9

11

15

16

18

21

22

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30

34

34

37

39

3.3.4 Biological Response to Biomaterials .

3.4 Femoral Component Design

3.4.1 Material .

3.4.2 Geometry

3.4.3 Surface Finish .

3.5 Performance . . . . .

Chapter 4 Bone 1\Iechanics

4.1 Structure . .

4.2 Composition .

4.3 Development, Growth, Modelling and Remodelling

4.3.1 Bone Formation .....

4.3.2 Mechanical Adaptation .

4.3.3 Mechanotransduction .

4.4 Mechanical Properties . . .

4.4.1 Constitutive Models

4.4.2 Elastic Modulus and Density .

4.4.3 Noninvasive Measurement of Bone Density

Chapter 5 Stress Analysis of the Femur

5.1 Experimental Stress Analysis

5.1.1 Strain Gauges ....

5.1.2 Strain Gauge Studies

5.2 Finite Element Stress Analysis .

5.2.1 Finite Element Modelling

5.2.2 Finite Element Studies

5.3 Remarks . . . . . . . . . . . .

Chapter 6 Bone Adaptation Models

6.1 Site-Specific Models . . . . . .

6.1.1 Adaptive Elasticity Theory.

viii

40

43

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44

46

48

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52

55

56

56

60

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81

81

82

84

92

92

95

108

110

113

113

6.1.2 Strain Energy Density Model .

6.1.3 Damage Accumulation Models .

6.2 Non-Site-Specific ]\:1odels ....... .

6.2.1 Self-Optimisation and Bone Maintenance Theories .

6.2.2 Global Models .

6.3 Remodelling Stimulus .

Chapter 7 Materials and Methods

7.1

7.2

Experimental Study .

7.1.1 Specimens

7.1.2 Implant

7.1.3 Mechanical Testing

7.1.4 Data Analysis .

Finite Element Study .

7.2.1 Model Construction .

7.2.2 Model Validation

7.2.3 Mesh Refinement

7.3 Bone Remodelling Study

7.3.1 Margron .....

7.3.2 Comparison with other Implants

7.3.3 Investigation of Parameters

Chapter 8 Results

8.1 Experimental Study.

8.2 Finite Element Study .




8.3.1 Margron .....


lX

115

117

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118

126

127

129

131

131

131

133

136

137

137

145

146

146

147

160

165

169

169

175

175

184

188

188

197


Chapter 9 Discussion

9.1 Experimental Study .

9.2 Finite Element Study .




9.3.1 Margron .....



9.3.4 Limitations .........

Chapter 10 Conclusions

10.1 Recommendations .

Appendix A Experimental Strain Gauge Data

Appendix B Strain Distributions

Appendix C Density Changes and Distributions

C.1 Margron ............. .

C.2 Comparison with Other Implants

C.3 Investigation of Parameters ...

C.3.1 Effect of Interface Conditions

C.3.2 Effect of Femoral Head Position

C.3.3 Effect of Dead Zone Width.

C.3.4 Effect of Activity Level . . .

C.3.5 Effect of Prosthesis Stiffness

Appendix D Bone Density Correlations

References

X

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217

218

221

221

225

227

228

237

247

254

257

259

262

270

274

274

275

282

282

282

285

285

285

287

291

List of Tables

2.1 Range of motion at the hip joint . . . . . . . . . . . . . . . . . 16

2.2 1\iiuscle activity and joint motion during the walking gait cycle 20

2.3 Peak hip joint reaction force for normal walking . 24

2.4 Hip joint and muscle force magnitudes during gait 26

2.5 Joint and muscle force magnitudes acting on the femur during gait . 27

3.1 Typical mechanical properties of implant materials . . . . . . . . . 36

4.1 Mechanical usage windows according to Frost's Mechanostat theory 65

4.2 Experimental values for the elastic modulus of human cortical bone

tissue ............ .

4.3 Experimental values for the elastic modulus of human trabecular

bone tissue . . . . . . . . . . . . . . .

4.4 Apparent density of human bone tissue

73

74

74

4.5 Emperical relationships between elastic modulus and apparent density 76

4.6 Emperical relationships between apparent density and CT data 80

7.1 Joint and muscle force components for the proximal femur

7.2 Margron clinical bone mineral density data .

7.3 Stability clinical bone mineral density data .

7.4 Epoch clinical bone mineral density data ..

7.5 Matrix of femoral head position parameters evaluated

8.1 Statistically significant strains before and after surgery

8.2 Finite element models to investigate convergence .

8.3 Effect of model complexity on computation time .

xi

154

160

163

165

167

171

184

186

8.4 Equivalent strain values and percentages for the Margron, Stability

and Epoch models . . . . . . . . . . . . . . . . . . . 200

A.1 Preoperative minimum principal strains (Load case 1) 262

A.2 Preoperative minimum principal strains (Load case 2) 263

A.3 Preoperative maximum principal strains (Load case 1) 263

A.4 Preoperative maximum principal strains (Load case 2) 264

A.5 Preoperative longitudinal strains (Load case 1) . 264

A.6 Preoperative longitudinal strains (Load case 2) . 265

A. 7 Postoperative minimum principal strains (Load case 1) 265

A.8 Postoperative minimum principal strains (Load case 2) 266

A.9 Postoperative maximum principal strains (Load case 1) 266

A.10 Postoperative maximum principal strains (Load case 2) 267

A.11 Postoperative longitudinal strains (Load case 1) 267

A.12 Postoperative longitudinal strains (Load case 2) 268

A.13 ?-values showing the statistically significant difference between the

strains before and after surgery . . . . . . . . . . . . . . . . . . . . 268

A.14 Postoperative strains as a percentage of preoperative strains (maxi-

mum and minimum principal strains and their corresponding errors) 269

A.15 Postoperative strains as a percentage of preoperative strains (longi

tudinal strains and their corresponding errors) . . . . . . . . . . . . 269

C.1 Predicted bone density changes in the Gruen zones for the Margron

model (dead zone 0.6, no distal contact, version angle 0°, neck length

+4 mm) ................................. 274

C.2 Predicted bone density changes in the Gruen zones for the Stability

model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275

C.3 Predicted bone density changes in the Gruen zones for the Epoch

model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275


model (fully bonded contact) . . . . . . . . . . . . . . . . . . . . . . 282

xii

C.5 Predicted bone density changes in the Gruen zones for the lVIargron

model (distal sliding contact) . . . . . . . . . . . . . . . . . . . . . 282


model (version angle 0°, neck length -4 mm) . . . . . . . . . . . . 282

C. 7 Predicted bone density changes in the Gruen zones for the Margron

model (version angle 0°, neck length 0 mm) . . . . . . . . . . . . . 283


model (version angle 0°, neck length +4 mm) . . . . . . . . . . . . 283

C.9 Predicted bone density changes in the Gruen zones for the l\1argron

model (version angle oo, neck length + 7 mm) . . . . . . . . . . . . 283


model (version angle - 20o, neck length +4 mm) . . . . . . . . . . . 283

C.ll Predicted bone density changes in the Gruen zones for the Margron

model (version angle -10°, neck length +4 mm) . . . . . . . . . . . 284


model (version angle +10°, neck length +4 mm) . . . . . . . . . . . 284

C.13 Predicted bone density changes in the Gruen zones for the 1\ifargron

model (version angle + 20°, neck length +4 mm) . . . . . . . . . . . 284


model (dead zone 0.55) . . . . . . . . . . . . . . . . . . . . . . . . . 285


model (dead zone 0.65) . . . . . . . . . . . . . . . . . . . . . . . . . 285


model (90% activity level) . . . . . . . . . . . . . . . . . . . . . . . 285


model (isoelastic properties) . . . . . . . . . . . . . . . . . . . . . . 286


model (cobalt-chrome properties) . . . . . . . . . . . . . . . . . . . 286

Xlll

List of Figures

2.1 Osteology of the pelvis and femur .............. .

2.2 The hip bone formed by the ilium, ischium and pubic bones

2.3 Neck-shaft angle of the femur

2.4 Version angle of the femur ..

2.5 Capsule and ligaments of the hip joint

2.6 Muscle attachment points of the pelvis and femur

2. 7 Location of the line of gravity

2.8 A complete gait cycle .....

2.9 Static equilibrium of the pelvis in single-legged stance .

2.10 Components and magnitude of the hip joint reaction force

3.1 The first total hip arthroplasty system

3.2 Early arthroplasty designs ...... .

6

7

8

9

10

12

17

19

23

25

31

32

3.3 Composition of some common orthopaedic biomaterials 35

3.4 Porous coating techniques . . . . . . . . . . . . . . . . 4 7

3.5 Zones around the femoral component for evaluating loosening 49

4.1 Architecture of the proximal femur . . . . . 51

4.2 Architecture of cortical and trabecular bone 53

4.3 Schematic diagram of intramembranous ossification 57

4.4 Schematic diagram of endochondral ossification . . 58

4.5 Endochondral ossification in the epiphyseal growth plate 59

4.6 Adaptation hypothesis for regulation for skeletal mass . . 60

4. 7 Bone remodelling due to the activity of basic multicellular units 63

XIV

408 Specific surface as a function of porosity 0 0 0 0 0 0 0 0 0 0 0 0 0 64

409 Rate of change of bone mass as a function of the strain history 0 66

501 Uniaxial strain gauge grid 82

502 \Vheatstone bridge 0 0 0 0 83

503 A collared implant increases axial compressive loads at the calcar 85

5.4 Load transfer mechanism for an uncemented prosthesis with and

without abductor muscle action present 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 87

505 Set up used for applying the hip joint and abductor forces to the femur 89

506 Representation of the femoral constraints for mechanical testing 0 0 90

50 7 Changed loading if the position of the prosthetic head does not co-

incide with the anatomic one 0 0 0

508 A two-dimensional finite element mesh

509 Nonlinearities in finite element modelling

91

93

95

5010 Two-dimensional side-plate model of the proximal femur 97

5011 Automatic mesh generation methods 98

601 Trilinear curve relating remodelling rate and stimulus 115

602 Graph of the surface area density as a function of apparent density 116

603 Piecewise linear curve relating remodelling rate and stimulus 120

6.4 Checker-board effect in density distribution 0 123

605 Effect of spatial influence function on trabecular morphogenesis 125

701 Flowchart of the study design 0 0 130

702 Anterior-posterior radiograph with 1\ilargron template overlying 132

703 The Margron hip prosthesis 0 0 0 0 0 132

7.4 Strain gauge positions on the femoral cortex 134

705 Mechanical testing of a femur under two load cases 135

706 Femoral geometry for the finite element model 0 0 0 138

70 7 10-noded tetrahedral element showing nodes and integration points 139

708 Finite element meshes for the Margron models 0 0 0 0 0 0 0 140

XV

7.9 Diaphyseal CT slice showing regions of interest to determine Houns-

field units of cortical bone . . . . . . . . . . . . . 142

7.10 "Ringing" phenomenon due to CT-scanning in air 143

7.11 3 and 7 mm finite element meshes used for convergence analysis 147

7.12 Remodelling rate as a function of the remodelling signal. . . . . 150

7.13 Polynomial fit of the bone surface area density-apparent density curve151

7.14 Overview of the bone adaptation simulation . . . . 152

7.15 Load and boundary conditions for the intact femur 155

7.16 Proximal load conditions for the intact femur 156

7.17 Gruen zone analysis of DEXA images . . . . . 159

7.18 Finite element meshes for the Stability models 162

7.19 Finite element meshes for the Epoch models 164

8.1 Medial and lateral principal strains . . 170

8.2 Anterior and posterior principal strains 170

8.3 lVIedial and lateral longitudinal strains 172

8.4 Anterior and posterior longitudinal strains 173

8.5 Medial and lateral percentage strains . . 17 4

8.6 Anterior and posterior percentage strains 174

8. 7 Density distribution of the femur . . . . 176

8.8 Contour plots of preoperative minimum principal strains 177

8.9 Contour plots of postoperative (no distal contact) minimum principal

strains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

8.10 Preoperative medial and lateral experimental and finite element prin-

cipal strains for load case 1 . . . . . . . . . . . . . . . . . . . . . . . 179

8.11 Preoperative anterior and posterior experimental and finite element

principal strains for load case 1 . . . . . . . . . . . . . . . . . . . . 179

8.12 Preoperative medial and lateral experimental and finite element prin-


XVI

8.13 Preoperative anterior and posterior experimental and finite element


8.14 Postperative medial and lateral experimental and finite element prin-


8.15 Postperative anterior and posterior experimental and finite element


8.16 Postperative medial and lateral experimental and finite element prin-


8.17 Postperative anterior and posterior experimental and finite element

principal strains for load case 2 183

8.18 Preoperative mesh convergence 185

8.19 Preoperative mesh convergence, distal . 185

8.20 Postoperative mesh convergence . . . . 186

8.21 Mesh convergence and element homogeneity 187

8.22 Minimum principal strain distribution . 189

8.23 Equivalent strain distribution 0 •••• 190

8.24 Density distribution of the remodelled femur 192

8.25 Simulated DEXA images during remodelling of the femur . 193

8.26 Change in bone density in the Gruen zones for increments 10 to 120 193

8.27 Incremental change in bone density in Gruen zone 7 ......... 194

8.28 Comparison of actual and simulated bone density changes for the

first 3 years after surgery . . . . . . . . . . . . . . . . . . . . . . . . 195

8.29 Comparison of actual and simulated bone density changes after 2 years196

8.30 Behaviour of the remodelling error over 120 remodelling increments 196

8.31 Preoperative strains for three femora under 45% gait cycle loading . 197

8.32 Postoperative strains for three femora under 45% gait cycle loading 198

8.33 Effect of implant design on the equivalent strain along the medial

cortex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

xvii

8.34 Effect of implant design on the change in bone density in the seven

Gruen zones at 2 years . . . . . . . . . . . . . . . . . . . . . . . . . 202

8.35 Effect of implant design on the change in bone density in the seven

Gruen zones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203

8.36 Effect of implant contact conditions on the equivalent strain along

the medial cortex . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204

8.37 Effect of contact conditions on the change in bone density in the

seven Gruen zones . . . . . . . . . . . . . . . . . . . . . . . . . . . 205

8.38 Effect of neck length on the equivalent strain along the medial cortex 206

8.39 Effect of neck length on the change in bone density in the seven

Gruen zones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

8.40 Effect of version angle on the equivalent strain along the medial cortex208

8.41 Effect of version angle on the change in bone density in the seven

Gruen zones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

8.42 Effect of dead zone width on the equivalent strain along the medial

cortex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210

8.43 Effect of dead zone width on the change in bone density in the seven

Gruen zones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

8.44 Effect of postoperative activity level on the equivalent strain along

the medial cortex . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

8.45 Effect of postoperative activity level on the change in bone density

in the seven Gruen zones . . . . . . . . . . . . . . . . . . . . . . . . 212

8.46 Effect of implant material on the equivalent strain along the medial

cortex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213

8.47 Effect of implant elastic modulus on the change in bone density in

the seven Gruen zones . . . . . . . . . . . . . . . . . . . . . . . . . 214

8.48 Immediately postoperative interface shear stress ( anteromedial, di

rection 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215

xviii

8.49 Immediately postoperative interface shear stress (posterolateral, di

rection 1) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 215

8050 Immediately postoperative interface shear stress (anteromedial, di

rection 2) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 216

8051 Immediately postoperative interface shear stress (posterolateral, di

rection 2) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 216

901 Nonlinear mechanoregulation rule including strain and damage me-

diated pathways 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 255

Bo1 Minimum principal strain distribution (Stability)

Bo2 Equivalent strain distribution (Stability) 0 0 0 0

Bo3 Minimum principal strain distribution (Epoch) 0

B.4 Equivalent strain distribution (Epoch) 0 0 0 0 0

270

271

272

273

Co1 Density distribution of the immediately postoperative Stability femur 276

Co2 Density distribution of the remodelled Stability femur 0 0 0 0 0 0 0 0 277

Co3 Simulated DEXA images during remodelling of the Stability femur 0 278

C.4 Density distribution of the immediately postoperative Epoch femur 279

Co5 Density distribution of the remodelled Epoch femur 0 0 0 0 0 0 0 280

Co6 Simulated DEXA images during remodelling of the Epoch femur 281

Do1 Correlation between simulated and clinical BMD changes (Margron,

1 year postop) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 287


2 years postop) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 288


3 years postop) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 288

D.4 Correlation between simulated and clinical BMD changes (Stability,

2 years postop) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 289

Do5 Correlation between simulated and clinical Bl\fD changes (Epoch, 2

years postop) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 289

Do6 Correlation between simulated and clinical BMD changes (all data) 290

xix

Nomenclature

a

BMD

Cres

Capp

CT

Strain tensor

Poisson's ratio

Remodelling error

Apparent density

Apparent density at integration point i

Convergence criterion

Function for surface area density of bone

Bone mineral density

Constant related to resorption rate

Constant related to apposition rate

Computed tomography

DEXA Dual-energy x-ray absorptiometry

E Elastic modulus

z Superscript indicating ith integration point

HA Hydroxyapatite

HU Hounsfield units

n Total number of integration points

s Dead zone width

S Current remodelling signal

Si Current remodelling signal at integration point i

Bref Reference remodelling signal

s:er Reference remodelling signal at integration point i

XX

t Current time

f::..t Remodelling time step

THA Total hip arthroplasty

N .B. Nomenclature refers to symbols used in the methodology for this thesis.

Within the background sections, terminology consistent with the original publi

cations are used.

xxi

Chapter 1

Introduction

Bone loss around uncemented femoral prostheses is believed to be a mechanically

mediated response to the altered postoperative loading environment, in accordance

with "Wolff's Law". Normally, the hip joint reaction force is carried entirely by

the bone. However, after hip replacement surgery it is shared between the implant

and the bone, with the stiffer component carrying the greater proportion (Huiskes,

1996). This causes bone to be stress-bypassed, or stress-shielded. Stress shielding

is clinically associated with bone resorption-particularly of the proximal-medial

femur-and occurs through adaptive bone remodelling. Although proximal bone

loss may not necessarily be a problem in terms of patient function or clinical scores

(McAuley et al., 1998), it reduces support of the prosthesis which may acceler

ate fatigue failure (Engh et al., 1990), may lead to late loosening, decreases bone

strength and complicates revision due to lack of bone stock (Kerner et al., 1999;

van Rietbergen et al., 1993).

Bone loss around uncemented hip prostheses has been attributed to the implant

design (Bobyn et al., 1990; Engh et al., 1990; McAuley et al., 2000; Sumner and

Galante, 1992; Sychterz et al., 2001) and preoperative bone quality (Engh et al.,

1994, 1992a; Sychterz and Engh, 1996), and has been investigated by radiographic

and dual-energy x-ray absorptiometry studies. Implant-dependent factors that de

termine the degree of stress shielding, and subsequent bone resorption, include elas-

1

1. INTRODUCTION 2

tic modulus, geometry and the characteristics of the implant-bone interface (fit,

surface coating and ingrowth) (Huiskes et al., 1992; Jacobs et al., 1992).

Stress shielding can be evaluated using experimental (e.g., Cristofolini et al.,

1995; Diegel et al., 1989; Finlay et al., 1991; Glisson et al., 2000; Jasty et al., 1994)

and finite element (e.g., Cheal et al., 1992; Huiskes, 1990; Keaveny and Bartel,

1993a; McNamara et al., 1996; Prendergast and Taylor, 1990) methods. Experi

mental methods include strain gauges and photoelasticity, which can only provide

stress information at the periosteal surface. Finite element analysis is able to deter

mine the stress distribution throughout a structure, however the output represents

an approximation of the true results, with accuracy depending on model complexity

and simplifying assumptions. Finite element analysis has been used in orthopaedic

research for over 30 years (Huiskes and Chao, 1983). 1,fodels were highly sim

plified initially, and the results were accordingly imprecise. Computing power has

increased considerably in this time, meaning complex finite element models can now

be analysed on personal computers-previously the domain of expensive worksta

tions. This allows less simplifying assumptions, with the models providing a better

representation of the physiological situation.

Bone remodelling theories have been developed to provide a mathematical for

mulation of "Wolff's Law", which can be combined with finite element analysis to

simulate bone adaptation (e.g., Beaupre et al., 1990a; Carter et al., 1987; Cowin

and Hegedus, 1976; Cowin et al., 1992; Hart et al., 1984a; Huiskes et al., 1992).

These investigations have predicted density distributions and periprosthetic bone

adaptation. Some of the remodelling theories have been compared with in vivo

studies in human (Huiskes, 1993b; Kerner et al., 1999; van Rietbergen and Huiskes,

2001) and canine (van Rietbergen et al., 1993; Weinans et al., 1993) subjects, with

moderate success.

Accurate simulation of strain-adaptive bone remodelling may provide a valuable

tool for selecting the most suitable prosthesis design for an individual patient. This

tool could also be used as one of a suite of pre-clinical tests to assess new implant

1.1 OBJECTIVES 3

designs. This has the potential to save industry vast sums of time and money, and

prevent the almost trial-and-error approach to clinical testing of designs that is

currently taking place.

1.1 Objectives

This study was undertaken to assess the stress distribution and remodelling of

a femur implanted with a femoral prosthesis. Specifically, the following research

questions were asked:

1. does the experimental femoral strain distribution change significantly after

hip replacement surgery with a cobalt-chrome, uncemented hip prosthesis?

2. can the experimental results be reproduced using finite element modelling?

3. is it possible to simulate the adaptive bone remodelling seen clinically, by

using finite element analysis coupled with bone remodelling theory?

The first question was addressed with an experimental strain gauge study in

which four femora were mechanically tested under simplified load conditions to

measure strains before and after reconstruction with a hip prosthesis, in order to

determine the degree of stress shielding. For the second research question, a femur

from the experimental study was used to create an anatomic finite element model.

A postoperative model was also constructed. Using the experimental loading con

figurations, the strain distribution was calculated and compared with the strain

gauge results for validation purposes. Mesh refinement was also examined. Finally,

a bone remodelling rule was developed and coupled with the finite element models

to predict mechanically-mediated adaptation around the hip prosthesis. The pre

dictions were compared with radiographic clinical data. Remodelling simulations

were performed for two other femora with different implant designs and compared

with clinical data to examine the robustness of the method.

1.2 THESIS OUTLINE 4

1.2 Thesis Outline

Before answering the research questions, a thorough literature review of the subjects

pertaining to this research is performed, including:

• Chapter 2-review of the anatomy and biomechanics of the hip joint.

• Chapter 3-review of the history of hip arthroplasty, biomaterials and implant

design.

• Chapter 4-review of bone structure, composition, development, maintenance

and mechanical properties.

• Chapter 5-review of experimental and finite element methods relating to

stress analysis of the femur.

• Chapter 6-review of theoretical bone adaptation theories.

The remainder of the thesis is concerned with addressing the research questions:

• Chapter ?-explanation of the methodology used to answer the research ques-

tions.

• Chapter 8-presentation of results.

• Chapter 9-discussion of the results in the context of previous studies.

• Chapter 10-conclusions and recommendations.

Chapter 2

Anatomy and

Biomechanics of the Hip

2.1 Anatomy of the Hip Joint

The hip joint, or coxofemoral joint, is a synovial, ball and socket joint that transmits

loads between the trunk and the lower limb and allows relative movement between

these segments to take place. Synovial joints have three general features: a joint

cavity, articular cartilage (usually hyaline), and an articular capsule lined with

synovial membrane. The joint capsule is discussed further in Section 2.1.3. The

bones of the hip joint consist of the hip bone, or os coxa, and the femur (Figure 2.1).

Articulation occurs between the femoral head and the acetabulum.

2.1.1 Proximal Articular Surface

The bony pelvis is formed by two hip bones which are joined anteriorly at the pubic

symphysis, and posteriorly to the lateral margins of the sacrum. The hip bone is

formed by the fusion of three bones: the ilium above, the ishcium below and behind,

and the pubis below and in front (Breathnach, 1965). The three parts, which are

joined only by cartilage until just before puberty, meet at the acetabulum on the

lateral side of the hip bone (Figure 2.2). The acetabulum provides a cup-like surface

5

2.1 ANATOMY OF THE HIP JOINT

Tubercle o! crest

lntertrot:hanteric line

Lesser t•ochanter

r----"' IHopub c (p€ct1neal) eminence ,. r-- Supenor ramus ol publs

/ ,~~--Pubic tubercle // Crest o! pubis

/ ~ P~cten PJb:~

U:r•+-1-- Body o! pubis

PublC arch, !eH heY

Ischia> tuberosity

(a) Anterior Aspect

Posterior supe1 or l!iac spine

Postenor inferior iliac spine

Medial supracondylar line--

Adductor tubercle

,.,~,~Iliac crest

\ '' ~ \r-Tubercle of crest

(1 .':J

Greater trochanter

Intertrochanteric crest

Lesser trochanter

Lateral supracondylar line

(b) Posterior Aspect

6

Figure 2.1: Osteology of the pelvis and femur showing common landmarks. Reproduced from 1\Ioore (1992).

2.1 ANATOMY OF THE HIP JOINT

Pubis

Acetabular fossa

Articular ridge

7

Figure 2.2: The hip bone is formed by the fusion of the ilium, ischium and pubic bones, which meet at the acetabulum. Adapted from Chung (1991).

for articulation with the femoral head. The rim of the acetabulum is deficient

distally, constituting the acetabular notch. The central part of the acetabulum

is deepened, forming the acetabular fossa. The acetabulum is directed laterally,

anteriorly, and inferiorly.

The acetabular surface is not all weight-bearing. Only a C-shaped area (the

lunate surface) is articular and covered with hyaline cartilage. The acetabular fossa

and the acetabular notch are nonarticular. The acetabular fossa is occupied by an

intracapsular, but extrasynovial, pad of fat. The peripheral edge of the acetabulum

is deepened by a rim of fibrocartilage, called the acetabular labrum, which acts to

increase joint congruency and thus stability. The acetabular labrum is continuous

across the acetabular notch as the transverse acetabular ligament.

2.1.2 Distal Articular Surface

The femur is the longest and strongest bone in the human skeleton. It extends

from the hip joint to the knee joint. Proximally, the femoral shaft is connected to

the femoral head by the neck. The greater and lesser trochanters provide muscle

attachment points. Distally, the two condyles articulate with the tibia.

2.1 ANATOMY OF THE HIP JOINT 8

The femoral head is two-thirds of a sphere and is directed upwards, forwards

and medially. It has a nonarticular pit (fovea) for attachment of the ligament of

head of femur (ligamentum teres). More than half of the femoral head is contained

within the acetabulum.

Two angles are used to characterise the proximal femur: the neck-shaft angle

and the version angle. As the name suggests, the neck-shaft angle is the angle

between the shaft of the femur and the neck, measured in the frontal plane. The

neck-shaft angle, or angle of inclination, is normally 125°. An angle less that this

value is a called coxa vara deformity, while an angle greater than 125° is a coxa

valga deformity (Figure 2.3). Deviations in either direction result in altered loading

Normal ""'-,

'

Coxa vara

Angle of inclination

Figure 2.3: Neck-shaft (or inclination) angle of the femur. Reproduced from Chung (1991) 0

conditions at the hip joint. Valgus angulation decreases joint stability-increasing

the likelihood of dislocation under some conditions. It also reduces the moment arm

of the abductor muscles, meaning that more muscle force is required to maintain

stability and increasing the hip joint reaction force. A varus angle increases the

abductor moment arm, but also increases the shear forces in the femoral neck. The

neck-shaft angle tends to become more varus with old age.


The version, or torsion, angle is the angle between the posterior condyles of

the knee and the axis of the femoral neck, measured in a horizontal plane. The

normal version angle is 12-15° in the anterior direction (Breathnach, 1965). If the

angle is greater than this, it is said to be anteverted, and if the angle is less, it is

retroverted (Figure 2.4). Retroversion enhances hip stability, but external rotation

(a) Normal

Axil: of heod lllfld ne.::k

....... -- ...,_-"-----"'-""'---..;.;::..

(b) Anteversion (c) Retroversion

Figure 2.4: Version (or torsion) angle of the femur. Reproduced from Norkin and Levange (1992).

of the femur may cause out-toeing of the feet. Anteversion predisposes the hip to

anterior dislocation and internal rotation of the femur can cause in-toeing of the

feet (Norkin and Levange, 1992).

The thick cortical buttress extending from the inferior femoral head along the

inferior neck to the medial femoral shaft is usually referred to as the calcar femorale

(Chung, 1991). This definition of the calcar region is important in terms of load

transfer from the femoral head to the shaft. According to Harty ( 1991), this def-

inition is incorrect, and the calcar in fact an interosseous vertical plate of bone

extending internally from the medial cortex of the femoral shaft around the level of

the lesser trochanter.

2.1.3 Joint Capsule and Ligaments

A strong, dense, fibrous capsule surrounds the hip joint. Proximally it is attached

to the acetabulum, just distal to the labrum, and also to the transverse acetabular

ligament. Distally the capsule is attached to the neck of the femur: anteriorly to the

intertrochanteric line, and posteriorly to the intertrochanteric crest. The capsule is

loose but very strong. From these attachments, the fibres of the capsule are reflected


back along the neck to blend with the periosteum. This reflected part forms the

retinacular fibres which bind down the nutrient arteries that supply most of the

head of the femur-primarily the anastomosis of the lateral and medial circumflex

femoral arteries.

The fibrous capsule is strengthened by three ligaments that spiral around the

long axis of the neck: the iliofemoral, pubofemoral and ischiofemoral ligaments

(Figure 2.5). The iliofemoral ligament is a thickening of the anterior part of the

(a) Iliofemoral and pubofemoral ligaments.

Jschiofemomt H!';p:ment

(b) Ischiofemoral ligament.

Figure 2.5: Capsule and ligaments of the hip joint. Reproduced from (Eftekhar, 1978).

capsule, and has the shape of an inverted "Y". The base arises from the anterior

inferior iliac spine and the acetabular rim, with the diverging limbs attaching to

the upper and lower ends of the intertrochanteric line. This is one of the strongest

ligaments in the body, helping to maintain upright posture during standing. It also

limits extension of the hip joint (Moore, 1992).

The pubofemoral ligament restricts abduction and extension of the hip. It passes

from the iliopubic eminence and obturator crest to the capsule on the inferior neck


of the femur. The ischiofemoral ligament is the weakest of the three, and attaches

to the posteroinferior margin of the acetabulum, passing laterally to the capsule.

The ligament of the head of the femur (ligamentum teres) is an intracapsular

ligament that is weak and appears to contribute little to the strength of the joint. Its

wide end is attached to the acetabular notch and the tranverse acetabular ligament,

and the narrow end is attached to the pit in the femoral head.

Synovial membrane lines the entire joint cavity, with the exception of those

regions covered with articular cartilage. The synovial membrane produces synovial

fluid to lubricate the joint. Bursae are also present around the hip joint to eliminate

friction between tendons and muscles rubbing against other tendons, muscles or

bones. The iliac bursa lies over the hip joint capsule and extends proximally into the

iliac fossa beneath the iliacus muscle. Other bursae in the area are positioned under

gluteus medius and gluteus minimus at their insertions to the greater trochanter,

and three under gluteus maxim us (over the ischial tuberosity, greater trochanter

and the upper part of vast us lateralis).

2.1.4 Muscles

The muscles around the hip joint can be grouped into the thigh muscles and the

gluteal muscles. The thigh muscles may be further subdivided into three groups

(anterior, medial and posterior) based on their locations, actions and innervations.

The origin and insertion points, and the actions, of the twenty four muscles crossing

the hip joint are listed according to these groups (Moore, 1992). Pelvic and femoral

attachment points are shown in Figure 2.6.

Muscles of the Anterior Thigh Region

Psoas Major Originates at the sides of the Tl2 to L5 vertebrae and intervertebral

discs between them. Inserts on the lesser trochanter. Acts conjointly with

iliacus to flex the thigh at the hip and to stabilise this joint.


G!u:eus max1nus

Gas1rncnemHJs, lateral head

(a) Anterior aspect. (b) Posterior aspect.

Figure 2.6: Muscle attachment points of the pelvis and femur. Reproduced from Moore (1992).

Iliacus Originates on the iliac crest, iliac fossa, ala of sacrum, and anterior sacroil-

iac ligaments. Inserts on the tendon of psoas major and the body of the femur,

distal to the lesser trochanter.

Tensor Fasciae Latae Originates on the anterior superior iliac spine and the an-

terior part of the external lip of the iliac crest. Inserts on the iliotibial tract,

which is attached to the lateral condyle of the tibia. Action is to abduct,

internally rotate, and flex the thigh. Also helps to keep the knee extended

and steady the trunk on the thigh.

Sartorius Originates on the anterior superior iliac spine and the anterior part of

the notch inferior to it. Inserts on the proximal part of the medial surface of


the tibia. Action is to flex, abduct and externally rotate the thigh at the hip

joint.

Rectus Femoris Originates on the anterior inferior iliac spine and the groove su

perior to the acetabulum. Inserts on the patella and via the patella ligament

to the tibial tuberosity. Action is to extend the leg at the knee joint. Also

steadies the hip joint and helps psoas major and iliacus flex the thigh.

Vastus Lateralis Originates on the greater trochanter and lateral lip of the linea

aspera. Insertion points as for rectus femoris. Action is to extend the leg at

the knee joint.

Vastus Medialis Originates on the intertrochanteric line and the medial lip of the

linea aspera. Insertion points and action as for vastus lateralis.

Vastus Intermedius Originates on the anterior and lateral surfaces of the body

of the femur. Insertion points and action as for vastus lateralis.

Muscles of the Medial Thigh Region

Pectineus Originates on the pectineal line of the pubis and inserts on the pectineal

line of the femur. Action is to adduct and flex the thigh.

Adductor Longus Originates on the body of the pubis, inferior to the pubic crest.

Inserts on the middle third of the linea asp era of the femur. Action is to adduct

the thigh.

Adductor Brevis Originates on the body and inferior ramus of the pubis and

inserts on the pectineal line and proximal part of the linea aspera of the

femur. Action is to adduct the thigh and to some extent flex it.

Adductor Magnus (adductor and hamstring parts) Originates on the infe

rior ramus of the pubis, ramus of ischium (adductor part), and ischial tuberos

ity. Inserts on the gluteal tuberosity, medial linea aspera, supracondylar line

(adductor part) and adductor tubercle of the femur (hamstring part). Ac

tion is to adduct the thigh. The adductor part also flexes the thigh, and the

hamstring part extends the thigh.


Gracilis Originates on the body and inferior ramus of the pubis, and inserts on

the proximal part of the medial surface of the tibia. Action is to adduct the

thigh, flex and help internally rotate the leg.

Obturator Externus Originates on the margins of the obturator foramen and

obturator membrane. Inserts on the trochanteric fossa of the femur. Action is

to externally rotate the thigh and steady the head of femur in the acetabulum.

Muscles of the Posterior Thigh Region

Semitendinosus Originates on the ischial tuberosity and inserts on the medial

surface of the proximal part of the tibia. Action is to extend the thigh, flex

and internally rotate the leg. When thigh and leg are flexed, it can extend

the trunk.

Semimembranosus Originates on the ischial tuberosity and inserts on the pos

terior part of the medial condyle of the tibia. Action is the same as for

semitendinosus.

Biceps Femoris Long head originates on the ischial tuberosity and short head

originates on the lateral lip of the linea aspera and lateral supracondylar line.

Inserts on the lateral side of the head of the fibula; the tendon is split at this

site by the fibular collateral ligament of the knee joint. Action is to flex the

leg and rotate it externally; extends the thigh.

Muscles of the Gluteal Region

Gluteus Maximus Originates on the external surface of the ala of the ilium, in

cluding the iliac crest, dorsal surface of the sacrum and coccyx, and the sacro

tuberous ligament. Most fibres insert in the iliotibial tract; some fibers insert

on the gluteal tuberosity on the femur. Action is to extend the thigh and

assist in its external rotation. Also steadies the thigh and assists in raising

the trunk from a flexed position.

2.2 BIOMECHANICS OF THE HIP JOINT 15

Gluteus Medius Originates on the external surface of the ilium between ante

rior and posterior gluteal lines. Inserts on the lateral surface of the greater

trochanter. Action is to abduct and internally rotate the thigh, and to steady

the pelvis.

Gluteus Minimus Originates on the external surface of the ilium between the

anterior and inferior gluteal lines. Inserts on the anterior surface of the greater

trochanter. Action as for gluteus medius.

Piriformis Originates on the anterior surface of the sacrum and the sacrotuberous

ligament. Inserts on the superior border of the greater trochanter. Action is

to externally rotate the extended thigh and abduct the flexed thigh; steadies

the femoral head in the acetabulum.

Obturator lnternus Originates on the pelvic surface of the obturator membrane

and surrounding bones. Inserts on the medial surface of the greater trochanter.

Action as for piriformis.

Gemelli (superior and inferior) The superior originates on the ischial spme,

and the inferior originates on the ischial tuberosity. Both insert on the medial

surface of the greater trochanter. Action as for piriformis.

Quadratus Femoris Originates ono the lateral border of the ischial tuberosity.

Inserts on the quadrate tubercle on the intertrochanteric crest of the femur

and inferior to it. Action is to externally rotate the thigh and steady the

femoral head in the acetabulum.

2.2 Biomechanics of the Hip Joint

The hip joint is a three degree-of-freedom joint which allows flexion-extension in

the sagittal plane, abduction-adduction in the frontal plane, and internal-external

rotation along the long axis of the femur. The biomechanics of the hip are governed

by the geometry of the joint and the functions of the soft tissues (ligaments and

muscles) surrounding the joint.


The hip is the most mobile joint of the lower limb, enabling correct positioning

of the foot (Table 2.1). A high degree of stability is needed due to significant weight

bearing requirements. The relatively large range of movement results largely from

the femur having a neck that is much narrower in diameter than the equatorial

diameter of the head.

Table 2.1: Range of motion at the hip joint. Reproduced from Norkin and Levange (1992).

Motion Range Comment

Flexion goo with knee extended 120-135° with knee flexed

Extension 10-30° may be reduced by knee flexion Abduction 30-50° Adduction 10-30° Internal Rotation 45-60° measured with knee flexed goo External Rotation 30-45° measured with knee flexed goo

Stability at the hip joint is produced both actively and passively. Passive sta

bility is provided by ligament tension, while active stability is provided by muscle

contraction during activity. The highly conforming articular surfaces also add to

stability. Active stability is generally provided by short muscles located close to the

axis of movement of the hip.

2.2.1 Stance

Bilateral

In erect bilateral, or two-legged, stance, the centre of gravity (COG) is located

around the height of the second lumbar segment-relatively distant from the fairly

small support base provided by the feet-making the body position unstable. De-

spite this, little energy is required to maintain the static erect posture in the form

of muscle contraction since ligaments, bones and joints are able to provide the

forces necessary to overcome the effects of gravity (passive stability). The constant

displacement and correction of the position of the COG within the support base

is called postural sway and the erect stance is maintained through motor control.


Small bursts of muscle activity, particularly in the legs, can be observed in response

to perturbations in the COG position. In bilateral posture each hip joint carries

approximately one-third of the total body weight (Norkin and Levange, 1992).

Under ideal circumstances the line of gravity (LOG), the vertical line between the

COG and the ground, would pass through all joint axes in the lateral view however

this is difficult to achieve because of normal body structures. During relaxed stance,

the ankle joint is in the neutral position and the knee is in full extension. The LOG

passes slightly anterior to the lateral malleolus at the ankle and just anterior to the

midline of the knee (Figure 2.7a). With the hip also in the neutral position, and no

(a) Location of the line of gravity (LOG) in bilateral stance.

(b) Lower limb moments due to the location of the LOG in bilateral stance.

(c) Location of the LOG (vertical line) in unilateral stance.

Figure 2.7: Location of the line of gravity. Reproduced from Norkin and Levange (1992).

deviation in pelvic tilt, the LOG passes slightly posterior to the hip joint axis. The

position of the LOG at the ankle causes a dorsiflexion moment which is corrected

by the soleus muscle (Figure 2. 7b). The extension moment at the knee is opposed

by the posterior joint capsule and associated ligaments-some low level hamstring

activity has also been identified. The extension moment at the hip is opposed by

the iliofemoral ligament and psoas major.


In the frontal plane, the LOG is equidistant from the hip, knee and ankle joints

on each side of the body. Little muscle activity is required to maintain medial

lateral stability since gravitational forces are balanced on each side of the body.

Any postural sway that occurs during normal bilateral stance changes the position

of the LOG relative to the joint axes and consequently, the level of muscle activity

required to maintain that stance.

Unilateral

In unilateral, or single-leg stance, the base of support is much smaller than for

bilateral stance, and hence the position of the centre of gravity is more unstable

(greater postural sway). Consequently, the line of gravity tends to move further

with respect to each of the joints. This results in greater muscle recruitment in

both the frontal and sagittal planes to maintain erect posture. The optimal LOG

in the lateral view remains in the same position as for double stance, however in

the anterior-posterior view, the LOG must pass through the base of support and

in so doing passes closer to the joint axes of the supporting limb (Figure 2. 7 c).

Unilateral stance produces a moment about the supporting hip joint which must

be balanced by abductor muscle forces. The magnitude of the moment depends

on the position of the spine, the position of the nonweight-bearing leg and upper

extremities, and most importantly, the inclination of the pelvis. If the trunk is

tilted over the hip joint, the gravitational moment is minimised by reducing the

distance between the hip joint and the COG. The hip joint supports about five

sixths of the total body weight in unilateral stance, however the additional hip

joint compression caused by abductor muscle action increases the joint load further

(Norkin and Levange, 1992).

2.2.2 Gait

Human locomotion is a translatory progression of the body as a whole, produced by

coordinated movements of the body segments. Normal gait is rhythmic and charac-


terised by alternating propulsive and retropulsive motions of the lower extremities

(Norkin and Levange, 1992). The gait cycle consists of the actions that take place

between initial contact of the reference extremity with the ground and the successive

contact of that extremity. Each limb passes through a stance phase and a swing

phase during a cycle (Figure 2.8). The stance phase begins with contact of the

Figure 2.8: A complete gait cycle from heel strike on the right leg (arrow), through stance and swing phases to the next heel strike (arrow). Reproduced from Norkin and Levange (1992).

reference extremity (heel strike) and continues while contact is maintained (until

toe off). The swing phase begins as soon as the reference extremity loses contact

with the ground and continues until the next occurrence of heel strike. The stance

phase constitutes approximately 60% of the gait cycle, and consists of heel strike,

foot fiat, midstance, heel off and toe off. The swing phase makes up the remaining

40%, and consists of acceleration, midswing and deceleration. During walking, a

period of double-limb support occurs at the beginning of the stance phase of one

leg and at the end of swing phase for the contralateral leg.

The action of gait is controlled by coordinated isometric, concentric and eccentric

muscle contractions. Table 2.2 outlines the pattern of muscle activity in the sagittal

plane during the normal gait cycle to produce the motions that occur at the hip

and knee joints.

In the frontal plane, joint movements are relatively small, so muscle activity

is mostly associated with providing dynamic support. During the early stage of

stance phase, the body weight is moving forward and shifting laterally over the

stance extremity. Muscular support is required at the joints during weight transfer.


Table 2.2: Muscle activity and joint motion during the walking gait cycle. Adapted from Norkin and Levange (1992)

Gait Cycle Motion

Heel strike to foot fiat Hip Flexion: 30 to 25° flexion

Knee Flexion: 0 to 15° flexion

Foot fiat to midstance Hip Extension: 25 to 0° flexion

Knee Extension: 15 to 5° flexion

Midstance to heel off Hip Extension: 0° of flexion to

10-20° of hyperextension

Knee Extension: 5° flexion to 0°

Heel off to toe off Hip Flexion: 10-20° of

hyperextension to 0°

Knee Flexion: 0 to 30° of flexion

Acceleration to midswing Hip Flexion: 0 to 30° of flexion

Knee Flexion: 30 to 60° of flexion

Extension: 60-30° of flexion

Midswing to Deceleration Hip Hip remains at 30° flexion

Knee Extension: 30° flexion to oo

Muscle

Gluteus maximus Hamstrings Adductor magnus

Quadriceps

Gluteus maximus

Quadriceps

Hip flexors

No activity

Iliopsoas Adductor magnus Adductor longus

Quadriceps

Iliopsoas Gracilis Sartorius

Sartorius Gracilis Biceps femoris

Gluteus maximus

Quadriceps Hamstrings

Contraction

Isometric to concentric

Concentric to eccentric

Concentric to no activity

Concentric to no activity

Eccentric

No activity

Concentric

Eccentric to no activity

Concentric

Concentric

Eccentric

Concentric Eccentric

2. 2 BIOMECHANICS OF THE HIP JOINT 21

The pelvis at the hip is stabilised by gluteus minimus, gluteus medius and tensor

fasciae latae, with gluteus medius resisting lateral dropping of the pelvis to the

contralateral side. The transfer of weight to the supporting limb creates a valgus

thrust at the knee, which is counteracted by vastus medialis, semitendinosis and

gracilis.

In the middle of stance phase, the requirements for medial-lateral stability at

the knee are reduced, however the tensor fasciae latae continues to provide stability

to the pelvis until toe off. Activity of the gluteus medius muscle decreases during

midstance. Adductor magnus and adductor longus begin acting towards toe off,

and work eccentrically during the acceleration part of swing phase to restrain the

lateral weight shift to the opposite extremity (Norkin and Levange, 1992).

2.2.3 Stair Climbing

Climbing stairs is a commonly performed task during normal activities of daily

living. Although similarities exist between level walking gait and stair climbing,

the significant differences are the greater ranges of joint motion, particularly hip

and knee flexion, and larger muscle forces involved. Bergmann et al. (2001) found

torque on the hip joint to be 23% greater during stair climbing than normal gait,

which certainly has strong implications for the stability of hip replacement implants.

Stair gait, like level walking gait, has both swing and stance phases. The stance

phase can be divided into weight acceptance, pull up and forward continuance.

The swing phase is subdivided into foot clearance and foot placement (Norkin and

Levange, 1992). Weight acceptance is comparable to the heel strike to foot flat

phases of walking gait. The pull up portion is a period of single-limb support. The

initial part of pull up is a time of instability at the joints, since all of the body

weight is shifted onto the supporting extremity when the hip, knee and ankle are

flexed. Most of the work during pull up is achieved by the knee extensors, rectus

femoris and vastus lateralis. The foot clearance period corresponds roughly to the

midstance to toe off phases of walking gait.


2.2.4 Joint and Muscle Forces

Both external and internal forces act on the hip. External forces are gravity, inertia,

and the ground reaction force. Internal forces are mainly created by the muscles.

Ligaments, tendons, joint capsule and bones work to resist, transmit, and absorb

forces.

The hip joint reaction force can be roughly estimated by the partial body weight

supported above. Joint compression due to muscle forces should also be taken into

account. Pauwels (1980) (originally published in 1965) used a graphical method to

estimate the joint reaction force during single-legged stance from anterior-posterior

view radiographs. Equilibrium of the pelvis was described in terms of balanced

moments due to the hip joint force and the abductor muscle force (Figure 2.9).

Moment arms and force directions were measured directly from the radiographs.

This method was also applied to the equivalent body position during slow gait. An

approach such as this should be limited to static or quasi-static analyses. Other

investigators have developed similar mathematical models (e.g., Bergmann et al.,

1997; Genda et al., 2001). During activity, inertia and muscle forces dramatically

alter the mechanical situation, and more robust methods are required.

In vivo hip joint reaction forces may be estimated more accurately using either

inverse dynamics or instrumented hip prostheses (Table 2.3). The modern inverse

dynamics approach uses three-dimensional video motion capture systems to measure

joint kinematics. Local coordinate systems are defined for each body segment by

three noncollinear markers. An array of video cameras determines the location of

each marker in global space, thus giving the orientation of each local coordinate

systems in global space. Relative movements between local systems are computed

using Euler/Cardan angles, assuming rigid body mechanics. The ground reaction

force is measured by an in-floor force plate and then used as an input, along with the

kinematic data, in a anthropometric model to determine the moments and forces

from the distal to proximal joints of the lower limb (hence inverse kinematics).


Figure 2.9: Static equilibrium of the pelvis in single-legged stance. The partial body weight (BW) is balanced by the hip joint force ( J) and the force of the abductor muscles (A). Reproduced from Cristofolini (1997).


Table 2.3: Peak hip joint reaction force for normal walking. ID, inverse dynamics; IP, instrumented prosthesis; MM, mathematical model. Remarks. *during slow gait; tused accelerometers fixed to the thorax as model input; +during single-legged stance.

Force Speed Average Authur Method (N/BW) (m/s) Subjects Age

Crowninshield et al. (1978) ID 4.3 1.0 1 25 Kotzar et al. (1991) IP 2.7 N/A 2 70 Bergmann et al. ( 1993) IP 3.5 0.83 2 76

IP 4.0 1.39 Bergmann et al. (1997) IP 3.2 0.83 1 89 Bergmann et al. (1997)* lVIM 2.7 N/A 1 89 Pedersen et al. ( 1997) IP 3.1 0.89 1 72 van den Bogert et al. (1999)t ID 2.5 1.5 9 41 Bergmann et al. (2001) IP 2.4 1.09 4 61 Genda et al. (2001)+ MM 2.3 N/A 56 25-6.5

To be realistic, muscle forces must be incorporated into the model. This leads

to quasi-static indeterminacy at each time increment because of the large number

of forces involved. An optimisation scheme, that minimises some objective func-

tion like muscle energy or stress, must be implemented to resolve the distribution of

forces between the various muscles. The force a muscle can generate is dependent on

muscle stretch and the physiological cross-sectional area. The line of action is gen-

erally represented by a straight line approximation, sometimes including wrapping

around bony structures. The advantage of the inverse dynamics system is its nonin-

vasive nature, and a large number of subjects can be examined. However, the results

are only as good as the musculoskeletal model used. Electromyography (EMG) is

often used either as model constraints or for validation purposes ( Crowninshield

et al., 1978). Furthermore, the action of antagonistic muscles is also often ignored.

These models can predict hip joint reaction force results within, at worst, 15-20%

of values from instrumented prostheses (Heller et al., 2001b; Stansfield et al., 2003).

Instrumented hip prostheses are able to measure in vivo hip joint reaction forces

experimentally using internal force sensors and telemetry systems. This is a highly

invasive procedure, and the number of subjects is consequently limited. It can only

be performed on patients requiring hip replacement. This makes it impossible to

obtain results for a "normal" active population. The biomechanics of a reconstructed


hip joint may also differ from a normal hip. This method allows data to be obtained

outside the laboratory environment, and therefore over a wide range of activities.

The large loads on the femoral head have a fairly constant direction regardless

of activity (Bergmann et al., 2001; Kotzar et al., 1991). Large loads are directed

downwards, laterally and posteriorly. Since muscle contractions produce many of

the loads experienced by the femur, it is not surprising that much of the loading is

in line with the femur, as this is the line of action of many of the larger muscles. In

contrast, the direction of loading in the acetabulum varies considerably (Pedersen

et al., 1997). Peak values of hip joint reaction force occur just after heel strike (first

peak) and just prior to toe off (second peak) (Figure 2.10). This joint reaction force

Forces. Femur System [%BW} 250

-50 0 25

F-

PFL\AIN1

%Cycle

Figure 2.10: Components and magnitude of the hip joint reaction force from an individual subject during a walking gait cycle. Reproduced from Bergmann et al. (2001).

is obtained from a single subject, and in this case, the largest peak occurs around

foot flat. A similar result was obtained by Cheal et al. (1992) (Table 2.4). Duda

et al. (1998), on the other hand, found the greatest hip joint force closer to toe off

(Table 2.5).

Most biomechanical models of the lower limb tend to adopt joint and muscle

data from studies by Brand et al. (1982, 1986), Crowninshield et al. (1978) and

Patriarca et al. (1981) (e.g., Cheal et al., 1992; Duda et al., 1998, 1997; Heller et al.,

2001b; Pedersen et al., 1997; Stansfield et al., 2003), often adapting them to include

wrapping around underlying structures. Cheal et al. (1992) calculated the force


components and magnitudes of muscles and the hip joint contact, for three stages

of the stance phase of gait (Table 2.4).

Table 2.4: Joint and muscle force magnitudes ( x BW) of the proximal femur for three phases of gait according to Cheal et al. (1992).

Force Heel Strike Midstance Toe Off

Adductor longus 0.20 0.30 Adductor magnus 0.20 0.30 Gluteus maximus (ant.) 1.28 Gluteus medius 0.72 0.80 1.18 Gluteus minimus 0.54 0.30 0.61 Iliopsoas 1.30 2.60 Piriformis 0.20 Vastus intermedius 0.40 Vastus lateralis 0.40 Vastus medialis 0.33 Joint contact 4.64 3.51 4.33

Duda et al. (1998) incorporated the small rotators of the hip, the short head

of biceps femoris and the ilioibial tract into their model (Table 2.5). The iliotibial

tract was modelled by tensor fasciae latae and a part of gluteus maximus, with

a pseudo-insertion point on the greater trochanter. The magnitudes of each force

are provided for three phases of the gait cycle. These are absolute values of force,

not scaled by body weight. Ten percent of the gait cycle corresponds to the the

instant of maximum abductor and adductor activity, 30% is the first peak in the

ground reaction force and 45% is the second peak, where the axial component of

the hip joint force reaches its maximum. Body weight in this case is 70 kg, which

corresponds to a joint reaction force of 3.19 BW at 45% of the gait cycle. This data

was also used in a study by Stolk et al. (2001).

Even with all of the biomechanical analysis tools available, the actions of some

muscles and soft tissues are not fully understood. The function of the iliotibial tract

is probably the best example of this, with little consensus in the literature. The

tensor fasciae latae muscle and about three-quarters of the fibres of gluteus max

imus insert into the iliotibial tract, which in turn attaches to the lateral condyle

of the tibia. The iliotibial tract is also attached to the linea aspera via the lateral


Table 2.5: Joint and muscle force magnitudes (Newtons) acting on the femur during three phases of the gait cycle. Adapted from Duda et al. (1998).

Force (N) 10% Gait Cycle 30% Gait Cycle 45% Gait Cycle

Hip joint contact 1408.96 1697.06 2190.18 Adductor longus 3.87 Adductor magnus (inferior) 61.99 Adductor magnus (superior) 86.40 Adductor minimus 56.01 Biceps femoris (short head) 49.66 61.28 91.97 Gluteus maximus 1 125.92 136.02 131.24 Gluteus maximus 2 99.87 110.63 90.98 Gluteus maximus 3 47.10 Gluteus medius 1,2,3 249.49 289.96 306.06 Gluteus minimus 1,2,3 168.76 246.83 284.32 Iliopsoas 72.16 174.21 Obturator internus,

superior & inferior gemelli 30.50 55.16 51.69 Pectineus 1.99 Piriformis 68.28 104.53 102.91 Quadratus femoris 44.57 Tensor fasciae latae 54.59 48.45 76.84 Vastus intermedius 62.93 Vastus lateralis 228.12 Vastus medialis 272.22 8.61

intermuscular septum. One theory is that the iliotibial tract acts as a lateral ten-

sion band during stance phase to keep the femur in axial compression, rather than

bending. The even distribution of bone mass on the medial and lateral cortices

of the femoral diaphysis is often used to back up this claim (Fetto and Austin,

1994; Ling et al., 1996; Taylor et al., 1996). Contrasting this, Cristofolini (1997)

proposed that it was unlikely for the femur to be optimised for a specific loading

position (i.e., single-legged stance) as this could lead to weakness during other daily

activities. Ling et al. (1996) pointed out that a hollow tube gives no mechanical or

weight advantage for resisting axial loads. They instead suggested that the shaft

is tubular in cross-section to resist torsion loads. A tube is, of course, suitable for

resisting bending also. Lanyon (1987) proposed that the cross-section was shaped

as it is to provide a high resistance to bending from abnormal directions, and only

low resistance to loads applied during normal activity.


Pauwels (1980), who considered the lower extremity in single-legged stance first

as a column, and then introduced joints, musculature, and ligaments one after the

other, proposed that a lateral tension band was needed to reduce large bending

moments in the femur. Under this condition, bending stresses in the femur were

predicted to decrease from proximal to distal, while axial stresses were constant

along the femoral shaft. Ling et al. (1996) likened this tension band effect to the

windward shrouds on a yachts rigging, which keep the mast in tension despite the

bending moment due to the wind on the sails and the righting moment of the keel.

Duda et al. (1997) indicated that at the proximal and distal ends of the femur,

the axial and shear forces showed their highest values. Internal loads were reduced

towards the diaphyseal part, which was mainly under axial compression, with shear

forces close to zero. This studies suggest that the lateral musculature probably does

contribute to the reduction of bending moments in the femur.

Because of these uncertainties, it will not be possible to produce an adequate

representation of the muscles until their forces and actions are reliably established.

Consequently, simplifications are inevitable when modelling the musculoskeletal sys

tem.

Chapter 3

Hip Arthroplasty

3.1 Indications

Total hip arthroplasty is a surgical procedure involving replacement of the bearing

surfaces of the hip with prosthetic devices. An intramedullary stem articulates with

an acetabular cup, via a ball and socket joint. The components may both be fixed in

place using a polymethylmethacrylate grouting agent (cemented), or by biological

fixation relying on direct bone ingrowth/ ongrowth to the material ( uncemented).

Hybrid fixation describes the situation where one component is cemented and the

other is uncemented. The fixation method, particularly when concerned with the

femoral component, strongly influences the transfer of load from the implant to

bone.

Total hip arthroplasty is generally indicated for end-stage arthritic involvement

of the hip in a patient with pain severe enough to cause disability and require med

ication, and is usually associated with loss of joint mobility. The most common ap

plication of total hip replacement is in primary or secondary osteoarthritis, caused

by trauma, congenital dysplasia, or other conditions. Other indications include

osteonecrosis, rheumatoid arthritis, gouty arthroplasty, calcium pyrophosphate de

position, ochronosis, displaced fractures of the femoral neck in elderly individuals,

primary and secondary tumours, and metabolic conditions such as Paget's disease.

29

3.2 EVOLUTION OF TOTAL HIP ARTHROPLASTY 30

Patient factors such as age, physical status, general medical condition, level of pain

and disability, response to conservative therapy, and desired lifestyle must be consid

ered before total hip arthroplasty is proposed (Eftekhar, 1978; Stulberg and Hupfer,

1991).

3.2 Evolution of Total Hip Arthroplasty

Early surgical efforts at alleviating pain from degenerate hip joints involved resection

or osteotomy of the proximal femur. No attempt was made to reform articular

surfaces, and ankylosis of the joint often resulted (McElfresh, 1991).

Interpositional arthroplasty was a procedure developed to restore motion to

ankylosed hip joints in the mid 1800s. The joint was separated, articular surfaces

were refashioned, and an interpositioning substance was placed to prevent subse

quent refusion (Fielding and Stillwell, 1987). Materials such as muscle, fibrous

tissue, celluloid, silver plates, rubber sheets, magnesium, zinc and decalcified bone

were used for interpositioning (Eftekhar, 1978).

In Boston, Smith-Peterson developed the "mould arthroplasty". From 1923, he

employed glass, Bakelite and Pyrex cups. Failure of the cups was a problem until

he experimented with Vitallium, a cobalt-chromium alloy, as an interpositioning

material (McElfresh, 1991). Vitallium was adopted following experimentation by

Venable and Stuck in Texas (Venable et al., 1937). The design was modified by

Otto Aufranc, an assistant to Smith-Peterson, and mould arthroplasty became a

successful procedure. From this concept came hip-socket, or cup arthroplasty, in

which a reshaped femoral head articulated with a polished metal cup fixed in the

acetabulum. This procedure never became popular (Fielding and Stillwell, 1987).

The search for dependable and effective techniques continued. Prosthetic fe

moral head replacement was attempted by Delbet in 1919, who used reinforced

rubber, and by Groves who fashion a hemispherical short stem device from ivory

in 1927. Neither was particularly successful (Fielding and Stillwell, 1987). In 1940,


Moore and Bohlman implanted a specially made Vitallium prosthesis to replace

the proximal femur. This is the first known metallic replacement hemiarthroplasty

(Eftekhar, 1978). Femoral head replacement, similar to Grove's design, was further

refined by the Judet brothers in 1950 using acrylic material (Figure 3.2A), by and

others. During the 1950s, short stem prostheses were replaced by intramedullary

long stem designs which gave greater stability. The devices proposed by Thompson

in 1950 and Moore in 1952 were the basis for many future designs (Figure 3.2B and

C).

Because of the bipolar nature of joint disease, most devices replacing only one

side of the joint were not successful. Wiles is credited with the first total hip arthro-

plasty (THA) in 1938 (Figure 3.1. This consisted of a ball and cup device fabricated

Figure 3.1: The first total hip arthroplasty is attributed to Phillip Wiles, 1938. Reproduced from Fielding and Stillwell (1987).

from stainless steel. A hemispherical ball was fixed by a bolt through the femoral

neck, and the cup was fixed by screws through a buttressed plate. No other work

with total hip replacement devices was reported until the 1950s. Surgeons tried to

articulate a Thompson or Moore stem with a large Smith-Peterson cup, but found

wear to be a problem. Subsequently IvicKee and Farrar designed a metal cup to

fit over a Thompson prosthesis in 1951, while in 1966, Ring developed a metal


acetabular cup which screwed into the pelvis and articulated with a Moore pros-

thesis (Figure 3.2D) (McElfresh, 1991). Parallel to Ring's work, Russian surgeons

developed a metal-on-metal system, but subsequently interpositioned polyethylene

(Figure 3.2E) (Eftekhar, 1978).

A a

c

F H

Figure 3.2: Hemiarthroplasty prostheses: (A) Acrylic Judet, (B) Moore, (C) Thompson. Total arthroplasty prostheses: (D) Ring, (E) Sivash, (F) McKee--Farrar, (G) Charnley, (H) Muller. Acrylic cement was employed for (F), (G), and (H). Reproduced from Fielding and Stillwell (1987).

Acrylic bone cement (polymethylmethacrylate, PMMA) fixation was introduced

to orthopaedics by Kiaer and Haboush in 1950 (Haboush, 1953; Kiaer, 1951), which

had a profound effect on the subsequent development of arthroplasty (Fielding and

Stillwell, 1987). Use of PMMA as a grouting agent for femoral and acetabular

components was popularised by Charnley, who showed that generous quantities

of cement were required to provide adequate support to an implant, and provide


uniform load transfer to the femur. McKee and Farrar redesigned their total hip sys

tem to incorporate cement, with increased success (Figure 3.2F) (Eftekhar, 1978).

The connection between the cement and the bone and between the cement and the

implant is mechanical, without any form of chemical bonding (Kiihn, 2000).

Charnley, who is considered the father of modern hip arthroplasty, also con

cerned himself with wear and lubrication at the joint interface. He initially inves

tigated using thin Teflon® (PTFE) shells on the femoral and acetabular sides to

reduce friction. Failure prompted the use of a small prosthetic head articulating

with a thick Teflon® socket. The small femoral head decreases frictional shear

forces at the bearing interface, theoretically improving socket fixation as well. Ad

verse tissue reaction and wear of the Teflon® led to the adoption of ultra-high

molecular weight polyethylene. The resulting total hip arthroplasty, termed "low

friction arthroplasty", with a cemented intramedullary femoral prosthesis having a

22 mm femoral head, bearing on a low friction polyethylene cup (Figure 3.2G), was

the inspiration for most future developments (Fielding and Stillwell, 1987). Charn

ley also showed the importance of concentrating on the details of surgical technique,

including infection control (Eftekhar, 1978).

Miiller followed Charnley and developed a system with variable neck sizes and

a 32 mm head diameter for greater stability (Figure 3.2H). Other cemented designs

were developed by Ling, Aufranc and Turner, Amstutz, Harris, and others (Fielding

and Stillwell, 1987).

During the first decades with cemented THA, high infection rates were a signifi

cant problem. Improved technique and use of systemic and local antibiotics helped

to reduce this problem. Aseptic loosening became the next major problem. This was

associated with the widening of indications for hip arthroplasty in the 1970s, with

procedures in young and active patients proving less satisfactory. Problems with

osteolysis and bone resorption, caused by "cement disease" (Jones and Hungerford,

1987), led to interest in uncemented implant fixation (Nivbrant, 1999).

3.3 BIOMATERIALS 34

The AML, Harris-Galante and PCA were early porous coated designs that were

widely adopted. Titanium was investigated as a prosthesis material, as bone was

found to grow directly onto its surfaces with certain roughness. Most uncemented

implants were released onto the market without undergoing clinical trials, and there

fore results were often worse than the cemented devices whose problems the implants

were designed to address. Success with cemented femoral stems has been improved

by better cementing techniques, however cemented acetabular components are still

a concern, leading to use of hybrid fixation, with cemented stems and uncemented

cups (Nivbrant, 1999). Aseptic loosening of components still proves to be the most

common cause of revision surgery today (Malchau et al., 2002).

3.3 Biomaterials

Selection of a material for an in vwo application in the body will depend on it

having the appropriate physical properties to perform the task, the ability to be

manufactured and sterilised easily, and biocompatibility.

3.3.1 Metals

The three common alloys used in orthopaedics are stainless steel, cobalt-chromium

alloy and titanium alloy. None of these materials was developed specifically for

biomedical applications, however their strength and corrosion resistance have led to

their use (Wright and Li, 2000).

Stainless Steels

The most frequently used form of stainless steel is 316L (ASTM F138), which is a

low carbon concentration, austenitic stainless steel (Park and Kim, 2000). 316L steel

is an alloy of iron and carbon, also containing chromium, nickel and molybdenum,

with small amounts of manganese, phosphorous, sulphur and silicon (Figure 3.3).

Stainless steel devices are passivated by immersion in a nitric acid bath to create

3.3 BIOMATERIALS

M<>(2·4%)

l(c§§:::::::::!j c {0-03%) ·-Mn,P. S.Sl.H.II"<.totall

Stainless Steel (3!6l)

Titanium {Ti • 6AI· 4V)

Cobalt Alloy (F151

35

Figure 3.3: Composition of some common orthopaedic biomaterials. Reproduced from Wright and Li (2000).

a chromium oxide (Cr20 3 ) layer on the surface. The low carbon concentration in

316L stainless helps maintain corrosion resistance by stopping formation of brittle

carbides. The carbides significantly weaken the material by making it susceptible

to corrosion-related fracture. Stainless steel is generally cold-worked by about 30%

for orthopaedic applications (Table 3.1), however it is prone to crevice and stress

corrosion, and is usually used for relatively short-term load bearing applications

(Wright and Li, 2000).

Cobalt-Chromium Alloys

Cobalt-chrome alloys are available in cast (ASTM F75), forged (ASTM F799) and

cold worked (ASTM F90, F562) compositions. These alloys are all primarily cobalt,

with significant amounts of chromium for corrosion resistance. The F75 and F799

alloys contain about 60% cobalt and 28% chromium (Figure 3.3), while the F90 and

F562 alloys have less cobalt and chromium, but large quantities of tungsten and

nickel. F75 alloy components are usually manufactured using investment casting,

or hot isostatic pressing (HIP) to improve the microstructure. F75 is often used

3.3 BIOMATERIALS 36

Table 3.1: Typical mechanical properties of implant materials. Reproduced from Wright and Li (2000).

I\1aterial Elastic Yield Ultimate Endurance (ASTM Modulus Strength Strength Limit Designation) Condition (GPa) (MPa) (l\1Pa) (MPa)

Stainless steels F55, F56, Annealed 190 331 586 241-276 F138, F139 30% Cold worked 190 792 930 310-448

Cold forged 190 1213 1351 820 Cobalt-chrome alloys

F75 As cast/ annealed 210 448-517 655-889 207-310 HIP 253 841 1277 725-950

F799 Hot forged 210 896-1200 1299-1586 600-896 F90 Annealed 210 448-648 951-1220

44% Cold worked 210 1606 1896 586 F562 Hot forged 232 965-1000 1206 500

Cold forged/aged 232 1500 1795 689-793 Titanium alloys

F67 30% Cold worked 110 485 760 300 F136 Forged annealed 116 896 965 620

Forged/heat treated 116 1034 1103 620-689

to fabricate porous coatings for biologic fixation of orthopaedic devices. The F799

alloy has superior mechanical properties to F75, achieved by hot forging. F90 and

F562 also have good mechanical properties due to cold-working (Table 3.1). Cobalt

chrome alloys are suitable for a wide range of orthopaedic applications, including

all metallic components of joint replacements. These alloys also have excellent

corrosion resistance and biocompatibility in bulk form (Wright and Li, 2000).

Titanium and Titanium Alloys

Titanium and its alloys also have excellent corrosion resistance and biocompatibility,

which makes them ideal for biomedical applications. The corrosion resistance is

superior to stainless steel and cobalt-chrome alloys, and is provided by a passivating

layer of Ti02 . The oxide layer is well tolerated by bone, becoming osseointegrated

with little evidence of intervening fibrous tissue. Commercially pure (CP) titanium

(ASTM F76) is frequently used in dental implants and for wire mesh that is sintered

on to titanium alloy implants for uncemented joint replacements. The most common

3.3 BIOMATERIALS 37

titanium alloy for orthopaedic devices is F136 alloy, which consists of aluminium

(about 6%) and vanadium (about 4%) alloying elements (Figure 3.3), so this alloy

is often called Ti-6Al-4V (Park and Kim, 2000). The alloy has excellent fatigue

resistance, and it can be worked to further improve its properties (Table 3.1). Ti-

6Al-4V is often used in joint replacements. Disadvantages associated with titanium

alloy include high notch sensitivity, which can substantially decrease fatigue life, and

low hardness, which give it poor wear resistance and makes the material unsuitable

for bearing surfaces (Wright and Li, 2000).

3.3.2 Polymers

Polyethylene and polymethylmethacrylate are the most commonly used polymers in

orthopaedic applications. Polyethylene is used extensively for load bearing surfaces

in joint replacements (Lee et al., 2000), while PMMA is used for bone cement as

popularised by Charnley.

Polyethylene

Polyethylene is a long-chain polymer consisting of ethylene molecules ( C2H4). The

mechanical properties are dependent on its chemical structure, organisation, molec

ular weight and thermal history. Polyethylene is a two-phase viscoplastic solid con

sisting of crystalline domains within an amorphous matrix. The crystalline regions

are connected by bridging molecules which improve strength. The polyethylene com

monly used in orthopaedic applications is ultra-high molecular weight polyethylene

(UHl\fWPE), with the polymer chains having a molecular weight of 3~6x106 gjmol

(Heisel et al., 2004).

Cross-linking of the polyethylene chains has been proposed to improve the wear

properties (e.g., Chiesa et al., 2000; Muratoglu et al., 2001). Cross-linking occurs

when free radicals located on the amorphous regions react to form a covalent bond

between adjacent molecules. This is thought to resist intermolecular mobility, de

creasing deformation and reducing wear. Unfortunately, cross-linked polyethylene

3.3 BIOMATERIALS 38

exhibits reduced yield strength and increased brittleness, in proportion to the de

gree of cross-linking (Heisel et al., 2004). Cross-linking also produces a large num

ber of submicron and nanometre-sized wear particles, which is thought to provoke

a greater inflammatory response than particles from non-cross-linked polyethylene

(e.g., Endo et al., 2002; Ingram et al., 2002).

Sterilisation methods also influence the mechanical properties of UHlVI\:VPE (Af

fatato et al., 2002; Muratoglu et al., 2003; Reeves et al., 2000). Polyethylene compo

nents are sterilised with gamma irradiation, gas plasma or ethylene oxide. Gamma

irradiation breaks covalent bonds within the polyethylene molecules, producing free

radicals which can react with oxygen. Oxidation causes chain scission which ulti

mately reduces strength and increases brittleness. Gamma irradiation in air and

long shelf life increase exposure of free radicals to oxygen, increasing oxidative ef

fects. Oxidation can be reduced by sterilisation in nitrogen or a vacuum. Remelting

the polymer can drive free radicals to a cross-linking reaction, removing the poten

tial for oxidation, however this induces changes in the crystalline structure which

can reduce some material properties (Heisel et al., 2004).

Polymethylmethacrylate

PMMA is generally available as a two part kit consisting of a liquid and a pow

der. The liquid is predominantly methylmethacrylate monomer, but also contains

hydroquinone which ensures that the monomer does not polymerise due to light

or heat. The liquid also contains N,N-dimethyl-p-toluiodine which helps accelerate

the polymerisation one the reaction has begun. Polymerisation is initiated when

the liquid comes into contact with the initiator, dibenzoyl peroxide, which is mixed

with the powder. In addition to the initiator, the powder mainly contains PMMA,

or a blend of Pl\IMA polymer with a copolymer of PMMA and polystyrene, or

PMMA and methacrylic acid. The copolymers provide toughness to the cement.

To make the cement radiopaque, Ba804 or Zr02 are also present in the powder.

3.3 BIOMATERIALS 39

Polymerisation occurs by an exothermic reaction, although thermal necrosis of tis

sue does not seem to an important factor in cemented prosthesis performance. Third

generation cementing techniques, involving vacuum or centrifuge mixing, pulsatile

lavage to prepare the femoral canal, pressurised cement injection and use of implant

centalisers, have enhanced the performance of cemented fixation (Wright and Li,

2000).

3.3.3 Ceramics

In orthopaedics, ceramics are used for two applications. The first is for bearing sur

faces in total joint replacements, and the second is for bone graft substitutes and as

coatings for metallic implants. Bearing surfaces required ceramics such as alumina

and zirconia that are hard, dense and bioinert, with high wear resistance. Ceramics

used for bone graft substitutes and coatings are generally less dense, bioactive or

bioresorbable materials that provide an osteoconductive surface to which bone will

bond. This type of ceramic includes calcium phosphate and bioglass (Wright and

Li, 2000).

Alumina

Aluminium oxide (Ab03 ) has excellent wear properties due to a very low coefficient

of friction (Park and Lakes, 1992). The alumina surface also has higher wettability

than other polyethylene and metal bearing materials, giving better lubrication.

Refinement of manufacturing techniques has led to a reduction in the incidence of

femoral head fracture (Wright and Li, 2000).

Zirconia

Zirconium oxide (Zr02 ) is also used for femoral heads, but only for articulation

against UHMWPE, because it does not wear well against itself or other ceram

ics (Wright and Li, 2000). Zirconia has low friction and wear resistance against

UHMWPE, and is tougher than alumina. Zirconia, unlike alumina, is unstable in

3.3 BIOMATERIALS 40

its pure form and must be stabilised~usually with yttrium oxide--to prevent it

changing phase. Zirconia implants must be sterilised at room temperature to pre

vent phases change, which can cause surface roughening (Li and Hastings, 1998).

Bioceramics and Glasses

Certain ceramics and glasses have been found to be osteoconductive in nature, with

osteoblasts forming bone in direct contact with the ceramic surface. This results in a

strong chemical bond between the ceramic and bone. Ceramics have therefore been

applied as coatings to uncemented prostheses to improve implant fixation to bone.

Hydroxayapatite (HA) is the most common ceramic coating. The composition of

the coating is not usually pure HA, and may consist of calcium oxide, tricalcium

phosphate, and amorphous calcium phosphate, depending on the manufacturing

process. Bioactive glasses are also being investigated for coating applications, and

include Si02 , CaO, NaO, and P 205 (Wright and Li, 2000).

3.3.4 Biological Response to Biomaterials

A biomaterial is defined as a synthetic material used to replace part of a living

system or to function in intimate contact with living tissue (Park and Lakes, 1992).

The biocompatibility of the material is a function of its ability to perform with an

appropriate reaction of a living system to the presence of the material (Black, 1992).

The biological performance of a material is determined by the interactions be

tween the host and material responses. The host response is the local or systemic

response, other than the intended therapeutic response, of living systems to the ma

terial. The host response may be both local and systemic. The material response

is the response of the biomaterial to living systems, and includes (Black, 1992):

• corrosion (pitting, galvanic, crevice, fretting, stress, microbiological)

• wear (adhesive, abrasive, third-body, corrosive, fatigue)

• dissolution

• degradation

3.3 BIOMATERIALS 41

• swelling

• leaching

• calcification

The host response may be dependent on the physical size of the material. Type I

and type IV hypersensitivity may be associated with biomaterials.

The primary considerations for biocompatibility testing are the type of tissue the

biomaterial contacts, the duration of intended contact, and the nature of contact

(direct or indirect). Biocompatibility is tested according to ISO Standard 19903-1.

The Standard describes a number of in vitro and short- to long-term in vivo tests

to determine a material's biocompatibility, including:

• cytotoxicityt

• sensitisation t

• irritation or intracutaneous reactivity

• systemic toxicity (acute)

• subchronic toxicity (subacute toxicity)

• genotoxicityt

• implantationt

• haemocompatibility

• chronic toxicityt

• carcinogenicityt

Tests marked with t are appropriate for joint replacement devices.

The metals, polymers and ceramics described above have been successfully used

in orthopaedic applications. These materials and their degradation products inter

act with the surrounding physiologic environment and may elicit a host response

that influences the performance of the surgical reconstruction (Jacobs et al., 2000).

Metals

Metals are released from implants in three ways: dissolution, corrosion and wear

(Brown and Merritt, 1991). Dissolution begins early as the implant and the body

3.3 BIOMATERIALS 42

fluid equilibrate, and involves the release of metal ions. Corrosion occurs when there

is a difference in electrochemical potential between two regions in a metal, and can

occur in a number of forms. Metals with a high negative electropotential are prone

to corrosion. However, for some metals corrosion is rapid and results in formation

of a thin passivating oxide layer which prevents further oxidation. \Vear can release

metallic debris as well as metal ions. The host response to metallic debris is initially

the same as that to other debris, however metals are usually eliminated by further

corrosion and dissolution. Metallic debris could migrate to the bearing interface,

causing third-body abrasive wear, and there is also concern about dissemination of

particles beyond the local tissues.

Three metallic elements-calcium, potassium and sodium-are present in large

quantities in the body and play major physiological roles. At least thirteen other

metallic elements are present in trace quantities only. Most of these are present as

non-trace constituents in orthopaedic implants: iron, aluminium, vanadium, man

ganese, nickel, molybdenum, titanium, chromium and cobalt. These trace elements,

with the exception of titanium, play vital physiological roles, and are termed essen

tial trace elements (Black, 1992).

Type IV, delayed-type hypersensitivity has been reported for nickel, cobalt and

chromium. Metal ions are thought to have too low a molecular weight to be capable

of directly activating either humoral or cell-mediated immune responses, however it

is thought that they bind to proteins to form complexes called haptens, which posses

antigenic qualities (Brown and Merritt, 1991). Specific responses to metal sensi

tivity include severe dermatitis, urticaria, and/or vascularitis (Jacobs et al., 2000).

Sensitivity may be related to other clinical symptoms, such as aseptic loosening

(Black, 1992).

Osteolysis

Osteolysis is characterised by destruction of bone and may be present as focal or

diffuse bone loss. Osteolysis has many etiologies, including primary and metastatic

3.4 FEMORAL COMPONENT DESIGN 43

bone tumours, infection, rheumatoid diseases and metabolic abnormalities. In rela

tion to joint prostheses, osteolysis presents as a slowly progressing, thin radiolucent

line surrounding a loose prosthesis, or progressive ballooning and scalloping in the

periprosthetic bony bed. A major cause of osteolysis is particulate wear debris

from articular surfaces, modular interfaces, areas of impingement, and at areas

of abrasion (Jacobs et al., 2000). Metallic, polymeric and ceramic particles have

all been associated with osteolysis, although polyethylene particles generated by

normal articular surface wear is the predominant particle type (Archibeck et al.,

2001). Intra-articular pressure generated during gait may serve to pump particles

throughout the joint and periprosthetic space (Jacobs et al., 2000).

Osteolysis results from increased local synthesis of bone resorbing factors by

macrophages. The cells phagocytose the small particles, but are unable to di

gest them. This stimulates increased macrophage accumulation, proliferation and

synthesis of bone resorbing factors. The reaction is self-sustaining as the indi

gestible particles are egested and recirculated. The cellular response is thought to

be determined by the size, composition and dose of the particulate. Improvements

in design, manufacturing, surgical technique and pharmacological treatments may

limit the amount of wear particles generated and consequently reduce the degree of

osteolysis and related implant loosening (Jacobs et al., 2000).

3.4 Femoral Component Design

3.4.1 Material

The choice of material for a femoral prosthesis will depend on strength, fatigue re

sistance, corrosion resistance, biocompatibility and wear resistance. Consequently,

cobalt-chrome and titanium alloys are frequently used for orthopaedic joint replace

ments. With cemented implants, reducing the elastic modulus has the effect of

increasing cement stress and accordingly the probability of cement failure (Crown

inshield, 1987).


The elastic modulus is particularly important for uncemented hips. Titanium

alloy has approximately half the stiffness of cobalt-chrome alloy, and should theoreti

cally share more load with the bone, reducing stress shielding (Huiskes, 1996). Stress

shielding causes adaptive bone remodelling changes in accordance with "Wolff's

Law". Implant stiffness has been cited as an important factor in determining the

extent of proximal bone loss (Bobyn et al., 1992; Engh et al., 1990; Sumner and

Galante, 1992), although implant-to-bone stiffness ratio has been proposed as a

more significant determinant (Jacobs et al., 1992; l\1cGovern et al., 1994; Sumner

and Galante, 1992; Sychterz et al., 2001). Some researchers have proposed that

there is little clinical benefit of titanium over cobalt-chrome (Jacobs et al., 1993;

Jones and Kelley, 2001; Mont and Hungerford, 1997).

3.4.2 Geometry

Cemented stem geometries can be classified as shape- or force-closed designs. A

shape-closed design implies that fixation is provided by a match of shapes. A force

closed design obtains stability by the action of forces (Huiskes et al., 1998). Shape

closed prostheses include collared designs, while force closed prostheses are tapered

and stability comes from subsidence into the cement as it creeps. Other design

parameters include stem size, stem cross-sectional shape, and stem length. These

factors contribute to the pattern of load transfer in the proximal femur. Cemented

implants are sized to create a circumferential cement mantle between the stem and

the bone, with the cement playing an important role in stress transfer to the femur.

Cement failure is a concern, and high cement stresses associated with sharp edges

and with thin cement mantles should be avoided (Crowninshield, 1987). The stem

should also resist rotation by using a flat or square cross-section, a curved stem, or

by stabilising grooves (Nivbrant, 1999)

Uncemented prostheses rely on intimate contact with bone for fixation. The

exact femoral geometry is impossible to predict, so line-to-line contact cannot be

expected over the implant surface. Implants can be divided into three categories:


wedge shaped, tapered and cylindrical (Jones and Kelley, 2001). ·wedge shaped

stems (e.g., PCA) aim to fill the proximal femur and transfer load proximally, and

may be curved, or "anatomic". Tapered stems (e.g., Synergy) obtain contact more

distally to provide more uniform load transfer, and fixation comes from a self-locking

mechanism (Bourne and R.orabeck, 1998). Cylindrical stems (e.g., AML) obtain

some degree of fixation in the diaphysis. The surface coating usually extends to

the level at which primary contact and fixation occurs. Implant fit is important for

stability and contact with bone, as well as load transfer. This is achieved through

precise instrumentation and bone preparation (Miller, 1991). Cylindrical stems are

more versatile for patients with abnormal femoral geometry, while wedge shaped

stems provide better stability in patients with normal femoral anatomy (Callaghan,

1993). No specific category of implant shape has yet proven to be more successful

than the others (Nivbrant, 1999).

Implant diameter has a significant effect on stem stiffness, particularly in bend

ing. Larger diameter stems have been associated with increased stress shielding and

bone loss (Engh and Bobyn, 1988; Engh et al., 1990). The stem cross-section is also

important for resistance of torsional loads. Use of a collar on uncemented implants

is contentious. The collar relies on accurate surgical technique to obtain collar

calcar contact, which may inhibit further subsidence of the implant and prevent

maximum fixation (Callaghan, 1993).

Femoral head size influences stability and wear at the hip. Small head sizes min

imise the amount of wear, because of the relatively small movement at the interface

for a given range of motion. The limitation of small head size is decreased range of

motion due to impingement of the neck on the acetabulum, which increases the risk

of dislocation. Small diameter heads are also associated with more polyethylene

creep (R.ubash et al., 1998). Development of stronger materials has led to decreased

neck diameters (undercut heads) for larger head sizes, to reduce wear while main

taining range of motion. The most common head diameter is 28 mm. Modular


components often have a thicker neck, particularly long neck length femoral heads,

which decreases the range of motion (Nivbrant, 1999).

3.4.3 Surface Finish

The surface finish of a cemented femoral prosthesis will depend on its shape and

material. Because of low abrasive wear resistance, titanium implants should be

polished. Force-closed implants, that are designed to subside within the cement

mantle to achieve secondary fixation, should also be polished. Stems that rely on

mechanical connection with the cement (shape-closed) should probably be matte or

roughened, however abrasive wear problems can arise if disengaging occurs. Wear

particles can lead to third-body wear at the articular surface. Precoating shape

closed designs with Pl\!Hv1A has been investigated as a means of increasing implant

cement interface strength (Nivbrant, 1999).

Uncemented stems are either grit-blasted or porous coated with beads or fibres.

The coating is usually restricted to the proximal part of the implant to improve

load transfer. A circumferential coating has been advocated to inhibit the passage

of wear particles to the periprosthetic space (Mont and Hungerford, 1997). Coat

ings are applied using sintering, diffusion bonding or plasma spraying techniques

(Figure 3.4), and the resulting pore size is important for bone ingrowth (Crownin

shield, 1987). Sintering is a high temperature process allowing particle-to-particle

and particle-to-substrate bonding, and is applicable to titanium and cobalt-chrome

alloys. Sintering can lower the fatigue strength of an implant by up to 40%. Diffu

sion bonding is a relatively low temperature process, and is used in the manufacture

of titanium fibre coatings. Plasma spraying creates textured surfaces, without the

interconnecting porosity of other methods. Metal powders are partially melted in

a hot plasma flame and deposited onto the substrate surface. The fatigue strength

of titanium alloy is weakened by all of these coating because of its high notch sen

sitivity (Callaghan, 1993).

3.4 FEMORAL COMPONENT DESIGN

(a) (A) Surface and (B) cross-sectional views of a cobalt-chrome beaded porous surface.

(b) (A) Surface and (B) cross-sectional views of a titanium plasma-sprayed surface.

(c) (A) Surface and (B) cross-sectional views of a titanium fibre surface.

Figure 3.4: Porous coating techniques. Reproduced from Crowninshield (1987).

47

3.5 PERFORMANCE 48

Hydroxyapatite (HA) layers have been applied to uncemented stems to increase

ingrowth rates and enhance stability. These coatings have not yet proved to be

significantly better than non-porous coated implants, however the coating may aid

in preventing passage of wear particles (D'Antonio et al., 1996; Tanzer et al., 2001;

To nino et al., 1999).

The extent of coating is an important factor in load transfer from the prosthesis

to bone. Proximally coated implants theoretically minimise stress shielding, how

ever the reduced surface area increases the interface stresses and the possibility of

interface failure. Extensively coated implants are more likely to achieve durable

fixation (Engh et al., 1987), however removal at revision becomes complicated.

3.5 Performance

The performance of total hip arthoplasty is assessed radiographically, by dual-energy

x-ray absorptiometry (DEXA), radiostereometric analysis (RSA), and clinical scores

(Nivbrant, 1999). Radiographic evaluation is the standard method for follow up of

hip arthroplasty. On the femoral side, delineation of the periprosthetic bone into

seven zones was proposed by Gruen et al. (1979) (Figure 3.5). Radiographs are

used for grading of cementing quality and evaluation of radiolucent lines and im

plant migration are considered important for predicting loosening (Nivbrant, 1999).

Estimation of density changes, even with standardised procedures, is not accurate,

with changes of more than 20% required (Engh et al., 2000).

DEXA is able to precisely measure changes in periprosthetic bone mineral den

sity. Density is often measured in Gruen zones, for comparison between subjects

and implants (Bryan et al., 1996; Glassman et al., 2001). DEXA is accurate to

within 5%, however limb rotation can influence the results (Kilgus et al., 1993;

Kiratli et al., 1992; Rahmy et al., 2000).

RSA is used to evaluate implant migration. The method relies on small tan

talum markers implanted in the bone and the prosthesis. The three-dimensional

3.5 PERFORMANCE 49

1

6 2

5 3

Figure 3.5: Zones around the femoral component delineated by Gruen for evaluating loosening. Reproduced from Gruen et al. (1979).

coordinates of the implant markers can be calculated by using a calibration cage

and two simultaneous x-ray exposures. The radiographs are digitised and relative

movements are calculated using the appropriate software. RSA has an precision of

about 0.1 mm and 0.5° (Nivbrant, 1999).

The performance of total hip arthroplasty can be assessed using clinical scores.

The Harris Hip Score is the most popular, and measures pain, function, activities

of daily living, motion and deformity. Other scores include the WOMAC (West

ern Ontario and McMaster Universities) Osteoarthritis Index and the SF36 (lVIed

ical Outcomes Study 36-Item Short-Form Survey). Although clinical scores give a

measure of patient satisfaction, they are unable to detect early loosening and are

inadequate for identifying poorly performing designs (Nivbrant, 1999).

Chapter 4

Bone Mechanics

Bone is a rigid and hard mineralised tissue. These characteristics allow it to perform

many important biomechanical and metabolic functions. The mechanical properties

of bone allow it to maintain the shape of the body, protect the contents of the

body cavities, transmit muscle and joint forces, and provide a location for bone

marrow. The mineral content of bone serves as a store for ions, particularly calcium.

In addition, bone is a self-repairing material and able to adapt its geometric and

material properties in response to mechanical requirements. Bone is capable of

performing these functions because of its material properties, which are a function

of its composition and structure, and its biological properties.

The ability of bone to adapt to its mechanical environment is often referred to

as Wolff's Law. In 1892, Wolff published his Law of Bone Remodelling (translated

as Wolff (1986)), which stated:

" ... the law of bone remodelling is the law according to which alterations

of the internal architecture clearly observed and following mathemati

cal rules, as well as secondary alterations of the external form of the

bones following the same mathematical rules, occur as a consequence of

primary changes in the shape and stressing or in the stressing of bones."

No mathematical law has yet been derived, and some researchers have questioned

his theories (Cowin, 1997; Lee and Taylor, 1999; Roesler, 1987).

50

4. BONE MECHANICS 51

During the 1860s, the anatomist Meyer sketched the trabecular structure of the

proximal femur in the frontal plane (Figure 4.la). An engineer named Culmann

noticed a similarity between the trabecular architecture and the stress trajectories

produced by his graphical statics method in a crane he was designing (Figure 4.1b).

From Culmann's graphical statics, Wolff presumed that trabeculae in the proximal

(a) tv1eyer's representation of the bone architecture of the proximal femur.

(b) Stress trajectories determined by Culmann's graphical statics method in a Fairbairn crane shaped like the proximal femur.

Figure 4.1: Architecture of the proximal femur. Reproduced from Wolff (1986).

femur followed principal stress trajectories, and that they must therefore cross at

right angles. This hypothesis, however, neglected some fundamental principals of

continuum mechanics. Firstly, there is no correspondence between the stress trajec

tories in a linear elastic, homogeneous, isotropic object in the shape of a bone, and

the architecture of the trabeculae in a real bone of the same shape, loaded in the

4.1 STRUCTURE 52

same manner. Secondly, there is an infinite number of stress trajectories between

two points in the homogeneous object, and a finite number of trabeculae between

two points in cancellous bone. Thirdly, bones are subjected to time-varying, not

static loads (Cowin, 1997). Wolff's concentration on statics led to criticisms of his

"law" in other area also.

The writings of Wolff up until the early 1880s made no reference to bone adap

tation as a dynamic process. Rather, he believed the form of bone to be determined

by static load (Lee and Taylor, 1999). It is Roux that is understood to have in

troduced the dynamic concept of functional adaptation. Roux proposed that bone

was a "quantitative self-regulating mechanism" controlled by a "functional stimulus"

(Lee and Taylor, 1999). Some of Raux's concepts were apparently adopted later by

Wolff. Consequently, some have proposed that the name "Raux's Law" may be more

appropriate for describing the stress-adaptive behaviour of bone (Cowin, 1997).

4.1 Structure

There are two types of bone tissue: trabecular (also called cancellous or spongy) and

cortical (also called compact). Trabecular bone is porous (75-95% porosity) and

found in cuboidal bones, fiat bones and at the ends of long bones. It consists of a

three-dimensional interconnected network of trabecular rods and plates interspersed

with bone marrow (Figure 4.2). The trabecular length scale is approxiately 200 J);m

(Keaveny, 1998).

Cortical bone is dense (5-10% porosity) and found in the shaft of long bones

and enclosing the trabecular tissue in other bones. The cortical bone structure

consists of Haversian systems (secondary osteons) made up of circumferential layers

of fibres with alternating orientations around a central canal carrying blood vessels

(Figure 4.2).

Cortical and trabecular bone contain two main types of bone tissue: woven and

lamellar (Martinet al., 1998). Woven bone is found in the developing embryo, and

4.1 STRUCTURE

lnterstttlaJ lamellae

Trabeculae Osteoclast

Circurnlerenl111! subperiosteal lamettae

53

s:eocy:e

Figure 4.2: Architecture of cortical and trabecular bone. Reproduced from Hayes and Bouxsein (1997).

in new bone formation in postfoetal osteogenesis (e.g., fracture healing). Woven

bone is a fairly disorganised matrix of interwoven collagen fibres with osteocytes

distributed throughout. It is eventually resorbed and replaced by lamellar bone.

Lamellar bone is built up of layers (lamellae), each approximately 3 to 7 pm thick

with parallel fibres. The fibre direction can vary by up to 90° between adjacent layers

(Jee, 2001). In adult cortical bone, lamellae appear in three patterns (Figure 4.2):

1. concentric-circular rings surrounding a longitudinal vascular channel that

together form a structural cone, the osteon or Haversian system;

2. circumferential-several layers of lamellae that extend around part or all of

the circumference of the shaft of a long bone; or

3. interstitial-angular fragments of what were formerly concentric or circum-

ferential lamellae, filling the gaps between Haversian systems.

4.1 STRUCTURE 54

Cortical bone may be further classified as primary or secondary (Martin et al.,

1998). Primary bone refers to tissue that is laid down de novo on an existing

bone surface during growth. The two general types are circumferential lamellar

bone, and plexiform bone, a mixture of lamellar and woven bone tissues. Blood

vessels incorporated in the circumferential lamellar bone are surrounded by several

concentric lamellae, forming a primary osteon with a primary Haversian canal at

its centre.

Secondary bone results from the resorption of existing bone and its replacement

by new lamellar bone. In cortical bone, secondary tissue consists of secondary os

teons. These are about 200 f-Lm in diameter and consist of about sixteen cyclindrical

lamellae surrounding the Haversian canal. Between the Haversian system and the

surrounding bone lies the cement line boundary.

Adult cortical and trabecular bone is almost entirely secondary bone. Most

compact bone is composed of secondary osteons and interstitial lamellae. Secondary

trabecular bone rarely contains osteons, as they do not generally fit within individual

trabeculae; instead containing cresent shaped hemiosteons and interstitial lamellae.

Hemiosteons are also delineated by cement lines.

Small cavities, or lacunae, connected by tubular canals, or canaliculi, are found

throughout woven and lamellar bone. Entrapped cells occupy the lacunae, and

communicate with cells in adjacent lacunae and nearby Haversian canals via cellular

processes within the canaliculi. Osteons are connected by transverse Volkmann's

canals, to form an interconnected network carrying neurovascular and lymphatic

vessels. Blood supply comes from nutrient, metaphyseal and epiphyseal arteries in

adult long bones.

Bone tissue has two major surfaces, periosteal and endosteal. The periosteal

surfaces are external while the endosteal surfaces are internal. The endosteal surface

is further subdivided into the intracortical (Haverian/osteonal), endocortical and

trabecular surfaces (Frost, 1987).

4.2 COMPOSITION 55

4.2 Composition

Bone is made up of 65% mineral and 35% matrix, cells and water (Jee, 2001). The

mineral phase of bone consists mainly of hydroxyapatite crystals, Ca10 (P04 ) 6 (0H)2.

The individual crystals are generally plate-like, measuring about 50 x 50 x 250 A

(Posner, 1985). The mineral is impure, in particular containing 4-6% carbonate

groups replacing the phosphate groups, making the material more realistically a

carbonate apapatite. The major cell types are osteoblasts, osteoclasts, osteocytes and

bone-lining cells. Osteoblasts, osteocytes and bone-lining cells are all descendants of

the osteoblastic cell lineage, representing different stages of maturation. Osteoclasts

represent the final differentiation stage of a line of the monocyte cell family.

Osteoblasts form new bone by secreting most of the components of the organic

matrix, or osteoid. The osteoid is made up primarily of type I collagen (90%) and

other noncollagenous proteins. Osteoblasts regulate the structural organisation of

the collagen matrix and facilitate the precipitation of mineral salts within the os

teoid from ions in the extracellular matrix. Active osteoblasts occur as a contiguous

layer of cuboidal cells 15 to 30 J-lm thick, wherever bone formation takes place. Os

teoblasts are differentiated from mesenchymal cells within the periosteal membrane

or bone marrow in a process taking 2-3 days. Osteoid is laid down at a rate of

about 0.55 [Lm/day (Jee, 2001) to 1 [Lm/day (Martinet al., 1998). This is referred

to as the bone apposition rate.

Bone-lining cells are inactive osteoblasts that are flattened, elongated cells cov

ering quiescent bone surfaces. They cover the majority of the adult bone surfaces.

Bone-lining cells are capable of forming bone without prior bone resorption in re

sponse to anabolic agents. They are also involved in resorption of the surface layer

of osteoid before giving access to osteoclasts. Bone-lining cells are believed to be

involved in mineral homeostasis by forming an ion barrier that regulates the flux of

calcium and phosphate in and out of the bone tissue ( J ee, 2001). Bone-lining cells

are thought to be influenced by strain within the bone, and thus involved with bone

adaptation.

4.3 DEVELOPMENT, GROWTH, MODELLING AND REMODELLING 56

Osteocytes are mature osteoblasts that have become embedded in lacunae within

the bone matrix. They are the most abundant cell type in mature bone, with

about ten times more osteocytes than osteoblasts (Jee, 2001). Osteocytes have little

synthetic activity. They form an extensive network with each other and with cells

at the bone surface, both physically and functionally, via slender cellular processes

which pass through the canaliculi. The cells are connected by gap junctions which

allows direct communication between the cells, through the passage of ions and

small molecules. Osteocytes and bone-lining cells together are believed to form a

sensory network that monitors mechanical load and tissue damage within bone, and

subsequently regulates adaptive responses (Majeska, 2001).

Osteoclasts are large, multinucleated cells that resorb bone by dissolution of

mineral and enzymatic digestion of organic macromolecules (Majeska, 2001). Active

osteoclasts are usually found in cavities on bone surfaces called resorption cavities

or H owship 's lacunae. Cessation of bone resorption is associated with migration of

osteoclasts from endosteal surfaces into adjacent marrow spaces where they undergo

apoptosis (Jee, 2001). Osteoclasts are regulated by numerous factors, including

hormones, growth factors and cytokines.

4.3 Development, Growth, Modelling and

Remodelling

4.3.1 Bone Formation

There are two major modes of primary bone formation, or osteogenesis, and both

involve the transformation of a preexisting mesenchymal tissue into bone tissue.

Mesenchymal tissue contains unspecialised cells that can readily self-proliferate and

differentiate into a number of different cell tissue types via well regulated lineage

cascades. The direct conversion of mesenchymal tissue into bone is called intramem

branous ossification. This process occurs primarily in the bones of the skull. In other


cases, the mesenchymal cells differentiate into cartilage, and this cartilage is later

replaced by bone in a process called endochondral ossification (Gilbert, 2000).

Intramembranous ossification is the characteristic way in which the fiat bones

of the skull are formed. During intramembranous ossification in the skull, neu-

ral crest-derived mesenchymal cells proliferate and condense into compact nodules.

Some of these cells develop into capillaries while others change their shape to be-

come osteoblasts, committed bone precursor cells. The osteoblasts secrete a matrix

(osteoid) that becomes calcified by the binding of calcium salts. As calcification

proceeds, bony spicules radiate out from the region where ossification began (Fig

ure 4.3). Furthermore, the entire region of calcified spicules becomes surrounded by

Calcifietl Rone cd1 (osteoq'le)

9lllf,lll' <JIIll>

Figure 4.3: Schematic diagram of intramembranous ossification producing a spicule of bone tissue. Reproduced from Gilbert (2000).

compact mesenchymal cells that form the periosteum (a membrane that surrounds

the bone). The cells on the inner surface of the periosteum also become osteoblasts

and deposit osteoid matrix parallel to that of the existing spicules. In this manner,

many layers of bone are formed.

Endochondral ossification involves the formation of cartilage tissue from aggre

gated mesenchymal cells, and the subsequent replacement of cartilage tissue by

bone (Figure 4.4). The process of endochondral ossification can be divided into five

stages. First, the mesenchymal cells are commited to become cartilage cells. During

the second phase, the committed mesenchymal cells condense into compact nodules

4.3 DEVELOPMENT, GROWTH, MODELLING AND REMODELLING

(Al (B)

!lyp<mophk d10ndroc-,1es I .

{C)

Ostcob!asts (bom::J

iLl)

.!lkmd

58

Figure 4.4: Schematic diagram of endochondral ossification. (A, B) Mesenchymal cells condense and differentiate into chondrocytes to form the cartilaginous model of the bone. (C) Chondrocytes in the centre of the shaft undergo hypertrophy and apoptosis while they change and mineralise their extracellular matrix. Their deaths allow blood vessels to enter. (D, E) Blood vessels bring in osteoblasts, which bind to the degenerating cartilaginous matrix and deposit bone matrix. (F ~H) Bone formation and growth consist of ordered arrays of proliferating, hypertrophic, and mineralizing chondrocytes. Secondary ossification centres also form as blood vessels enter near the tips of the bone. Reproduced from Gilbert (2000).

and differentiate into chondrocytes, the cartilage cells. In the third phase, the

chondrocytes proliferate rapidly to form the model of the bone. As they divide, the

chondrocytes secrete a cartilage-specific extracellular matrix. In the fourth phase,

the chondrocytes stop dividing and increase their volume dramatically, becoming

hypertrophic chondrocytes. These large chondrocytes alter the matrix they produce

to enable it to become mineralised. The fifth phase involves the invasion of the carti-

lage model by blood vessels. The hypertrophic chondrocytes die by apoptosis. This

space will become bone marrow. As the cartilage cells die, a group of cells that

have surrounded the cartilage model differentiate into osteoblasts. The ostoblasts

begin forming bone matrix on the partially degraded cartilage. Eventually, all the

cartilage is replaced by bone. Thus, the cartilage tissue serves as a model for the

bone that follows. The skeletal components of the vertebral column, the pelvis, and

the limbs are first formed of cartilage and later become bone.


In the long bones of humans, endochondral ossification spreads longitudinally

outwards in both directions from the diaphysis of the bone (Figure 4.4). As the

ossification front nears the ends of the cartilage model, the chondrocytes near the

ossification front proliferate prior to undergoing hypertrophy, pushing out the car

tilaginous ends of the bone. These cartilaginous areas at the ends of the long bones

are called epiphyseal growth plates. These plates contain three regions: a region

of chondrocyte proliferation, a region of mature chondrocytes, and a region of hy-

pertrophic chondrocytes (Figure 4.5). As the inner cartilage hypertrophies and the

'

Pml!ftnling cartilag<: cells

I Hypcrlmphk ' and .;,~akifir·ing f <>H;],g«<lls

Zone of cartila)!,C' degeneration and ossit1,ation

Figure 4.5: Endochondral ossification in the epiphyseal growth plate.

ossification front extends further outwards, the remaining cartilage in the epiphy-

seal growth plate proliferates. As long as the epiphyseal growth plates are able to

produce chondrocytes, the bone continues to grow.

General bone growth is controlled by a combination of genetic and circulating

systemic factors, while systemic and regional factors, mechanical usage in partie-

ular, can modulate it locally. Longitudinal bone growth adds new spongiosa to


preexisting spongiosa and new length of cortical bone to preexisting cortex. Radial

or periosteal bone growth adds new width by apposing subperiosteal bone to the

cortex (Jee, 2001).

4.3.2 Mechanical Adaptation

The form of adult bone is regulated by two main factors: the predetermined genetic

template that explains intersubject variations, and the ability of bone to react to

changes in the level of loading, according to "Wolff's Law" (Goodship and Cun

ningham, 2001). Thus, in the absence of mechanical loading, the form and mass of

a bone will return to the genetic baseline. Reduced functional loading can occur

due to generalised conditions, such as bed rest and microgravity experienced during

space flight. More localised disuse occurs with cast immobilisation and around or-

thopaedic implants such as joint replacements. Conversely, increased physiological

exercise will stimulate bone formation. An hypothesis for mechanical adaptation is

presented in Figure 4.6.

I BONE DEPOSITION ~

INCREASE ACTIVITY DECREASE STRAINS

1 /,./ ,

/ I I I DECREASE ACTIVITY INCREASE STRAINS

I L. ..... , .... ,,. -t : ' I •

FUNCTION DISUSE

't ) ,, ;~ ' ,, ....._ __ GENETIC BASELINE+--..,..

Figure 4.6: Adaptation hypothesis in which skeletal mass is adjusted to maintain an optimal strain environment, genetically predetermined for each specific location. Reproduced from Rubin and Lanyon (1987).

Carter (1984) proposed that the net rate of change of bone mass is a function

of the time rate of change of the strain history function. The strain history is a


function of the cyclic strain range, mean strain, and the number of loading cycles.

Other potential components of the strain history function include strain rate and

frequency.

Lanyon and Rubin (Lanyon, 1984; Lanyon and Rubin, 1984; Rubin and Lanyon,

1984, 1987) developed the functionally isolated avian ulnar model to investigate the

effects of loading parameters on long bone morphology in vivo. Importantly, this

model isolated the bone from any mechanical loading other than that applied as

part of the experimental protocol. The unknown factor associated with loading from

normal activity between sessions of experimentally applied loading was eliminated.

In contrast, studies such as that by Meade et al. (1984) in which a constantly applied

load was applied to the canine femur via external springs, produced results which

are difficult to interpret, since additional dynamic loads from normal activity were

superimposed.

Lanyon and Rubin's investigations demonstrated that dynamic loading within

the physiological strain range led to an osteogenic response, sensitive to the magni

tude, rate of change, and distribution of the dynamic strain. Static loading within

the physiological range produced similar results to those observed in disuse. The

osteogenic response becomes saturated after as few as 36 consecutive loading cy

cles per day, and only 4 loading cycles per day were needed to prevent resorption.

Turner (1998) termed this the "case of diminishing returns". Turner et al. (1995)

proposed that bone cells responded to stress-generated fluid flow within the bone

matrix proportional to strain rate. In a cylinder, strain rate is proportional to the

amplitude of the applied dynamic load-a stimulus previously proposed by Lanyon

and Rubin. Zernicke et al. (2001) reported an osteogenic response after 3 weeks

of running in mature roosters. This was correlated with the peak circumferential

strain. High impact jump drops with immature roosters showed significant bone

formation which correlated with strain rate. Strain rate increased considerably more

than peak strain during this activity. Mi et al. (2002) reported strain gradients to

be strongly related to bone interstitial fluid flow. In another isolated avian ulna


study, Brown et al. (1990) observed osteogenic bone responses that correlated with

strain energy density, longitudinal shear stress, and tensile principal stress/strain.

Some of these experiments indicate that bone does not adapt to the predomi

nant mechanical environment, but rather to the predominant osteogenic stimulus.

Accordingly, bones may not be concerned with the entire strain history, but only

with a small component of the strains (Mosley, 2000). The frequency and mag

nitude of strains during normal activity in animals was assessed by Fritton et al.

(2000). They determined that large strains(> 1000 J-lE) occur relatively few times a

day. On the contrary, small strain ( < 10 J-lE) occur thousands of times a day. Lower

magnitude strains ( < 200 J-lE) were more uniform around the bone cross-section.

Production of functionally and mechanically purposeful architecture is achieved

by modelling, while remodelling produces and maintains bone that is biomechani

cally and metabolically competent. Modelling is the alteration of size and shape of

bones (macromodelling) by resorption drifts and formation drifts over wide regions

of bone surfaces. Modelling is predominantly associated with changing geometry.

Growth, surface drifts, and functional adaptation are various forms of modelling.

Primary bone is structurally inferior to secondary bone, and secondary bone

quality deteriorates with time due to accumulation of fatigue cracks which occur at

osteon cement lines and as diffuse shear microcracks throughout the bone (Carter,

1982). Remodelling is the coupled process by which primary and damaged bone

is removed in small packets by basic multicellular units (BMUs). Remodelling

limits resorption and formation to one location and affected bone is simply replaced

by new bone without changing bone geometry (Smit and Burger, 2000). With

increasing age, bone remodelling throughout the skeleton progressively diminishes

the distinction between the primary bone formed by growth and modelling, and

secondary bone (Carteret al., 1996). This process occurs in four stages:

1. resorption-activation of osteoclasts;

2. reversal-coupling of formation to resorption;

3. formation-formation of new bone matrix by osteoblasts; and


formation resorption

resting reversal

(a) Cortical bone remodelling by EMUs.

~~~ ~a~(7~a

resorption reversal t ~--~

resting formation

(b) Trabecular bone remodelling by B~IUs.

Figure 4.7: Bone remodelling due to the activity of basic multicellular units. Reproduced from Smit and Burger (2000).

4. resting/ quiescence-bone surfaces lined by inactive osteoblasts (bone-lining

cells).

Remodelling takes place on all of the skeletal envelopes/surfaces, although in

adult humans, about 80% of the cancellous and cortical surfaces (periosteal and

endosteal), and about 95% of the intracortical surfaces are inactive with respect

to remodelling at any given time ( J ee, 2001). In cortical bone, remodelling occurs

by osteonal tunnelling in which the osteoclasts of a BMU excavate a canal that is

refilled by osteoblasts. Haversian systems, oriented along the main loading direction,

that are 100-200 p,m wide and up to 10 mm long are the result. Trabecular bone

remodelling results in surface grooves (Howship's lacunae) with a depth of 60-70 p,m

that are refilled by osteoblasts (Figure 4.7). For each BMU, the amount of bone

replaced is generally less than that removed, leading to a net decrease in the amount

of bone. Consequently, increased remodelling leads to greater losses of bone, while

decreased remodelling reduces these losses and conserves bone (Frost, 1987).

The total surface area available for remodelling at any site is dependent on

the local bone porosity. Martin (1984) developed a relationship for this area per

unit volume (specific surface) as a function of the porosity, presented graphically in

Figure 4.8.

According to Burr (2002), bone remodelling achieves three goals:


E E

7

6

. 5 w u ~ 4 a: :::J (f)

u 3

D

-----------:'_ B ,..... 0 -- ........

/', .. ·"' 0 0 ................. 0 ' . ... ....

/ 0 0 ......

' . ' / 0 •!..------- 0 • \ . . . '

(,'. ~ 0~ ••• \ . ' /• ...... ---------..!') A • \'

,' ... - - ... --........... ...... \ lL ,'t ........ ~ .p \ u 2 :• - .... ~ "' . lLJ ... ~ ~ \

~ ................. \ ' ' ' ...... \

.2 .3 .4 .5 6 .7 .8 .9 1.0

POROSITY

64

Figure 4.8: Specific surface as a function of porosity. Reproduced from Martin (1984).

1. it provides a way for the body to alter the balance of essential minerals by

increasing or decreasing their serum concentrations;

2. it provides a mechanism for the skeleton to adapt to its mechanical environ-

ment, reducing fracture risk; and

3. it provides a mechanism to repair damage created by fatigue loading.

The first of these goals can be accomplished without site-specific (nontargeted)

remodelling, since it matters little where bone is removed and replaced, provided

structural integrity is maintained. Bone turnover for participation in calcium home

ostasis is highest in the central bone (e.g., iliac crest) where the bone is in contact

with red marrow, as apposed to peripheral bone where it is in contact with yellow

or fatty marrow (Parfitt, 2002). The other two goals require site-dependent, or

targeted, remodelling.

The osteoregulatory mechanisms controlling bone modelling and remodelling

are deemed to be modulated locally by cellular activity. Controlling inputs include

functional load bearing, the influence of microdamage and the local effects of sys-

temic influences including calcium regulating hormones, nutrition, age and drugs

(Lanyon, 1992).

To explain the behaviour of bone in response to mechanical usage, Frost (1987)

proposed the "Mechanostat" theory. This likened mechanically-mediated adaptation


to a domestic thermostat, where modelling and remodelling could be turned on or

off, depending on the set point, or minimum effective strain (MES). Under disuse,

remodelling is activated, while modelling is inhibited, leading to bone loss. Overload

inhibits remodelling and activates modelling, leading to bone gain. Frost's theory

does not consider what happens during pathologic overload. This strain range

would be characterised by significant fatigue or creep damage, increased remodelling

to repair this damage, and periosteal/ endosteal woven bone modelling (Iv1artin,

2000). Approximate strain ranges for physiologic, disuse, overload and pathological

overload are indicated in Table 4.1.

Table 4.1: Mechanical usage windows according to Frost's Mechanostat theory. Each window is separated by a minimum effective strain (MES) with approximate values in microstrain. Reproduced from Martin (2000).

Disuse Range Physiologic Range Overload Range Pathologic Overload

0-50 J1E 50-1500 p,c 1500-3000 p,c > 3000 J1E

resorption > formation resorption = formation resorption> formation resorption> formation

increased remodelling homeostasis rising remodelling maximal remodelling

decreased modelling increased modelling maximal modelling

The concept of a minimum effective strain, or strain range, is similar to the idea

of Carter (1984), who identified the existence of a physiological band for mature

bone, wherein bone tissue is unresponsive to changes in loading history. Carter

proposed a curve relating the rate of change of bone mass to the strain history

function (Figure 4.9). The strain history is a function of the cyclic strain range .6-E,

the mean strain Em and the number of loading cycles N. The two curves suggest

growing bone is more sensitive to strain history changes than mature bone. The

width of the physiological band is thought to be site-specific.

4.3.3 Mechanotransduction

Bone cells within the bone matrix are believed to act as sensors of local mechani-

cal loading~adjusting remodelling and modelling activity via a mechanobiological

feedback system. Frost (1987) proposed a scheme in which a mechanical load on a


m1- c "0 '0 0

(,!)

<l.J c 0 m

t 0

' ~ 0 ...J v § m

IMMOBIL- NORMAL IZATION ACTIVITY

SEVERE LOADING

STRAIN HISTORY RATE

dS(l:\E, Em,N)

dt

-GROWING BONE

-MATURE BONE

66

Figure 4.9: Relationship between the rate of change of bone mass and the strain history function. Reproduced from Carter (1984).

bone would generate a primary mechanical signal, which is then detected by cells

that would generate secondary signals. The secondary signals would be addressed

to modelling and remodelling systems. This was expanded on by Turner and co

workers (Duncan and Turner, 1995; Turner and Pavalko, 1998), and divided into

four phases of mechanotransduction:

1. mechanocoupling~transduction of a mechanical force on the bone (skeletal

level) into a local mechanical signal that can be perceived by the sensor cells;

2. biochemical coupling~transduction of a local mechanical signal into a bio-

chemical signal, and ultimately, gene expression;

3. cell-to-cell communication~transmission of the signal from the sensor cell to

the effector cell; and

4. effector response~final tissue-level response by the effector cells.

This process of mechanotransduction in bone has been likened to the same process

in vascular endothelial cells, in which shear stress due to blood flow results in sensor


cells locally producing paracrine factors which act on vascular smooth muscle cells

to alter blood pressure (Duncan and Turner, 1995; Turner et al., 1995).

The first step, mechanocoupling, has been the most thoroughly investigated.

There is general agreement among researchers that cells of the osteoblast lineage

are the most likely transducers of mechanical strain. Osteocytes are the most likely

derivatives of this cell line, due to their distribution within the bone matrix, and

their ability to communicate with other osteocytes and cell lines (Cowin et al.,

1991; Harrigan and Hamilton, 1993a; Lanyon, 1987; Martin, 2000; Turner et al.,

1995; Turner and Pavalko, 1998). Each osteocyte is connected by 50 to 70 gap

junctions at the ends of cellular processes to other osteocytes, bone-lining cells or

osteoblasts on all adjacent bone matrix surfaces. Connection to endothelial cells in

the bone vasculature is also probable (Cowin, 1993). This network of cells forms a

functional syncytium.

The manner in which the local mechanical state of a bone is measured by this cell

population is not fully understood. Some of the possibilities include direct strain,

fluid shear and streaming potentials (Cowin et al., 1991). Tissue level strains, due to

deformation of the osteocytic lacunar walls, cell and cell-process membranes, may be

very small when considered in terms of bone-cell displacement. The physiological

strain range, measured on the periosteal surface, of adult load-bearing bone in

most species is 2000-3000 fJ£ (Rubin and Lanyon, 1984). Some investigators, such

as Turner et al. (1995), have questioned whether bone cells can sense such small

strains, however, it is possible that strain concentrations exist around osteocyte

lacunae (Cowin et al., 1991; Smit and Burger, 2000). Nicolella and Lankford (2002)

estimated strains around lacunae up to 16 000 fJ£, and 30 000 fJ£ within a distance

of one lacunar diameter.

Another possibility is that strain is amplified by stress-generated fluid flow

through the porous bone matrix. Bone cells may be capable of detecting fluid

shear stress. The other effect of fluid flow is streaming potentials. The flow of fluid

containing charged solutes through a solid matrix containing oppositely charged


chemical groups causes charge separation. This results in streaming potentials due

to the balance between electrical forces and fluid density. This creates a poten

tial difference between two sites in the bone tissue of up to 2 m V (Cowin et al.,

1991). The physical quantity cells may sense is the disparity between intra- and

extracellular electric potentials (Harrigan and Hamilton, 1993a). Becket al. (2002),

however, were unable to find a relationship between streaming potential magnitudes

and strain or strain gradients in an experimental study.

It is probable that bone cells react to more than one component of their mechan

ical environment, allowing for a more structurally relevant remodelling response in

different anatomical locations or in bone with different structural properties (Ehrlich

and Lanyon, 2002).

Damage accumulation caused by fatigue loading has also been hypothesised to

influence bone remodelling, particularly under pathological overload conditions. Mi

crodamage accumulates slowly under normal loading conditions, and for this reason

it is unlikely that microcracks trigger increased remodelling due to disuse (Carter,

1984). Microcracks can accrue rapidly when strains exceed 3000 f-1£ (Duncan and

Turner, 1995), and increased remodelling is required to repair the damaged bone

tissue. Due to the low number of osteogenic loading cycles required to induce

modelling, it is improbable that damage accumulation plays a role in this process

(Duncan and Turner, 1995; Lanyon, 1992; Rubin and Lanyon, 1987; Turner et al.,

1995).

The biochemical coupling phase involves measurement of the local mechani

cal signal. Possibilities include force transduction from the extracellular matrix

to the cytoskeleton and nuclear matrix through integrins, stretch-activated cation

(Ca2+) channels within the cell membrane, protein-dependent pathways in the cell

membrane, and linkage between the cytoskeleton and the phospholipase pathways

(Duncan and Turner, 1995). Ingber (1997) proposed a form of cellular architecture

relying on tensional intregrity for stability (tensegrity) as a mechanism for coupling

of the local signal to a cellular response. Compression members within the cell

4.3 DEVELOPJ\1ENT, GROWTH, MODELLING AND REMODELLING 69

resist the contractile pull of the cytoskeleton. This theory predicts that the cells

are hard-wired to respond immediately to mechanical stress transmitted over the

cell surface receptors, that physically couple the cytoskeleton to the extracellular

matrix (integrins) or other cells ( cadherins, selectins).

Candidates for cell-to-cell communication of bone adaptation information in

clude prostaglandin E2 , insulin-like growth factors I and II, and nitric oxide (Bakker

et al., 2001; Blankenhorn et al., 2002; Duncan and Turner, 1995; Turner and Pavalko,

1998; van't Hof and Ralston, 2001). Prostaglandin E2 has important anabolic ac

tions in bone, demonstrated by its ability to promote recruitment of osteoblast

precursor cells and increase osteoblast proliferation. Nitric oxide has been shown

to act as a mediator of mechanically-induced bone formation. Insulin-like growth

factors could couple bone formation to bone resorption (Ehrlich and Lanyon, 2002).

The effector response resulting from the initial local mechanical signal involves

differentiation and recruitment of cells to the bone surface to facilitate an adaptive

response (Duncan and Turner, 1995). Other hormones, particularly calcium regu

lating, may interact with the local mechanical signals to change the sensitivity of

the sensor or effector cells to mechanical load.

The mechanotransduction pathway still requires considerable investigation to

determine how all of these components fit together. According to Martin (2000),

bone-lining cells are restrained from activating remodelling by the strain-generated

signals arriving from the network of osteocytes within the adjacent bone matrix.

Lanyon (1984) also proposed that the osteogenic stimulus in normally loaded bone

prevents high remodelling activity. Martin (2000) went on to suggest that the bone

formation rate of functioning osteoblasts was also inhibited by osteocytic signals.

This seems counterintuitive in terms of loading being conducive to bone formation,

however this leads to creation of new osteocytes, rather than altering osteoblast

differentiation and recruitment to BMUs.

The strain-generated signal produced by osteocytes is most likely interrupted by

fatigue cracks, by direct injury to osteocytes or their processes. According to Martin

4.4 MECHANICAL PROPERTIES 70

(2000), loss of this signal would trigger bone-lining cells to activate remodelling to

repair the bone tissue. Tami et al. (2002) observed a high degree of interconnection

in the osteocyte syncytium of healthy bone. A marked decrease in interconnectivity

was observed under osteoporosis. This situation, in a manner similar to fatigue

damage, decreases the ability of the cells to communicate, subsequently increasing

remodelling and decreasing bone mass.

To account for the fact that bone is not completely resorbed under disuse con

ditions, possible only as far as a genetic baseline level (Figure 4.6), Turner (1998)

introduced a "principle of cellular accommodation". This rule postulated that bone

cells accommodate to an altered mechanical loading environment, making them less

responsive to routing signals over time. Rubin et al. (2002) also proposed that bone

cells are capable of accommodating new loading environment. An osteocyte may be

able to "normalise" the local mechanical environment by modulating its cytoskeletal

architecture, attachment to the matrix, configuration of the periosteocytic space,

and communication channels to surrounding cells. In this manner, the osteocyte

can accommodate most changes in local loading without needing to alter tissue

architecture, except under severe changes in which case site-specific remodelling oc

curs. Cowin et al. (1991) thought it possible for an osteocyte to remodel the shape

of its lacunae, thereby mechanically adjusting its sensitivity to a particular type of

loading.

4.4 Mechanical Properties

The load-bearing capacity of a skeletal structure is dependent on its intrinsic mate

rial properties as well as the size and shape of the bone tissue. From a mechanical

point of view, the allocation of these parameters represents a compromise between

the need for stiffness to make muscle actions efficient, the need for compliance to

absorb energy and avoid fracture, and the need for minimum skeletal weight. The


best solution for the conflicting mechanical demands will depend on the specific

bone and its function.

4.4.1 Constitutive Models

Bone is generally assumed to be a linear elastic material. Elasticity, being a con

tinuum theory, assumes that the model of the material is continuous, although the

material itself may not be. No material is continuous to any level, but trabecular

bone is not continuous even at the macroscopic level. Hence it is a structure rather

than a material. For trabecular bone to be modelled as a continuum, a length scale

over which the material properties are averaged to smooth out the holes should be

established. The length scale is about five intertrabecular lengths (Harrigan et al.,

1988), or about 5 mm according to Cowin (1993). When considering trabecular

bone, it is common to discuss continuum level or structural properties, rather than

tissue level properties. The density of trabecular bone is often reported as the ap

parent density, which is related to the tissue level density Pt by the bone volume

fraction Vt or the porosity P

p=ptxVf

= Pt X (1- P) ( 4.1)

Keeping all of this in mind, for a linear elastic continuum material, Hooke's law

may be applied (Chung, 1988). The generalised Hooke's law for small strain is

(4.2)

where O"ij is the stress tensor, and /ij is the small strain tensor. For an anisotropic

material, the fourth order stiffness tensor, Eijkm, is symmetric and 21 independent

4.4 1\ilECHANICAL PROPERTIES

coefficients are needed to characterise it

~1111 ~1122 ~1133 ~1112 ~1123 ~1131

~2222 ~2233 ~2212 ~2223 ~2231

~3333 ~3312 ~3323 ~3331

symm. ~1212 ~1223 ~1231

~2323 ~2331

~3131

72

( 4.3)

For most materials, this number of constants is reduced due to symmetry. A ma

terial that has properties varied along three perpendicular axes (e.g., longitudinal,

radial and circumferential) is said to be orthotropic. Nine independent coefficients

are required to describe orthotropy. Trabecular bone is accepted to be effectively

orthotropic (Yang et al., 1998), with the principal axes governed by the trabecular

orientation.

A special type of orthotropic material, with the properties equal in two of the

three principal directions, is a transverse isotropic material. In this case the number

of independent constants is reduced to five. For cortical bone, the average orienta

tion of the mineralised collagen fibres is approximately parallel to the bone's long

axis. This causes a significant difference in the mechanical properties associated

with the longitudinal direction. The microstructure of primary bone presents a dis

tinct difference in the radial and transverse directions, suggesting that cortical bone

is orthotropic. However, osteonal remodelling tends to convert the bone from an

orthotropic to a transversly isotropic material (Huiskes, 1997; Martinet al., 1998).

An isotropic material is symmetric with respect to every plane and axis, and

has material properties that are identical in all directions. Only two constants are

needed to define an isotropic material-generally expressed as the Young's or elastic

modulus ~ and Poisson's ratio v, or in terms of the the Lame constants f-1 and >..

Isotropic materials have the advantage that the stresses and strains can be de

composed into hydrostatic (dilatational) and deviatoric (distortional) components.


For structural metals, the deviatoric stress and its second invariant play a large

part in yielding. The second invariant of the deviatoric stress is a scalar referred

to as the octahedral shear stress or von Mises stress. For anisotropic materials,

it is still possible to decompose stress and strain into hydrostatic and deviatoric

components, however the advantage of decomposition is lost because the modes are

coupled. For example, a deviatoric stress will produce a strain that is a combi-

nation of deviatoric and hydrostatic components. A further disadvantage is that

yielding of anisotropic materials is generally not independent of hydrostatic stress,

and therefore it is the total stress, not just the von Mises stress, that contributes

to yielding (Cowin, 1990). Suitable presentation of stress analysis results is thus

important when dealing with anisotropic materials.

4.4.2 Elastic Modulus and Density

The mechanical properties of cortical and trabecular bone tissue have been investi-

gated experimentally using a variety of methods. To calculate the elastic modulus,

techniques include uniaxial tension and compression testing, 3- or 4-point bending,

ultrasound, and indentation testing (Tables 4.2 and 4.3). These tables show that

the elastic modulus of bone varies with testing direction, testing method, region

and bone type.

Table 4.2: Experimental values for the elastic modulus of human cortical bone tissue in the femoral diaphysis.

Author Method Direction E (GPa)

Bargren et al. (1974) Tension/ compression (wet) Longitudinal 16.1 ± 0.4 Bargren et al. (1974) Tension/ compression (dry) Longitudinal 19.1 ± 0.3 Reilly et al. (1974) Tension/ compression Longitudinal 17.1±3.2 Reilly and Burstein (1975) Tension/ compression Longitudinal 17.0 Reilly and Burstein (1975) Tension/ compression Transverse 11.5 Keller et al. (1990) 4-point bending Longitudinal 12.1 ± 4.1 Lotz et al. (1991) 3-point bending Longitudinal 12.5 ± 2.1 Lotz et al. (1991) 3-point bending Transverse 6.0 ± 1.5 Turner et al. (1999) Acoustic microscopy Longitudinal 20.6 ± 0.2 Turner et al. (1999) N anoindentation Longitudinal 23.5 ± 0.2


Table 4.3: Experimental values for the elastic modulus of human trabecular bone tissue.

Author Site Method Direction E (MPa)

Ashman and Rho (1988) Distal Ultrasound Parallel to 1300 ± 150 femur trabeculae

Odgaard and Linde (1991) Proximal Compression Longitudinal 689 ± 438 tibia ( extensometer)

Odgaard and Linde (1991) Proximal Compression Longitudinal 871 ± 581 tibia (optical)

Rho et al. (1993) Tibia Tension (dry) Individual 1040 ± 350 trabeculae

Rho et al. (1993) Tibia Ultrasound (wet) Individual 1480 ± 140 trabeculae

Rohlmann et al. (1980) Femoral Compression Longitudinal 394.6 head

Rohlmann et al. ( 1980) Femoral Compression Longitudinal 322.2 condyles

Keaveny (1998) Femur Compression Longitudinal 389 ± 270

Turner et al. (1999) Femoral Acoustic Individual 1750±110 condyles microscopy trabeculae

Thrner et al. (1999) Femoral N anoindentation Individual 1810 ± 170 condyles trabeculae

Most of the variation between these values of elastic modulus can be attributed

to anisotropy, tissue mineralisation, viscoelasticity, experimental errors and most

importantly, the porosity. Table 4.4 shows some of the variation in apparent density

between locations in the femur.

Table 4.4: Apparent density of human bone tissue.

Author Type Site p (g/cm3)

Rohlmann et al. (1980) Cancellous Femoral head 0.426 Rohlmann et al. (1980) Cancellous Femoral condyles 0.347 Lotz et al. (1991) Cortical Femoral diaphysis 1.72 ± 0.10 Lotz et al. (1991) Cortical Femoral diaphysis 1.73 ± 0.07 Crolet et al. (1993) Cortical 1.8-2.2 Currey (1998) Cortical 1.99 Keaveny (1998) Cancellous Femur 0.5 ± 0.16 Bruyere Garnier et al. (1999) Cancellous Femoral head 0.56 ± 0.11


Because of the significant effect of porosity on the mechanical properties of bone,

many empirical relationships have been derived to calculate these properties as a

function of the apparent density. The most frequently cited is the cubic relationship

between compressive elastic modulus and apparent density, published by Carter and

Hayes (1976, 1977), in which

( 4.4)

where Ec is the compressive modulus of cortical bone and Pc is the density of cortical

bone. If Ec = 22 000 MPa and Pc = 1.8 g/ cm3 for bone tested at E- = 0.1 s-1,

Equation 4.4 becomes

( 4.5)

This relationship assumes cortical and trabecular bone are effectively the same ma

terial, differing only in porosity. The strain rate-dependence of the elastic modulus

is due to viscoelasticity. All biological materials display at least some viscoelasticity

(Reilly and Burstein, 1974). Experimental testing has shown that elastic modulus

and ultimate stress increase with strain rate, while strain to failure decreases with

strain rate. Viscoelastic phenomena include creep, stress relaxation and dynamic re

sponse. These properties arise from the combined behaviour of the mineral, organic

and fluid components of bone. Collagen, motion at cement lines between osteons

and between lamellae within osteons, thermoelastic damping from heat flow be

tween osteons and stress-induced fluid flow through the porous bone matrix are all

potential sources of viscoelasticity (Garner et al., 2000). The mineral phase of bone

is effectively elastic (Yamashita et al., 2000).

Researchers have argued that trabecular and cortical bone should have sepa

rate relationships to describe their mechanical properties (e.g., Ashman and Rho,

1988; Evans, 1973; Keller, 1994; Rho et al., 1993; Rice et al., 1988; Schaffier and

Burr, 1988), since cancellous bone is more metabolically active, is remodelled more


frequently than cortical bone, and is consequently younger (Rho et al., 1998). Re

cently, Parfitt (2002) has disputed the commonly held belief that cancellous bone

is necessarily turned over more rapidly, although this does not imply that the min-

eralisation of trabecular and cortical tissue is automatically the same. Some of the

empirical relationships for elastic modulus as a function of apparent density are

presented in Table 4.5.

Table 4.5: Emperical relationships between elastic modulus and apparent density.

Author

Carter and Hayes ( 1 977) Rice et al. (1988)

Schaffier and Burr (1988) Keller et al. (1990) Lotz et al. (1990) Goldstein et al. (1991)

Snyder and Schneider (1991) Keaveny and Hayes (1993) Rho et al. (1993) Rho et al. (1995)

Sttilpner et al. (1997)

Relationship

E = 3.790i0·06 p3

E = 0.06 + 0.90 p2 (compression) E = 0.06 + 1.65 p2 (tension) E = 0.09p7·4

E = 6.4 Pl. 54

E = 1.31 p1.4o E = 1.353 pl.48

E = 34.634 p - 46.246 E = (109.59 P2.39) x 10-9

E = 0.613 pl.44

E = -0.29 + 0.0042 p + (1.8 X 10-6 ) p2

E = 5.05 pu28

E = 9.11 Pl.326

E = 2.01p2·5

E = 1.76 p3·2

Density Range

all cancellous cancellous cortical p > 0.5 gjcm3

cancellous p < 1.4 gjcm3

p > 1.4 gjcm3

cortical cancellous cancellous p < 1.0 gjcm3

p > 1.5 g/cm3

p < 1.2 gjcm3

p > 1.2 g/cm3

Rice et al. (1988) pooled elastic modulus-apparent density data. for trabecular

bone from a. number of studies. Although the methodologies were not consistent

amongst these studies, they predicted a. quadratic relationship. Rho et al. (1993)

showed that the elastic modulus of cancellous bone could be estimated from a.

quadratic relationship, which they were able to extend to include individual trabec

ulae. This could not, however, be extrapolated to cortical bone. Other studies of

cancellous bone have also obtained power law exponents closer to two than three.

Odga.a.rd and Linde (1991) asserted that the compressive modulus of cancellous bone

was generally underestimated by about 20% because of end effects associated with

the mechanical testing method. The trabeculae on the cut surface undergo higher

than normal deformation-resulting in overestimation of the strain averaged over


the compression specimen. This may account for some of the variation between the

many modulus~density relationships in Table 4.5.

Empirical relationships based on the apparent density have also been determined

for bone strength (e.g., Carter and Hayes, 1977; Keller et al., 1990; Rice et al., 1988;

Snyder and Schneider, 1991).

4.4.3 Noninvasive Measurement of Bone Density

To determine bone apparent density in the laboratory, the bone tissue weight is

measured and divided by the bulk volume of the sample. Noninvasive methods

for measuring bone apparent density include quantitative computed tomography,

single- and dual-energy absorptiometry, and ultrasonography (Lotz et al., 1990).

Problems with these methods include beam hardening, radiation scattering and

effects of marrow and overlying tissue.

X-ray absorptiometry methods quantify the total bone mineral content (BMC)

contained within a three-dimensional region scanned by an x-ray beam. This is a

projection method, in which all information on bone mass is scanned down to a

two-dimensional plane. The BMC is often normalised by the projected area of the

region scanned, to obtain areal bone mineral density (BMD) (Kaufman and Siffert,

2001).

Dual-energy x-ray absorptiometry (DEXA) provides a measure of the bone min

eral density (BMD) by using two different energy sources and comparing the differ

ence in attenuation. This allows the effects of soft tissue to be separated out. Early

systems used gamma rays rather than x-rays for the photon source, with less accu

rate results. DEXA systems can use either a fan source beam coupled to an array

of detectors, or a pencil beam with a single detector. The fan beam configuration

allows for a straight path scan along the region of interest, whilst the pencil beam

follows a slower two-dimensional raster scan path (Blake et al., 1993). Single-energy

x-ray absorptiometry measures x-ray absorption at a single energy only, and thus

cannot compensate for varying amounts of soft tissue. Consequently, single-energy


methods are useful for anatomical sites where the amount of soft tissue is negli

gible. Unfortunately, x-ray absorptiometry methods do not discriminate between

cortical and trabecular bone, lumping together the bone mass from cortical and

trabecular portions at a particular site. In addition, only areal BMD is measured,

not volumetric density. In vivo studies show DEXA has precision errors of less than

5% (Kilgus et al., 1993; Kiratli et al., 1992; Rahmy et al., 2000). However, Kiratli

et al. (1992) found that rotations of ±5° of the femur has a significant influence on

the area of the scanning region, leading to a variation in BMD of over 5%, while

Rahmy et al. (2000) measured variation up to 20% for femoral rotation of ±15°.

The most significant changes occurred in smaller regions of interest, where the area

measurement is strongly influenced by rotation of the femur.

Computed tomography (CT), like x-ray absorptiometric methods, are available

in single- or dual-energy modes. The single-energy method provides the most re

producible results over the majority of conditions and is most widely used (Mirsky

and Einhorn, 1998). An x-ray source is also employed. CT scanners have developed

considerably over the years to reduce scan times and radiation exposure.

First generation scanners use parallel-beam geometry. Multiple measurements

are obtained using a single x-ray pencil beam and detector. The beam is translated

in a linear motion across the patient to obtain a projection profile. The source

and detector are then rotated by about 1 o around the patient and another projec

tion profile is obtained. This translate-rotate scanning motion is repeated until

the source and detector have been rotated by 180 degrees. The second generation

scanners use a narrow fan beam with multiple detectors to increase scan speed. A

translate-rotate scanning motion is still employed, with a larger rotation increment

(up to 30°). With third generation scanners, a curved detector array consisting

of several hundred independent detectors is mechanically coupled to the fan beam

x-ray source, and both rotate together. The fan beam is larger (30-60°), keeping

the patient in view at all times. For the fourth generation of computed tomography

scanners, the x-ray fan beam rotates while the detector array remains stationary.


The detector array consists of 600 to 4800 (depending on the manufacturer) inde

pendent detectors in a circle that completely surround the patient.

The requirement for faster scan times, and in particular fast multiple scans

for three-dimensional images, has resulted in the development of spiral (helical)

scanning systems. Helical scanners employ continuous rotation of the x-ray source

and/ or detector array, coupled with simultaneous translation along the scanning

axis, to create uninterrupted three-dimensional data. Both third and fourth gener

ation systems achieve this using slip rings to replace cumbersome electrical cables.

Data acquired from all of these scanners are reconstructed using computer soft

ware. Naturally, the reconstruction algorithms become more sophisticated as the

scanner technology improves. A computed tomography scan image consist of many

cells (pixels) each assigned a H ounsfield unit (HU or CT number), which is a di

mensionless number relating the linear attenuation coefficient of the material in the

pixel to the attenuation coefficient of water. A pixel is a two-dimensional represen

tation of a corresponding tissue volume, called a voxel. Voxel size is determined by

the pixel size and the CT slice thickness.

CT measurements can be quantified by scanning alongside calibration phantoms

of known density, such as liquid dipotassium hydrogen phosphate (Esses et al., 1989;

Lotz et al., 1990; Marom and Linden, 1990; Revak, 1980), solid tricalcium phosphate

(Snyder and Schneider, 1991) and solid hydroxyapatite (Cody et al., 1996). One of

the benefits of quantitative CT (QCT) is a linear relationship between attenuation

coefficients and equivalent mineral density. The equivalent mineral density is ex

pressed in terms of mg/mm3 of the calibration material (e.g., mg/mm3 of K2HP04).

Bone apparent density is similarly related to the attenuation coefficients and equiv

alent mineral density (Table 4.6). Other advantages include direct measurement

of a volume of bone, and ability to separately assess trabecular and cortical bone.

Individual bones are usually scanned in water to reduce beam hardening artefacts.


Table 4.6: Emperical relationships between apparent density (g/cm3) and CT data (CT number, HU; equivalent mineral density, QCT). Note. tonly 2 points used.

Author

Esses et al. (1989) Lotz et al. (1990) Snyder and Schneider (1991) Rho et al. (1995) Cody et al. (1996) Couteau et al. (1998) (prox. femur) Couteau et al. (1998) (dist. femur)

Relationship

p = 1.9 X 10-3 QCT + 0.105 p = 0.0012 QCT + 0.17 p = 0.701 HU X 10-3

p = (1.076 HU + 131) X 10-3

p = 0.002QCT- 2 p = (1.5 HU + 17.2) X 10-3

p = (1.2HU + 303) X 10-3

Correlation

R 2 = 0.60 R2 = 0.73 R 2 = 0.65 R 2 = 0.84 t

R 2 = 0.80 R 2 = 0.74

Chapter 5

Stress Analysis of the Femur

This chapter reviews the literature on the subject of experimental and finite element

stress analysis of the femur, with respect to the alteration of load transfer pathways

following hip arthroplasty. Both of these techniques have intrinsic advantages and

disadvantages when applied to this subject.

In the natural femur, the joint force is distributed across the entire cross-section

of the femur through a combination of bending and axial loads, with relatively

minor loads. When the femur is implanted with a prosthesis, the applied load

is redistributed in a quite different manner. The bending loads are transmitted

by localised contact stresses between the implant and bone, while axial loads are

transferred by shear at the interface (Joshi et al., 2000b). Experimental and finite

element stress analysis methods are able to evaluate this redistribution of loads to

the femur.

5.1 Experimental Stress Analysis

Experimental methods for stress analysis of the femur include strain gauge (reviewed

here) and photoelastic (e.g., Engh et al., 1992b; Finlay et al., 1989; Glisson et al.,

2000; Hua and \Valker, 1995) techniques. Strain gauge studies are most abundant in

the literature as they give quantitative strain values at discrete locations, although

they have the disadvantage of only measuring site-specific strains, thus giving no

81

5.1 EXPERIMENTAL STRESS ANALYSIS 82

clear indication of strain fields. Another difficulty is that strain gauges are inaccu

rate in regions of high strain gradient (Finlay et al., 1991). Photoelastic procedures

give a good indication of strain gradients and principal strain directions, however

calculated shear strains tend to underestimate those measured with gauges (Glisson

et al., 2000). The photoelastic method is useful for selecting sites for quantitative

strain gauge measurement. The primary drawback of any experimental stress anal

ysis method is that internal and interface stresses are unavailable.

5.1.1 Strain Gauges

Strain gauges are sensing elements that change resistance when deformed along the

active axis. The gauge generally consists of metal foil, cut into a grid structure by a

photoetching process, and mounted on a resin film backing (Figure 5.1). Grids may

Passive Axis

Figure 5.1: Uniaxial strain gauge grid. Adapted from Bentley (1995).

be stacked at various angles to measure deformation along multiple axes. The film

backing is bonded to the structure to be measured with adhesive. The resistance of

an element of length l, cross-sectional area A and resistivity p is given by

R= pl A

(5.1)

In general, p, l, and A can change if the element 1s strained, so the change in

resistance is given by p pl l

~R = -~l- -~A+ -~p A A2 A

(5.2)


and dividing through by R = pl /A yields

!:1R !:1l !:1A !:1p -=---+-R l A p

(5.3)

The ratio f1l/l is the longitudinal strain in the element. The strain E is related to

the change in resistance by the gauge factor G

!:1R = Gc: Ro

(5.4)

where R0 is the unstrained resistance of the gauge. Strain gauge elements are

incorporated in resistive, or Wheatstone bridge circuits, to convert the output into

a voltage signal (Figure 5.2). The output voltage Erh is a function offour resistances

~----o~o-----~

Figure 5.2: Wheatstone bridge. Reproduced from Bentley (1995).

R 1 to R4 and the input, or source, voltage Vs

(5.5)

If R 1 is the sensing element (strain gauge), and R 2 to R4 are fixed resistors, it is

required that the fixed resistances are all equal to the unstrained resistance of the

sensing element R0 , for the sensitivity to be as high as possible (Bentley, 1995).

This leads to the linear relationship between output voltage and strain

Vs Erh = 4 cc: (5.6)


The output voltages are typically amplified and recorded using analogue-to-digital

conversion.

5.1.2 Strain Gauge Studies

Most experimental strain gauge studies in orthopaedic research have investigated

the mechanical response of the femur to hip arthroplasty. The cortical strain dis

tribution of the intact femur is first determined by mechanical testing under a pre

scribed loading, and then tested again after implantation of a hip prosthesis. These

investigations give a measure of the load transfer for the implant-bone system.

The loading employed by most researchers is static and often pseudo-physiological.

The strain distribution for the intact femur usually shows the femur bending in

the coronal plane, with compressive strains medially and tensile strains laterally.

The highest strains are proximal, decreasing distally (e.g., Cristofolini et al., 1995;

Huiskes et al., 1981; McNamara et al., 1997a; Oh and Harris, 1978; Otani et al.,

1993), with this situation reversed following surgery.

Stress Shielding

Significant reductions in strain in the proximal medial femur have been reported

for both cemented (Cristofolini et al., 1997; Finlay et al., 1989; Oh and Harris,

1978; Rohlmann et al., 1987, 1983) and uncemented (Cristofolini et al., 1997; Diegel

et al., 1989; Engh et al., 1992b; Finlay et al., 1991, 1989; Kim et al., 2001; Vanderby

et al., 1990) implant types. Calcar strains are not significantly increased with more

flexible prosthesis materials (Diegel et al., 1989; Oh and Harris, 1978; Simoes and

Vaz, 2002), with all producing significant stress shielding. Stem length (Huiskes

et al., 1981), diameter (Jasty et al., 1994) or surface features (Gillies et al., 2002)

also have little effect. Many authors agree that the congruency between the implant

and the prepared femur is most important for load transfer (Diegel et al., 1989; Jasty

et al., 1994; Simoes and Vaz, 2002), with precise calcar-collar contact (Figure 5.3)

also helpful if present (Jasty et al., 1994; Oh and Harris, 1978; Vander Sloten et al.,


1993), although the effectiveness of a collar in vivo is not assured. The significance

Figure 5.3: A collared implant (A) with intimate bone contact, increases axial compressive loads at the calcar compared with an implant without a collar (B).

of the extent of porous coating layer on uncemented prostheses is difficult to evaluate

in vitro, since bone ingrowth has not occurred. McNamara et al. (1997a) glued a

noncemented implant into a synthetic femur to simulate a fully ingrown situation,

and measured strains consistently lower than a standard press-fit stem, indicating

a stiffer system.

Strain gauge testing has been applied to femora obtained post-mortem from hu-

man (Engh et al., 1992b) and canine (Vanderby et al., 1990) subjects with unilat-

eral hip replacement. Strains were measured on the unimplanted femora before and

after surgery, representing the preoperative and immediately postoperative condi-

tions, and also on the in vivo remodelled femora. Stress shielding seen immediately

after surgery was not consistently normalised to the intact condition by remodelling

in either study, possibly because adaptation was still progressing or the bone had

accommodated to the new loading environment.

Other applications of strain gauges with respect to femoral stress measurement

include evaluation of new implant designs (Kim et al., 2001; Vander Slaten et al.,


1993; Viceconti et al., 2001a), measurement of strain during femoral canal prepara

tion and prosthesis insertion (Elias et al., 2000), and verification of finite element

models (McNamara et al., 1994; Rohlmann et al., 1982, 1983; Stolk et al., 2002).

The femora tested in all of these studies are either fresh frozen (Diegel et al.,

1989; Elias et al., 2000; Gillies et al., 2002; Glisson et al., 2000; Kim et al., 2001;

Oh and Harris, 1978; Otani et al., 1993), embalmed (Cristofolini et al., 1995; Hua

and Walker, 1995; Huiskes et al., 1981; Jasty et al., 1994; Sedlacek et al., 1997), dry

(Vander Slaten et al., 1993), or synthetic (Cristofolini et al., 1997; McNamara et al.,

1997a; Simoes and Vaz, 2002; Viceconti et al., 2001a). Synthetic bones are produced

from composite materials to recreate the mechanical properties of cadaveric bone,

without the inter-specimen variability or the difficulty of obtaining specimens.

Loading and Constraints

The systems of forces found in the literature vary widely with different numbers of

muscles and force magnitudes and directions. This is partially due to the differ

ent situations simulated, for example, single-legged stance, two-legged stance, and

various phases of the gait cycle. Some authors tried to make the set up as sim

ple as possible with a single force, while others included a high number of muscle

forces. Some of the common arrangements include a single force on the femoral

head (Diegel et al., 1989; Huiskes et al., 1981; Oh and Harris, 1978; Otani et al.,

1993), the hip joint force and the action of the abductor muscles grouped together

(Cristofolini et al., 1994; Engh et al., 1992b; Finlay et al., 1989; Gillies et al., 2002;

Glisson et al., 2000; Tanner et al., 1988; Vander Slaten et al., 1993), or the hip joint,

abductor and iliotibial tract forces (Finlay et al., 1991; Kim et al., 2001; Rohlmann

et al., 1982). A minority of authors have simulated additional forces such as the

vastus muscles, adductors and rectus femoris (Cristofolini et al., 1995; Munting and

Verhelpen, 1993; Simoes et al., 2000), however Cristofolini et al. (1995) excluded


the iliotibial tract. Figure 5.4 shows the difference in load transfer when the ab-

ductor muscles are not included, and the potential for overestimating lateral stress

shielding.

(a) Load transfer path with the hip joint reaction force alone.

(b) Load transfer path with the hip joint reaction and abductor muscle forces.

Figure 5.4: Load transfer mechanism for an uncemented prosthesis with and without abductor muscle action present. Reproduced from Cristofolini (1997).

Some methodological studies have been performed to evaluate how the loading

conditions affect the stress distribution of the femur. Rohlmann et al. (1983) found

that a single force applied parallel to the femoral shaft produced strains similar to

loading with hip joint, abductor and iliotibial tract forces. The iliotibial tract force

reduced the bending from hip joint abductor actions. Finlay et al. (1991) concluded

that loading should at least incorporate the abductor muscle force, the iliotibial

tract, or both, in addition to the hip joint force. The iliotibial tract in conjunction

with the joint force increased proximal strains on the medial aspect, while decreasing

tensile strains distally on the lateral aspect, both before and after arthroplasty with

a noncemented hip. The iliotibial tract applied additional compressive loads to the

proximal femur, reducing large tensile bending strains laterally.


Finlay et al. (1989) found that abductor muscle forces increased medial and

lateral strains while reducing proximal bending. Similarly, McNamara et al. (1997a)

measured strains without abductor simulation that were typically one-third of those

measured with the abductor forces present.

Cristofolini et al. (1995) estimated the importance of simulating various muscle

groups in in vitro mechanical testing of the femur at heel strike. The gluteal mus

cles, adductors, vasti and rectus femoris were investigated. The iliotibial tract was

not included as it was thought to be inactive at heel strike. The gluteal muscles

dominated over all others, with axial strains always at least twice as high as those

generated by other muscles. Rectus femoris was the second most significant muscle,

producing strains 10-50% of those due to the glutei. The vasti were found to be

the least relevant muscle group. This study formed the basis of the development of

a standard heel strike loading test protocol (Cristofolini et al., 1994), in which only

the hip joint and abductor muscles forces were incorporated (Figure 5.5). Rulers

and goniometers were used to ensure force directions and positions were controlled.

A load cell monitored the abducting force.

Aamodt et al. (1997) measured strain on the lateral femur in vivo at a position

35 mm below the lateral eminence of the greater trochanter in two patients. Strains

were measured in single- and two-legged stance, during walking and stair climbing.

Strains during activity were tensile, with maximum principal strains aligned with

the long axis of the femur during stance. These results suggested that the action of

the lateral musculature is not sufficient to overcome the bending moment imposed

by the joint force.

The distal constraints on the femur are also varied. The literature reports the

femur either fixed at the diaphysis (Engh et al., 1992b; Gillies et al., 2002; Hua and

Walker, 1995; Otani et al., 1993; Tanner et al., 1988), or at the condyles (Cristofolini

et al., 1994; Diegel et al., 1989; Finlay et al., 1989; Glisson et al., 2000; Kim et al.,

2001; Munting and Verhelpen, 1993; Oh and Harris, 1978; Vanderby et al., 1990).

Translations are usually fixed distally, however some rotational degrees-of-freedom

5.1 EXPERIMENTAL STRESS ANALYSIS

on lesser trochanter

c

89

®

Figure 5.5: Set up used for applying the hip joint and abductor forces to the femur. (1-5) Rulers and goniometers to measure force directions. (6) Load cell to monitor the abdcutor force. Reproduced from Cristofolini (1997).

may be unconstrained. Proximal constraints are also important to ensure that the

femur is loading isostatically. Figure 5.6 shows how the femur may by constrained

to reproduce physiological loading, even with nonphysiological constraints.

Experimental Errors

Viceconti et al. (1992) examined the effects of some factors not controlled in most

experimental strain gauge studies. They investigated the importance of loading

rate, bone preservation method, strain gauge preservation, bone temperature and

bone hydration on strain measurement. Strain rate was found to be unimportant,

freezing altered mechanical properties less than embalming, moisture penetration

under the gauge could be reduced with a thin layer of polyurethane film, while bone

5.1 EXPERIMENTAL STRESS ANALYSIS

B.W.

(a) (b) (c) LATERAL VIEW A N T E A I 0 A

(d) VIEWS

90

Figure 5.6: Representation of the femoral constraints for mechanical testing. (a) The femur is presented with the adjacent bone segments. (b) The tibia can be assumed to be fully constrained, the knee joint is represented by a hinge, and the hip joint is joined to the pelvis with a spherical joint. (c) and (d) represent options to distally constrain the knee and apply loads to the femoral head while avoiding unwanted force components. Reproduced from Cristofolini (1997).

temperature should be controlled. Bone dehydration caused deformation of up to

1500 Jl£ over 24 hours.

Errors associated with mechanical testing were further elucidated by Cristofolini

et al. (1997), using a standard heel strike protocol (Cristofolini et al., 1994). A para

metric model derived from beam theory, developed in a previous study ( Cristofolini

et al., 1996), was employed to interpolate the strain data and estimate the strain

gradient around the gauge positions. This parametric model can also be used to

describe changes in strain distribution and to predict strain distributions under

changed load. Using composite femora instrumented with uniaxial gauges, a sensi

tivity analysis was performed to examine the effect of gauge position and alignment,

and the size of the gauge grid. Gauges on the anterior and posterior cortices were

found to be highly sensitive to positioning errors due to their proximity to the

neutral axis. Uniaxial gauges are probably not suitable for this location. For me-

dial and lateral gauges, alignment was found to be important. Finlay et al. (1991)


has previously mentioned that strain gauges are not accurate around high strain

gradients.

Continuing on with this work into uncontrolled factors, Cristofolini and Vice

conti (1999) examined the effect on femoral strains of head position change following

hip replacement. A femur loaded in an identical manner before and after surgery,

should have equal strains in the cortex below the distal tip of the implant. To

minimise errors, the same moment should be applied when comparing intact and

reconstructed femoral strains (Figure 5. 7).

BEFORE IMPLANTATION

AFTER , IMPLANTATION

Figure 5.7: Loading changes if the position of the prosthetic head does not coincide with the anatomic one. Forces must be altered to generate the same moments. Reproduced from Cristofolini (1997).

To compare the variability between pairs of femora, Sedlacek et al. (1997) sub

jected ten embalmed pairs to single-legged and stair climbing loads using the method

of Engh et al. (1992b). Endosteal gauges, as well as the usual periosteal gauges were

used in this study. No significant difference was reported between left and right fe-

mora, however, considerable variations was found between subjects. Oh and Harris

(1978) also reported large variations between individual femora.

5.2 FINITE ELEMENT STRESS ANALYSIS 92

5.2 Finite Element Stress Analysis

The femur is the bone most commonly analysed theoretically, probably due to its

historical developments (i.e., the work of Wolff and Roux), and also its common

involvement in clinical procedures such as hip arthroplasty. Early finite element

studies were aimed at establishing validity of the procedure by comparison with

clinical observations. Techniques were refined and used to address specific problems

associated with femoral implants including interface failure, micromotion, prosthesis

failure, cement fatigue, and stress shielding.

5.2.1 Finite Element Modelling

The finite element method involves cutting a structure into several elements (pieces

of the structure), describing the behaviour of each element in a simple way, and then

reconnecting the elements at nodes as if nodes were pins that hold elements together

(Cook, 1995). For analysis of three-dimensional structures, the elements can be

brick, wedge or tetrahedral shapes. For two-dimensional analysis, quadrilaterals

and triangles are used. The assembly of all of the elements is called the finite

element mesh.

An example of a two-dimensional mesh is given in Figure 5.8. Each node is

able to move in two directions (two degrees-of-freedom) and each force has two

components. The displacement vector u and the force vector f at each nodal point

i can be written in terms of their components

i [u~] i [ f~] u = ; f = ui fi

y y

(i = 1,2,3) (5.7)


F

CD 3

3 f. -fJc:- u3 y y

Figure 5.8: A two-dimensional finite element mesh and definition of nodal forces and displacements. Reproduced from Huiskes and Verdonschot (1997).

For a structure with a total of n elements, the vectors at the lh element can be

written ul

X J]; ul f~ ul

y

uJ = u2

fj = J;

u2 X (j = 1, ... , n) (5.8) u2 t;

u3 y

u3 X t:

u3 y Jt

For each element

fJ = QJ uJ (5.9)

where QJ is the stiffness matrix of the jth element and consists of 6 x 6 components.

The components are determined by assuming the deformation in the element takes a

specific form in such a way that the deformation within the element is determined by

the relative displacements of the nodal points. For instance, the strain distribution

in the element is assumed to be uniform. The components of the stiffness matrix can

then be determined from the shape and volume of the element, the elastic modulus

and Poisson's ratio (Huiskes and Verdonschot, 1997).


The equations for each element (Equation 5.9) can be assembled together, in

the sense that all displacements and forces of the different elements belonging to

the same nodal point are collected. This produces a vector u containing all nodal

point displacement components and a vector f containing all nodal point force

components. For a linear elastic material with small deformations, these two vectors

are related by the m x m stiffness matrix Q, giving

f= Qu (5.10)

where m is the number of degrees-of-freedom in the model (usually 2n for a two

dimensional mesh and 3m for a three-dimensional mesh). The force components

are either zero where no external force is applied, or have a known value equal to

the external force. Displacements are unknown except where boundary constraints

are applied. The nodal displacements are calculated by solving Equation 5.10 for u

(5.11)

The result is usually obtained by some form of Gauss elimination or an iterative

method. The solution is always approximate because of two important simplifi

cations. The deformation of each is limited to a uniform strain field (i.e., linear

displacement), and all load transmission is assumed to occur at the nodal points.

The accuracy of the approximation depends on the element type and the degree of

mesh refinement. The solution converges to the exact solution as the mesh density

approaches infinity.

Different types of elements use different interpolation functions to represent the

coordinates and displacements in the subsequent calculations of stress and strain.

Simple elements with linear displacement fields have a limited number of degrees-of

freedom and therefore low computation time, however they are not able to represent

bending. A larger number of elements can be used, or a more sophisticated element

with a quadratic displacement field, and more nodes per element, may be employed.


The number of nodal points or elements required for appropriate accuracy can be

determined using convergence tests.

In linear analysis, the solution is directly proportional to the load. The equilib-

rium equations are written for the initial structure conditions, and can be solved

in a single step. Often linear assumptions are at odds with reality. Displacement

of the structure may be large enough for the equilibrium equation to be rewritten

in terms of the deformed configuration, the material may yield and contact area

may increase with force. These are examples of geometric, material and contact

nonlinearities (Figure 5.9). Nonlinearities in the finite element model increase the

/ /

///~ /

~~=I =-==--=---/==it'

{a)

-------;· !v ,l

p p

L v L/ (b) {c)

Figure 5.9: Sources of nonlinearity. (a) Slender elastic beam loaded by a follower force. (b) Elastic-plastic beam loaded by a fixed direction force. (c) Contact stress in a roller bearing. Reproduced from Cook (1995).

complexity of the problemm since they cannot be solved explicitly, and instead a se

ries of linear steps are required. Incremental methods such as the Newton-Raphson

and modified Newton-Raphson methods are used. The solution is reached when

a convergence criterion is satisfied (Cook, 1995). This is often determined by the

sum of the residual forces for all degrees-of-freedom of the model at the end of each

equilibrium increment.

5.2.2 Finite Element Studies

One of the first applications of finite element modelling in orthopaedic biomechanics

was a stress analysis of the femur by Brekelmans et al. in 1972. The entire femur


was modelled in two dimensions, with 936 3-noded triangular elements of uniform

thickness (approximately 1074 nodal degrees-of-freedom). A three-dimensional, but

fairly coarse (around 969 degrees-of-freedom), model of the proximal femur was later

published by Valliappan et al. (1977). The three-dimensional model of the femur

developed by Rohlmann et al. (1982) was quite sophisticated by previous standards,

with 7188 degrees-of-freedom. Results from both of these three-dimensional studies

were compared with experimental data, showing conformity in a qualitative sense

only. These method-oriented studies were aimed at demonstrating the possible

applications of finite element modelling to biomechanics, rather than tackling any

specific problems.

Modelling the Femur

Expensive computational demands have meant that the femur is often modelled in

a simplified manner. Although the femur has asymmetric geometry and loading,

two-dimensional models have been created in the plane of the femoral neck. To

account for the structural stiffness of the normal femur, a side-plate is used by some

authors (e.g., Huiskes, 1990; Svensson et al., 1977; Weinans et al., 1992b, 1994).

The thickness of the side-plate is calculated so that the cross-sectional moment of

inertia of the model is equal to that of the three-dimensional femur being approx

imated (Figure 5.10). Further simplified side-plate models of a straight femoral

shaft are also in the literature (Huiskes, 1990; Huiskes et al., 1987; Kuiper and

Huiskes, 1997), along with three-dimensional axisymmetric models of the diaphysis

(Estok and Harris, 2000; Gross and Abel, 2001; Keaveny and Bartel, 1994; Nuno

and Amabili, 2002; Nuno and Avanzolini, 2002).

Anatomic three-dimensional finite element models more accurately represent the

geometry of the femur. The mesh can be created in either a "geometry-based" or

"voxel-based" process. Geometry-based meshing is most common and requires the

extraction of bone contours from CT scans using thresholding and edge-following


side plate

e-n

Figure 5.10: Two-dimensional side-plate model of the proximal femur accounting for three-dimensional rigidity in the frontal plane. Reproduced from Huiskes (1990).

algorithms (Huiskes et al., 1992; Keaveny and Bartel, 1993a; Mann et al., 1995; Mc

Namara et al., 1994), or by digitising contact radiographs of sectioned femurs (Cheal

et al., 1992; Kerner et al., 1999; Rohlmann et al., 1987; Weinans et al., 1993). The fe-

mur geometry must be reconstructed from the contours using computer-aided draw-

ing (CAD) packages or finite element pre-processors before meshing. This method

requires considerable time investment to perform manually, and consequently many

studies refer to a single bone geometry when, in many cases, anthropometric vari-

ability should not be neglected (Viceconti et al., 1998b).

Automated mesh generation (AMG) methods have been developed, which allow

relatively quick construction of patient-specific finite element models. Voxel-based

meshing is one of these automated procedures that creates nodes to form a cubic lat-

tice along orthogonal axes defined by the CT scanner. Bone contours are extracted

using the method described for geometry-based models, and the structure is created

by converting a voxel (see Section 4.4.3), or several adjacent voxels, directly into


brick elements if some part of the voxellies within the nearest bone contour. This

method tends to produce somewhat irregular surfaces (Figure 5.11a) and stresses

calculated here tend to oscillate around the theoretical solution (Guldberg et al.,

1998). Nevertheless, voxel-based models have been studied quite extensively by

(a) Voxel-based mesh. Reproduced from Skinner et al. (1994b).

(b) Geometry-based mesh. Reproduced from Viceconti et al. (1998b).

Figure 5.11: Automatic mesh generation methods.

some research groups (Keyak et al., 1993, 1990; Keyak and Skinner, 1992; Lengsfeld

et al., 1998; Weinans et al., 2000). Results from assessment of interface behaviour

when femoral prostheses are introduced (Namba et al., 1998; Skinner et al., 1994a,b)

are somewhat uncertain as the surfaces are not smooth. Cody et al. (1999, 2000a,b)

created subject-specific voxel-based models to predict fractures of the proximal fe-

mur giving reasonable correlation with mechanical testing.


Geometry-based automated mesh generation procedures have also been estab

lished that create meshes with smooth surfaces and larger element sizes (Fig

ure 5.11 b). These methods tend to alleviate some of the problems associated with

the voxel-based variety (Merz et al., 1996a,b; Viceconti et al., 1998b, 1999).

Material Properties

The majority of finite element models of the femur assume all bone to be a linear

elastic, continuum material. As stated in Section 4.4, some assumptions about the

material behaviour, particularly with respect to trabecular bone, are required for

bone to be modelled in such a manner. The trabecular length scale over which ma

terial properties should be averaged is about five intertrabecular lengths (Harrigan

et al., 1988), or about 5 mm according to Cowin (1993). When considering finite

element modelling of implant-bone systems, a significant issue is that within three

to five intertrabecular lengths of the implant or osteotomy, continuum modelling is

not valid and should be replaced by statistical models for the interface. The results

of continuum level studies around interfaces are correct if the actual compliances

of the region are similar to the continuum model. The continuum limitations do

not limit the degree of refinement necessary for accurate finite element analysis

(Harrigan et al., 1988).

Bone is assumed to be isotropic by most researchers; defined by two indepen

dent constants, the elastic modulus E and Poisson's ratio v. Cortical bone can be

approximated as transversely isotropic (Huiskes, 1997; Martinet al., 1998), and this

constitutive relationship is occasionally applied in finite element models (Pancanti

et al., 2003; Vichnin and Batterman, 1986). Vichnin and Batterman (1986) reported

that transversely isotropic properties in the diaphysis caused higher implant stresses

than isotropic properties. Transverse isotropy is a simplification of orthotropy, and

not as appropriate for describing the material behaviour of trabecular bone. Con

sequently, Wirtz et al. (2003) assigned orthotropic material axes to each element,

based on the trabecular orientation and Haversian system orientations for cortical


bone. Other researchers who have also applied orthotropic material properties to

their finite element models include Cheal et al. (1992) and Taylor et al. (2002).

Nevertheless, the use of isotropy and transverse isotropy are justified in many sit

uations, as the error due to simplification of the material model is often less than

the error from other sources (Cowin, 1993).

The elastic moduli assigned to the finite element meshes are typically homo

geneous for the bone type (cortical or cancellous), or inhomogeneous, with elastic

modulus dependent on the CT density at each element or integration point. The

elastic modulus-density relationships are empirical relationships, such as presented

earlier in Table 4.5. The relationship derived by Carter and Hayes (1977) (Equa

tion 4.5) is one of the most commonly used. For AMG models, inhomogeneous ma

terial properties are relatively straightforward to implement. Heterogeneity of bone

properties was investigated in a series of papers by Edinin and co-workers (Edinin

and Taylor, 1992; Edinin et al., 1991). The values of Poisson's ratio reported from

finite element studies is invariably constant for both cortical and cancellous bone,

ranging between 0.2 and 0.4, but 0.3 is the most common (Ando et al., 1999; Estok

and Harris, 2000; Harrigan and Harris, 1991; Kang et al., 1993; Keaveny and Bartel,

1993a,b; Mann et al., 1995; Taddei et al., 2003).

Investigators have also implemented homogenisation theory to model the porous

microstructure of trabecular bone (e.g., Bagge, 2000; Fernandes et al., 1999; Ped

ersen, 2002; Pettermann et al., 1997). The aim of homogenisation is to represent a

heterogeneous medium as a homogeneous continuum that has the same macroscopic

behaviour (Prendergast, 1997). The isotropy of the homogenised material depends

on the behaviour of the microstructural building blocks.

The advent of high resolution J.LCT scanners has led to geometry-based AMG

models for small volumes of trabecular bone (Ladd and Kinney, 1998; Ulrich et al.,

1998). Ladd and Kinney (1998) showed that for a small volume of trabecular bone,

variation of Poisson's ratio between 0.15 and 0.35 had negligible effects on stiffness

of the structure. It is unlikely that whole bones will be modelled from J.LCT scans in


the foreseeable future, due to the massive computational expense linked with mesh

generation and solution solving.

Convergence

Mesh refinement and convergence analysis is rarely reported due to the large amount

of time required to produce a mesh manually (Viceconti et al., 1998b). Some re

searchers that have reported convergence include Valliappan et al. (1977), Vichnin

and Batterman (1986) and Biegler et al. (1995). Others have assumed convergence

by similarity with experimental results. Keyak et al. (1990) and Keyak and Skinner

(1992) examined convergence of a voxel-based model, but the use of strain energy

density as a measure of convergence in this case was disputed by Marks and Gardner

(1993).

Experimental verification

Early studies showed relative agreement with experimental results, but generally

not in an absolute sense (Rohlmann et al., 1982, 1983; Valliappan et al., 1977).

Rohlmann et al. (1983) attributed the difference in results to a number of errors,

due to: extrapolation of stresses from Gauss points, irregular element shapes, bone

geometry, bone properties, contact conditions, geometric linearity, deviations in

strain gauge positions, and ubiquitous experimental errors. The voxel-based model

of Keyak et al. (1993) tended to underestimate experimentally measured strains,

most likely due to imprecise modelling of the bone surface. Finite element models

of synthetic femora have been quite successfully verified at some length. MeN amara

et al. (1994) found better quantitative agreement with experimental results using

synthetic bones as opposed to cadaveric. Experimental testing of synthetic femora,

with and without hip replacement, was done under 4-point bending (McNamara

et al., 1994) and heel strike loading ( Cristofolini et al., 1997; MeN amara et al.,

1997a, 1996; Stalk et al., 2002).


Stress Shielding

Methods of reducing stress shielding have been studied in detail with finite element

modelling. These include the use of a collar and reduction of implant stiffness, either

by changing elastic modulus or moment of inertia. Rohlmann et al. (1987) stated

that a collar was unimportant for proximal bone stress, although cement stresses

were elevated proximally without it. Contrary to this, Keaveny and Bartel (1993a)

showed that loss of collar support greatly reduced proximal axial forces. Prendergast

and Taylor (1990) also found that a collar on a cemented stem increased stresses in

the calcar region. A low modulus (25 MPa) stem with a collar produced a stress

distribution most like the intact femur.

Unlike the experimental studies described above, elastic modulus of the pros

thesis has been found to have a significant effect on stress in the proximal femur

when modelled numerically. 1v1any researchers have reported a nonlinear inverse

relationship between cortical bone stress and implant modulus (Cheal et al., 1992;

Huiskes et al., 1992; McNamara et al., 1996; Namba et al., 1998; Rohlmann et al.,

1987; Tensi et al., 1989; Weinans et al., 2000) with a greater change in bone stress

for lower prosthesis moduli. The problem of severe stress shielding, however, is

not necessarily resolved (McNamara et al., 1996; Namba et al., 1998). Tensi et al.

(1989) reported that a low modulus (15 GPa) stem is not necessarily ideal for un

cemented hip arthroplasty in terms of stresses in the proximal femur, since high

compressive stresses exist proximally for the low modulus stem, which may exceed

the compressive strength of trabecular bone.

Another issue associated with low modulus implants is the greater interface

stresses and relative motion between the implant and surrounding bone. Optimisa

tion techniques were employed by Kuiper and Huiskes (1997) to obtain an elastic

modulus distribution for an intramedullary stem, in an idealised model, that pro

duced a uniform stress distribution along the implant~bone interface. This was

achieved distally with an elastic modulus that gradually decreased distally. The


proximal stress peak could not be avoided. Chang et al. (2001) were also inter

ested in minimising interface stresses. They developed a more flexible design with

a reduced mid-stem diameter. A larger diameter distal tip was retained to prevent

instability. Gross and Abel (2001) examined the effect of having a hollow distal

stem on bone and cement stresses. This led to increased proximal bone and cement

stresses relative to a solid stem. By optimising the taper of the hollow section~by

variation of the inner diameter~proximal bone stress could be increased without

overstressing the cement. Cement stresses are important within the context of fa

tigue cracking and release of particulate matter, and have been examined further

in other papers (Estok and Harris, 2000; Kleemann et al., 2003; Mann et al., 1995;

N uno and Amabili, 2002).

The effect of prosthesis stem length appears relatively unimportant with respect

to bone stress, as was found experimentally. Rohlmann et al. (1987) showed that

stem length had little effect on implant, bone or cement stresses, except for stems

shorter than 100 mm. McNamara et al. (1996) found little difference in bone stress

proximally, but a longer stem had greater distal stress shielding. Similarly Toni et al.

(1996) reported that for a proximally bonded implant, stem length had little effect,

however short stems performed better clinically, perhaps due to different bonding

behaviour caused by the level of micromotion. In a remodelling simulation, van

Rietbergen and Huiskes (2001) found no difference in bone adaptation between

a normal implant and the same implant without the distal stem. Vichnin and

Batterman (1986), however, predicted a reduced load bearing capacity for bone

under torsion with the standard version of a cemented stem, as opposed to the

extended.

The fact that finite element models predict increased calcar strains for low mod

ulus materials, where no difference is detected experimentally, underlines the im

portance of the implant-bone and/ or implant-cement interfaces for proximal load

transfer. The method by which they are theoretically modelled is therefore fun

damentally important. Most of the early studies assumed all interfaces to be fully


bonded, with equal displacements at the nodes across the interface. Subsequently,

many researchers have routinely used springs, gap elements and Coulomb friction

to model interface stress and micromotion. A large range of friction coefficients

have been quoted for implant-cement and implant-bone interfaces. Load transfer

to bone occurs primarily across these interfaces, so any inaccuracies in modelling

the interface characteristics can significantly effect the load transfer (Joshi et al.,

2000b). For example, Mann et al. (1995) found that the largest tensile stresses

in the proximal cement mantle were increased by 95% when Coulomb friction was

used, rather than perfect bonding, to model the cement-implant interface.

Cemented prostheses have two interfaces to be simulated. The cement-bone

interface is predominantly considered bonded, due to the interdigitation of the two

materials in practice. The implant-cement interface is generally modelled as bonded

or with Coulomb friction. Some more complex arrangements have also been investi

gated, for example, Rojek and Telega (1999) developed a contact model accounting

for adhesive forces. This was implemented in a geometrically simplified symmetric

model of a cemented hip in the proximal femur. Shear and tensile stresses could be

transmitted at the interface until separation occurred.

Modelling a porous coated surface poses a few challenges since in reality the

interface behaviour alters with time in vivo. During the immediate postoperative

period, there is no bone ingrowth, so tensile stresses and shear stresses above those

due to friction are not transmitted at the interface. As ingrowth progresses, more

of the coated surface is able to transmit shear and tensile forces. Often the two

extremes are modelled, with frictional contact to represent the immediate postop

erative condition, particularly when initial stability is of interest, or fully bonded

to represent the completely ingrown scenario.

One of the first studies to include nonlinear friction at the implant-bone interface

was published by Tensi et al. (1989). Transverse and normal springs were rigid and

transmitted all forces in regions of porous coating, while only compressive and

Coulomb shear forces were transmitted at smooth surfaces.


A somewhat elaborate procedure was adopted by Keaveny and Bartel (1994)

to model implant-bone contact. Thin interface elements, 0.25 mm thick, were

defined. A nonlinear constitutive law was applied to each of the 8 Gauss points per

element, allowing debonding (tensile separation) or shear failure to occur at any or

all of the Gauss points. Following separation or shear failure, the modulus at that

point is reduced and the stress distribution is recalculated. An interface element

was considered as being a contact region, transition region (partially debonded) or

separation region depending of the number of debonded Gauss points.

To evaluate interface stress for bonded surfaces, representing porous coated re

gions of noncemented implants, Huiskes and van Rietbergen (1995) employed the

Hoffman criterion. This gives a scalar value that interrelates the roles of differ

ent stress components in the initiation of interface failure. Uncoated regions were

modelled with nonlinear interface elements allowing frictionless sliding and incor

poration a 10 11m gap to simulate a thin fibrous tissue layer. The technique was

later applied by van Rietbergen and Huiskes (2001).

Modelling porous coated surfaces with Coulomb friction and frictionless sliding

elsewhere, Keaveny and Bartel (1993a) showed that axial forces were higher for un

coated implants, when compared with partially and fully coated surface treatments.

Torsional forces are similar for uncoated and partially coated implants, and lower

for fully coated. For a two-thirds coated implant (Keaveny and Bartel, 1995), axial

load transfer was greatest proximally for the no-ingrowth case, compared with typ

ical and ideal interfaces. Micromotion and subsidence was reduced for the typical

and ideal ingrowth cases.

With a simplified three-dimensional model, Keaveny and Bartel (1994) examined

the effect of surface treatment on contact area. The friction coefficient had negligible

effect on the contact region, while the amount of coating and the applied loads had

a small effect. A larger contact area was predicted with the use of a partial coating,

while a combination of axial and bending loads, as opposed to bending alone, caused

greater interface separation. For fully coated stems, axial load were transferred by


large shear forces at the lateral stem tip, while for partially coated stems, axial load

is transferred by small shear stresses just above the medial aspect of the coating

junction. Tensi et al. (1989), however, detected high shear stresses at the distal

margin of the porous coating for both partially and fully coated prostheses.

Skinner et al. (1994b) used a voxel-based model to asses the extent of porous

coating on an uncemented implant. The length of coating had negligible effect

on femoral stress proximal to the lesser trochanter. A fully coated prosthesis was

recommended based on proximal stresses and reduced distal stress concentration.

Biegler et al. (1995) adopted the same contact method as Keaveny and Bartel

(1994) to study the effect of surface finish on regions of contact. Contact patterns

were similar for the smooth and porous coated versions of an implant, and between

the two designs examined. Stair climbing loading increased interface separation,

which may reduce bone ingrowth.

In a series of papers, the effects of interface conditions around a particular unce

mented hip under heel strike loading in a synthetic femur were reported (McNamara

et al., 1997a, 1996; Toni et al., 1996). Highest bone stresses were obtained with a

proximally bonded stem without any distal contact conditions (representative of an

over-reamed femoral canal). The fully bonded case gave the worst load transfer,

while a proximally bonded implant with sliding distally fell between these two cases.

Further applications of finite element modelling of the femur include measure

ment of prosthesis micromotion (e.g., Ando et al., 1999; Biegler et al., 1995; Vice

conti et al., 2001c, 2000), pre-clinical testing of new implant designs (e.g., Ando

et al., 1999; Joshi et al., 2000a; Viceconti et al., 2001a) and subsequent design

revision (e.g., Viceconti et al., 2001b).

Loading and Constraints

According to a review by Cristofolini (1997), the most common loading arrangement

( 44% of the experimental and finite element literature they reviewed) involved a

single force on the femoral head. The next most common set up (39% of the


literature) included the action of the abductor muscles. The third most common set

up (14%) simulated the hip joint force, the abductor muscles and the iliotibial tract,

although there is little agreement about the action of the iliotibial tract. Simulations

with additional muscle forces are essentially limited to finite element models, where

control of the magnitude and direction of the forces is easily implemented.

Most of the finite element modelling papers in this review employed the hip joint

and abductor muscle forces only to represent stance or gait loading. Some have

included the iliotibial tract also (Lengsfeld et al., 1996; Prendergast and Taylor,

1990; Rohlmann et al., 1987), or the iliotibial tract and iliopsoas muscle forces

(Taylor et al., 1996). Nonphysiological moments were applied in addition to a hip

force by Biegler et al. (1995) to represent stair climbing. Lengsfeld et al. (1996)

found the strain energy density distribution of the femur to be most sensitive to the

iliotibial tract force, when applied in combination with the hip joint and abductor

forces. Taylor et al. (1996) discovered that the direction of the joint reaction force

most heavily influenced the stress distribution. The iliotibial tract reduced coronal

plane bending, but increased sagittal plane bending.

A few researchers have used a more comprehensive muscle set (Cheal et al.,

1992; Duda et al., 1998; Joshi et al., 2000a; Kleemann et al., 2003; Stolk et al.,

2001). Cheal et al. (1992), however, did not include the iliotibial tract for loading

at heel strike, midstance or toe off. A methodological paper by Duda et al. (1998)

analysed a model of a full synthetic femur at 10, 30 and 45% of the gait cycle. A

complete muscle set was compared with simplified cases, for example, abductors,

iliotibial tract and hip joint force. Principal strains were less than 2000 JLE using

the complete muscle set, but nearly 3000 JLE under simplified load cases. A simple

muscle set including the iliotibial tract action produced a large bending moment

distally, and thus did not recreate the strain distribution from a complete muscle

set. Neglecting muscle forces led to overestimation of shear forces and bending

moments, whilst torsional effects were underestimated. Duda et al. (1998) suggest

5.3 REMARKS 108

that at the least the abductors, iliotibial tract, adductors and hip joint force should

be included in in vitro studies.

A similar style of investigation by Stolk et al. (2001) set out to determine which

muscle forces should be included in in vitro testing of cemented hip arthroplasty.

The same complete muscle set as Duda et al. (1998), again at 10, 30 and 45% of

the gait cycle, was applied to a model of the proximal femur containing a cemented

implant. Inclusion of the abductor group had the largest effect on deflection of

the model, with further inclusion of the iliotibial tract, vasti and adductors having

relatively small effects. The abductor muscles also had the greatest influence on

the femoral strain distribution. Based on these results, it was concluded that hip

joint and abductor muscle forces were sufficient to adequately reproduce in vivo

bone loading for cemented hip implants. This conclusion was not extrapolated to

loading on the intact femur. It was also suggested that the iliotibial band could be

justifiably excluded on the basis of the lack of consensus on its action and the small

effect it had on load transfer in cemented hip arthroplasty.

In reference to the iliotibial band, Cristofolini (1997) also commented that: "if

a force is unknown or its effect is irrelevant, assigning any value is no less arbitrary

than assigning a value of zero." Cristofolini (1997) further recommended that a

loading set up should begin with a simple starting point, with the hip joint force

only, and other forces should be investigated one by one and retained only if it is

physiological, is shown to affect the results, and its magnitude is known.

5.3 Remarks

Strain gauges and finite element modelling have been used in a large number of

studies concerned with stress shielding following hip arthroplasty. Both methods

have been effective in simulating clinical studies, however it is almost impossible

to quantitatively compare results between studies due to varied loading protocols

and subject-specific models. The conflicting requirements of a flexible stem having

5.3 REMARKS 109

low interface stress, the difficulty of practically implementing a collar, and the

discrepancy between the experimental and theoretical methods when considering

implant stiffness, imply that the mechanism of load transfer to the femur is probably

the most important aspect in the design of a hip prosthesis.

According to Rojek and Telega (1999), the load transfer mechanism and associ

ated stress patterns in prosthetic fixation depend on four aspects: loading charac

teristics, implant geometry, material properties and boundary /interface conditions.

It is the interface conditions that are most difficult to simulate experimentally and

theoretically, especially for porous coated implants. Finite element models, with

few exceptions, assume perfectly congruent surfaces at the implant-bone interface,

whereas in reality, the contact area is highly dependent on difficult to control factors

like surgical technique. This situation with discrete contact points can be repro

duced experimentally, and for this reason has been cited as an important aspect of

load transfer (Diegel et al., 1989; Jasty et al., 1994). Van Rietbergen et al. (1993)

in fact found better agreement with in vivo bone adaptation results when a proxi

mal interface gap was included, while Weinans et al. (1994) showed that proximal

overreaming resulted in dramatic proximal bone loss.

Although pre-clinical evaluation methods for implant designs have progressed

considerably, the importance of in vivo verification is still important. Further stan

dardisation of pre-clinical test protocols, such as ISO 7206 which has considerably

reduced the occurrence of stem fractures (Stolk et al., 2002), will also help improve

the success of hip arthroplasty.

Chapter 6

Bone Adaptation Models

Section 4.3 described the adaptive properties of bone in response to mechanical

load in terms of what has been observed experimentally and possible mechanobi

ological systems that governs that adaptation. Many mathematical models have

been proposed by researchers to simulate these systems theoretically. Since the

exact adaptation process at the cellular/microstructural level is not fully under

stood, most of these mathematical models seek to describe remodelling in terms

of cause-and-effect relationships, essentially with a "black box" in between. Such

models are classified as phenomenological. Optimisation theories have also been

applied to studying the adaptive behaviour of bone, but these models have some

limitations. A mechanistic approach is needed to properly elucidate the interplay

of the biological and mechanical environments. These models should include the

effects of genetics, hormones and drug therapy. Some progress has been made in

this direction, however much more work is needed before reliable results can be

obtained.

This chapter reviews some of the bone adaptation models found in the literature.

The models are either conceptual, or in a form for inclusion in bone adaptation sim

ulations. The adaptation simulations consist of a remodelling theory coupled with

the finite element method in most cases. Boundary element methods have also been

used (e.g., Luo et al., 1995), but are beyond the scope of this review. The advantage

110

6. BONE ADAPTATION ]'v10DELS 111

of finite element modelling is that it provides mechanical quantities, or field vari

ables (e.g., stress, strain), throughout a structure, which can be used to determine

local remodelling stimuli at all of these locations. The finite element model is incre

mentally updated according to the change in material properties and/ or geometry

predicted by the remodelling theory. The theories are quasi-static, i.e., independent

of loading rate, viscoelastic and inertia effects.

In Section 4.3.2, the differences between modelling and remodelling are dis

cussed. Appropriately, computational models tend to simulate these processes sep

arately. Somewhat confusingly though, both modelling and remodelling are often

classified as "remodelling". The alteration of bone geometry brought about by mod

elling is termed surface or external remodelling, while the change of porosity and

ultimately stiffness due to remodelling is called internal remodeling. This distinc

tion was made by Frost (1964). Since all bone remodelling occurs by resorption

and deposition onto surfaces, it would be most precise to use surface remodelling

equations to simulate both modelling and remodelling processes for bone. However,

this would be a massive computational task if applied to all of the envelopes of

the skeleton, particularly the trabecular bone, due to the vast surface area. Most

simulations include only one of the "remodelling" processes.

Mathematically, internal remodelling can be described by a change in apparent

density. The rate of change of apparent density at a particular point can be de

scribed by an objective function F, which is dependent on a particular remodelling

stimulus at location (x, y, z) (Weinans et al., 1992a). The objective function is as

sumed to be related to the local stress tensor a-= a-(x, y, z), the local strain tensor

€ = e(x, y, z), and the local apparent density p = p(x, y, z)

dp dt = F(a-,e,p), 0 < p::::; Pc (6.1)

where the density cannot decrease below 0 (total resorption) or above Pc (density of

cortical bone). Remodelling equilibrium (net rate of change of bone density is zero)

6. BONE ADAPTATION l\10DELS 112

occurs when the objective function F reaches zero. Equation 6.1 can be written as

d: = B(S- k), 0 < p '5. Pc (6.2)

where B is a constant, S = S(x, y, z) is the mechanical stimulus, and k = k(x, y, z)

is a reference value. The mechanical stimulus strives to equal the reference value

(Equation 6.2), which can either be site-specific or non-site-specific (constant over

the model). Surface remodelling can be simulated in a similar manner, with the

rate of change of apparent density replaced by the rate of change of a position.

Section 4.3.3 describes the process by which mechanical quantities within bone

are locally transduced by sensors throughout the structure, producing a stimulus

to provoke an appropriate cellular reaction to maintain or modify the bone archi-

tecture, as hypothesisd by Roux and Wolff. Based on this concept, many numerical

bone remodelling theories use locally derived, site-specific, mechanical stimuli to

drive adaptation. Consideration for the structure of the bone as a whole is not

given. The other school of thought is that bone is an optimised structure, satisfying

either local or global objective functions. These are the non-site-specific models.

The different implementations of the various site- and non-site-specific models are

reviewed below. Some theories include addition nonlinearities not described by

Equation 6.2.

Since most remodelling equations are given in rate form, they must be integrated

in time so the adaptation from that period of time may be introduced into the finite

element model to determine the new field quantities in the bone. A forward Euler

integration algorithm is generally used as it is easy to implement and computational

costs are small dm(t)

m(t + l:lt) = m(t) + l:lt~ (6.3)

where t is the current time, l:lt is the time step, and m is the time-dependent

variable. This time integration scheme is only conditionally stable, so the time

step must be kept below a critical value for the results to be meaningful (Smolinski

6.1 SITE-SPECIFIC MODELS 113

and Rubash, 1992). Instabilities can usually be detected for linear problems, since

the solution oscillates with time. This behaviour is not so obvious with nonlinear

problems, and thus may go undetected. Another option is the backward Euler

method, which is an implicit integration method in which the equations are solved

at a future time based on information at a given time. This method is used for

nonlinear problems in which there is only a single time derivative (Harrigan and

Hamilton, 1993b).

6.1 Site-Specific Models

Site-specific remodelling simulations associated with adaptation around hip replace

ments require two finite element models: one representing the reference, or preopera

tive, mechanical state and one representing the treated, or postoperative mechanical

state. Both models require identical external loads. The local stimuli in the treated

state are driven towards the site-specific reference values by adapting the apparent

density and/ or geometry. In the calculation of change in density /position, the for

ward Euler integration time step must be chosen small enough to ensure monotonic

convergence.

6.1.1 Adaptive Elasticity Theory

A consistent mathematical theory for prediction of bone remodelling in accordance

with "Wolff's Law", was not proposed until the 1970's. The theory of adaptive elas

ticity developed by Cowin and Hegedus (1976) and Hegedus and Cowin (1976) is

a thermomechanical continuum theory that assumes that the load adapting prop

erties of cortical bone can be modelled by a chemically reacting porous medium in

which the rate of reaction is strain controlled. For small strains, the remodelling

rate can be expressed as

(6.4)


where e is the change in solid fraction, EiJ is the strain tensor (small strain theory),

AiJ(e) is a strain-rate coefficient, and a( e) is a function of the current solid fraction.

According to this theory, bone has a characteristic equilibrium configuration of

apparent density distribution and shape. The equilibrium condition is assumed to

produce an equilibrium (reference or homeostatic are also used interchangeably in

the literature here) strain field in response to a typical external load. A deviation

in the strain field, due to change in the load (either by change in external load or

the presence of an implant) becomes the driving force for local adaptation of shape

(surface/external remodelling) and apparent density (internal remodelling) towards

the equilibrium strain field.

The adaptive elasticity theory was later incorporated into an axisymmetric finite

element model by Hart et al. (1984a) to investigate surface remodelling of long

bones. Adequate results were obtained under axial loads only. One problem with

this method is the large number of constants required.

Based on the phenomenological framework of the adaptive elasticity theory,

Hart et al. (1984b) developed a more mechanistic approach. They proposed that

both internal and surface remodelling could be described by the manifestation of

surface cellular processes. In this model, net surface remodelling is calculated from

the sum of the osteoblast and osteoclast activity per unit surface area. Cellular

activity is modulated by genetic, hormonal and metabolic factors, as well as the

strain remodelling potential. The strain remodelling potential has a cumulative

nature due to past strain history. This model uses constants that are not purely

phenomenological, but are related to biological parameters that could possibly be

measured.

A poroelastic version of Cowin's small strain adaptive elasticity theory was em

ployed by Papathanasopoulou et al. (2002) to investigate the forced fit of a medull

ary pin in a hollow cylindrical bone model.


6.1.2 Strain Energy Density Model

Huiskes et al. (1987, 1992) used a formulation of the adaptive elasticity theory with

strain energy density (SED), U, instead of the strain tensor, as the stimulus. This

model has undergone more clinical verification than most. The actual remodelling

stimulus was the strain energy density, normalised by the apparent density, and

averaged over n load cases

S=]:_tUi n i=l P

(6.5)

where 1

U = 2 Eij rYij (6.6)

and Eij is the strain tensor, rYij is the stress tensor.

Huiskes discovered that a nonlinear relationship between strain energy density

and adaptation rate (Figure 6.1) was needed to replicate radiographic clinical find-

ings. A "dead" or "lazy" zone was implemented following a proposal from Carter

gain

Stimulus (S)

loss

Figure 6.1: Trilinear curve relating remodelling rate and stimulus. Reproduced from (Huiskes, 1993b).

(1984) suggesting the existence of a site-specific, physiological band wherein bone

tissue is unresponsive to changes in loading history. The idea of a minimum thresh

old change in stimulus was also conceived by Frost with his "minimum effective

strain" (Frost, 1987).

6.1 SITE-SPECIFIC MODELS

The internal remodelling rule for apparent density adaptation is written

dp

dt

C a(p)(S- (I+ s)Sref),

0,

C a(p)(S- (I- s)Sref ),

S > (I+ s)Sref

(I- s)Sref ~ S ~(I+ s)Sref

S <(I- s)Sref

116

(6.7)

where Cis the slope of the curve in Figure 6.1. Sis the stimulus from Equation 6.5,

Sref is the reference, or homeostatic, stimulus, and s is a constant describing the

width of the dead zone. This formulation also includes the function a(p) for the

free pore surface area expressed as a function of apparent density per unit volume

of bone, originally proposed by Martin (I972) (Figure 6.2). Since modelling and

>. 4 0 -·v; M' t: ;:;: <1) s 3 0 0

"' ....__

<1) "' ... ,.. <l: :: 2 0

<1) ~ u

"' r.n 1.0 't: :::s

(.f)

00 0.0 0.2 OA 0.6 0.8 1.0 1.2 1 4 1.6 18 2.0

Apparent Density

p (g / cm3)

Figure 6.2: Graph of the surface area density as a function of apparent density. Reproduced from Beaupre et al. (1990b).

remodelling take place on all of the bone surfaces (periosteal, endosteal, trabecular

and osteonal), more adaptation is predicted on those volumes of bone with higher

free surface area. This factor also accounts for some of the nonlinearity of the

proportionality constant.

The early version of the theory (Huiskes et al., I987) defined internal and sur

face remodelling separately. Remodelling of bone around an intramedullary stem

was simulated in a two-dimensional side-plate finite element model. Pronounced

resorption of the upper part of the cortical shaft was observed, due to the stress

shielding causes by the implant.

6.1 SITE-SPECIFIC MoDELS 117

The model defined by Equation 6.7 has been used by a number of authors with

three-dimensional finite element models to investigate the effect on periprosthetic

remodelling of dead zone width, initial bone quality, stem stiffness (Huiskes, 1993b;

Huiskes et al., 1992; Weinans et al., 1991), and extent of porous coating (Huiskes

and van Rietbergen, 1995). The study by Huiskes (1993b) compared their results

with clinical bone mineral density measurements from Engh et al. (1992a) and

found reasonable agreement. A similar study comparing patient-specific remodelling

results with radiographic data was performed by Kerner et al. (1999). They found

that bone loss in the region of the lesser trochanter was overestimated by the model

in all cases, and that convergence was not reached after 60 increments. Excessive

bone loss in the calcar region was also reported by van Riet bergen and H uiskes

(2001) when comparing a model incorporating the ABG stem with a clinical study.

Weinans et al. (1993) compared theoretical results with two year data from a canine

study, but better results were obtained for press-fit stems when a proximal interface

gap was included (van Rietbergen et al., 1993).

6.1.3 Damage Accumulation Models

A different approach was taken by Prendergast and Taylor (1992), who proposed a

remodelling theory based on the hypothesis that damage accumulation drives bone

remodelling. The remodelling stimulus is the difference between the current damage

rate and the remodelling equilibrium repair rate value. An advantage of this theory

is that it automatically accounts for dynamic loading history as the driving force of

the remodelling process. Surface remodelling of the femoral diaphysis under reduced

torsional loading (Prendergast and Taylor, 1994) and around an intermedullary rod

(Prendergast and Taylor, 1992) was investigated with this model. McNamara et al.

(1997b) showed that the damage stimulus was equivalent to the strain energy density

stimulus used by other researchers, when damage is measured as a function of crack

length.

6.2 NON-SITE-SPECIFIC MODELS 118

Ramtani and Zidi (2001, 2002a,b) explored this topic further, and created a

general continuum thermodynamic framework, along the lines of Cowin and Hege

dus (1976), to describe damage-induced remodelling. This model requires further

identification of constants and understanding of the damage evolution during the

adaptation process (Ramtani and Zidi, 2001).

6.2 Non-Site-Specific Models

Many scientists have assumed that bones are structurally optimised for their me

chanical environment (e.g., Thompson, 1961; Wolff, 1892). It is not clear exactly

what they are optimal for, but possibilities include deformation, strength and

weight. Most non-site-specific remodelling theories involve optimisation, and are

concerned with morphogenesis of the trabecular architecture of the proximal femur,

due to its fairly predictable distribution. These theories are generally coupled with

two-dimensional finite element models.

According to Hart (2001), optimisation studies help to further understanding of

bone as a mechanical structure, but do not provide particularly useful information

about the physiological process of adaptation.

6.2.1 Self-Optimisation and Bone Maintenance Theories

One of the first optimisation approaches was the self-optimisation model of Fyhrie

and Carter (1986), which predicted changes in trabecular orientation and apparent

density resulting from a change in applied stress. The stimulus was either a stress

ratio (a/ a ult) or energy stress ( V2f!E). The bone maintenance theory of Carter

et al. (1987) followed on from this, and proposed that bone in remodelling equilib

rium (i.e., no net bone gain or loss) is exposed to a constant daily stimulus that is

a function of the loading history.

Fyhrie and Carter (1990) applied Carter's model to predicting the apparent

density distribution in a three-dimensional finite element model of the femoral head


and neck, with limited success. Whalen et al. (1988) used a form of the bone main-

terrance theory to examine calcaneal bone density as a function of activity level.

Carter et al. (1989) used the theory to predict density in the proximal femur. Tra-

becular orientation was then calculated from the principal stress direction after each

iteration. Using the same assumptions, Orr et al. (1990) predicted density distribu

tions in the natural femur and tibia, and around a femoral surface arthroplasty and

tibial knee arthroplasty component. Other than the attempt by Fyhrie and Carter

(1990), all other simulations were incorporated with two-dimensional finite element

models.

A time-dependent version of the bone maintenance theory (Carteret al., 1987)

was developed by Beaupre et al. (1990b). An error that drives the density adapta-

tion was defined between the actual and attractor state tissue level stress stimuli,

(6.8)

in which CJ = V2U E is the energy stress, n is the number of loading cycles and m

is a weighting factor subject to the relative dependence of the stimulus on energy

stress and loading cycles.

Previous, non-time-dependent, studies forced the error to zero during each iter

ation, whereas this study used a piecewise linear function (Figure 6.3) expressing

the remodelling rate with respect to the tissue level stimulus, given by

c1 ('1/Jb - '1/JbAs) + ( c1 - c2)w1, '1/Jb- '1/JbAs < -w1

C2 ( '1/Jb - '1/Jb AS)' -wl ::; '1/Jb - '1/JbAs < 0 (6.9) r=

c3('1jJb- '1/JbAs), 0 ::; '1/Jb - '1/JbAs ::; W2

c4('1jJb- '1/JbAs) + (c3- c4)w2, '1/Jb- '1/JbAs > W2

The time rate of change of apparent density was then calculated from

p = r Sv Pt (6.10)

6.2 NON-SITE-SPECIFIC MODELS

Tissue Stress Stimulus -.j,, (MPa /day)

120

Figure 6.3: Piecewise linear curve relating remodelling rate and stimulus (Beaupre et al., 1990b).

where Sv is the bone surface area density from Martin (1984) (Figure 6.2) and

Pt is the mineralised tissue bone density. This theory was put into practice in

Beaupre et al. (1990a) with a two-dimensional finite element model of the proximal

femur. A simplified tri-linear remodelling rate curve, similar to Figure 6.1, was

compared with a linear function. The tri-linear model converged much more quickly

than the linear version. The density distribution predicted by the tri-linear model

at convergence was a reasonable representation of the actual distribution. The

distribution predicted by the linear model was similar to previous studies early on,

but after further iterations, the model converged to something less representative.

Other investigators used the model proposed by Beaupre et al. (1990b) as the

basis for their own studies. Nauenberg et al. (1993) converted density changes from

clinical studies into linear bone apposition/resorption rates, according to the tri

linear model with a dead zone. The data was obtained from studies investigating

the effects of exercise and injury on bone density. The slopes of the rate laws ranged

from 0.0014 to 0.0045 (pm/day)/(MPa/day) for resorption and 0.004 to 0.0013 for

apposition. These slopes indicate resorption occuring approximately 3.5 times faster

than apposition. Rapid initial bone loss was found during the first year with steady

state density achieved 2-3 years post-injury.


Levenston et al. (1994) modified the daily stimulus to included an exponentially

fading memory of past loading. This model gives the same result as Beaupre et al.

(199Ga) under simplified conditions. Time constants of 5 and 2G days in the remod

elling stimulus also converged to this result. Consideration of previous loading may

be important for short-term implications of use and disuse. Fischer et al. (1996)

implemented the theory of Beaupre et al. (199Gb) to see if a density distribution

could be produced or maintained by more than one set of loads. Similar results

were reported, except near boundaries and high density gradients.

Sti.ilpner et al. (1997) used an equivalent strain E as the stimulus in the theory

of Beaupre et al. (199Gb), defined by E = -JEijEij· This is used to calculate the

remodelling error e, which is the difference between the actual and optimal stimulus

levels

(6.11)

where N is the total number of load cases, i is the ith load case, ni is the number of

load cycles per day of load case i, mi are weighting factors, and Erem is the homeo-

static strain value. The bone apposition rate was determined from a double sigmoid

curve incorporating a dead zone, and also a saturation level. Internal remodelling

proceeds according to Equation 6.10. It was concluded that more complex loading

was required to create a physiological density distribution in three dimensions.

Hernandez et al. (2GGG) expanded the description of Beaupre et al. (199Gb) to

include the influence of biological factors on osteoblasts and osteoclasts. Cellular

activity was then regulated by the both metabolic and mechanical setpoints. A

large number of parameters was required to describe this model, and it is not yet

in a state where it could be used for a whole structure.

Strain Energy-Dependent Model

Huiskes et al. (1987) presented a theory for predicting the density distribution of

bone, as well as an application to stress sheilding as discussed previously. Internal

remodelling, was defined with a relation similar to Equation 6. 7, except that the


reference stimulus was constant throughout the structure, and the surface area

density function was not included. A linear version of the equation was used ( s = 0)

to predict the apparent density distribution of the proximal femur.

A similar formulation was used (Huiskes et al., 1989) to predict the density dis

tribution in a two-dimensional side-plate model of the proximal femur, with three

loading cases to represent daily activity. The resulting density was first used to

assess stress-shielding following hip arthroplasty, and then used to simulate re

modelling around a hip stem until the objective was reached again. Quite severe

proximal medial bone loss was noted, and the remodelling mechanism illustrated a

self-propagating effect.

Weinans et al. (1992b) also used a similar model, except with a dead zone curve,

that reflected experimental findings indicating resorption occurs more readily than

apposition. The effect on remodelling of stem stiffness for cemented and uncemented

hip replacements was then investigated. The same model was used by vVeinans et al.

(1994) to investigate the effects of fit and implant-bone integration characteristics.

Anisotropic Models

A number of anisotropic models have been proposed to predict trabecular density

and orientation. These include a modified version of the adaptive elasticity theory

of Cowin and Hegedus (1976), supplemented by Cowin et al. (1992) to simulate

changing anisotropy of the material. An elastic constitutive relation for trabecular

bone was defined, that includes the fabric tensor which is a symmetric second rank

tensor that is a stereological measure of the microstructural arrangement of the

trabeculae and pores. This was called the noninteracting microstructure theory.

The fabric tensor was also incorporated in a model by Tsubota et al. (2002), which

used local nonuniformity of stress as the driving force for remodelling.

Other anisotropic models include those of Pettermann et al. (1997) and Miller

et al. (2002). Anisotropic models are important for predicting the evolution, struc

ture and arrangement of trabecular bone.


Behaviour of Non-Site-Specific Remodelling Theories

Weinans et al. (1992a) investigated the behaviour of the optimisational approaches

employed by Carter et al. (1989), Huiskes et al. (1989, 1987), and Beaupre et al.

(1990a), and discovered that they produced a discontinuous patchwork not unlike

trabecular bone. This had previously been masked by the averaging/ smoothing

used by finite element post-processors (Figure 6.4). The system was found to be

Figure 6.4: Checker-board effect in density distribution hidden by finite element postprocessors. Reproduced from Weinans et al. (1992a).

liable to chaotic behaviour with an irregular structure as the solution, describable

by a fractal. Chaotic behaviour describes the transition from expected behaviour

to unexpected, but deterministic behaviour. The origin of the unstable behaviour

was apparently a positive feedback loop in the regulation model, and not the fi

nite element implementation. The only stable solution was one in which elements


were either empty or saturated to the maximum permissible density. The solu

tion obtained violates the continuum assumption on which it is based, however the

emerging morphology is not unlike the trabecular structure of bone itself.

This paradox was further investigated by Cowin et al. (1993), who showed that

the discrete time algorithm investigated by Weinans et al. (1992a) has a well known

chaos mechanism for ranges of the parameters of physiological interest. The con

tinuous time solution, however, is smooth, monotonic and nonchaotic. The chaotic

nature of the discrete time solution is similar to a logistic equation employed in

population biology to predict the population of a species with nonoverlapping gen

erations at generation n + 1, from the population at generation n, written as

(6.12)

where A is a control parameter that controls the propensity of the population to

grow. Cowin determined that a very small time step was required to ensure mono

tonic convergence.

In a series of papers, Harrigan and Hamilton (1992a,b, 1993b, 1994a,b) per

formed a rigorous study into the behaviour of this form of remodelling theory.

Necessary and sufficient conditions were determined for stability of the solution,

which placed restrictions on the elastic modulus-density relationship and remod

elling stimulus.

Jacobs et al. (1995) suggested the use of higher order elements and applica

tion of the remodelling rule to nodes, rather than element centroids or integration

points. This essentially smooths the discontinuous stress and strain quantities by

averaging them at the nodes before calculating strain energy density at the nodes.

The change in density can then be extrapolated back to the integrations points.

In this way, large density gradients across elements were avoided, and a continuous

density distribution was produced. Further stability studies based on the prediction

of density distribution in two-dimensional finite element models were undertaken

by Levenston (1997) and Capello et al. (1998).

6.2 NoN-SITE-SPECIFIC MODELS 125

A more physiological approach was taken by Mullender et al. (1994) to produce a

continuous solution to the self-optimisation problem. They proposed a modification

to the theory which incorporated a spatial influence function to remove the sensor

density dependence on the finite element mesh. Remodelling simulations up until

this time had determined the remodelling stimulus either at the element centroid or

integration point, so the number of sensor sites was dependent on the mesh density.

Mullender's model contained a lattice of equally spaced sensor sites, whose position

was independent on the finite element mesh. They hypothesised that osteocytes act

as the sensors for mechanical signals, and that each sensor produces a stimulus which

diminishes exponentially away from that sensor's location. The stimulus value at

a location is determined by the contributions from all sensors, depending on their

distance from the that location. The model produced trabecular-like structures

(Figure 6.5a), without the check-board patterns seen in earlier models (Figure 6.5b).

The thickness of the trabecular struts and the degree of branching was determined

(a) Prediction by Mullender et al. (1994). (b) Prediction by Weinans et al. (1992a).

Figure 6.5: Effect of spatial influence function on trabecular morphogenesis.

by the range of action of the sensors. The result was independent of the finite

element mesh as long as the elements were sufficiently small.


This spatial influence function model was used to demonstrate changes in tra

becular orientation due to varied loading conditions (Mullender and Huiskes, 1995)

including direction and magnitude. Van Rietbergen et al. (1996) applied this theory

to remodelling of a simple 3D lattice structure, while the effect of stimulus on the

resulting equilibrium trabecular structure were examined by Keller (2001). Xinghua

et al. (2002) introduced two nonlinearities into the model, which effectively sped

up convergence of the solution and altered "osteoclast activation", by increasing the

change in density for a change in stimulus. The behaviour of Mullender's model

was the subject of investigation by Zidi and Ramtani (1999, 2000).

Huiskes et al. (2000) reformulated the model of Mullender et al. (1994) in terms

of osteoblast recruitment level relative to a threshold value, and osteoclast activity.

Results were similar to Mullender, except clinical situations could be described in

a more relevant way.

6.2.2 Global Models

Global optimisation models to predict the density distribution and anistotropy of

bone have been assessed in more recent years. These models assume that bone is an

optimal structure, and an optimisation problem (e.g., minimal compliance subject

to a constraint of given mass) is solved to predict bone architecture. The solution

to the problem is generally obtained by utilising Lagrange multipliers to convert

the global problem into a criterion that can be satisfied locally. Local models can

be viewed as a simulation of a local biological process, or a structural "optimality

criterion". The advantage of global models is a clear statement of what bone is

optimal for, although the corresponding local criterion may not be simple for bone

to follow (Miller et al., 2002). Interestingly, some similarities can be found between

the converted local criterion from global models and the criteria from other local

models.

Jacobs et al. (1997) developed an anisotropic model based on density adaptation

and anisotropy reorientation using the principal stress as the external stimulus. The

6.3 REMODELLING STIMULUS 127

adaptive response of bone was proposed to be a globally efficient mechanical struc

ture. The global efficiency function was found to imply a local regulation process.

This theory was applied to a two-dimensional model of the proximal femur. Pan

dorf et al. (1999) looked at adding non-mechanical components to the remodelling

stimulus. These included the effects of parathyroid hormone, calcitonin, calcitriol

and plasma concentrations of calcium and phosphate.

Fernandes et al. (1999) used homogenisation of a porous unit cell in a global

optimisation model for prediction of bone architecture in a three-dimensional prox

imal femur. A cost function accounting for structural stiffness and a biological

constraint associated with metabolic maintenance was optimised. Anisotropy was

accounted for by rotation of the homogenised material properties tensor. The lo

cal formulation of the optimal criterion was shown to be equivalent to the models

used by Beaupre et al. (1990b) and Weinans et al. (1992a). Later, Fernandes et al.

(2002) used the same global optimisation theory to examine bone density around

hip stems. Other models using homogenisation in global optimisation schemes were

proposed by Bagge (2000) and Pedersen (2002).

Subbarayan and Bartel (2000) proposed a global criterion that is a trade off

between the competing costs of metabolic growth and use, represented by mass, and

the cost of failure, represented by total strain energy. This model was not dissimilar

to Fernandes et al. (1999). A local formulation with strain error terms was derived

under the assumption that the shape of the bone is fixed. It was suggested that the

rules of local remodelling models may be thought of as approximations to global

models.

6.3 Remodelling Stimulus

A large number of stimuli have been proposed to regulate bone adaptation. These

include the strain tensor, strain energy density, energy stress, failure stress, von

6.3 REMODELLING STIMULUS 128

Mises stress, average principal strain and equivalent strain. Others are not so spe

cific, proposing as yet unknown functions of mechanical quantities. These stimuli

are all based on continuum mechanics theory. Some are invariant, while others have

direction-dependence.

Stress is usually considered as the force acting over an area, while strain is a non

dimensional measure of change in length. These concepts are not, however, so simple

or intuitive (Humphrey, 2001). Stress, as defined by Cauchy, is a volume-averaged

tensor that transforms outward unit normal vectors, that define orientations of

differential areas about a point of interest, into traction vectors that are a measure

of the intensity of the forces acting on that neighbourhood. Similarly, strain is also

a volume-averaged tensor, defined in terms of a deformation tensor. Consequently,

scalar functions of these quantities will also be volume averaged. Strain energy

density is a popular choice in the literature, however its selection is essentially

based on the fact that it is an easily interpreted scalar function of stress and strain

(Weinans et al., 1992a).

Tensors transform vectors into vectors, and are therefore independent of coordi

nate system. To be computationally useful, components relative to an appropriate

coordinate system are identified. The chosen coordinate system, of which there are

an infinite number, generally depends on convenience of calculation. One of these

possibilities is the principal coordinate system, where the only non-zero components

of the stress or strain tensor are along the diagonal.

Considering these points, it is questionable whether a cell is able to sense a

particular component of a specific volume-averaged tensor that is resolved to a

particular coordinate system that is convenient for computation. It is, nevertheless,

possible that cellular responses may correlate with coordinate-invariant mechanical

quantities. In the case of correlations, there is no need to address causation, and

consequently similar stimuli can be correlated to different responses, and vice versa

(Humphrey, 2001).

Chapter 7

Materials and Methods

This study is divided into three principal sections. The objectives of each section

are to:

1. Experimental Study

• Determine the effect of hip arthroplasty with the ~'largron hip prosthesis,

on the cortical strain distribution of a group of femora.

2. Finite Element Study

• Construct an anatomic finite element model of an intact femur, selected

from the experimental group, and model the femur implanted with the

Margron.

• Validate the finite elerrl'ent models by comparing strain data with exper

imental results.

• Analyse the effects of mesh refinement.

3. Bone Remodelling Study

• Develop a theoretical algorithm to simulate bone adaptation.

• Employ this algorithm to simulate bone adaptation using the finite ele

ment models created in the Finite Element Study.

• Simulate adaptation that is consistent with radiographic clinical data.

129

7. MATERIALS AND METHODS 130

• Simulate remodelling in two other femora, implanted with two other im

plants with differing design philosophies, and produce results consistent

with their respective radiographic clinical data.

• Determine the approximate time scale of the simulation process.

• Investigate the effects of some parameters on the remodelling outcome.

The structure of the investigation is presented more clearly in a flowchart (Fig-

ure 7.1).

Experimental Study

Mechanical Testing -I Validation Strain Analysis '--· -------.------J

l Finite Element Study

Construct Finite Element Model

l r--------·._I ___ C_o_n_v_e~~~e_n_ce __ ~

I Bone Remodelling Study I

Margron

-

! Develop Mathematical

Remodelling Rule

l Other Implants

Radiographic Data from Patients

Predict Bone Density Changes

1-

I Investigate Parameters I

Figure 7.1: Flowchart of the study design.

7.1 EXPERIMENTAL STUDY 131

7.1 Experimental Study

The experimental study was concerned with obtaining the cortical strain distribu

tion of four cadaveric femora, before and after hip arthroplasty with a cobalt-chrome

femoral prosthesis. This was undertaken using strain gauges and mechanical test

ing. The change in strain after surgery, caused by stress shielding, may provide a

stimulus for adaptive bone resorption.

7.1.1 Specimens

For the experimental strain gauge study, four fresh-frozen human femora were ob

tained from a tissue bank (mean age: 53 years, range: 34-73 years). The sample

size was limited for a number of reasons. Firstly, it is difficult to obtain fresh human

tissue. Secondly, repeated measures statistics were to be used, so the sample size

could be reduced. Also, the experimental part of the study was essentially aimed

at validating the finite element model.

Each femur was stripped of soft tissue and x-rayed in the medial-lateral and

anterior-posterior planes for the purposes of identifying abnormalities and for im

plant size selection (Figure 7.2).

7.1.2 Implant

The implant investigated was the Margron TM hip prosthesis (Portland Orthopae

dics, Pty. Ltd., Sydney, NS\V, Australia) (Figure 7.3). The Margron hip replace

ment is modular, consisting of separate stem and neck components manufactured

from forged cobalt-chrome alloy, which are joined by a taper. The stem is circular in

cross-section, with a "cone" shape proximally, and a straight cylinder distally (Fig

ure 7.3b ). Two different speed external threads and longitudinal derotation columns

provide immediate resistance to torsional and axial movement (Figure 7.3a). The

proximal part is coated with a 70 J1m hydroxyapatite layer to encourage fixation.

The adjustable neck component allows for selection of the optimum version angle,

7.1 EXPERIMENTAL STUDY

Figure 7.2: Anterior-posterior radiograph with Margron template overlying.

A-~.~

PrD>>'Tial

c --

8 l\h~d

Tl!r,'<.ul

(a) External features.

(b) Section view showing neck-stem connection.

Figure 7.3: The Margron hip prosthesis.

(c) Assembled implant.

132


medial offset and vertical height for the prosthetic femoral head (Figure 7.3c). The

neck length can be additionally altered by selecting the appropriate femoral head.

Adjustment of the femoral head position provides the ability to restore the normal

biomechanics of the joint, including range of motion and stability.

The surgical steps for insertion of the Margron hip prosthesis consist of neck

resection, vertical reaming, milling to the shape of the implant and tapping of the

distal thread. The stern is introduced by screwing the implant horne using a torque

wrench. During this process, the distal thread engages with the tapped section,

while the proximal thread cuts a path through the proximal metaphyseal bone.

Since the proximal thread lags behind the distal thread by 0.5 rnrn per turn (for

the Number 1 size), the endosteal bone between the two threads is theoretically

compressed. There is the potential for nearly 2.5 rnrn of compression when the

implant is fully inserted, at which point, the cone section of the implant is in

intimate contact with bone. Below the distal thread, the femoral canal is reamed

to a diameter 1 rnrn greater than the stern.

7.1.3 Mechanical Testing

Triaxial strain gauge rosettes (Showa Measuring Instruments Co. Ltd., Tokyo,

Japan) were fixed with cyanoacrylate cement to the periosteal surfaces of the femora

at four levels (Figure 7.4) after careful preparation of the gauge site. The gauges

were placed with one of the axes aligned with the long axis of the femur. Triaxial

rosettes are necessary for finite element validation (Cristofolini, 1997). The strain

gauges used for this study had the following specifications:

• Gauge grid length: 1 rnrn

• Measurable strain: 2 to 4% maximum

• Temperature range: -30 ac to +80 ac • Thermal output: within ±2f.I£j ac at room temperature up to +80 ac • Gauge factor: 2.00 (nominal)

• Gauge factor change with temperature: ±0.015%/ ac


Figure 7.4: Strain gauge positions on the femoral cortex.

• Gauge factor tolerance: within 81% gauge factor for the respective package of

strain gauges

• Fatigue life: more than 106 reversals at 1000 fJ£

• Excitation: 1 Volt DC

• Strain gauge resistance: 120 n

The strain gauge base material was a polyester, with Cu-Ni alloy for the foil mate

rial, giving the strain gauge up to 10% measurable strain. The strain gauges were

also self-temperature compensating.

The femora were embedded distally in the diaphysis to facilitate fixation for

mechanical testing according to Gillies et al. (2002), with 10° of valgus angulation

and the femoral shaft vertical in the coronal plane ( 0° of flexion). Others have

used a similar form of distal fixation (Hua and Walker, 1995; Otani et al., 1993;

Tanner et al., 1988). The literature reports valgus embedding angles of between

9~12° (Cristofolini et al., 1995; Diegel et al., 1989; Engh et al., 1992b; Finlay et al.,

1991, 1989; Kim et al., 2001; Otani et al., 1993). Two simplified loading conditions

were examined:

(a) LOAD CASE 1, axial force of -820 N, 0° flexion; and

(b) LOAD CASE 2, axial force of -820 N, 10° flexion.

7.1 EXPERI!VIENTAL STUDY 135

Flexion was applied by altering the position of the testing jig (Figure 7.5). These

configurations are pseudo-physiological at best, but are appropriate for assessing

the influence of stress shielding, and for validation of the finite element model as

they are easily replicated. They also introduce a variety of loading types including

bending and torsion.

Each load cases was applied to the intact femora three times with an MTS 858

Bionix testing machine (MTS Systems Corporation, Eden Prairie, MN, USA) (Fig

ure 7.5) and the strain gauge data was acquired at 100 Hz with a 2100 System

signal conditioner/ amplifier and a Model 2000 analogue-to-digital converter (Mea

surements Group, Inc., Raleigh, NC, USA). The loading profile was applied to the

(a) Load case 1. (b) Load case 2.

Figure 7.5: Mechanical testing of an intact femur under the two load cases. The flexion angle is adjusted by the distal fixture.

test samples in force control, in the form of a -20 N preload followed by a ramped

function at -200 N/sec to a 10 second hold phase at -820 N.

The four femora were implanted with Margron implants using the prescribed

technique by a surgeon. The position of the centre of the femoral head was kept


constant by selecting the appropriate neck length and version angle for the pros

thetic femoral head. Mechanical testing was repeated under identical loading.

7.1.4 Data Analysis

Strains were averaged during the hold phase of loading. Maximum and minimum

principal strains were subsequently calculated for each gauge using the formula

(7.1)

where a, b and c are respectively the oo, 45° and 90° grid elements on the triaxial

gauges (Craig, 2000).

Means and standard deviations for the principal and longitudinal strains were

calculated and plotted for each gauge location using Matlab v5.3 (The J\1athworks,

Inc., Natick, MA, USA). The standard deviations included the inter-specimen, but

not the intra-specimen variation. Horizontal bar charts were used, and a Matlab

function was developed to draw the error bars, which was beyond the standard

functionality. Preoperative and postoperative strains were compared using analysis

of variance (ANOVA) with repeated measures (Statistica, Statsoft, Inc., Tulsa, OK,

USA). The extent of stress shielding was assessed by determining the strains after

hip replacement as a percentage of the intact values. To propagate the standard

deviations into the percentages, the following formulae were used

Z =X± y,

z=:E. y'

~z = J~x2 + ~y2

~z = J ( ~x) 2 + ( ~) 2

where ~x, ~y and ~z are the standard deviations of the means x, y and z.

(7.2)

7. 2 FINITE ELEMENT STUDY 137

7.2 Finite Element Study

The primary aim of the finite element study was to produce finite element models

representing the intact and postoperative conditions for one of the femora from the

experimental group. To reproduce the mechanical response of the biological bone

tissue, geometry and material properties of the femur were obtained from computed

tomography ( CT) scanning. By applying loads and boundary conditions identical

to the experimental situation, the finite element model could be validated by the

experimental strain data. l'v1esh refinement was performed to investigate solution

convergence.

7.2.1 Model Construction

A representative cadaveric femur (right, 34 year old female) from the experimental

testing group was selected by a surgeon, and scanned in air using a Toshiba Whole

Body X-Ray CT Scanner (X Series), using a pixel matrix of 512 x 512 and exposure

settings of 120 kV, 100 rnA and 1.0 sec. Slices were taken at 3 mm intervals

proximally and 5 mm intervals distally. A slice thickness of 2 mm was used in all

cases. In-house software was used to extract the periosteal surface contour for each

slice by a thresholding and edge detection process. The contours were exported in

the form of a number of points, along with their corresponding position along the

scanning axis, to MSC.Patran (MSC.Software Corporation, Santa Ana, CA, USA).

Closed loop interpolating B-splines were run through the points from each contour

(Figure 7.6a), and surface sections were subsequently constructed to form the outer

surface of the femur (Figure 7.6c). The surfaces must be created with consideration

to the placement of the implant, particularly with respect to the osteotomy cut.

Creating the geometry of the femoral shaft is a relatively straightforward task of

joining adjacent contours to form surfaces. The geometry of the proximal femur is

not trivial to create, and construction of many new curves is required to regenerate

the shape (Figure 7.6b).

7. 2 FINITE ELEMENT STUDY

(a) CT contours. (b) Reconstruction of proximal geometry.

(c) Intact femur surfaces.

Figure 7.6: Femoral geometry for the finite element model.

138

The surfaces were meshed with two-dimensional, 6-noded, triangular elements

using a global edge length of 5 mm to form a closed volume. This surface mesh was

subsequently used to create a three-dimensional solid mesh with 10-noded, modified,

tetrahedral elements (Figure 7.7). Second order elements were chosen to model the

femur, as they can accurately reproduce bending. The additional computational

cost was considered acceptable considering the more accurate results.

Modified tetrahedral elements were used to address certain problems with the

regular second order tetrahedral elements, mainly related to their use in contact

problems. Regular second order tetrahedral elements usually give accurate results

in problems with no contact, however, in uniform pressure contact situations, the

contact forces are significantly different at the corner and midside nodes (they are


4

3

1

2

Figure 7.7: 10-noded tetrahedral element showing nodes (dots) and integration/Gauss points (crosses).

zero at the corner nodes of a second order tetrahedron), which may lead to conver

gence problems (Abaqus User's Manual; Hibbitt, Karlsson & Sorrensen, Inc.).

The finite element model of the intact cadaveric femur (Figure 7.8c) was created

in two parts. Firstly, the part of the femur that would remain after preparation

for implantation with the Margron femoral stem (Figure 7.8a), and secondly the

remaining bone consisting of the femoral head and neck, and the elements in place

of the implant (Figure 7 .8b). This ensured that the mesh of the bone in the post

operative femur (Figure 7.8d) was identical to that part of the bone in the intact

femur.

The finite element model of the Margron prosthesis (Figure 7.8f, g) was de

veloped from a computer-aided drawing (CAD) file from the manufacturer (Fig

ure 7.8e). To facilitate meshing, some of the geometrical details were removed

including the derotation columns and threads. The taper between the stem and

neck components was not modelled, with the prosthesis assumed to be solid. The

implant was positioned using the endosteal contours of the femur and by consul

tation with the experimental radiographs. The centre of the prosthetic head was

aligned as closely as possible with the centre of the physiological femoral head.

The bone tissue was assumed to be a linear elastic, isotropic continuum. Material

properties for the finite element models were obtained from the CT slices. To extract

the material properties from the CT data, the coordinates of each integration point

(Figure 7.7) of the intact femur must be output to file. This was achieved by running

7.2 FINITE ELEMENT STUDY

(a) Prepared femur.

(b) Additional elements to make up the complete femur.

(c) Intact femur. (d) Operated femur.

(e) Margron geometry.

(f) Margron implant (anterior).

(g) Margron implant (medial).

Figure 7.8: Finite element meshes for the Margron models.

140


a "dummy" analysis for the intact femur. An arbitrary elastic modulus was given to

the elements, no loads were applied, and the Abaqus user subroutine UVARM was

called. User subroutines allow additional user control over the inbuilt functionality

of Abaqus, and are written in the Fortran language. The UVARM subroutine is

generally employed to create user output variables. In this case, however, it was

used because the material point coordinates are automatically passed from Abaqus

to this subroutine, where they can be written to file.

In-house software matched the integration point coordinates with the corre

sponding CT density. This was achieved by finding the nearest slice above the

integration point, and then finding the pixel with the same ( x, y) coordinates. The

final Hounsfield unit value written to file is the average of that pixel and the four

other pixels immediately adjacent to it. The elastic modulus at each integration

point was then calculated from this data file, by using two relationships: 1) be

tween apparent density and Hounsfield units, and 2) between elastic modulus and

apparent density.

As stated in Section 4.4.3, the first relationship is linear. Ideally, a number

of calibration phantoms should be used when CT-scanning the femur from which

the linear equation could be derived. Unfortunately this option was not available.

Therefore the apparent density had to be estimated from two bone regions with

high and low values of Hounsfield units. The centre of the femoral head and the

cortical bone in the mid-diaphysis were chosen. The average Hounsfield unit value

in these two locations were determined over a series of CT slices using Analyze

VW software (AnalyzeDirect, Inc., Lenexa, KA, USA) (Figure 7.9). The upper

average Hounsfield unit for dense cortical bone was HU = 2280, and HU = 470 for

trabecular bone in the femoral head. The apparent density of cortical bone in the

diaphysis was assumed to be 2.0 gfcm3 , while the apparent density of trabecular

bone in the femoral head was assumed to be 0.56 gfcm3 (Table 4.4). A linear

7.2 FINITE ELEMENT STUDY 142

Figure 7.9: Diaphyseal CT slice showing 3 regions of interest chosen to determine Hounsfield units of cortical bone.

relationship between apparent density and Hounsfield unit was thus derived

p = 0.801 HU + 173.5 (7.3)

The second relationship was taken from Carter and Hayes (1977).

(7.4)

where i is the strain rate and p is the apparent density of bone. The typical strain

rate for bone during normal activity is i = 0.01 s-1 (Bostrom et al., 2000; Lanyon

and Rubin, 1984), therefore Equation 7.4 becomes

E = 2785l (7.5)

These equations were used to assign the site-dependent elastic moduli to the

bone mesh. To include these relations in the finite element analysis, the *ELAS-

TIC, DEPENDENCIES and *USER DEFINED FIELD Abaqus options were used

in the material definition, in conjunction with the USDFLD user subroutine. The

USDFLD subroutine is used to redefine field variables at a material point (integra

tion point). In this analysis, the elastic modulus field was defined at the integration

points by reading in the file containing the Hounsfield units (data was stored as a


state variable), calculating the elastic modulus using Equations 7.3 and 7 .5, and

returning this value to the analysis. A constant value of Poisson's ratio, v = 0.3,

was used for cortical and cancellous bone (Section 5.2.2).

A problem was identified when looking at the density distribution along a line

across a CT slice (Figure 7.10a). The femur was scanned in air, and high and low

frequency signals at the air-bone junction were observed. This artefact is known as

"ringing" (Snyder and Schneider, 1991) (Figure 7.10b). Low Hounsfield unit read-

ings, below air values, were observed immediately adjacent to the air-bone interface,

with elevated values, above normal cortical bone, also present. The "ringing" arte-

(a) CT slice through the femoral diaphysis showing a line of interest.

n t e n s i t y

4329

2902

1475

-1379

-2806......,. __ ,.._ __ _ 0 Profile

(b) Intensity profile (in Hounsfield units) along the line of interest. Note extreme values either side of the air-bone interface.

Figure 7.10: "Ringing" phenomenon due to CT-scanning in air.

fact was overcome by determining a maximum cut-off value for the Hounsfield units

of cortical bone. The value for cortical bone (HU = 2280) was selected as the

maximum allowable value. All values above the cutoff were assumed to be equal

to this value. A lower bound was also placed on the CT data, with all Hounsfield

units below -90 taken as equal to this value. This included intramedullary tissue,

and was equivalent to an apparent density of 0.1 gjcm3 using Equation 7.3. Lower

densities were found to collapse some elements under high loading. Therefore, all

element were assigned densities between 0.1 and 2.0 g/cm3.

7.2 FINITE ELEIV1ENT STUDY 144

For the operated femur, the bone properties were applied in exactly the same

way as for the intact femur, given that this part of the mesh is identical. The

Margron elements were assigned the properties of forged cobalt-chrome alloy-an

elastic modulus of E = 210 GPa (Breme and Biehl, 1998) and Poisson's ratio of

v = 0.33. The implant was assumed to be isotropic and linear elastic.

The implant-bone interface was modelled using a combination of fully bonded

and small-sliding contact. In Abaqus, one surface definition provides the master

surface and the other surface definition provides the slave surface. For fully bonded,

or tied contact, each node on the slave surface is constrained to have the same value

of displacement as the point on the master surface that it contacts. This allows

transmission of tensile, compressive and shear forces at the interface. The small

sliding capability of Abaqus allows comparatively small sliding of two bodies relative

to each other. A kinematic constraint ensures that the slave surface nodes do not

penetrate the master surface. The small-sliding contact capability is implemented

by internal contact elements which allow three-dimensional contact between a slave

node and a deformable master surface (Abaqus User's Manual; Hibbitt, Karlsson &

Sorrensen, Inc.). Small-sliding contact does not allow the transfer of tensile forces,

while transfer of shear forces depends on the specified friction coefficient. A friction

coefficient of zero produces frictionless sliding, and thus no transfer of shear at the

interface.

The nonlinear analyses were all run with Abaqus Standard, using the USDLFD

subroutine to define the elastic moduli at the bone integration points, on a personal

computer with parallel1133 MHz Pentium 3 processors and 2GB RAM. The effects

of geometric nonlinearites were included using the Abaqus NLGEOM option. The

output databases (.odb files) were viewed using Abaqus CAE. Field quantities were

plotted with 75% nodal averaging. These were output to a report file by creating a

PATH of nodes and then choosing XY DATA to obtain the field output along the

path. Paths were created along the medial, lateral, anterior and posterior aspects

7. 2 FINITE ELEl'vfENT STUDY 145

of the femur. Python scripting was then used to repeat the extraction of results

from the various finite element models.


The intact and postoperative finite element models were validated by applying loads

and boundary conditions identical to those employed in the experimental study. A

force of 820 N was applied to 3 nodes on the surface of the intact femoral head

to replicate load cases 1 and 2, with the line of action passing through the head

centre. The same procedure was used for the hip joint force on the femoral head of

the hip implant. It was ensured that the hip force was positioned along the same

line of action before and after virtual implantation of the stem. The distal femur

was constrained against all translations at the level the experimental femur was

embedded.

Validation of the reconstructed finite element model was performed with the

implant-bone contact represented as:

(a) no distal~proximal contact surface (between and including the two threads)

bonded, with no contact defined distally (representing an over-reamed med

ullary canal);

(b) fully bonded~all implant surfaces tied to the bone interface; and

(c) distal sliding~the proximal region tied to the bone interface, while the distal

part was allowed to slide and transmit compressive loads.

These conditions were similar to those examined by McNamara et al. (1997a). In

practice, the femoral canal is reamed out to a diameter 1 mm larger than the

distal stem, and therefore condition (c) is most representative, assuming the stem

is inserted straight. A condition with friction at the proximal contact surface was

not analysed as the friction coefficient between the implant and bone was unknown

and would have only introduced additional uncertainties.

Compression of the bone between the proximal and distal threads on the implant,

caused during introduction to the femoral canal, was mentioned in Section 7.1.2.

7.3 BONE REI'v10DELLING STUDY 146

Residual strains, assuming they are appreciable on the periosteal surface and/ or

are not dissipated by viscoelastic effects, are not detected using strain gauges since

the amplifiers must be zeroed before measurement, assuming a state of zero strain.

Therefore, residuals were not incorporated in the finite element model.

Principal strains were obtained along the medial, lateral, anterior and posterior

aspects of the intact and reconstructed models. These were output to file and

plotted using Matlab, alongside the corresponding principal strains for the femur

used to create the finite element models. Comparison of results led to selection of

the contact conditions for use in further studies.


To examine convergence of the finite element solution, two additional models of

the intact femur were created, with 7 and 3 mm element edge lengths, to compare

with the existing 5 mm model (Figure 7.1la, c). After evaluation of convergence

results for the intact femur, only one additional model of the implanted femur was

constructed, with 3 mm element edge lengths (Figure 7.11b). Loads and bound

ary conditions corresponding to load case 1 were applied. The minimum principal

strains along the medial aspect of the femur gave a measure of solution convergence.

The effect of element material homogeneity on solution convergence was also

examined. This was achieved by applying material properties either directly to the

element integration points, or averaging the four integration point values across the

element, and applying the same value to each. This was undertaken for the 3 and

5 mm preoperative models under load case 1.


Adaptive bone remodelling, in accordance with "Wolff's Law", is a phenomenon

observed clinically in response to uncemented hip arthroplasty. The most common

adaptive change is bone resorption over time at the proximal-medial femur, resulting

7.3 BONE REMODELLING STUDY

(a) Intact femur (3 mm mesh).

(b) Operated femur (3 mm mesh).

(c) Intact femur (7 mm mesh).

Figure 7.11: 3 and 7 mm finite element meshes used for convergence analysis.

147

from stress bypassing, or stress shielding of this bone, caused by the implant. Bone

resorption comes about from increased remodelling activity, activated by a complex

osteoregulatory system. In this section an algorithm, which is coupled with finite

element modelling, is developed to predict bone remodelling in response to hip

replacement surgery.

7.3.1 Margron

Remodelling Rule

One of the aims of this thesis was to investigate remodelling of a femur implanted

with the l\1argron hip prosthesis. The first step in achieving this aim was to develop

an anatomic CT-based finite element model of a femur, and a model of this femur

7.3 BONE REMODELLING STUDY 148

reconstructed with the Margron hip. This process was discussed in the preceding

section (7.2). Having achieved this, the second step was to conceive an algorithm

to describe the bone adaptive changes seen clinically. This involved development of

a mathematical remodelling rule, and selection of the remodelling signal that will

be the stimulus for adaptation.

The remodelling rule was based on that proposed by Huiskes et al. (1992),

which is a site-specific, strain-adaptive remodelling thoery. This is a phenomeno

logical theory, which is appropriate because there is insufficient understanding of

the mechanobiological processes for a mechanistic model. The majority of three

dimensional models used to simulate bone adaptation in response to stress shielding

have been of this type (Cowin and Hegedus, 1976; Hart et al., 1984a; Huiskes et al.,

1992; Kerner et al., 1999; van Rietbergen and Huiskes, 2001). Details of these

models can be found in Section 6.1.

Huiskes' remodelling theory integrates finite element modelling with a strain

adaptive bone remodelling simulation procedure, which relates local deviations in

the bone mechanical environment from the homeostatic condition (due to inser

tion of a prosthesis), to gradual changes in bone density. Adaptation of the bone

apparent density was defined as "internal" remodelling by Frost (1964).

In Huiskes' model, the remodelling signal was based on the assumption that bone

strives to normalise the strain energy density per unit mass for specified loading

conditions. This choice was initially proposed by Carter et al. (1987). Based on

results using this remodelling signal, from the literature and my own experience,

I decided against using it. Instead, I adopted the equivalent strain proposed by

Sttilpner et al. (1997), similar to TvfikiC and Carter (1995)

(7.6)

where Eij is the strain tensor. This remodelling signal is also a positive, direction

invariant scalar that is easy to interpret. Other signals I considered besides this

one included minimum principal strain (Turner et al., 2003), hydrostatic strain,


deviatoric strain and shear strain. The deviation in equivalent strain, S, away from

the physiological value, Sref, is the stimulus for remodelling. A reduction in strain

leads to a decrease in apparent density, while increased strain causes an increased

density, in accordance with "Wolff's Law".

Damage accumulation caused by fatigue loading is another possible stimulus for

remodelling. Fatigue cracking tends to occur when loading is above the physiological

range (Duncan and Turner, 1995). When concerned with periprosthetic adaptation

however, bone resorption caused by underloading is the major problem. Fatigue

cracks accumulate slowly under normal loading conditions, and are therefore not

likely to trigger remodelling due to disuse (Carter, 1984). Hence the influence of

damage accumulation was not considered to be significant for the current applica

tion.

The model accounts for the physiological range of equivalent strains where bone

is unresponsive to load by including a "dead zone" or "lazy zone". This concept was

proposed by Carter (1984) and Frost (1987). This means that a threshold change

in equivalent strain from the reference situation is required before remodelling is

activated. Hsieh et al. (2001) recently showed that the strain threshold increases in

regions of higher peak strains. Others have also assumed the dead zone width to

be site-specific (Beaupre et al., 1990b; Carter, 1984). This suggests that the dead

zone width should be proportional to the reference strain.

The remodelling rate, of either resorption or apposition, is dependent on the

local difference between the equivalent strains before and after reconstruction with a

femoral implant, and the width of the physiological range, or dead zone. This can be

represented with a piecewise linear curve consisting of three sections (Figure 7.12).

To the left of the reference strain, where the actual equivalent strain is less, net

bone resorption occurs. To the right of the reference strain, net bone apposition

takes place. The region with zero slope immediately adjacent to the reference

signal denotes the dead zone, where there is no change in density. The width of the

dead zone at any location depends on the constant parameter s, and also on the


Remodelling Rate

{1-s)Sref Sref 1---------7---+---~--------- Equivalent

I : Strain I I

!- Dead Zone --1

Figure 7.12: Remodelling rate as a function of the remodelling signal.

150

magnitude of the reference equivalent strain Sref· The parameter s is important,

because it can be adjusted to alter the extent of adaptation. In this study, s was

"tuned" to produce simulation results consistent with those found clinically.

Unlike Huiskes' model, the resorption and apposition rates were not assumed to

be the same. Although changes of bone apparent density are all referred to here as

internal remodelling, the biological processes leading to increases and decreases of

density are not the same (Frost, 1987). It is thought that resorption takes place more

quickly than deposition (Beaupre et al., 1990b; Weinans et al., 1992b). Nauenberg

et al. (1993) converted radiographic data relating to use and disuse, into linear

apposition rates and found that resorption occurred approximately 3.5 times faster

than deposition. Thus the slope to the left of the dead zone in Figure 7.12 was

set 3.5 times higher than the slope to the right. The slope of the resorption curve

was limited by the maximum allowable change in density within a remodelling

increment.

Bone remodelling takes place on all of the skeletal surfaces: periosteal, intra

cortical, endocortical and trabecular (Frost, 1987). The potential for remodelling is

therefore related to the amount of free surface area within a given volume. Martin


(1972) developed a relationship for the bone surface area density. Using a geomet

ric model for the pore shape, this was expressed as a function of porosity (Martin,

1984), which was later adapted by Beaupre et al. (1990b) to produce the surface

area density as a function of apparent density (Figure 7.13). The surface area den-

4.5

""~ 4 E E ~ 3.5 E ~ 3 ~ "iii a5 2.5 0

al 2 ~ 8 1.5 C1l 't:

~ 1

0.5

OL-----L---~----~----~----~----~----~----~----~----~

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Apparent Density (g/cm3)

Figure 7.13: Polynomial fit of the bone surface area density-apparent density curve from Beaupre et al. (1990b).

sity function was determined by fitting a 5th order polynomial to this curve using

Matlab

a(p) = 0.0426 + 6.7579p- 2.1026/- 2.5502p3 + 2.6883p4- 0.8581l (7.7)

Putting all of this together, the mathematical remodelling rule for rate of change

of density is given by

dp

dt

Capp a(p)(S- (1 + s)Srer),

0,

Cres a(p)(S- (1- s)Srer),

S > (1 + s)Sref

( 1 - S) Sref :::; S :::; ( 1 + S) Sref

S < ( 1 - S) Sref

(7.8)


where Capp is the slope of the apposition curve, Cres is the slope of the resorp

tion curve (equal to 3.5 x Capp), and a(p) is the surface area density defined by

Equation 7. 7.

The strain-adaptive bone remodelling procedure is outlined in Figure 7.14. Two

FE MODEL -1 Change in I 1 Postoperative

Femur - Material Properties -. Remodelling Theory I

I Dead Zone I

I Loads/BCs J

I Actual Remodelling I

Signal (S) J

FE MODEL I Reference Remodelling I Preoperative I Signal ( Sref) Femur

l --... 0-----'

_j Figure 7.14: Overview of the bone adaptation simulation.

finite element models are required: one representing the reference, or intact femur,

and one representing the treated, or operated femur. The same mesh is required for

the bone elements remaining after implantation so that site-specific strains can be

directly compared at each integration point. Development of these finite element

models was discussed in Section 7.2. Identical loads and boundary conditions must

also be applied.

The difference between the actual and reference local remodelling signals ( equiv

alent strains), relative to the dead zone width, drives the change in local density,

according to Equation 7.8. The new density distribution in the operated finite

element model is updated using a forward Euler integration algorithm

p(t + ~t) = p(t) + ~t d~~t) (7.9)

where t is the current time and ~t is the analysis time step. This integration scheme

is only conditionally stable, so the time step must be sufficiently small for mean

ingful results (Smolinski and Rubash, 1992). Density changes alter the mechanical


properties of bone (Equation 7.5), so new equivalent strains are calculated at the

beginning of the next remodelling iteration. Each remodelling iteration consists of

one pass around the loop represented by the thicker arrows in Figure 7.14. The

simulation continues to pass around this loop until all of the equivalent strains have

reached the dead zone, or the density has reached the maximum (2.0 g/cm3 ) or

minimum (0.1 gjcm3 ) values. This is when a new density distribution is reached

(remodelling equilibrium), and the simulation is terminated.

Implementation

The next part of the remodelling study was to put the adaptation theory into prac

tice. The finite element models had already been created, but it was necessary to

apply new loads and boundary conditions, and to implement the remodelling theory

using Abaqus. The contact conditions for the Margron-bone interface consisted of

fully bonded contact at the proximal surface with no contact defined distally ( condi

tion (c), Section 7.2.2), to represent the slightly over-reamed canal found clinically.

A physiological muscle force configuration was applied to both models. Duda

et al. (1998) proposed that remodelling simulations should include the abductors,

iliotibial band, adductors and hip contact forces. Other researchers have suggested

that site-specific remodelling theories are insensitive to the precise loading condi

tions, as long as the load applied in the model represents a typical loading pattern

that includes axial, bending and torsional components (Huiskes et al., 1987, 1992;

Weinans et al., 1993). For these reasons, a complete muscle set was employed.

The largest hip joint reaction force occurs at 45% of the gait cycle, just prior

to toe off (Duda et al., 1998). The joint and muscle forces at this moment of the

gait cycle were assumed to be representative of the peak loading experienced by

the femur during daily activity (Cristofolini, 1997). The magnitude and direction

of the muscle forces are taken from Duda et al. (1998), assuming a 70 kg subject

(Table 7.1). For a right femur, as used for the current study, the x direction is

anterior, they direction is lateral and the z direction is superior. Only the proximal


femur was CT -scanned, so it was assumed to have a version angle of 15°, which is

within the normal range (Breathnach, 1965).

Table 7.1: Joint and muscle force components for the proximal femur.

Name x component y component z component

Hip joint reaction force -466.34 962.62 -1911.22 Gluteus Maximus 1 35.10 -87.87 90.95 Gluteus Maximus 2 0.08 -57.73 70.32 Gluteus Medius 1,2,3 111.23 -179.68 221.40 Gluteus Minimus 1,2,3 186.22 -193.69 92.98 Piriformis 5.35 -77.90 67.03 Pectineus 1.30 -1.01 1.12 Psoas Iv1ajor, Iliacus 115.24 -62.89 114.51 Superior and Inferior Gemelli 7.07 -35.18 37.20 Tensor Fasciae Latae 51.42 -40.70 -40.04 Vastus Medialis 2.93 0.18 -8.09 Vastus Intermedius 9.13 5.01 -62.06 Vastus Lateralis 69.58 -25.73 -215.72

These forces were applied to the reference and treated finite element models by

selecting a group of nodes representing the attachment area of the muscles (Fig

ures 7.15 and 7.16). Polgar et al. (2003) found that forces at single nodes lead to

stress concentrations which can pass through the thickness of the bone cortex. It

was hoped to avoid this situation by spreading the muscle forces over a larger area.

The femur was constrained distally, 60 mm below the stem tip.

Before the treated femur could be remodelled, the mechanical state of the refer-

ence femur had to be obtained. This was achieved by running a three step Abaqus

analysis. In the first step, the coordinates of the underformed integration points

were written to file, for future reference. In the next step, the bone material prop-

erties were applied to the model with the user subroutine USDLFD, as they were in

Section 7.1, and with the forces shown in Table 7.1. The GETVRM function was

employed within USDLFD to access integration point volumes, which were written

to file along with the corresponding coordinates and densities. This file was later

used to create a simulated DEXA scan of the time zero condition. After conver-

gence of the second step solution, loading was maintained throughout the third

7.3 BONE REl\10DELLING STUDY 155

J

(a) Anterior. (b) Lateral. (c) Posterior. (d) Medial.

Figure 7.15: Load and boundary conditions for the intact femur.

analysis step. The purpose of this step was to calculate, and output to file, the

equivalent strain for each integration point. This was facilitated by the UVARM

user subroutine containing GETVRM to access integration point mechanical quan

tities. The *USER OUTPUT VARIABLE option in the material definition of the

analysis input file instructs Abaqus to call UVARM, which allows the definition of

output quantities that are functions of any of the available integration point quanti

ties. The equivalent strain was computed from these quantities and written to file.

Defining the reference equivalent strain as a user output variable also allowed it to

be viewed in the post-processor.

Remodelling of the postoperative femur could now be implemented. This was a

multi-step process. The first step was identical to the second step of the previous

analysis. The forces and initial bone material properties were applied and the


(a) Anterior. (b) Lateral.

(c) Posterior. (d) Medial.

Figure 7.16: Proximal load conditions for the intact femur.


resulting equilibrium position of the model was calculated by Abaqus. The forces

were kept constant from this point on, by using a tabular amplitude function. In the

second step, the adaptation process began. Again the USDFLD user subroutine was

employed to define the elastic moduli. The reference equivalent strains s;ef at each

integration point i, were read in and stored in a state variable for future reference,

along with the values of (1- s )s;ef and (1 +s )s;ef· The current equivalent strains for

the operated femur Si, were calculated at each integration point using GETVRM to

access the current mechanical quantities. The remodelling error at each integration

point was then calculated according to the magnitude of the current strain relative

to the nearest extremity of the dead zone

(7.10)

The change in density at the integration point, during the remodelling increment,

was then calculated using a discrete time implementation of Equation 7.8

(7.11)

where the value of the constant C depended on if the remodelling error, ~i, was pos

itive (apposition) or negative (resorption). The integration point density was then

updated, within the upper and lower limits of 2.0 g/cm3 and 0.1 g/cm3 respectively

i i .6.i Pt+l = Pt + P, 0 .1 ::; Pt+l ::; 2. 0 (7.12)

The new integration point densities were stored as state variables and passed to the

next analysis step, where new values of the elastic modulus field variable and equiv

alent strain were calculated. The changes in density were updated again according

to Equations 7.10 to 7.12, and passed to the next step. This process continued until

the average value of~' calculated at the end of each adaptation step, reached an


asymptote

(7.13)

where n is the total number of integration points for elements with bone properties.

The closeness of this function to zero indicates how close the remodelling error is

equal to zero throughout the bone.

The value of tlpi (Equation 7.11) for each integration point was monitored dur

ing the first remodelling step to ensure that the changes in density were not greater

than half of the maximum density (~Pmax = 1.0 gjcm3 ) (van Rietbergen et al., 1993;

Weinans et al., 1993). The greatest change in density occurred during the first step,

and if the density change at any integration point was greater than ~Pmax, the

analysis was terminated and the time step, tlt, was reduced accordingly before the

analysis was restarted. This has the effect of decreasing the slope in Figure 7.12.

In this instance, the slope of the resorption curve was equal to 40 gjmm2 for each

remodelling increment.

Data Analysis

Principal strains were obtained along node paths, as explained in Section 7.2.1, on

the femoral cortex preoperatively, postoperatively and at remodelling equilibrium.

Contour plots of these circumstances were also created. The same was done for

the equivalent strains. Contour plots of the density distribution before and after

remodelling were produced, to show the effect of remodelling at the bone surface.

At designated stages throughout the analysis, simulated dual-energy x-ray ab

sorptiometry (DEXA) images were output. The density and volume of each integra-

tion point were written to file and read in, along with the undeformed coordinates,

by in-house software to produce DEXA images in any orientation, with respect to

the coordinate system of the finite element model. Anterior-posterior images were

produced, and quantitatively analysed using Global Lab Image/2 (Data Transla

tion, Inc., Marlboro, MA, USA) to calculate the percent change in bone density,

relative to the preoperative case.


Before analysing the DEXA images, an image of the implant, oriented within

Patran in the same manner as the DEXA image, was created. This was scaled

and positioned over the preoperative DEXA image using Adobe Photoshop (Adobe

Systems, Inc., San Jose, CA, USA), to mask out the bone behind. This image was

opened in Global Lab Image and rectangular regions of interest were drawn to rep

resent the seven Gruen zones (Gruen et al., 1979). This image was then thresholded

(Figure 7.17a), and an additional region of interest was created within each rect

angular region, that contained only the bone that would be seen by a conventional

DEXA scanner. These regions were saved and used to analyse subsequent DEXA

(a) Masking of image and thresholding procedure

•;I&U!Iiimml IV~ Tramfer ~&ackSCtt>t

Nll11lbet or

3

(b) Measurement of greyscale value in region of interest

Figure 7.17: Gruen zone analysis of DEXA images.

images, without the need to overlay the implant image or perform thresholding

(Figure 7.17b).

7.3 BONE REI\IODELLING STUDY 160

The percent changes in bone mineral density for the seven Gruen zones were

plotted using Matlab. Results were compared with radiographic bone mineral den

sity data from the Department of Nuclear Medicine, St. George Hospital, Kogarah,

NSW, Australia (Table 7.2), by calculating correlation coefficients (Statistica, Stat

soft, Inc., Tulsa, OK, USA) for 1, 2 and 3 year time points. Convergence of the

remodelling simulation was evaluated by plotting the average remodelling error

against remodelling increment number.

Table 7.2: Margron clinical bone mineral density data. 1 year: n = 64, 2 years: n = 56 and 3 years: n = 31 patients.

Time Point Zone 1 Zone 2 Zone 3 Zone 4 Zone 5 Zone 6 Zone 7

%Change BMD 1 year -7.6% -15.5% -2.0% -0.6% 0.6% -15.6% -27.3% 2 years -10.1% -20.4% -2.0% -0.6% 1.8% -14.8% -31.4% 3 years -15.2% -22.5% -4.0% -3.8% -1.8% -18.0% -34.7%

±%Error 1 year 37.7% 29.6% 26.9% 25.8% 24.2% 32.9% 32.1% 2 years 37.7% 30.2% 26.9% 26.7% 24.6% 31.8% 31.2% 3 years 39.7% 29.2% 26.9% 27.7% 25.0% 31.4% 32.5%


To show that the strain-adaptive remodelling theory was not specific to the single

situation identified in the previous section, I created subject-specific models using

other femora, with two distinctly different designs. The Stability™ (DePuy Inter

national, Ltd., Leeds, UK) and Epoch® (Zimmer, Inc., Warsaw, IN, USA) femoral

stems were selected because of the availability of bone mineral density databases.

Correlation with bone mineral density changes from the simulations would imply

that the simulation was not unique to a particular femur or implant design.

For the Stability and Epoch models, the same loading as the Margron model

was applied (Table 7.1), which assumed equal body weight/activity level, and these

femora were also assumed to have the same version angle as the Margron model

(15°). Both femora were constrained distally, 60 mm below the stem tip. Re

modelling was simulated for the Stability and Epoch stems, following an identical


procedure. For these two cases, the greatest change in density at any integration

point during the first remodelling increment was approximately half that of the

Margron model. Therefore, the slope of the resorption curve was set at 80 g/mm2

per remodelling increment, allowing the simulation to proceed at twice the rate.

Principal strains from the intact and reconstructed finite element models were

plotted for the medial and lateral cortices, and contour plots produced. The equiva

lent strains along the medial cortex were also plotted before and after implantation,

and at remodelling equilibrium, with corresponding contour plots. Simulated DEXA

images were created for the Stability and Epoch models using the method outlined

previously. Percentage change in bone mineral density for the seven Gruen zones

at a simulated time point of 2 years were graphed.

Stability

The Stability is a proximal fit-and-fill implant made from titanium alloy. The

proximal part has small steps and a beaded porous coating. The distal part is

fluted and has a slot in the coronal plane to reduce the bending stiffness, while

allowing for canal filling to prevent toggling. The implant relies on metaphyseal

filling for load transfer.

The Stability finite element models were constructed in the same manner as

the Margron model. The femur model was created from CT scans of a left, 54

year old male bone (Figure 7.18a-d). The implant geometry was obtained from the

manufacturer. To facilitate meshing, the proximal steps and distal flutes were not

modelled. The distal slot, however, was retained (Figure 7.18e-g). The implant was

assigned an elastic modulus of E = 115 GPa (Breme and Biehl, 1998). The porous

coated surface was fully bonded to the bone, while frictionless sliding contact was

defined for the remaining surface area.

The simulation data was compared with radiographic data from a clinical DEXA

study undertaken at the Department of Nuclear Medicine and Bone Mineral Den

sitometry, St. Vincent's Hospital, Sydney, NSvV, Australia (Table 7.3).


(a) Intact femur (anterior).

(b) Intact femur (posterior).

(c) Operated femur (anterior).

(d) Operated femur (posterior).

(e) Stability implant (medial).

(f) Stability implant (anterior).

(g) Stability implant (lateral).

Figure 7.18: Finite element meshes for the Stability models.


Table 7.3: Stability clinical bone mineral density data. 6 months: n = 30, 1 year: n = 24, and 2 years: n = 10 patients.


%Change BMD 6 month -8.8 -6.4 -8.2 -7.4 -7.5 -7.9 -12.6 1 years -7.4 -6.7 -5.1 -5.2 -1.1 -5.6 -20.5 2 years -6.3 -8.2 -6.4 -6.5 -0.2 -4.1 -22.7

±%Error 6 month 30.2 22.0 38.8 18.8 28.3 22.4 24.1 1 years 34.0 25.2 34.8 21.4 30.9 23.7 27.7 2 years 39.7 28.9 33.3 24.4 40.0 35.9 39.0

Epoch

The Epoch hip prosthesis is a low modulus, composite implant, designed to reduce

femoral stress shielding while achieving stable fixation. The implant incorporates

multilayer construction, with a forged cobalt-chrome core satisfying most of the load

bearing requirements. The core is surrounded by low modulus polyaryletherketone

polymer, and a full length coating of titanium fibre metal is applied to the outside

of the polymer for bone ingrowth (Swarts et al., 1997).

The proximal part of the implant is anatomic, with an anterverted neck. Distally,

the stem is straight and cylindrical. It is designed for proximal and distal canal

filling, while maintaining maximum surface area for bone ingrowth (Glassman et al.,

2001). The implant is conceptually similar to a cemented prosthesis.

The finite element models of the femur and Epoch prosthesis were created ac

cording to Section 7.3. The femur model was created from CT scans of a left, 47

year old male bone (Figure 7.19a-d). Geometry of the Epoch stem was obtained

from the manufacturer. The cobalt-chrome core was assigned an elastic modulus of

E = 210 GPa, and the polyaryletherketone outer layer a modulus of E = 4 GPa

(Swarts et al., 1997). The thin porous coated layer was not modelled (Figure 7.19e

h). The implant was assumed to be fully ingrown, with bonded contact over the

area where porous coating exists.


(a) Intact femur (anterior).

(e) Epoch implant (metal part).

(b) Intact femur (posterior).

(f) Epoch implant (polymer part).

(c) Operated femur (anterior).

(g) Epoch implant (anterior).

164

(d) Operated femur (posterior).

(h) Epoch implant (medial).

Figure 7.19: Finite element meshes for the Epoch models.


The Epoch model was compared with 2 year radiographic clinical data (Ta

ble 7.4) from a multicentre study of 46 patients (Glassman et al., 2001). The

variation in the data was not available from this paper.

Table 7.4: Epoch clinical bone mineral density data. 2 years: n = 46 patients.


%Change BMD 2 years -2.4% -3.4% -1.6% -0.1% 1.4% -7.7% -15.8%

7 .3.3 Investigation of Parameters

A mathematical remodelling rule to simulate femoral bone adaptation in response

to hip arthroplasty was developed, and implemented using finite element models.

Remodelling around three different hip replacement stems, inserted in three different

femora was simulated. This technique was then applied to investigate the effects of

varying some of the parameters used to date.

In each case, the influence of the specific parameter was analysed by plotting

the equivalent strains at a series of nodes along the medial cortex for the preopera

tive, immediately postoperative and remodelling equilibrium conditions. The effect

on the simulated density distribution was also examined by comparing percentage

changes in bone mineral density in the seven Gruen zones. The Gruen zone analysis

was performed at a 3 year time point, unless otherwise stated.

Effect of Interface Conditions

The contact condition with a bonded Margron-bone interface proximally and no

contact defined for the distal part implant, representing an over-reamed medullary

canal, produced strains most like the experimental conditions, particularly distally

(Section 8.2.1). This condition was also used for all other simulations involving the

Margron model.

7.3 BONE REJ\WDELLING STUDY 166

To examine the effect of the contact conditions on remodelling, the same contact

conditions were investigated as were used for validation of the postoperative finite

element model (Section 7.2.2):

(a) no distal-proximal surface fully bonded, with no contact defined distally;

(b) fully bonded-all implant surfaces tied to the bone interface; and

(c) distal sliding-the proximal region tied to the bone interface, with frictionless

sliding at the distal cyclindrical part.

No residual stresses or strains from insertion of the Margron stem were included.

This is because static loads do not promote remodelling (Lanyon and Rubin, 1984),

and the variation in strain produced by the external loading is important, rather

than the sum of residual and loading strains (Cristofolini, 1997).

Effect of Femoral Head Position

The Margron is a modular implant that allows for a relatively high degree of vari

ation of the femoral head position. Consequently, remodelling simulations were

performed to evaluate the influence of the femoral head position on bone adapta

tion. The position of the prosthetic femoral head was varied by changing the neck

length and the version angle.

The physiological position of the femoral head was obtained with a +4 mm neck

according to the template. This was varied to the other available neck lengths of

-4, 0 and + 7 mm. The version angle was varied from the physiological position

( +4 mm neck and oo relative angle) by 10° and 20° degrees of anteversion, and the

same quantities of retroversion. The matrix of parameters is shown in Table 7.5.

Effect of Dead Zone Width

The width of the dead zone is an important parameter in the mathematical remod

elling rule, determining the threshold change in strain required to induce adaptation.

This parameter was earlier varied to tune the simulation bone density changes to


Table 7.5: Matrix of femoral head position parameters evaluated. Negative neck lengths refer to shorter necks. Negative version angles denote retroversion (relative to the physiological position), positive version angles denote anteversion.

Neck Length Version Angle

-4mm oo Omm oo

+4mm -20° +4mm -100 +4mm oo +4mm +100 +4mm +20° +7mm oo

the radiographic measurements in patients. A dead zone width of s 0.6 was

selected.

In this section, the effect of changing the dead zone width by 0.05 either side of

the selected value was examined for the Margron simulation. Therefore remodelling

was simulated for s = 0.55, s = 0.6 and s = 0.65.

Effect of Activity Level

The preoperative and postoperative finite element femur models are both loaded

with identical joint and muscle forces. This implies that the forces experienced by

the femur are the same, before and after surgery. In reality, preoperative activity

may be limited due to difficulty of movement (pain, etc.), or postoperative activity

may be reduced due to rest after surgery.

To analyse the effect of activity level on the adaptation process, a simulation

was run for the Margron model with the postoperative forces at only 90% of their

preoperative levels. This is a 10% reduction of the forces experienced before surgery.

Effect of Prosthesis Stiffness

Implant stiffness is known to strongly influence adaptive bone remodelling due to

stress shielding by implants (Bobyn et al., 1990; Engh et al., 1987; Huiskes et al.,

1992; Sumner and Galante, 1992; Weinans et al., 1992b). High stiffness stems cause


greater stress shielding than low modulus stems, with a corresponding effect on

bone adaptation.

The Epoch model was used to investigate the effect of prosthesis stiffness on the

amount of bone adaptation, because it has quite unique material properties to begin

with. Remodelling simulations were run with the Epoch entirely fabricated from

cobalt-chrome (CoCr model), and with a material having the elastic modulus of

cortical bone (isoelastic model). For the Epoch, the effect of the prosthesis material

properties on the percentage changes in bone density was evaluated at 2 years.

Flexible stems are likely to induce greater interface stress (with a bonded in

terface) than conventional implant materials, and therefore this result was also

examined. Abaqus gives the interface shear in two perpendicular directions on the

slave contact surface defined by the surface normal. Both components need to be

considered. Contour plots of the shear stresses were produced.

Chapter 8

Results


Preoperative and postoperative maximum principal, minimum principal and lon

gitudinal strains were determined under two load cases (load case 1: 0° flexion,

load case 2: 10° flexion) at the sixteen gauge sites on the four femora. Means and

standard deviations were calculated for each strain gauge.

The important results have been plotted in this section. A complete list of the

data, including results for individual femora, can be found in Tables A.1 to A.12

(Appendix A). The two experimental load conditions place the femora in bending

in the coronal plane, while load case 2 introduces additional bending in the sagittal

plane. In most instances, this causes compression medially and posteriorly, and

tension laterally and anteriorly. For this reason, minimum principal strains are

plotted for the aspects of the femur in compression and maximum principal strains

are plotted for those in tension (Figures 8.1 and 8.2). The longitudinal components

of the strains are also presented (Figure 8.3 and 8.4).

The strains before and after surgery were compared for statistical difference at

each gauge using analysis of variance (ANOVA) with repeated measures. Table 8.1

shows the significantly different results for the strains plotted in Figures 8.1 to

8.4. P-values for other strains are given in Table A.13. Comparisons were not

169


~---~---··2 ci 10

-1200-1000 -800 -600 -400 -200 0 Medial (!J-E, Minimum Principal)

z Q) C) :J <1l

(!J

3 11

4 12

- Preop Case 1 - Postop Case 1 D Preop Case 2 D Postop Case 2

170

0 200 400 600 800 1 000 1200 Lateral (!J-E, Maximum Principal)

Figure 8.1: Preoperative and postoperative experimental minimum principal strains on the medial cortex (left) and maximum principal strain on the lateral cortex (right) for load cases 1 and 2.

13

14 ci z Q) C) :J <1l

(!J

15

-1200-1000 -800 -600 -400 -200 0 Posterior (!J-E, Minimum Principal)

5

6

7

- Preop Case 1 D Postop Case 1 D Preop Case 2 D Postop Case 2

0 200 400 600 800 1 000 1200 Anterior (!J-E, Maximum Principal)

Figure 8.2: Preoperative and postoperative experimental minimum principal strains on the posterior cortex (left) and maximum principal strain on the anterior cortex (right) for load cases 1 and 2.


made between the two load cases. A repeated measures design is used to evaluate

changes within subjects, and allows for a smaller sample size to show a significant

difference, as variation in data is reduced.

Table 8.1: P-values showing the statistically significant strains before and after surgery for each load case (bold indicates p < 0.05).

Principal Strains Longitudinal Strains Gauge No Case 1 Case2 Case 1 Case 2

1 0.0016 0.0018 0.0007 0.0013 2 0.0136 0.0127 0.0215 0.0261 3 0.0596 0.5915 0.0561 0.3081 4 0.4068 0.2303 0.4033 0.3502

5 0.8816 0.2990 0.0783 0.7004 6 0.1790 0.4176 0.0302 0.3744 7 0.0051 0.6933 0.0069 0.7915 8 0.0142 0.2712 0.0131 0.2831

9 0.0007 0.0006 0.0005 0.0004 10 0.0056 0.0052 0.0066 0.0060 11 0.0318 0.0658 0.0331 0.0637 12 0.8790 0.4832 0.7430 0.7945

13 0.0056 0.4573 0.0126 0.8311 14 0.3255 0.0007 0.2148 0.0080 15 0.0985 0.5241 0.0701 0.7245 16 0.0272 0.0972 0.0241 0.1024

Figures 8.1 shows high strains proximally for the intact femur, medially and

laterally under both loading conditions. These strains tend to decrease distally

on the medial side, while remaining relatively constant laterally. On the anterior

and posterior aspects (Figure 8.2), intact strains increase distally. There is no

obvious difference between the two load cases for the intact strains on the medial

and lateral cortices. A difference is evident when the anterior and posterior cortices

are examined. Load case 2, with the femur in 10° of flexion, produces much higher

strains at all but the most proximal level. The maximum principal strains on the

anterior aspect under load case 1 are small for all gauges.

The strains measured after the femora were reconstructed with the Margron

hip generally increase from proximal to distal on all sides. Examining the medial

and lateral cortices in Figure 8.1, the strains at the proximal two gauge levels are


significantly lower (p < 0.05) than the intact values for both load cases. Distal to

this, the strains approach the preoperative values, except at gauge 11 under load

case 1, where the postoperative strain continues to be significantly less than before

surgery (p = 0.03).

As with the intact strains, load case 2 causes higher postoperative strains than

load case 1 at the two distal levels anteriorly and posteriorly (Figure 8.2). On these

cortices, significantly different pre- and postoperative strains occur at gauges 7, 8,

13 and 16 for load case 1, and gauge 14 for load case 2 (p < 0.05).

Longitudinal strains (Figures 8.3 and 8.4) are almost identical to the principal

strains on the medial, lateral and posterior cortices, indicating compression medially

and posteriorly, and tension laterally. The anterior longitudinal strains show a

change from small compressive strains proximally to larger tensile strains distally.

2 10 ci z Q) Cl ::::! ell 0

3 11

4 12

-1200-1 000 -800 -600 -400 -200 0 Medial (J.lE, Longitudinal)

- Preop Case 1 - Postop Case 1 - Preop Case 2 - Postop Case 2

0 200 400 600 800 1 000 1200 Lateral (J.lE, Longitudinal)

Figure 8.3: Preoperative and postoperative experimental longitudinal strains on the medial and lateral cortices for load cases 1 and 2.

The similarity between the longitudinal and principal strains is reflected by the

statistically significant results. Of the data plotted in Figures 8.1 to 8.4, the only


~ - Preop Case 1

13 5 rl - Postop Case 1 I - Preop Case 2

f--{1-i D Postop Case 2

~ 14 6 •

ci I • . I

z ~ Q) O'l :J

+ (1j (.!) -15 7

~

16 8

-1200-1 000 -800 -600 -400 -200 0 -200 0 200 400 600 800 1 000 Posterior (~Jc, Longitudinal) Anterior (Jlc, Longitudinal)

Figure 8.4: Preoperative and postoperative experimental longitudinal strains on the posterior and anterior cortices for load cases 1 and 2.

difference is that the results at gauge 6 under load case 1 are significant for the

longitudinal strains, where they are not for the maximum principal strains.

To assess the level of stress shielding caused by the introduction of the femoral

component, the average postoperative strains are expressed as a percentage of the

preoperative values. Percentage strains are calculated for the principal strains shown

in Figures 8.1 and 8.2, and presented in Figures 8.5 and 8.6. A complete list of the

percentage strains for all gauges and load conditions is given in Tables A.14 and

A.15 (Appendix A).

The percentage strains follow a similar tendency both medially and laterally un

der the two loading conditions, with significant stress shielding at the most proximal

level ( 4.4-16.0%) and a trend towards the preoperative values at the most distal

level (88.5-132.8%) (Figure 8.5). At the intermediate gauge levels, the percentages

ranged from 31.5-44.9% at the more proximal of these, and 65.9-90.8% at the next

level down. Percentage strains under load case 2 were larger than those obtained

with the femur loaded vertically. This situation is reversed for the anterior and


9

....---=! 2 1 0 F-----, ci z Q) Ol ::J ctS

C)

.---------~3 11r-------~

200 150 100 50 0 0 50

-Load Case 1 D Load Case2

100 150 Medial (% Minimum Principal) Lateral (% Maximum Principal)

174

200

Figure 8.5: Postoperative strains expressed as a percentage of preoperative strains on the medial and lateral cortices for load cases 1 and 2.

14 ci z Q) Ol ::J ctS

C)

15

200 150 100 50 0 Posterior (% Minimum Principal)

5

6

7

0 200

-Load Case 1 D Load Case2

400 Anterior (% Maximum Principal)

600

Figure 8.6: Postoperative strains expressed as a percentage of preoperative strains on the posterior and anterior cortices for load cases 1 and 2. Note different scale for anterior

cortex.


posterior cortices, where percentage strains are higher under loading condition 1

for all gauges except the most proximal on the posterior side (Figure 8.6). The

postoperative strains are considerably larger than their intact values at the distal

two levels anteriorly under load case 1 (note different scale on Figure 8.6 right).


A subject-specific anatomic finite element model of a femur was created, and loads

and boundary conditions were applied as outlined in Chapter 7. This model was

implanted with the Margron hip prosthesis and identical loading was applied.

The intact femur consisted of 17046 elements with 25778 nodes and 77334 nodal

degrees-of-freedom. The operated femur model was comprised of a total of 13695 el

ements with 22364 nodes and 67092 nodal degrees-of-freedom. The operated model

has 9817 bone elements and 3878 implant elements.

Figure 8. 7 shows the density distribution of the femur model, shown in Houns

field units. High density cortical bone (larger Hounsfield unit) is seen along the

femoral diaphysis and up the medial aspect as far as the osteotomy. Proximal to

the level of the lesser trochanter, the cortical shell is thinner, and the density is

reduced, and also appears more variable from the outside. The cortical shell can

also be seen in cross section, where the bone has been prepared to accept the im

plant. Some Hounsfield unit values appear to be outside the specified range of -90

to 2280 HU.


Finite element strains were compared with experimental strains to determine how

effectively the finite element models replicated the experimental situation. Compar

isons were made for the intact femur and the femur reconstructed with the l\hrgron


SDV2 (Ave . Cr i t . : 75%)

+5 .4 25e+03 +2.800e+03 +2 . 500e+03 +2 .2 00e+03 +1 . 900e+03 +1 .600e+03 +1 . 300e+03 +1 . 000e+03 +7 . 000e+02 +4 . 000e+02 +1 . 000e+02 -2 . 000e+02 -3 . 235e+03

(a) Anteromedial view

• .

•

(b) Posterolateral view

Figure 8.7: Density distribution (Hounsfield units) of the femur .

176

prosthesis under the two simplified load cases used experimentally. The postoper

ative model was investigated with three contact conditions for the implant- bone

interface:

(a) no distal- proximal contact surface (between and including the two threads)

bonded, with no contact defined distally;

(b) fully bonded- all implant surfaces t ied to the bone interface; and

(c) distal sliding- the proximal region tied to the bone interface, while the distal


From the results it was hoped to ascertain which postoperative condition was most

representative of the experimental situation.


Finite element strains were calculated at the integration points and extrapolated

to the nodes, for the intact and operated models under load cases 1 and 2. Con

tour plots for the intact (Figure 8.8) and reconstructed models (Figure 8.9) were

produced, where only the elements remaining after surgery are shown. Figure 8.9

EE , Min . Pr i ncipal (Ave . Cr it. : 75%)

+4 . 819e-04 +O . OOOe+OO - 2 . 500e-04 -s . oooe-0 4 - 7 . 500e- 04 -l . OOOe-03 -1 . 250e-03 - l. SOOe-03 - 1.750e-03 - 2 . 000e-03 -2 . 250e-03 -2 . 500e-03 - 2 . 152e-02

(a) Load case 1 (b) Load case 2

Figure 8.8: Contour plots of preoperative minimum principal strains (anteromedial view; postoperative elements only).

represents the interface condition with no distal contact.

Under both preoperative load conditions (Figure 8.8a, b), the minimum principal

strain is quite high (around 1250 1-.u::) in the calcar region. For load case 1 (0° flexion),

the strain decreases quite quickly until a short distance below the lesser trochanter.

Flexion of 10° causes the region of high strain to continue much further distally,

and the bending introduced in the sagittal plane causes the strained area to move

posteriorly.


EE, Min. Princ ipa l (Ave . Cr i t.: 75%)

+2 . 068e- 04 +0 . 00 0e+ 00 -2 .5 00e-0 4 -s . oooe - 04 -7 . 500 e- 04 - l. OOOe-03 -1 . 250e - 03 - l. SOOe-03 - 1.75 0e-03

- -2 . OOOe- 03

i -2 . 250e-03 -2 .500e-03 -l . OSSe-02

(a) Load case 1

178

(b) Load case 2

Figure 8.9: Contour plots of postoperative (no distal contact) minimum principal strains ( anteromedial view).

Postoperatively (Figure 8.8a, b), the minimum principal strains are reduced

significantly. This is especially apparent proximally, although there is a small zone of

high strain adjacent to the implant. Distally, the strains appear similar in magnitude

and distribution to the respective preoperative load cases.

To compare the finite element results with the experimental data, nodal principal

strains were obtained along the anterior, posterior, medial and lateral cortices.

These are plotted as a curve, beside the corresponding experimental data for the

modelled femur, shown as horizontal bars at the gauge locations (Figures 8.10 to

8.17).

For the two preoperative loading conditions, agreement between the experimen-

tal and finite element results is generally good for the medial and lateral principal

strains at the three distal gauge levels (Figures 8. 10 and 8.12). At the level of the

8. 2 FINITE ELEMENT STUDY

-1200-1 000 -800 -600 -400 -200 0 Medial (JlE, Minimum Principal)

179

0 200 400 600 800 1 000 1200 Lateral (JlE, Maximum Principal)

Figure 8.10: Preoperative experimental (bar) and finite element (line) principal strains on the medial and lateral cortices for load case 1.

-1200-1 000 -800 -600 -400 -200 0 Posterior (Jl£, Minimum Principal)

13 5

14 ci z (]) Cl ::J ((!

0 15

6

7 ·.

0 200 400 600 800 1 000 1200 Anterior (JlE, Maximum Principal)

Figure 8.11: Preoperative experimental (bar) and finite element (line) principal strains on the posterior and anterior cortices for load case 1.


1"7"":':~~~~~~ 2 10 F;:;;;;;;;::;:r:;;;;::;:r:;;;;::;:r::;:j

ci z Q) C> :J (1j

c:l fJ!!ilmlm. 3 11

-1200-1 000 -800 -600 -400 -200 0 Medial (J..LE, Minimum Principal)

0 200 400 600 800 1 000 1200 Lateral (J..LE, Maximum Principal)

Figure 8.12: Preoperative experimental (bar) and finite element (line) principal strains on the medial and lateral cortices for load case 2.

14

15

-1200-1000 -800 -600 -400 -200 0 Posterior (j..t£, Minimum Principal)

ci z Q) C> :J (1j

c:l

6

7

0 200 400 600 800 1 000 1200 Anterior (f.l£, Maximum Principal)

Figure 8.13: Preoperative experimental (bar) and finite element (line) principal strains on the posterior and anterior cortices for load case 2.


proximal gauges, there is considerable deviation between the experimental and nu

merical results. This is also a feature of the proximal gauges on the anterior and

posterior cortices (Figures 8.11 and 8.13). Distally on the anterior and posterior

cortices, the finite element results agree well with the experimental data under load

case 2, where the strains are relatively large. Under load case 1 the strains are small

and are underestimated in some instances by the finite element model.

For the two postoperative loading conditions, some of the problems detected

preoperatively are seen. The theoretical strains at the most proximal gauges are

again much larger than those measured experimentally, except at gauge 1 under both

load cases (Figure 8.14 and 8.16) and gauge 5 under load case 1 (Figure 8.15). The

strains produced by load case 1 on the anterior and posterior aspects (Figure 8.15)

underestimate the experimental values also. For the other graphs (Figures 8.14,

8.16 and 8.17), the strains for the middle two gauge levels match up reasonably

with the experimental strains. Distally, the strains are underestimated medially

and laterally under load case 1, and laterally under load case 2, but match well for

the remainder.

The effect of the contact conditions was really only evident at the third level of

gauges (3, 7, 11 and 15). Medially, anteriorly and posteriorly, strains were largest

at this level for the model with no distal contact, with the smallest strains for the

fully bonded interface. On the lateral aspect, the model with no distal contact

again produced the highest strains at this level, however the model with sliding

contact distally produced the smallest strains. Across all of the postoperative graphs

(Figure 8.14 to 8.17), the model with no distal contact, gave results closest to those

achieved experimentally. This model was used for further analysis.


-1-- Fully bonded -e- Distal sliding -a- No distal

-1200-1000 -800 -600 -400 -200 0 Medial (f.l£, Minimum Principal)

182

0 200 400 600 800 1 000 1200 Lateral (f.l£, Maximum Principal)

Figure 8.14: Postoperative experimental (bar) and finite element (lines) principal strains on the medial and lateral cortices for load case 1.

-1200-1 000 -800 -600 -400 -200 0 Posterior (f.l£, Minimum Principal)

15

ci z Q) 0> ::J cO

<!J

6

7

-1-- Fully bonded -e- Distal sliding -a- No distal


Figure 8.15: Postoperative experimental (bar) and finite element (lines) principal strains on the posterior and anterior cortices for load case 1.


--+-- Fully bonded -e- Distal sliding -a- No distal

-1200-1000 -800 -600 -400 -200 0 Medial (f.l£, Minimum Principal)

183

0 200 400 600 800 1 000 1200 Lateral (f.l£, Maximum Principal)

Figure 8.16: Postoperative experimental (bar) and finite element (lines) principal strains on the medial and lateral cortices for load case 2.

13

14 ci z (J) C'l ::J ctS

(!)

15

-1200-1000 -800 -600 -400 -200 0 Posterior (f.l£, Minimum Principal)

5

6

7

--+-- Fully bonded -a- Distal sliding -a- No distal


Figure 8.17: Postoperative experimental (bar) and finite element (lines) principal strains on the posterior and anterior cortices for load case 2.


8. 2. 2 Mesh Refinement

Finite element models were prepared and run under the conditions indicated in

Table 8.2. Solution convergence was monitored by plotting minimum principal

strains along the medial aspect of the femur under load case 1 (0° flexion).

Table 8.2: Finite element models to investigate convergence.

Femur Edge Length Material Properties Contact

Intact 3mm integration point NjA 3mm element average NjA 5mm integration point N/A 5mm element average N/A 7mm integration point N/A 7mm element average NjA

Reconstructed 3mm integration point fully bonded 5mm integration point fully bonded

The position of the point of force application was kept constant for all models.

The strain distribution was found to be extremely sensitive to this parameter, with

a load applied only a millimetre or two more medially increasing strains by up to

10% in some cases.

Figure 8.18 shows the minimum principal strain distribution along the medial

aspect of the intact model. The y axis shows the normalised position along the

longitudinal axis of the femur, where zero is located at the level of the osteotomy

and one is the distal prosthesis tip. These results reveal the strain magnitudes

decreasing with mesh refinement from 7 to 5 mm. The data also becomes more

smooth. The difference between the 5 and 3 mm strains is much reduced, indicating

solution convergence. This is particularly evident in the diaphysis, where material

properties are more uniform (Figure 8.19).

Since the 7 mm mesh size was obviously overestimating the strains, postoperative

models were created with 3 and 5 mm mesh densities only. Figure 8.20 shows good

agreement between these mesh sizes again, considering the strains are relatively

small.


r-~--~~~~~~--~--~~~~~0 I -1-- 5 mm Integ Pt

-e- 3 mm Integ Pt -e- 7 mm Integ Pt

0.2

0.4

c g ·u;

0.6 6:

0.8

-2000 -1800 -1600 -1400 -1200 -1 000 -800 -600 -400 -200 0 Medial (f..le, Minimum Principal)

Figure 8.18: Preoperative minimum principal strains on the medial cortex for load case 1, with finite element mesh densities of 3, 5 and 7 mm.

rf---=========::!:=l:S~=-----.---,--..,--?~~~~;1 o.5 -1-- 5 mm Integ Pt -e- 3 mm Integ Pt -e- 7 mm Integ Pt 0.6

0.7

c 0

0.8 ~

0.9

~----~----~------~----~------~----~------~----~----~1.1

-700 -650 -600 -550 -500 -450 -400 -350 -300 -250 Medial (f..le, Minimum Principal)

Figure 8.19: Distal data from Figure 8.18.

0 a.


rr===~====~-----,-----,-----,-----,~7-10 -+- 5 mm Integ Pt --e- 3 mm Integ Pt

-350 -300 -250 -200 -150 Mediai(JJ£, Minimum Principal)

-100 -50 0

0.2

0.4

c 0

:;:: "iii

0.6 6:..

0.8

Figure 8.20: Postoperative minimum principal strains on the medial cortex for load case 1, with finite element mesh densities of 3 and 5 mm.

Finite element analysis provides only approximate solutions to stress analysis

problems. l\1odel accuracy is generally improved by increasing mesh density, how

ever this is offset by the much larger computation time. Table 8.3 shows the change

in computation time associated with the higher number of degrees-of-freedom of the

more refine models.

Table 8.3: Effect of model complexity on computation time.

Femur

Intact

Reconstructed (fully bonded)

Edge Length

3mm 5mm 7mm

3mm 5mm

Nodal Degrees-of-Freedom

291096 77334 35850

250881 67092

CPU Time

9855.6 sec 864.1 sec 301.8 sec

6555.9 sec 673.7 sec

The effect of homogeneity of element material properties on mesh refinement

is shown in Figure 8.21. The 5 mm mesh with material properties averaged over

the element gives much higher strains than the other material and mesh options,


which are difficult to distinguish due to their similarity. The 3 mm mesh with

inhomogeneous elements produces the most accurate results.

-+- 5 mm Integ Pt - 5mmEimAve -e- 3 mm Integ Pt - · 3 mm Elm Ave

-2000 -1800 -1600 -1400 -1200 -1 000 -800 -600 -400 -200 0 Medial (J.L£, Minimum Principal)

0.2

0.4

c 0

:;::: ·u;

0.6 &.

0.8

Figure 8.21: Preoperative minimum principal strains on the medial cortex for load case 1, with mesh densities of 3 and 5 mm and material properties applied to integration points or averaged over elements.

Figures 8.18 to 8.20 show a small increase in accuracy with mesh refinement,

however Table 8.3 indicates a massive increase in computation time to achieve this.

Figure 8.21 also implies an increase in accuracy by using inhomogeneous element

properties as a substitute for mesh refinement. For these reason, the 5 mm mesh

was considered suitable to be used for further study.



8.3.1 Margron

The remodelling rule was used to predict changes in bone density due to the dif

ference in equivalent strain between the "normal" femur and the femur implanted

with the ?vlargron hip prosthesis. The remodelling simulation was run for a total

of 120 remodelling increments. The time step was kept relatively small, to ensure

that the greatest change in density at any integration point during the first remod

elling increment was less ~Pmax· Consequently, the gradient of the resorption curve

was 40 gjmm2 for each remodelling increment, and the apposition gradient was 3.5

times less.

The dead zone width was adjusted parametrically to obtain results that were

within the clinical range. By examining multiple time points, the most suitable

value for the dead zone width turned out to be s = 0.6, therefore equivalent strains

greater or less than (1 ± s )Sref, or ±60% of the value of the reference remodelling

strain, caused bone adaptation.

Principal Strains

A contour plot of the minimum principal strain distribution of the femur is shown for

the preoperative, immediately postoperative, and remodelled cases (Figure 8.22).

Contour plots give a semi-quantitative appreciation of the strain situation. Before

surgery (Figure 8.22a), the forces representing 45% of the gait cycle produce high

strains proximally and medially. The high medial strains extend distally to the

point of fixation, and also a little anteriorly. After arthroplasty (Figure 8.22b),

the proximal strain is reduced considerably at the medial cortex. Distal to the

mid-stem level, the strain distribution is similar to the intact bone. Remodelling

(Figure 8.22c) doesn't change the strain magnitudes distally, but proximally, strains

are closer to their preoperative values, except for a small band around the mid-stem

level, where strains remain small.

8.3 BONE R EMODELLING STUDY

EE, Min . Principal (Ave . Crit .: 75 %)

+2 . 79le - 03 +O . OOOe+OO -2 . 500e-04 -s . oooe-04 -7 . 500e-04 -l . OOOe-03 -1.250e-03 -l . SOOe-03 -1.750e-03 -2.000e - 03 -2.250e-03 - 2 . 500e-03 -1.687e-01

(a) Intact femur

189

(b) Postoperative (c) Remodelled

Figure 8.22: Minimum principal strain distribution (anteromedial view).

Plots of maximum and minimum principal strain values at nodes on the medial

and lateral aspects of the femur, before and after surgery, are also presented in

Figures 8.31 and 8.32. The vertical axis of these graphs is normalised with repect

to the medial intersection of the osteotomy with the cortex (position = 0) and the

distal stem tip (position= 1.0).

Medially at the osteotomy level, the preoperative minimum principal strain is

-2066 fl£, decreasing to less than half of this value at the distal tip of the implant

( -930 p,c). On the lateral side, the maximum principal strains are extreme for

the proximal 20% of the implant , as was seen previously in Figures 8. 10 and 8. 12.

This reduces to about 1300 fl£ at a posit ion of 0.2. The maximum principal strain

decreases further to 512 p,c at the level of the distal stem tip.

Postoperatively, the minimum principal strain on the medial cortex is reduced

to -235 p,c, or 11% of the intact value. The effect of stress shielding is apparent

8.3 BONE R EMODELLI NG STUDY 190

for the proximal 60% of the implant length, whereafter the strain approaches the

preoperative value. At the distal tip, the minimum principal strain is -758 J-LE,

or 83% of the preoperative value. Laterally, stress shielding is also seen along the

proximal 60% of the implant , however extreme values are evident at the proximal

nodes again. Twenty-percent of the distance down the implant , the maximum

principal strain is about 500 J-LE, increasing to 612 J-LE at position equal to 0.6, and

then down to 372 J-LE at position equal to 1.0.

Equivalent Strains

The change in equivalent strain distribution after hip arthroplasty is the stimu

lus for bone adaptation. A situation almost identical to the principal strains is

obtained for the equivalent strain distribution (note different scale, Figure 8.23).

Equivalent strains are high proximally in the preoperative femur (Figure 8.23a).

UVARM3 (Ave . Cri t .: 7 5%)

+2 . 516e- 01 +S . OOOe-03 +4 . 500e-03 +4.000e- 03 +3 . 500e- 0 3 +3 . 000 e-0 3 +2 . 500e- 03 +2 . 000 e-0 3 +l . SOO e-03 +l. OOOe-03 +S . OOOe - 0 4 +O. OO Oe +OO - 1. 2 46e-0 1

(a) Intact femur (b) Postoperative (c) Remodelled

Figure 8.23: Equivalent strain distribution ( anteromedial view).

8.3 BONE R EMODELLING STUDY 191

Surgery reduces the strains, particularly at the medial cortex (Figure 8.23b) , and

then remodelling increases the strain magnitude in this region (Figure 8.23c).

A graph of the equivalent strains along a path of nodes on the medial cortex

of the femur before and after surgery, and after remodelling, is presented in Fig

ure 8.33 (left). The vertical axis is again the normalised position relative to the

osteotomy level and the distal stem tip. Preoperatively, the equivalent strain is

equal to 2111 f-lc at the osteotomy level. This falls away to 1010 f-lc at the distal

tip of the prosthesis. Immediately following implantation with the hip replacement

device, the equivalent strain is reduced to only 45 f-lc at the osteotomy, and 844 f-lc

distally. After 120 remodelling increments, the distal value remains the same, how

ever at the osteotomy level, the strain is now equal to 954 f-lc, which is 45% of the

preoperative value.

Bone Density

The density distribution of the femur after remodelling is shown in Figure 8.24

( c .f. Figure 8. 7). This indicates cortical bone loss around the proximal half of the

Margron stem, particularly medially and anteriorly, however the images do not show

what occurs closer to the implant .

Simulated DEXA images give an appreciation of the density distribution across

the interior of the femur. Figure 8.25a shows the situation before surgery, while

Figure 8.25d gives the result after 120 remodelling increments. Figure 8.25b illus

trates the density distribution after 10 remodelling increments. Bone resorption at

the level of the osteotomy down to the lesser trochanter is the most obvious feature ,

both medially and laterally. This continues , particularly on the medial aspect, until

remodelling increment 60 (Figure 8.25c). Litt le change in density can be detected

visually between the 60 and 120 increment images.

Figure 8.26 shows the percent change in bone density from the preoperative

condition at the seven Gruen zones. Each curve represents the percent change for a

given number of remodelling increments. As the number of increments approaches

8.3 BONE R EMODELLING STUDY

SDV2 (Ave. Crit .: 75%)

•

+5.425e+03 +2.800e+03 +2.500e+03

'- +2. 200e+03 +1 . 900e+03 +1 . 600e+03 +1.300e+03 +1 . 000e+03 +7 . 000e+02 +4.000e+02 +1 . 000e+02 -2 . 000e+02 -3.235e+03


• .

•


Figure 8.24: Density distribution (Hounsfield units) of the remodelled femur.

192

120, the curves start to overlap as the solution converges. Numerical values for the

bone density changes are provided in Table C.1 (Appendix C).

In zone 1, there is a small increase in bone density (2.4%) during the first 10

increments, but this approaches zero as the remodelling progresses. At remodelling

equilibrium, zone 2 exhibits bone loss of 8.5%. Approximately half of this resorption

( -4.5%) occurs during the first 20 increments. In zones 3, 4 and 5, there is negligible

change in density during the remodelling process. Zone 6 sees a change in bone

density of 26.5%, while maximum bone adaptation of -30.7% occurs in zone 7. In

zone 7, more than half of the density change (-16.6%) takes place within the first

10 remodelling increments.

Figure 8.27 shows how the bone in zone 7 adapts to the postoperative condition,

according to the remodelling theory. The bone density decreases monotonically to

reach a remodelling equilibrium value of -30.7%. This value is approximately


(a) Preoperative (b) Increment 10 (c) Increment 60 (d) Increment 120

Figure 8.25: Simulated DEXA images during remodelling of the femur.

5.---.--------,-------,,-------.--------.--------.--------.--~

0

-5

~ -~ -10 Q)

0

~ -15 0 co ~ -20 c co .c () -25 cf?-

-30

-35

- Increment 1 0 Increment 20

-+- Increment 40 -e- Increment 60 -a- Increment 80 -A- Increment 100 ~ Increment 120

-40~--~------~------~~------~------~--------L-------~--~

2 3 4 Gruen Zone

5 6 7

Figure 8.26: Change in bone density in the Gruen zones for remodelling increments 10 to 120.


0

-5

~ -~ -10 Q)

0

~ -15 0 Ill

~-20 c ca

.r:. () -25 ~ 0

-30

-35

194

-40~--------~--------~--------~--------~--------~------~

0 20 40 60 Remodelling Increments

80 100

Figure 8.27: Incremental change in bone density in Gruen zone 7.

120

reached after 60 increments, although some small changes in zones 2 ( -0.8%) and

6 ( -1.8%) continue until increment 120.

Comparing this remodelling data with the clinical DEXA database, it was deter

mined that 10 remodelling increments was approximately equivalent to 6 months in

vivo. This idea was further examined using two other subject-specific models with

different implants (see Section 8.3.2). Accordingly, 20 increments corresponds to 1

year, 40 to 2 years, and 60 to 3 years for the Margron model. Figure 8.28 plots the

simulated DEXA data for 20, 40 and 60 remodelling increments with the clinical

data for 1, 2 and 3 years. The most notable differences are in Gruen zones 1 and

2, where bone resorption is underestimated by the model. Better agreement is seen

for the remaining zones, although actual bone loss in zone 6 is less than predicted.

Significant correlations were found between the radiographic clinical and simulated

data at all three time points (1 year: R 2 = 0.80, p = 0.006; 2 years: R 2 = 0.68,

p = 0.022; and 3 years: R 2 = 0.67, p = 0.022; Figures D.1 to D.3, Appendix D).

Figure 8.29 presents the actual and simulated results at 2 years postoperatively.

Ninety-five percent confidence intervals are indicated on the actual data, which


5.---.--------.-------,,-------.-------~--------~------~--~

0

-5

-30

-35

-->< • Clinical 1 Year -o · Clinical 2 Years -o · Clinical 3 Years _.,._ Simulation 1 Year -e- Simulation 2 Years --a- Simulation 3 Years

\ D

-40~--~------~--------~------~------~--------L-------~--~

2 3 4 Gruen Zone

5 6 7

Figure 8.28: Comparison of actual and simulated bone density changes for the first 3 years after surgery.

were obtained using error propagation methods. The average error is approximately

±30% at 2 years, with similar values for 1 and 3 years. The simulated data is well

within the range of the clinical data, with an average difference of 5.4% (maximum

of 13.7% at zone 2, minimum of 0.6% at zone 4). At zone 7, the difference between

the clinical and predicted change in density is 1.7%, compared with 1.1% and 4.4%

at 1 year and 3 years respectively.

Convergence

The remodelling error was obtained at each increment and averaged over all of the

model integration points (Figure 8.26). The average error starts at 215.5 x 10-6 at

the beginning of the analysis, and decreases monotonically to an asymptote with

a value of 9.5 x 10-6 after remodelling. After 10 increments, the error drops to

20.2 x 10-6 , while after 60 increments, the error is 10.2 x 10-6 . In the first 10

increments, the error changes by 206 x 10-6 , however in the last 60 increments, the

error is further reduced by only 0. 7 x 10-6 .


30.---.--------.-------.--------,--------.--------.-------.---~

20

10

.?:- 0 ·c;; c: Q)

0 -10 Q) c: s -20 Q) Ol

ffi -30 .r:. ()

<f- -40

-50

/

-60 - - Clinical2 Years -- Simulation 2 Years

...... '>. ..

"

-70~--~-------L------~~------~------~--------L-------~--~

2 3 4 Gruen Zone

5 6 7

Figure 8.29: Comparison of actual and simulated bone density changes at 2 years (error bars show 95% confidence interval for clinical data).

.... 2 ....

UJ

x10-4 2.5.---------,---------.----------~---------.----------.---------~

2

1.5

0.5

0~--------~--------~--------~--------~~--------~--------~

0 20 40 60 Remodelling Increments

80 100

Figure 8.30: Behaviour of the remodelling error over 120 remodelling increments.

120



Two other subject-specific finite element models of femora were created. One of

these was implanted with the Stability hip, while the other received the Epoch

prosthesis. Remodelling simulations were performed in the manner as for the Mar

gron model, however in this case the resorption gradient was set at 80 g/mm2

per remodelling increment, rather than 40 gjmm2, based on the maximum change

in density during the first remodelling increment being smaller. This effectively

doubled the time step for each increment, and accordingly, 10 increments is now

equivalent to 1 year in vivo, with 20 and 30 increments corresponding to 2 and 3

years respectively. Remodelling was run for a total of 60 increments.

Principal Strains

The medial minimum and lateral maximum principal strain distributions were calcu-

lated under 45% gait cycle loading, and plotted for the Stability and Epoch models,

and the Margron for comparison (Figures 8.31 and 8.32). Contour plots of the

0.8

- Margron --e-- Stability 1 -a- Epoch

-3000 -2000 -1000 0 Medial (f..L£, Minimum Principal)

0.2

c ~ 0.4 (/) 0

0... "0 Q) (/) :m o.6 E .... 0 z

0.8

0 1000 2000 3000 Lateral (f..L£, Maximum Principal)

Figure 8.31: Preoperative strains for three femora under 45% gait cycle loading.


- Margron

0.2 0.2

c: 0.4 g 0.4

"(i.j

0 0... "0 Q)

0.6 ~ 0.6 E ..... 0 z

0.8 0.8

-a- Stability 1 -a- Epoch

-3000 -2000 -1000 0 Medial (!1£, Minimum Principal)

0 1000 2000 3000 Lateral (!1£, Maximum Principal)

Figure 8.32: Postoperative strains for three femora under 45% gait cycle loading.

minimum principal strains are shown in Figures B.l and B.3 (Appendix B).

These graphs show similar strain distributions in the three femora under identical

loading. The preoperative distribution (Figure 8.31) shows the strains decreasing

distally on both the medial and lateral aspects. The Epoch femur appears to be

undergoing slightly less bending than the two others, with fairly constant principal

strains most of the way along the femoral shaft. Again, large strains are seen

proximally on the lateral aspect for the Margron femur. This situation is also

evident for the Stability femur.

The postoperative strain distributions (Figure 8.32) are again similar for the

three models. Laterally, the maximum principal strains do not change much after

arthroplasty for the Epoch model. For the Stability, the change in strain is more ap

parent proximally, but occurs as a gradual change from the distal tip. The Margron

model shows strain reduction along the proximal 60% of the implant.

Medially, the minimum principal strains are reduced proximally for all models.

Strain reduction occurs along the medial cortex adjacent to the upper 60% of the


Margron stem as seen in Figure 8.22, and along the proximal 40% or so of the

Stability and Epoch implants.

Equivalent Strain

Figure 8.33 shows the variation of the equivalent strain along the medial cortex

for the preoperative, immediately postoperative and remodelled conditions, for the

three femora and implants examined. Note the similarity in the magnitude (different

0 0 0 .....

....... ' / < 0.2 0.2 ·\. 0.2 I

/ .I I ( (

c: I I I 2 0.4 0.4 0.4 ·;n )

I 0 a_ I '0 CD \ ~ 0.6 0.6 / 0.6 E

( . 0 z

0.8 0.8 0.8

- Preoperative -+- lmmed. Postop. -e- Remodelled

0 1000 2000 0 1000 2000 0 1000 2000 Margron (J.L£, Equivalent) Stability (J.L£, Equivalent) Epoch (J.L£, Equivalent)

Figure 8.33: Effect of implant design on the equivalent strain along the medial cortex.

sign) between the preoperative and immediately postoperative equivalent strains,

and the corresponding minimum principal strains from Figures 8.31 and 8.32. This

implies that the minimum principal strain is effectively the driving force for adap

tation medially. Contour plots of the equivalent strains are provided in Figures B.2

and B.4.

The graphs in Figure 8.33 show substantial differences proximally between the

preoperative and immediately postoperative strains, indicating substantial stress

shielding, for the three implants. These disparities are reduced following remod-

elling, however the preoperative conditions are never reached because of the effect


of the dead zone. Distally, the changes in equivalent strain are relatively small

following surgery for all models, and therefore the strains remain fairly constant

during the remodelling process.

Table 8.4 presents the equivalent strains from Figure 8.33 as absolute strain

values and as percentages of the preoperative values at the levels of the osteotomy,

the lesser trochanter and the distal stem tip. Stress shielding is apparent for all

implants, with a trend towards normalisation of the equivalent strain due to adap-

tation.

Table 8.4: Preoperative, immediately postoperative and remodelled values of the equiv-alent strain for the Margron, Stability and Epoch models at 3 locations on the medial cortex. The immediately postoperative and remodelled values are given as percentages of the preoperative.

Position Immed Postop Remodelled Preop Immed Postop % Remodelled %

:tvfargron 0 45 fiE 954 fiE 2111 fi£ 2% 45% 0.2 364 J-tf 761 J-tf 1985 f-tc 18% 38% 1.0 844 f-tc 844 J-tf 1010 J-tf 84% 84%

Stability 0 351 f-tc 633 fJ,f 2005 J-tf 18% 32% 0.2 1284 f-tc 1241 J-tf 2254 J-tf 57% 55% 1.0 1489 f-tc 1483 J-tf 1664 J-tf 89% 89%

Epoch 0 81 J-tf 719 f-tc 1096 J-tf 7% 66% 0.2 882 J-tf 878 J-tf 1599 J-tf 55% 55% 1.0 1186 J-tf 1175 J-tf 1315 J-tf 90% 89%

Bone Density

The pre- and post-remodelling contour plots of the Epoch and Stability femora are

shown in Figures C.l, C.2, C.4 and C.5 (Appendix C). Simulated DEXA images

are shown in Figures C.3 and C.6. Appreciable changes in density are evident at the

calcar region, with some densification seen distally. The percent changes in Gruen

zone bone density for the Epoch and Stability models are provided in Tables C.2

and C.3, and were compared with clinical bone mineral data from DEXA studies.

Figure 8.34 plots the simulated change in bone density for the Margron, Stability


and Epoch models at 2 years (120, 60 and 60 remodelling increments respectively)

and the corresponding clinical results at 2 years. The Margron model results are

mentioned previously in Section 8.3.1.

The Stability model shows good agreement with the clinical data, with an av

erage difference of 3.4%. The largest discrepancy is at zone 2 (7.4%), while the

smallest is at zone 6 (0%). In zones 1 and 2, there is a tendency for the simula

tion to underestimate the change in bone mineral density. At zone 7, the predicted

decrease in bone density is 20.4%, which is 2.2% less than measured in the clin

ical subjects. At 2 years, the average error on the percentage change in density

measured clinically at each Gruen zone is 34% (Table 7.3). The simulated data

correlated strongly with the clinical (R2 = 0.72, p = 0.016; Figure D.4).

The Epoch simulation predicts a small increase in bone density in zones 1 to

6. This is contrary to the clinical data for zones 1 to 4 and 6, in which a small

decrease in density is found. The bone loss in zone 7 (9.7%) is less than that

expected for the average patient (15.8%) at 2 years. The average difference between

the clinical data and the simulated results is 3.9%, with the largest difference in

zone 6 (7.8%). Confidence intervals were not available for the clinical data with this

implant. Again, agreement between the simulation and clinical data was quantified

by a statistically significant correlation (R2 = 0.76, p = 0.010; Figure D.5). A

significant correlation was present when the 1, 2 and 3 year Margron time points

were combined with the 2 year time points for the Epoch and Stability density

changes (R2 = 0.73, p < 0.00001; Figure D.6).

Convergence

Convergence of the remodelling solutions was monitored using the average sum of

the remodelling errors (Figure 8.35). With the Stability model, the average error

in equivalent strain starts at 163.8 x 10-6 at the beginning of the analysis, and

decreases to an asymptotic value of 5. 7 x 10-6 after remodelling. The average error


0 z-. ·u; c (!)

-10 0 (!) c 0 co (!) -20 C> c CIS .c 0 ~ -30 0

z-. ·u; c

-40

0

~ -10 (!) c 0 co (!) -20 C> c CIS .c 0 ~ -30 0

- - -)'

/

... / .,. '- /

'- / '-

'y/.

-->< • Margron Clinical _,._ Margron Simulation

2 3 4

-X--- -X ......... ,._ - -->t----

- · Stability Clinical --- Stability Simulation

202

-'\

" " ·'\. "

"" . . " .

" " ... \; .

5 6 7

-40L---~------~--------~------~---------L--------L--------L--~

2 3 4 5 6 7

X

0 ....... ·x

z-. ,._ - -x- '-- - ,._ '-·u; '-c .,._ ~ -10 ....... ··"'-··

' (!) ' c '-x 0 co (!) -20 C> c CIS .c 0 ~ -30 0

I~ Epoch Clinical I Epoch Simulation

-40 2 3 4 5 6 7

Gruen Zone

Figure 8.34: Effect of implant design on the change in bone density in the seven Gruen zones at 2 years.


X 10-4

2.5,-----,---~-------r----,-----;:c======:::;-1

1

-e--- Stability I ----- Epoch

2

1.5 ..... g w

0.5

10 20 30 Remodelling Increments

40 50 60

Figure 8.35: Effect of implant design on the change in bone density in the seven Gruen zones.

with the Epoch model begins much lower at 73.6 x 10-6 , and falls to 0.7 x 10-6 by

the time remodelling equilibrium is reached.


Remodelling was simulated using the I'viargron models to evaluate the effects of some

of the parameters involved with the finite element modelling and the remodelling

theory. All density changes in the Gruen zones are plotted at 3 years, with additional

data in Tables C.4 to C.16 (Appendix C). The Epoch model was also used to

investigate the effect of prosthesis material properties on the remodelled density

distribution. In this case density changes are plotted at 2 years, with additional

data in Tables C.l7 and C.l8.


Remodelling simulations were performed to determine if the contact conditions de

fined at the implant-bone interface would be an important factor in the outcome of


the results. The type of contact definition can strongly affect the total computation

time. For this reason, three cases were investigated with the Margron implant:

(a) no distal-proximal contact surface (between and including the two threads)

bonded, with no contact defined distally;

(b) fully bonded-all implant surfaces tied to the bone interface; and

(c) distal sliding-the proximal region tied to the bone interface, while the distal


The equivalent strains along the nodes on the medial aspects of the femur are

presented for the three contact conditions (Figure 8.36). These are shown imme

diately postoperatively (left) and after 120 increments of remodelling simulation

(right). Immediately after surgery, no difference can be seen along the medial cor-

0.2

c .g 0.4 -~ a.. "'0 Q)

~ 0.6

E 0 z

0.8

0

- - Preoperative -1-- No Distal -e- Fully Bonded -e- Distal Sliding

/

I /

I

I I I

500 1 000 1500 2000 2500 lmmed. Postoperative ~e., Equivalent)

0

/

\

0.2 I /

/

I /

0.4

0.6

0.8

0 500 1 000 1500 2000 2500 After Remodelling (J.lc, Equivalent)

Figure 8.36: Effect of implant contact conditions on the equivalent strain along the medial cortex.

tex for the proximal 30-40% of the implant, however distally the interface does

influence the load transfer to the bone, and subsequently the equivalent strain. The

largest strains in the distal region are evident with proximal contact only (no dis

tal), while the fully bonded stem had the lowest strains. This situation is repeated


after remodelling, however remodelling causes the equivalent strain to increase in

the proximal 40% for all models by the same amount.

Figure 8.37 indicates little difference between the three contact conditions in

terms of the degree of bone lost after 3 years. There is a fraction more bone loss

in Gruen zone 6 for the fully bonded model, while all other points on the plot are

approximately coincident.

5.---.--------.-------.--------.--------.--------.-------.---~

0

-5

c -~ -10 Q)

0

~ -15 0 co ~ -20 c: ctl ..c: () -25 rl

..... ,.._. -......1

X

I

I I

-30 1-.-------------, - ·Clinical -1- No Distal Contact

-35 -e-- Fully Bonded -e- Distal Sliding

... /-1

I I

----+:-

\ .. -40L---~------~------~--------~-------L--------L-------~--~

2 3 4 Gruen Zone

5 6 7

Figure 8.37: Effect of contact conditions on the change in bone density in the seven Gruen zones.

For this reason, the fact that the postoperative experimental strain distribution

was best represented (Section 8.2.1), and by taking computation time into account,

the model with the proximal contact surface tied and no contact defined distally

was used for all other remodelling simulations.


The effects of neck length and version angle on remodelling were analysed. The

physiological neck length was determined as +4 mm from the template. This po

sition was varied to the other available neck lengths, which are -4, 0 and + 7 mm.


The effect of the neck length on the equivalent strain is presented in Figure 8.38.

The variation in the immediately postoperative equivalent strain between the four

0.2

c ,g 0.4 '2 [)_

'0 Q)

~ 0.6

E 0 z

0.8

0

- - Preoperative -+- Neck Length +4 -e- Neck Length 0 -e- Neck Length -4 -A- Neck Length + 7

)

I

I /

500 1 000 1500 2000 2500 lmmed. Postoperative~£, Equivalent)

0

0.2

0.4

0.6

0.8

0

/

\ )

/ /

I /

500 1 000 1500 2000 2500 After Remodelling (!l£, Equivalent)

Figure 8.38: Effect of neck length on the equivalent strain along the medial cortex.

models is most pronounced distally. The situation is unchanged distally following

remodelling, however the strains converge to a single curve from just above the nor-

malised position of 0.4. The difference between the preoperative and immediately

postoperative equivalent strains is greatest for the shorter neck lengths, i.e., shorter

neck lengths produce smaller strains, and for the + 7 mm neck length, the strains

are approximately equal below the normalised position of 0.6.

The corresponding change in bone density in the seven Gruen zones is indicated

by Figure 8.39. This shows greatest femoral bone loss for the shorter neck lengths 3

years postoperatively. The greatest effects of this parameter are seen in zones 2 and

6. In zone 2, the percentage bone loss varies from 5.0% ( + 7 mm neck length) to

12.6% ( -4 mm neck length), while in zone 6, bone density decreases by 19.3% for

the + 7 neck length and 32.6% for the -4 mm neck length. For the -4 mm length,

percentage bone loss in Gruen zone 6 is greater than zone 7 (32.1%).


5.---.--------.-------.--------.--------.--------,-------.---~

0

-5

c ·~ -10 Q)

0

~ -15 0 co ~-20 c Cll ..c () -25 ;,!!., 0

-30

-35

" I ......... , ,I

X

--Clinical -+- Neck Length +4 --e- Neck Length 0 -e- Neck Length -4

! I

---A- Neck Length + 7 -40~~====~~~--~----_L ______ L_ ____ J_ ____ _L~

2 3 4 Gruen Zone

5 6 7

Figure 8.39: Effect of neck length on the change in bone density in the seven Gruen zones.

The effect of version angle on the equivalent strain is shown in Figure 8.40.

The immediately preoperative curves are similar to those in Figure 8.38, with the

most difference between models distally. For the version angle parameter evaluated

in this case, the immediately postoperative equivalent strains are greatest for the

retroverted femoral necks. The strains decrease as the version angle passes through

the physiological position (0°) and becomes anteverted. The -20° version angle

model produces equivalent strains similar to the intact femur values along the distal

one-third of the data presented.

After 120 increments of remodelling simulation, the strains again tend to con-

verge towards a single curve above the 0.4 position for all models, with little change

in the strains distally. At the most proximal two nodes however, the -20° and

20o models end up converging to a slightly lower equivalent strain value (average

of 827 f.LE at position = 0) compared with the other three (average of 933 J-LE at

position= 0)


o~~~~==~~~~ - · Preoperative

0.2

t:

:2 0.4 ·u; 0 a.. "0 Q)

~ 0.6 § 0 z

0.8

0

-1- Version Angle oo -e- Version Angle +10° -a- Version Angle -1 oo -~>-- Version Angle +20° -+- Version Angle -20°

)

I

/

500 1 000 1500 2000 2500 lmmed. Postoperative Q..t£, Equivalent)

0.2

0.4

0.6

0.8

0

I

I

I

/

)

I

/

\. )

/

208

500 1 000 1500 2000 2500 After Remodelling {/-lE, Equivalent)

Figure 8.40: Effect of version angle on the equivalent strain along the medial cortex.

The plot of bone loss in the seven Gruen zones (Figure 8.41) for the models with

varying version angle, indicates that bone loss generally increases with anteverted

angles at 3 years after surgery. In zone 7, bone loss is proportional to the version

angle. Anteversion increases bone loss ( + 20o, 37.7%), while retroversion decreases

it ( -20°, 24.1 %). This trend is not consistent across the other Gruen zones, with

the 10° anteversion model causing the most bone loss in zones 3-6, while the other

conditions produce similar results. Some densification is apparent for the -20° and

+20° models (3.4% for both). In zone 1, all of the version angles produce similar

results within about 2%. In zone 2, pronounced resorption of 30% and 21.8% occurs

for the +20° and +10° models respectively. Interestingly, the +10° variation gives

results most similar to the clinical mean in four out of the seven zones (2-4 and 7).


Models were run with dead zone widths of s = 0.55, s = 0.6 and s = 0.65 to

demonstrate the effect of this parameter on the remodelling simulation. Figure 8.42

shows that the dead zone has no effect on the immediately postoperative equivalent


0

-5

Z' -~ -10 Q)

0

~ -15 0 m ~ -20 c co .c () -25 -;!?_ 0

-30

-35

209

--Clinical --+-- Version Angle oo --e- Version Angle +10° -e-- Version Angle -1 oo --A-- Version Angle +20° -+- Version Angle -20°

-40L---~-------L------~--------~-------L--------L-------~--~

2 3 4 Gruen Zone

5 6 7

Figure 8.41: Effect of version angle on the change in bone density in the seven Gruen zones.

strains as expected. After remodelling however, it is the model with the lowest dead

zone width (s = 0.55) that has most approached the preoperative curve, indicating

a greater degree of medial bone resorption. Changes in the equivalent strains occur

mostly over the proximal half of the implant as observed with other models. At the

level of the osteotomy, the equivalent strain equals 816 ILE for the s = 0.55 model,

954 fLE for the s = 0.6 model, and 1095 fLE for the s = 0.65 model, compared with

2111 fLE preoperatively. These values equate to 38.7%, 45.2% and 51.9% of the

preoperative value for the 0.55, 0.6 and 0.65 models respectively. The percentage

of the preoperative values correlate perfectly ( R 2 = 1) with the dead zone width,

indicating a linear relationship between the dead zone width and the remodelled

strain expressed as a percentage of the intact value at remodelling equilibrium, for

the small range of widths considered.

Figure 8.43 indicates what looks like, and is, a linear relationship between dead

zone width and the percent change in bone density in the Gruen zones (R2 > 0.96

in all cases), for the small range of widths. There is close to zero change in density


0~---r----r----r----~---.

0.2

c 2 0.4 "Cii 0 a.. "0 Q)

~ 0.6 § 0 z

0.8

0

- - Preoperative -1- s = 0.60 -e- s = 0.65 -e- s = 0.55

I

I

I

)

I /

500 1 000 1500 2000 2500 lmmed. Postoperative ij.te, Equivalent)

0.2

0.4

0.6

0.8

0

I I

)

I

/

I

/

\. l

/

210

500 1 000 1500 2000 2500 After Remodelling (f.le, Equivalent)

Figure 8.42: Effect of dead zone width on the equivalent strain along the medial cortex.

for the distal zones (3-5), however in the remaining zones the change is inversely

proportional to dead zone width. In zone 7, bone loss is increased from 30.3% at

3 years for the s = 0.6 model, to 33.8% for the s = 0.55 model. Alternatively, the

amount of bone resorption is reduced to 26.4% for the s = 0.65 model.


The effect of postoperative loading on the femur was evaluated by reducing all

of the muscle and joint forces applied to the femur by 10% of the values applied

to the intact model. Figure 8.44 shows how this influences the equivalent strain

postoperatively and after 120 remodelling increments. Reduction of the loads to

90% of their preoperative values causes a decrease in the equivalent strains medially,

that becomes more apparent towards the mid-stem region. Below this level, the

difference between the 90 and 100% activity curves is approximately constant. After

remodelling, the two models have essentially the same strain curves above a position

of 0.4 on the medial cortex, while the distal values remain the same as immediately

postoperative.


5.---.--------r--------.-------.--------.--------r-------~--~

0

-5

~ -~ -10 Q)

0 )g -15 0

(l)

gj, -20 c ctl ..c () -25 6'2-

I

.... I I

....._ I

-30 h--------, -- Clinical --t- s = 0.60

-35 ---e--- s = 0.55

-----K-

I

... X •

-e- s = 0.65 -40L=~====~L_ ____ ~ ____ _i ______ L_ ____ ~----~--~

2 3 4 Gruen Zone

5 6 7

Figure 8.43: Effect of dead zone width on the change in bone density in the seven Gruen zones.

0 0 - - Preoperative / --+- 1 00% Activity \. ---e--- 90% Activity

0.2 } 0.2 / /

/ /

I I c / / 2 0.4 0.4

) "iji 0 a.. "0

I I Q)

~ 0.6 I 0.6 I E ..... 0 z

0.8 0.8

0 500 1 000 1500 2000 2500 0 500 1 000 1500 2000 2500 lmmed. Postoperative ()l£, Equivalent) After Remodelling ()l£, Equivalent)

Figure 8.44: Effect of postoperative activity level on the equivalent strain along the medial cortex.


Bone loss due to remodelling increased in all but the distal three Gruen zones for

the lower postoperative activity level (Figure 8.45). Bone loss at 3 years is increased

5.---.--------.-------.--------.--------.--------.-------,---~

0

-5

c ·~ -10 Q)

0

~ -15 0 co ~ -20 c: co

..c: () -25 -;12. 0

-30

'- I . , .. ,I

X

_, - Clinical -35 -+- 1 00% Activity

-e- 90% Activity

I

I

I .

-----+<-

... ~.

-40L---~-------L------~--------~------~--------~------~--_J

2 3 4 Gruen Zone

5 6 7

Figure 8.45: Effect of postoperative activity level on the change in bone density in the seven Gruen zones.

in zone 1 by 2.6%, in zone 2 by 2.9%, in zone 6 by 5.0% and by 3.1% in zone 7, when

compared with the model that assumes identical loading before and after surgery.


This variable was investigated using the Epoch model. Epoch remodelling simula

tions were run with the normal implant properties and two variations: 1) cobalt

chrome properties for the entire implant, and 2) isoelastic (cortical bone properties)

for the entire implant.

The immediately postoperative equivalent strain showed a similar degree of

stress shielding for all three implants at the level of the osteotomy (81-142 J-LE

compared with 1096 J-lE preoperatively), however the difference between the differ

ent modulus implants became apparent just distal to this. The equivalent strains

were then highest for the most flexible (isoelastic) implant and lowest for the most


rigid, all cobalt-chrome implant with the standard Epoch in between (Figure 8.46).

After remodelling, the equivalent strain is only changed over the proximal 25-30%

0.2

c 2 0.4 -~ a.. -o

CD

~ 0.6 E 0 z

0.8

0

- Preoperative --+-- Epoch --e- lsoelastic

./ /

I

I \

I

I

I

I •

--e- Cobalt Chrome

500 1 000 1500 2000 2500 lmmed. Postoperative (l.t£, Equivalent)

0.2

0.4

0.6

0.8

0

./ /

I \

I

I

I

I

I •

500 1 000 1500 2000 2500 After Remodelling (~-t£, Equivalent)

Figure 8.46: Effect of implant material on the equivalent strain along the medial cortex.

of the implant on the medial cortex. The three curves have all moved closer to the

preoperative curve in this region, and end up with similar values close to the level

of the osteotomy.

The quantity of bone lost in the Gruen zones is shown in Figure 8.4 7 for 3

year predictions. The clinical data is not available for plotting at this time point.

Significant changes in bone density for zones 6 and 7 are evident for the different

prosthesis material properties. In zone 7, the change in bone density ranges from

+0.8% for the isoelastic stem, to -34.5% for the cobalt chrome stem, with the

normal Epoch in between ( -10.2%). There is also some bone accumulation at the

distal tip of the cobalt chrome implant ( +2.6% in zone 4). In zones 1 to 5, the

differences betweent the three models are less than 2%.

The immediately postoperative interface stress distributions were calculated for

the three material properties. Figures 8.48 and 8.49 gives the interface stress in

direction 1, as defined by Abaqus, which is approximately in the inferior-superior


5.---.--------.-------,,-------,--------,--------,--------.---,

0

-5

z--~ -10 (])

0

~ -15 0 co ~ -20 c Cll .c () -25 ;{?_ 0

-30

-35 -+- Epoch -e- lsoelastic --a- Cobalt Chrome

-40L---~-------L------~~------~------~--------~-------L--_J

2 3 4 Gruen Zone

5 6 7

Figure 8.47: Effect of implant elastic modulus on the change in bone density in the seven Gruen zones.

direction. Anteromedial and posterolateral views of the contact surface are given.

The area of highest stress is at the proximal-medial interface, and is greatest for

the isoelastic implant and smallest for the cobalt-chrome. Some regions of distal

shear stress are also evident for the cobalt-chrome stem.

The stress in direction 2 (Figure 8.50 and 8.51) is approximately in the horizontal

plane, and relates to torsion of the implant. The area of high proximal-medial

shear stress was greatest again for the isoelastic stem, and least for the cobalt-

chrome. Stresses in this direction were smaller than direction 1. There is evidence

again of a distal stress concentration for the cobalt-chrome implant.


CSHEARl (Ave . Crit . · 75%)

~ +5 . 575e+00 +1. oooe~ oo +8. SOOe-01 +7 . OOOe-01 +5. SOOe-01

I +4 . OOOe-01 -+2. SOOe-01 +1. oooe-ot -5. OOOe-02 -2. OOOe-0 1

I -3 . SOOe-01 -5. OOOe-01 -2. 456e+OO

CSHEARl (Ave . Cri t . · 75%) • +7. 335e+OO

~ =~: ~g~~~g~ +7 . OOOe-01 +5. SOOe-01

-

+4. OOOe-01 +2 . SOOe-01 +1. OOOe-0 1 -5. OOOe-02 -2 . oooe-o1

I -3. SOOe-01 -5 . OOOe-01 -3 . 368e+OO

CSHEARl (Ave. Crit. · 75%)

~ +7. 580e+OO +1. OOOe+OO +8 . SOOe-01 +7 . OOOe-01 +5 . SOOe-01

-

+4. OOOe-01 +2. SOOe-01 +LOOOe-01 -5 . OOOe-02 -2 . OOOe-01

• - 3 . 500e-01 -5 . OOOe-01 -4. 015e+OO

215

Figure 8.48: Immediately postoperative interface shear stress (direction 1) for (left) Epoch, (middle) isoelastic, (right) cobalt-chrome (anteromedial view).

CSHEARl (Ave. Crit .: 75%)

~ +5. 575e+OO +1. OOOe+OO +8 . SOOe-01 +7. OOOe-01 +5 . SOOe-01 +4. OOOe-01 +2 . SOOe-01 +1 . OOOe-01 -5 . OOOe-02 -2. OOOe-01 -3 .SOOe-01 -5 . OOOe-01 -2.456e+OO

CSHEARl (Ave . Crit . · 75%)

~ +7. 335e+OO +1 . OOOe+OO +8 . 500e-01 +7. OOOe-01 +5 .500e-01 +4 . OOOe-01 +2 . 500e-01 +1. OOOe-01 -5 . OOOe-02 -2 . OOOe-0 1

• -3 .500e-01 -5. OOOe-01 -3 . 368e+OO

CSHEAR1 (Ave . Crit. · 75%)

~ +7 . 580e+OO +1 . OOOe+OO +8. 500e-01 +7. OOOe-01 +5. 500e-01 +4. OOOe-01 +2. SOOe-01 +1. OOOe-01 -5 . OOOe-02 -2. OOOe-01 -3 . SOOe-01 -5. OOOe-01 -4 . 015e+OO

Figure 8.49: Immediately postoperative interface shear stress (direction 1) for (left) Epoch, (middle) isoelastic, (right) cobalt-chrome (posterolateral view).


CSHEAR2 (Ave. Crit. · 75%)

~ +6. 608e+OO +1 . OOOe+OO +8. SOOe-01 +7. OOOe-01 +5 . SOOe-01

-

+4. OOOe-01 +2 . SOOe-01 +1. OOOe-01 -5. OOOe-02 -2. OOOe-01

I -3. SOOe-01 -5 . OOOe-01 -2 . 467e+OO


111 :i: zgg~:85 +8 . SOOe-01 +7. OOOe-01 +5. SOOe-01 +4. OOOe-01 +2. SOOe-01 +1. OOOe-01 -5 . OOOe-02 -2. OOOe-01 -3. SOOe-01 -5. OOOe-01 -3. 922e+OO

CSHEAR2 (Ave. Crit . · 75%)

~ +5.932e+OO +1 . OOOe+OO +8. SOOe-01 +7. OOOe-01 +5. SOOe-01 +4. OOOe-01 +2 . SOOe-01 +1. OOOe-01 -5. OOOe-02 -2. OOOe-01 -3. SOOe-01 -5. OOOe-01 -4 . 859e+OO

216

Figure 8.50: Immediately postoperative interface shear stress (direction 2) for (left) Epoch, (middle) isoelastic, (right) cobalt-chrome (anteromedial view).


~ +6. 608e+OO +1. OOOe+OO +8. SOOe-01 +7. OOOe-01 +5. SOOe-01 +4 . OOOe-01 +2. SOOe-01 +1. OOOe-01 -5. OOOe-02 -2. OOOe-01 -3. 500e-01 -5. OOOe-01 -2 .467e+OO


• +1.748e+01 ~ - +1. OOOe+OO

+8. SOOe-01 +7 . OOOe-01 +5. SOOe-01 +4. OOOe-01 +2. 5ooe-01 +1 . OOOe-01 -5. OOOe-02 -2. OOOe-01 -3. SOOe-01 -5. OOOe-01 -3. 922e+OO


~ +5. 932e+OO +1. OOOe+OO +8. 500e-01 +7. OOOe-01 +5. 500e-01 +4 . OOOe-01 +2. 500e-01 +1. OOOe-01 -5. OOOe-02

il -2. OOOe-01 -3 . 500e-01 -5. OOOe-01 -4. 859e+OO

Figure 8.51: Immediately postoperative interface shear stress (direction 2) for (left) Epoch, (middle) isoelastic, (right) cobalt-chrome (posterolateral view).

Chapter 9

Discussion

Total hip arthroplasty has one of the highest success rates of contemporary surgeries

(Cristofolini, 1997), relieving pain and immobility. Between July 2001 to June

2002, 26 689 hip replacement procedures were performed in Australia, of which

65% were primary total hips replacements. This represented an increase of 13% in

the primary total hip category from the previous 12 months. Cementless fixation

currently accounts for 41% of primary hip procedures in this country (Graves et al.,

2003). The ageing population and success in younger patients are contributing to

the growing demand.

Implant failure, necessitating revision, can occur for a number of reasons includ

ing aseptic loosening, infection, fracture of the bone or implant, dislocation, wear,

pain and technical error (Graves et al., 2003; Lucht, 2000; Malchau et al., 2002). Of

these, aseptic loosening is the most common. Revision surgery, particularly early

revision, is related to an increased rate of re-revision (Graves et al., 2003; Malchau

et al., 2002). Revision is also associated with higher cost and mortality (Cristofolini,

1997; Graves et al., 2003). Consequently, all measures must be taken to limit the

rate of revision surgery.

A large number of hip prosthesis designs are available on the market, although

many new design aspects have been clinically tested in a somewhat trial-and-error

fashion, with variable results. According to Herberts et al. (1989), to compare two

217


types of prostheses with probabilities of failure of 5% and 3% over 5 years, a series

of almost 3000 patients would have to be followed before one design could be proven

to be significantly better than the other. This does not seem likely, and therefore

pre-clinical tests to predict implant longevity would be advantageous.

Bone resorption around hip replacements due to strain-adaptive remodelling

in accordance with "vVolff's Law" is a common concern. Although clinical failures

associated with bone resorption are infrequent, bone loss reduces bone strength and

increases the risk of fracture. This also reduces the support of the implant which

increases the load it carries, possibly leading to fatigue fracture (Engh et al., 1990).

Sufficient bone stock for revision is a major issue. Development of a in vitro tool

to accurately predict bone remodelling changes around hip prostheses would be a

beneficial design instrument to gain confidence in the performance of an implant,

before moving to in vivo experimentation.

This study first examined the experimental strain distribution of cadaveric fe

mora, before and after hip arthroplasty with the Margron prosthesis, under simple

loading. One of these femora was subsequently taken and used as the basis for an

anatomic finite element model. This finite element model was validated by compar

ison with the strains from the actual femur. Mesh refinement was also examined.

The finite element model was subsequently coupled with a strain-adaptive bone

remodelling theory to investigate changes in periprosthetic bone density.


Mechanical testing of four cadaveric femora was undertaken to assess the cortical

strain distribution before and after hip replacement with the Margron prosthesis.

Preoperative strains decreased from proximal to distal on the medial cortex, as seen

by many others, even under different loading conditions (e.g., Cristofolini et al.,

1995; Jasty et al., 1994; Oh and Harris, 1978). This points to bending of the femur

in the coronal plane under the two applied load conditions. Under load case 1 (0°


hip flexion), strains were reasonably constant on the anterior and posterior aspects,

however under load case 2 ( 10° flexion), the strains increased from proximal to distal

due to bending introduced in the sagittal plane. Load case 2 also introduces torque

to the femur.

In the coronal plane (under load cases 1 and 2), bending was highest towards

the metaphysis, while in the sagittal plane (under load case 2), bending was more

significant in the diaphysis. Coronal plane bending can be explained by fixation of

the femur in 10° valgus, where the moment arm for bending in this plane reduces

from proximal to distal. With the femur in 0° flexion, the moment arm for bending

in the sagittal plane remains constant, and consequently the anterior and posterior

strains remain essentially constant along the femur. However, with the femur placed

in 10° flexion, the moment arm for bending in the sagittal plane increases from

proximal to distal, and the strain magnitudes increase accordingly.

Insertion of the cobalt-chrome Margron stem decreased strains from proximal to

distal all around the femur. A statistically significant reduction in proximal strain

was observed medially and laterally at the proximal two gauge levels under both

load conditions, which implies the potential for disuse atrophy of bone in these

regions. Longitudinal strains were generally similar to the principal strains with

compression medially and posteriorly, and tension laterally and mostly anteriorly.

Similar strain magnitudes imply that the principal strains were aligned with the

longitudinal axis of the femur. This is due to loading predominantly in the coronal

plane, a result corroborated by Finlay et al. (1991). Some differences between

the longitudinal and principal strains were evident at the proximal gauges on the

anterior aspect, where strains were compressive rather than tensile. Small strain

magnitudes in these locations could be responsible.

McNamara et al. (1997a) tested a synthetic femora under joint reaction force

alone, with the femur in neutral flexion and constrained at the condyles. They

found compressive strains medially and tensile strains laterally. Anterior strains

were compressive, while posterior strains went from very small compressive at the


most proximal level, to larger tensile strains, and then back to small compressive

strains distally. Using a loading protocol more like load case 1 in the current study,

Oh and Harris (1978) also observed compression medially and tension laterally,

while strains on the anterior aspect were compressive at the proximal two gauges

levels and tensile distally, while posterior strains changed from tensile proximally,

to compressive distally. The trends reported by Oh and Harris (1978) agree very

well with those found in this study.

Expressing the postoperative strains as a percentage of the preoperative values

provides a depiction of the degree of stress shielding. The medial and lateral results

show a high degree of stress shielding proximally, with a trend towards normalisation

of strains distally. There is an additional tendency for stress shielding to be reduced

under load case 2. This tendency is reversed on the anterior and posterior cortices,

where load case 1 appears to produce less stress shielding. At gauges 7 and 8, the

percentage strains are dramatically high (485.9% and 297.4% respectively) under

load case 1. This is due to very small preoperative strains, compared with their

values after surgery. It can be hazardous expressing strains as a percentage of

preoperative values when small values are involved. Finlay et al. (1991) advised

that it was only legitimate for large strains, as insignificant changes in small strain

can translate into large percentage changes.

Direct comparison with the literature is difficult due to the varied testing meth

odologies. The systems of applied forces and constraints differ significantly from

study to study. In the current case, the load conditions are only pseudo-physiological

and the configuration may not give an accurate representation of the degree of

stress shielding expected in vivo. The joint reaction force alone was applied, yet

Cristofolini (1997) advise that excluding the abductor muscle group may lead to

overestimation of lateral stress shielding (see Figure 5.4).

The setup was primarily used for validation of the finite element model, since

the loads and boundary conditions could be easily replicated. More than one femur

was tested to ensure that the results were representative of a group, remembering


that inter-specimen variation can be significant when dealing with human tissue

(Sedlacek et al., 1997). The femur was fully constrained at the diaphysis in this

study, similar to other investigations (Gillies et al., 2002; Hua and \Valker, 1995; Oh

and Harris, 1978; Otani et al., 1993; Tanner et al., 1988). Proximally, the femoral

head was allowed to translate freely in the horizontal plane, to ensure that the

system was not overconstrained. If the setup is overconstrained, the force applied

by the setup depends on the stiffness of the bone-jig-testing machine ( Cristofolini

and Viceconti, 1999).


An anatomic finite element model of a femur was constructed from CT scans of a

cadaveric femur from the experimental study. CT data files provided the geometry

and apparent density properties for the three-dimensional model (Marom and Lin

den, 1990). A finite element model of the femur reconstructed with the Margron

hip prosthesis was also created.

Under simple load configurations, strains from finite element analysis of these

models were compared with experimental strains for validation purposes. The in

fluence of mesh refinement on the accuracy of the finite element results was also

investigated.


A finite element model should always be validated against experimental strains

measured in the femur from which its geometry has been derived (Cristofolini,

1997). Consequently, the subject-specific finite element model used in this study

was loaded under the same conditions as the experimental femur from which it was

constructed, and principal strains were compared with the experimental strains on

the medial, lateral, anterior, and posterior surfaces.


Preoperatively, discrepancies were seen between the experimental and finite ele

ment results at the proximal level of gauges on all sides of the femur and under both

load cases. This situation was also noted after arthroplasty on the lateral and pos

terior aspects. Part of this problem could be associated with creation of the initial

geometry of the femur. At the level of the proximal gauges, the geometry changes

quite rapidly from the fairly straight shaft to the variable metaphyseal region. This

makes it difficult to accurately reproduce the geometry. The most significant prob

lem resulting from this comes about if the finite element mesh ends up outside the

actual femoral geometry, particularly if integration points are outside the geometry.

If this is the case, the integration point will be assigned the minimum value, and

a high density gradient across the element will ensue. This will also cause a high

strain gradient across the elements (perpendicular to the periosteal surface), with

particularly large deformations at the integration points near the surface. Extrapo

lation of strains from the integration points where they are calculated, to the surface

nodes, will exacerbate the problem in the presence of a strain gradient.

The geometric problem just described is probably what is happening at the most

proximal gauges on the lateral and posterior aspects, as strains at these two locations

are significantly overestimated by the finite element model under all conditions.

Examination of the preoperative surface density distribution (Figure 8. 7) shows an

abrupt decrease in density going from distal to proximal around the level of the

lesser trochanter on the proximal and lateral aspects, lending some weight to this

idea. This problem could be resolved by applying homogeneous properties to each

element, however the mesh would need to be refined (Section 9.2.2), increasing

computation time substantially.

The strain values calculated by the finite element analysis are dependent on the

elastic modulus-apparent density relationship. The Carter and Hayes (1977) rela

tionship (Equation 4.5) is considered to represent an upper bound for the elastic

modulus of bone compared with other relationships in Table 4.5 (Weinans et al.,


2000), and therefore may produce lower strains from the model. However, consis

tently lower finite element strains were not a problem here.

At the medial and anterior proximal gauges, the difference between the experi

mental and finite element results was evident under both load cases preoperatively,

but not after surgery. Strain gauges give only a site-specific measurement of strain,

and give no indication of the strain gradient. Strain gauges are known to be inaccu

rate in regions of high strain gradient (Finlay et al., 1991), which may be the case

at the medial and anterior proximal gauges. The averaging effect in areas of high

strain gradient will depend on the size of the gauge grid (Cristofolini et al., 1997).

Other possible sources of experimental error include bone dehydration or moisture

penetration under the gauge (Viceconti et al., 1992), gauge positioning (Cristofolini

et al., 1997; Rohlmann et al., 1983), ubiquitous experimental errors (Rohlmann

et al., 1983), or gauge calibration, data acquisition, and load cell calibration.

Anterior and posterior strains were underestimated by the finite element model

under load case 1 before and after surgery. Preoperatively, these strains are quite

small to begin with, making differences appear large. The larger experimental

strains suggest more bending of the experimental femur in the sagittal plane, pos

sibly caused by slight misalignment of the femur during testing. Gauges on the

anterior and posterior cortices are also close to the neutral axis of bending in the

frontal plane. Consequently, the strains will be sensitive to measurement location.

It is only when bending is introduced in the sagittal plane that strains are increased

and in better agreement. When using uniaxial strain gauges, Cristofolini et al.

(1997) recommended that anterior and posterior strain gauges be avoided because

of reliability problems related to positioning. The effect may not be as drastic with

triaxial gauges, but could still be important.

Postoperative strains are also sensitive to the position of the prosthetic femoral

head (Cristofolini and Viceconti, 1999) and the characteristics of the implant-bone

interface (Diegel et al., 1989; Huiskes et al., 1992; Jasty et al., 1994; Simoes and Vaz,

2002). Care was taken experimentally and with the finite element model, however


some positioning errors of the femoral head are possible. Cristofolini and Viceconti

(1999) showed that lateralisation of the prosthetic head by 7 mm can produce strain

errors as high as 50% compared with the physiological position, using heel-strike

loading if the same forces are applied. In terms of congruency, error in preparation

of the femoral canal is minimised with the Margron system since a circular cross

sectioned mill is used for shaping, rather than more difficult to control broaches.

Thus, the likelihood of discrete implant-bone contact points is reduced. In the finite

element model, the interface is assumed to be perfectly congruent.

Strains below the mid-stem region were dependent on the contact conditions

simulated at the interface. Generally, the model with the proximal coated surface

fully bonded to the bone, with no contact defined distally, produced the highest

strains distally, which was also most like the experimental case. Increasing the

contact area tended to decrease the distal strains. This effect was also reported

with finite element modelling of an uncemented hip under heel-strike loading in a

synthetic femur (McNamara et al., 1997a, 1996; Toni et al., 1996). Highest bone

stresses were obtained with a proximally bonded stem without any distal contact

conditions (representative of an over-reamed femoral canal). The fully bonded case

gave the lowest load transfer, while a proximally bonded implant with sliding distally

fell between these two cases. Bonding of the implant-bone interface was simulated

experimentally by gluing the stem into the femoral canal. This produced lower

strains than the standard press-fit stem, but gave better agreement with the finite

element model with a similar interface.

Much of the literature that reports experimental validation of their finite ele

ment models have used homogeneous properties for cortical and cancellous bone.

The studies using composite bones have been able to report good agreement be

tween the strain gauge and finite element results (McNamara et al., 1997a, 1996;

Stolk et al., 2002; Viceconti et al., 1998a, 2001a). Anatomic models with homo

geneous properties based on cadaveric geometry have also been validated. Keyak


et al. (1993) validated a voxel-based model using strain gauges, with loading ap

plied to the femoral head. A significant correlation was shown between experimental

and finite element strains, although the finite element strains tended to underes

timate measured values. Similarly, the automatic mesh generation models created

by Lengsfeld et al. (1998) produced results that correlated well with experimental

data. Certainly, the behaviour of composite bones should be easier to model than

the more complex biological material, while applying homogeneous properties to ca

daveric models represents a significant simplification. There seemed to be a distinct

lack of validated finite element models in the recent literature with inhomogeneous

material properties, either within the material or the element.

Due to the numerous simplifying assumptions made in finite element models,

comparison of the numerical results with experimental strains values can only be

of a qualitative nature (Joshi et al., 2000b). This is partially due to the fact that

the response of bone is difficult to model. In this study, the finite element model of

the femur was made as accurate as possible by using a relatively refined mesh (see

Section 9.2.2) and by applying inhomogeneous material properties to the elements.

Mesh refinement (see next section) ensures that local stress variations are not over

looked, while inhomogeneous elements are capable of reproducing the effects of the

varying elastic modulus field found in bone. Considering these points, and that the

comparisons with strain gauges are limited to a small number of discrete locations,

the finite element model developed here was thought to be sufficiently accurate for

the purpose of determining the stress distribution of the femur, particularly in the

important proximal-medial region.


Solution convergence is an important part of any finite element analysis (Cook,

1995), although it is seldom reported in the biomechanical literature. The finite

element method produces field quantities that are an approximation of the actual

solution. Mesh refinement reduces the error between the approximate and required


results, however model complexity and therefore computation time, are substan

tially increased. Accordingly, a compromise must often be found between these two

competing factors.

In this study, the model of the intact femur was investigated with 3, 5 and

7 mm average element sizes. Solution convergence was monitored by the minimum

principal strain along the medial aspect of the femoral cortex. Model accuracy may

be evaluated using structural displacement (Biegler et al., 1995; Valliappan et al.,

1977; Viceconti et al., 1998b; Vichnin and Batterman, 1986) and/or surface stresses

(Keyak et al., 1990; Keyak and Skinner, 1992; Viceconti et al., 1998a). In this case,

as with Viceconti et al. (1998b), surface strains were employed.

With the material properties applied to each element's integration point, there

sults approached a solution as the mesh was reduced. This was particularly evident

in the diaphysis, where material properties were less variable. The 7 mm mesh was

consistently different from the 3 and 5 mm meshes, and therefore was not examined

for the reconstructed femur model. Good agreement was again seen between the 3

and 5 mm meshes for the postoperative model, especially considering strains were

less than 300 f.l£.

Based on similarity between the 3 and 5 mm mesh results, the 5 mm element

size was accepted for further modelling. This decision was backed up by the com

putation time being 11 times greater for the more refined intact femur mesh. For

the reconstructed model, the time difference was closer to 10, however this would

probably increase further if more complex contact interactions were included.

The effect of applying the material properties to each integration point, or av

eraging them over each element and thereby applying homogeneous properties to

individual elements, was also examined. The results indicate that the least accu

rate solution is produced by the 5 mm mesh with average properties, while the most

accurate solution comes from the 3 mm mesh with distinct properties applied to

the integration points. It is difficult to distinguish between the 5 mm integration

point and 3 mm average strains, which suggests that the use of inhomogeneous

9.3 BONE REivfODELLING STUDY 227

material properties may be used in place of mesh refinement. This finding was also

noted by Edinin and Taylor (1992), where bone stresses were underestimated and

local stress peaks were smoothed out by not using intra-element variation in elastic

modulus. One problem associated with inhomogeneous element properties is that

if the gradient across the element is high, the material properties can be high when

extrapolated to the nodes. This issue was not seen when constant properties were

applied across each element. Extrapolation of strains to the nodes did not appear

to be a problem with variable modulus elements, where in fact some of the local

peak strains found with the average modulus elements were smoothed out.

Another important factor that affects model accuracy is mesh conditioning. Dis

torted elements, or elements with large aspect ratios are sources of ill-conditioning,

which can lead to inaccurate results (Rohlmann et al., 1983; Viceconti et al., 1998b,

1999). Slender elements may possess higher stiffnesses than expected (Cook, 1995).

There were no distorted elements detected in the 5 mm mesh.


A strain-adaptive bone remodelling algorithm was coupled with finite element mod

elling to predict bone density changes in response to reconstruction with a femoral

prosthesis. The optimal strain environment for bone is thought to be genetically

predetermined for each specific location (Carter, 1984; Lanyon, 1987; Rubin and

Lanyon, 1987), which implies the need for a site-specific formulation of the remod

elling rule. Incorporation of a dead zone, as suggested by Carter (1984) and Frost

(1987) is necessary to obtain valid simulation results (Huiskes et al., 1992). There

modelling process has many unknown variables, and the theory is usually simplified

to minimise the number of parameters.

The remodelling rule used in the present study differs from that of Huiskes et al.

(1992) on which it was based, in three key areas: 1) choice of remodelling signal,

2) different rates of resorption and deposition, and 3) use of physiological loading.


In this model, equivalent strain, equal to the magnitude of the strain tensor, was

assumed to be the mechanical signal that bone responds to. This may not be

the actual signal that is transduced at the cellular level, however it does produce

results that correlate with the clinical data, which is acceptable considering this is

an empirical model.

The rate of resorption was taken to be 3.5 times greater than the rate of ap

position, based on data from Nauenberg et al. (1993), and general agreement that

resorption occurs more quickly (Beaupre et al., 1990b; Weinans et al., 1992b). In

Huiskes' model, the rates are assumed to be the same, however this simplification

is probably not significant since most of the density changes are reductions.

In the current study, physiological muscle and joint forces from 45% of the gait

cycle were applied. This is in contrast to the simplified loading configurations used

by Huiskes and others, consisting of femoral head and greater trochanter loads only.

9.3.1 Margron

Remodelling of a femur implanted with the Margron hip prosthesis was simulated.

Bone density changes were in accordance with the model theory, with large differ

ences between the pre- and postoperative remodelling signals driving the largest

changes in density. Remodelling did not take place in regions where the difference

in remodelling signals was less than the threshold value, dictated by the dead zone

width.

Literature pertaining to simulation of periprosthetic bone adaptation is primar

ily limited to the model proposed by Huiskes and co-workers (1992). Other pa

pers examining bone adaptation generally refer to trabecular morphogenesis (e.g.,

Beaupre et al., 1990a; Cowin et al., 1992; Mullender et al., 1994) or are mechanistic

models in a form not suitable for implementation due to undetermined biological

parameters (e.g., Fyhrie and Schaffier, 1995; Hart et al., 1984b; Hernandez et al.,

2000).


Principal and Equivalent Strains

The physiological load case, representing 45% of the gait cycle, produced bending

of the normal femur in the coronal plane, with minimum principal strains dominat

ing medially, and maximum principal strains laterally. This is primarily due to the

action of the joint reaction force and the muscles inserting on the greater trochanter

(gluteus medius and minimus, piriformis and tensor fasciae latae). There was also

bending in the sagittal plane, with some compression anteriorly, and tension pos

teriorly. In this case, gluteus medius, gluteus maximus and iliopsoas are the major

force components at work. Duda et al. (1998) obtained similar results, with medial

bending and strains below 2000 jJ£. However, bending in the sagittal plane was in

a posterior direction, rather than anterior. This can be attributed to Duda using

an entire femur, a balanced set of forces in static equilibrium, and point loading.

After surgery, minimum principal strains on the medial cortex of the femur were

considerably reduced proximally due to stress shielding (11-22% of the intact val

ues). Remodelling decreased the bone densities, and correspondingly the elastic

moduli in this region, thereby increasing deformations and strains ( 45-54%). Dis

tally, the strains did not change significantly, and remained at about 85% of the

preoperative values during the remodelling simulation. The strains at remodelling

equilibrium were not identical to those found before surgery because of the presence

of the dead zone.

The equivalent strains behaved in a similar manner to the principal strains.

Stress shielding reduced the strains around the region of the lesser trochanter (2-

18% of the reference values), and subsequent remodelling caused the strain to ap

proach the preoperative value (38-45%). After remodelling, the equivalent strains

should all be at least 40% of the reference value, due to a dead zone width of 60%.

Some discrepancies are presumably due to extrapolation of the strains from the

integration points, where the remodelling rule is applied, to the nodes.

Engh et al. (1992b) obtained 5 pairs of femora with unilateral Anatomic Med

ullary Locking (AML) stems (DePuy, Warsaw, IN, USA), obtained at autopsy.


Cortical strains were measured in the remodelled femur, the intact femur and the

post-mortem implanted femur. Large strain reductions were observed in the post

mortem implanted femur, which were most pronounced proximally ( 4-10% of intact

strain). Extensive bone adaptation after an average of 7.5 years did not restore

strains to their normal values (4-43% of intact strain), although there was improve

ment similar to that found with the Margron simulation.

In an in vivo canine study, Vanderby et al. (1990) obtained intact, immediately

postoperative, and 4 month remodelled strains. Adaptations were generally con

sistent with the change in strain subsequent to surgery, but this was not strongly

correlated with magnitude. There was no consistent trend identified towards nor

malisation of altered strains. Longer time in vivo may have been required.

Bone Density

This is the first time that changes in bone mineral density predicted by bone re

modelling theory have correlated strongly and significantly with clinical results.

The correlations existed, not only for the seven Gruen zones, but also at three time

points. Up until now, the pattern of density distribution has been qualitatively sim

ilar to clinical observations, or only correlated with change in total bone mineral

content across all regions.

Predictions of BMD changes in this study are on average within 5.4% of the

clinical data at 3 years, with a maximum of 13. 7%. The simulation underestimates

bone loss in zones 1 and 2, while slightly overestimating it in zone 6. The shape

of the curve is the same as that found clinically, and the predictions are within the

range of clinical data. Correlations between the simulated and clinical data were

strong at 1, 2 and 3 years.

Insufficient resorption laterally in zones 1 and 2, and excessive resorption medi

ally in zone 6, could be attributed to a variety of factors. These include the choice of

loading, implant-bone interface conditions, geometric changes, preoperative bone


mineral content, or a combination of these. However, it is also important to re

member that the simulation is for a single femur, compared with DEXA data from

a larger population, meaning that the exact pattern of bone resorption should not

necessarily be the same as the group mean.

The somewhat asymmetrical pattern of bone loss predicted by the simulation

may be influenced by the applied loading. One load case is used, representing

physiological muscle forces from 45% of the gait cycle. Some remodelling theories

have used the load history function defined by Carter et al. (1987), where the

remodelling signals were averaged over multiple load cases. This was initially used

for trabecular morphogenesis studies, where one load case was unable to produce

realistic density distributions. Simple configurations were used, with forces applied

to the femoral head and greater trochanter only. Usually three load cases have

been used (e.g., Beaupre et al., 1990a; Huiskes and van Rietbergen, 1995; Huiskes

et al., 1992), although sometimes only one (van Rietbergen et al., 1993; Weinans

et al., 1993). It is possible that additional load cases, e.g., heel strike and stair

climbing, would stress shield a region of bone differently. Nevertheless, it has been

proposed that the actual loading configuration is not important for site-specific

remodelling theories, as long as it represents a typical loading pattern that includes

axial, bending and torsional components (Huiskes et al., 1987, 1992; Weinans et al.,

1993).

Ingrowth is not an immediate process, and therefore only compressive forces

and shear due to friction can be transmitted across the interface until bone in

growth becomes established. After this time, tensile forces can also be transferred

across the interface. It is quite likely that the applied loading in my simulation

causes transmission of tensile loads at the bonded interface of the proximal~lateral

femur, straining the bone and creating an "osteogenic" signal to inhibit bone re

sorption that would not normally be present. Ingrowth occurs via a response to

the trauma created at the time of surgery. Intramembranous formation of woven

bone is followed by creation of lamellar bone. Woven bone is present within 1 week,


and mechanical fixation occurs some time thereafter. The exact time in humans is

not certain, however fixation strength plateaus at 2 weeks in canine models, and

clinicians recommend 6~ 12 weeks of protected weight-bearing with humans (Jacobs

et al., 2000). This period of lower usage could stimulate additional resorption not

predicted by the model.

Adaptive changes in the geometry of bone occur in vivo after hip arthroplasty,

such as rounding off of the femoral neck at the osteotomy. This theory does not

account for these changes, although bone resorption is simulated by very low den

sity bone that contributes little to the total density of a region of interest. Since

bone mineral density is a measure of the bone mineral content normalised by the

measurement area, the effect of changing area is hopefully not that significant. The

proximal Gruen zones (1, 2, 6 and 7) are also more liable to measurement errors

in the clinical setting, due to the smaller areas of the regions (Kiratli et al., 1992;

Rahmy et al., 2000). DEXA is accurate to within 5%, however positioning errors

can decrease the precision further (Kilgus et al., 1993; Kiratli et al., 1992; Rahmy

et al., 2000).

Preoperative bone mineral content has been cited as an important predictor of

bone loss following hip arthroplasty (Engh et al., 1994, 1992a; Sychterz and Engh,

1996). This variable is probably not that significant here, as medial bone loss is

overestimated medially at zone 6, but underestimated laterally at zones 1 and 2,

rather than being excessive or too little on both sides of the implant.

Despite small differences between the simulation and clinical percentage density

changes in zones 1, 2 and 6, the predicted values are still well within the 95%

confidence intervals. The error bars are quite large (±30%) because errors can

propagate quickly when numbers are divided. Consider what would happen if a

data point in the high range of one group is divided by a data point in the low

range of the other group, or vice versa. This could lead to large deviations from

the mean when calculating percentage change. The error bars could potentially be


reduced by increasing the number of subjects in the study and by stratifying the

data by age. Uncontrolled patient factors are difficult to account for.

The remodelling theory proposed by Huiskes et al. (1992) has been used to sim

ulate apparent density adaptation around hip prostheses. This model predicted

severe proximal bone resorption around an unspecified uncemented titanium pros

thesis, except on the lateral side, when applied to a finite element model of an

"average" femur. Densification was found halfway down the stem laterally, and at

the tip of the stem. The model predicted 68% bone loss at the most proximal

level examined and 35% at the mid-stem level. Twenty increments of remodelling

were simulated, during which convergence was almost reached, althouth the time

scale was not related to a realistic one. This model has been further explored and

compared with in vivo results in human (Huiskes, 1993b; Kerner et al., 1999; van

Rietbergen and Huiskes, 2001) and canine (van Rietbergen et al., 1993; Weinans

et al., 1993) subjects.

Huiskes (1993b) compared the simulation results from Huiskes et al. (1992)

with clinical data from Engh et al. (1992a) and found qualitative agreement, even

though different implants were used in the two studies with respect to both geometry

and materials. Similar trends were noted between the two studies in terms of the

effects of preoperative bone mass. This investigation was a useful first step towards

validation of the simulation model.

Kerner et al. (1999) obtained four pairs of femora with unilateral AML stems

at autopsy. The contralateral femora were used to create intact and postoperative

finite element models for remodelling analysis. The distal parts of the finite ele

ment models were patient-specific, whilst the proximal parts were from the average

femur by Huiskes et al. (1992). Remodelling was simulated on the post-mortem

implanted model and DEXA images were produced for comparison with the in vivo

remodelled femur with the stem. Progressive bone loss in the proximal part of the

bone occurred, with the greatest reductions in the proximal~medial region and lat

erally, distal to the greater trochanter. In all four simulations, bone disappeared


completely in the region of the lesser trochanter, while bone densification at the

proximal-lateral region and the distal stem tip was overestimated, compared with

the in vivo remodelled specimens. However, gradual filling of gaps between the

implant and bone was apparent and this was also seen clinically. In this study,

the authors were unable to correlate DEXA measurements in individual scanning

regions from the in vivo remodelled femora with simulations. Instead, total BMC

measured from the lateral direction was compared. This most likely reduced the

influence of the extensive medial bone loss, and suggests that BMC measured from

the anterior direction did not correlate with the clinical results. The simulation was

terminated in all cases after 60 increments, even though the remodelling time in

vivo was different (17, 84, 77 and 72 months) for the specimens. This was before

equilibrium was reached, but gave results closest to the retrievals.

Van Rietbergen and Huiskes (2001) compared simulation data from their aver

age femur model with clinical data for the anatomic, titanium, uncemented ABG

femoral stem (Osteonics, Allendale, NJ, USA). The implant was bonded at the

one-third proximally coated area, with frictionless sliding and a 10 p,m gap distally

to represent a thin fibrous interface. The model was run to equilibrium, with no

mention of real time. The clinical data reported endosteal apposition and densifi

cation in the mid-stem region, and bone resorption in the most proximal sections.

Resorption was predicted by the model in the proximal-medial cortex and in the

proximal greater trochanter. In the calcar region, approximately 40% bone loss was

predicted, compared with the mean of 27.1% for the clinical study. Some densifi

cation occured close to the HA coating on the medial and lateral sides, but not as

much as seen clinically. Distal endosteal apposition seen in the simulation was not

symmetric as found in the clinical study.

In all of these examples, the major problem in my mind, is that bone loss due

to adaptation is overestimated and appears to be self-propagating to some extent.

The degree of bone loss can be lessened by increasing the dead zone width, however

the value of 0. 75 used for the simulations is already a significant proportion of


the preoperative mechanical state. In such a case, resorption does not occur until

the remodelling signal is less than one-quarter of the intact value. The problem

can mostly be attributed to the choice of mechanical signal and how it behaves in

response to changes in density. In preliminary studies, I evaluated the signal used

by Huiskes et al. (1992) and found considerably more proximal bone loss for the

Margron model.

Bone remodelling occurs predominantly in the first year and rarely beyond two

years (Bobyn et al., 1992; Bugbee et al., 1997; Engh and Bobyn, 1988; Kroger et al.,

1998). This certainly agrees with the results from the current study, where 86%

of the total change in bone density in zone 7 occurred during the first 2 years ( 40

increments), and 97% by 3 years ( 60 increments). Similar findings were present

in the other Gruen zones. Kilgus et al. (1993) detected small density changes by

DEXA for up to 5~7 years postoperatively, and by Kiratli et al. (1996) up to 8 years

postoperatively. In the present study, very small changes were also present out to

6 years (120 increments), when remodelling equilibrium was reached.

In response to overestimation of proximal bone loss, Kerner et al. (1999) pro

posed that the adaptive process was limited to a finite postoperative period reached

before predicted remodelling equilibrium. They hypothesised that the bone does

not remember its preoperative mechanical state after a certain time and terminates

the remodelling process before the original state is established. This concept has

been explored by others. Turner (1998) hypothesised that bone cells accommodate

to an altered mechanical loading environment, making them less responsive over

time. Cowin et al. (1991) thought it possible for osteocytes to remodel the shape of

their lacunae, thereby mechanically adjusting their sensitivity to a particular type

of loading, while Rubin et al. (2002) proposed that bone cells can accommodate

some degree of change in loading environment, without altering tissue architecture,

by modulating cytoskeletal architecture, attachment to the matrix, configuration of

the periosteocytic space, and communication channels to surrounding cells.


The dead zone ensures that the preoperative mechanical environment at a site

consists of a wide range of strains either side of the actual value. This means that

bone need only reach the edge of this range by the time remodelling equilibrium

is reached. This means that the bone has essentially adapted to a new loading

environment, and thus there may be some flaws in Kerner's argument.

Convergence

Remodelling equilibrium was monitored by a function equal to the error between the

actual remodelling signal and the reference value, averaged over all of the integration

points of the bone elements in the model. Some integration points will naturally

begin the simulation with strains within the threshold of no remodelling, and these

will not be changed. Others will have large error values, and therefore the change

in density will be large (within limits). The greatest error is found at the start of

the remodelling simulation, and falls away quickly during the first few remodelling

increments. After this time, only small changes in the error occur as the solution

approaches equilibrium in a monotonic fashion. The convergence function never

reaches zero, as some integration points are unable to reach a state of zero error.

This is because they reach either maximum or minimum density values.

Uniqueness of the solution was not examined closely in this study, however the

greatest change in density during a remodelling increment was limited to half of the

maximum possible value according to Huiskes and co-workers (Huiskes et al., 1992;

van Rietbergen et al., 1993; Weinans et al., 1993). This determined the remodelling

rate, which was kept constant for the remainder of the analysis.

The chaotic behaviour reported with two-dimensional trabecular morphogenesis

studies (Weinans et al., 1992a) was not seen here. This could be related to the

particular remodelling rule, use of higher order elements, and application of the

remodelling rule to the integration points.



The Margron model simulated remodelling results that agreed well with those found

clinically. To demonstrate that the theory was not specific to a particular femur

with a particular implant, remodelling was simulated for two other femora implanted

with two quite distinct implants. This process was also needed to "tune" the dead

zone width. Tuning was performed by comparing the percent change in bone density

predicted by the three models, with the respective 2 year clinical data.

Principal and Equivalent Strains

Preoperative principal strains follow much the same trend for each of the three

prostheses, since all finite element models have the same loading applied. Differences

are probably due to inter-specimen variations in bone density and bone geometry.

Distally, strains are smallest with the 1v1argron femur. This was also the youngest

and smallest femur. Consequently strains could be reduced in this case due to a

small diaphyseal diameter, less femoral head offset and high bone density. The

Epoch femur appears to have fairly constant bending in the coronal plane, rather

than increased bending proximally. This is probably attributable to the geometry

of the femur.

Examining the minimum principal strains along the medial cortex before and

after surgery for the three models, stress shielding is evident proximally in all cases.

The degree of stress shielding can be assessed in terms of the reduction in strain

magnitudes and the distance this effect is propagated distally. All of the implants

caused substantial stress shielding proximally, but this continued for the greatest

distance distally with the Margron implant.

Medial pre- and postoperative equivalent strains were similar to the minimum

principal strains for the Margron, Stability and Epoch models. After remodelling,

the equivalent strains were most changed, compared with the immediately postop

erative situation, for the Margron model, where signals were increased along the

9.3 BONE REr,IODELLING STUDY 238

proximal 40% of the implant. An increase in strain points to a decrease in den

sity, and this was reflected by the Margron losing bone in zones 6 and 7. For the

Epoch and Stability models, the equivalent strains were only altered by remodelling

along the proximal 20% of the respective implants, and accordingly bone loss was

recorded in zone 7, but not significantly in zone 6. Interestingly, the remodelling

signals changed more during the simulation for the Epoch model (7% to 66% of the

preoperative value at the osteotomy) than for the Stability model (18% to 32%),

while the Stability model predicted more bone resorption in zone 7. This implies

that the strain measured at the cortex only gives a partial measure of the internal

strain state of the bone. Higher interface stress with the more flexible Epoch stem

could provoke an osteogenic signal to inhibit resorption.

The different strain distributions for the three implants can be attributed to a

number of factors relating to their material, geometric and interface properties. The

Margron, made from cobalt-chrome, has an elastic modulus around twice that of

the titanium Stability, while the composite Epoch is less stiff again. The Epoch and

Stability both rely on metaphyseal filling with cortical contact medially to provide

some degree of load transfer. Alternatively, the tapered cylindrical Margron stem

initially relies on the two external threads to engage bone for load transfer. Implant

stiffness is related to both material and geometric properties, and is one of the

most significant determinants of stress shielding. The stiffness is dependent on the

elastic modulus and the cross-sectional properties. Axial stiffness is related to the

cross-sectional area (diameter squared), while bending stiffness is proportional to

the moment of inertia, or second moment of area (diameter raised to the fourth

power). While elastic modulus has only a linear effect on stem stiffness, diameter

has a more significant effect, particularly in bending. The distal bending stiffness

of the Stability is decreased by incorporation of a distal slot in the coronal plane

and flutes. The Epoch is more flexible because the rigid cobalt-chrome core has a

relatively small moment of inertia, while the compliant polymer layer has a larger,

but less significant, moment of inertia. Because the Margron does not rely on


filling of the metaphysis for load transfer, the proximal cross-sectional area of the

Margron is actually smaller than the Stability and Epoch stems. The Margron

could potentially be more flexible in this region than the Stability.

Increased proximal bone loading associated with flexible uncemented stems has

been studied at length in the finite element literature. Huiskes et al. (1992) eval

uated stress shielding in a three-dimensional model with 110 GPa (titanium) and

20 GPa (isoelastic), as well as 80 and 50 GPa stems. A nonlinear relationship

was evident, with stress shielding increasing with stem stiffness. The influence of

implant stiffness was most significant for lower modulus stems. This scenario was

also encountered by Cheal et al. (1992) who examined three implant materials for a

collared AML implant model (cobalt-chrome, 234.4 GPa; titanium, 110.2 GPa; and

composite, 51.8 GPa), and by Weinans et al. (2000) looking at 200 GPa (cobalt

chrome), 110 GPa (titanium) and 40 GPa (reduced modulus) implants.

Namba et al. (1998) used a voxel-based model to evaluate a collared stem with

cobalt-chrome or titanium material properties. Von Mises stress below the collar

with the titanium implant was twice that found with the cobalt-chrome stem, how

ever this was still only one-tenth of the intact value, indicating stress shielding was

still pronounced. Stress concentration at the distal tip was also reduced using the

titanium stem. McNamara et al. (1996) found reduced stress shielding proximally

for the lower modulus implant when examining 105 and 210 GPa uncemented stems.

This was also associated with lower distal tip stress concentrations.

Looking at cemented stems, Rohlmann et al. (1987) noted reduced bone stress

in the proximal femur for higher modulus implants when comparing 100, 200 and

400 GPa fully bonded and collared stems. Similarly, Prendergast and Taylor (1990)

compared stresses in the medial calcar using high (200 GPa) and low (25 GPa)

modulus cemented implants. The low modulus (collared) stem produced a stress

distribution most like the intact femur. Using a simplified three-dimensional model

of the diaphysis, Gross and Abel (2001) were able to increase proximal bone stress

by tapering the internal diameter of hollow stems.


The effect of stem stiffness on results from experimental strain gauge studies

is not so clear cut, with sometimes conflicting conclusions. Examining cemented

implants, Oh and Harris (1978) found no difference in cortical strains for 6 ce

mented stem types with variable stiffness. The work of Diegel et al. (1989) found

no significant difference between strains with uncemented stainless steel (200 GPa)

and composite (72 GPa) stems. Simoes and Vaz (2002) examined 5 modified Free

man uncemented stems, with different materials for the proximal and distal parts,

including steel, aluminium and a composite material. Again little variation was

detected between the stems of differing stiffness. Jasty et al. (1994) found little ef

fect of implant diameter on experimental stress shielding. McNamara et al. (1996),

however, was able to distinguish between 105 and 210 GPa uncemented stems in

the experimental setting. The implants were glued into synthetic femora, to repre

sent the fully-bonded contact situation used in finite element modelling. Likewise,

Bobyn et al. (1992) measured axial strains on the medial cortex of femora retrieved

from dogs implanted bilaterally with uncemented cobalt-chrome and hollow tita

nium implants for 3 years. These were compared with normal femora. Strains for

the flexible side were closer to those on the normal femur ( > 75% of intact values)

compared with the rigid side ( < 50%) for the distal three guages levels. These last

two examples show that ingrowth seems necessary to discriminate between different

modulus stems in the experimental setting.

The experimental studies highlight the importance of the implant~bone interface

in load transfer to bone. In finite element modelling, the interface is generally

perfectly matched to the shape of the prosthesis, with implant~bone contact across

large surface areas. In reality, load transfer probably occurs at discrete points, with

separation at other areas. The characteristics of the implant~bone interface have

justifiably been emphasised by researchers as significantly affecting stress shielding

(Diegel et al., 1989; Huiskes and van Rietbergen, 1995; Huiskes et al., 1992; Jasty

et al., 1994; Simoes and Vaz, 2002; Weinans et al., 1994).


Another factor relating to stress shielding is the surface treatment of the implant.

The Margron has an hydroxyapatite (HA) coating over the proximal two-thirds

of its surface, the Stability has a beaded porous coating over the proximal one

third, while the Epoch is fully coated with a titanium fibre mesh. The coatings

are circumferential in all cases. Surface treatment influences the implant-bone

interface, and therefore effects load transfer. The behaviour of these surfaces will

be significantly different in vivo, and will depend on the area available for ingrowth,

and the proportion of this that is actually ingrown.

The effect of extent of coating is quite obvious with the Margron finite element

model when examining the postoperative principal strains. There is a noticeable

increase in medial and lateral strain towards the distal coating junction, at which

point the strains begin to decrease again. The model with the one-third coated Sta

bility stem shows the medial strains increasing more proximally, with peak strains

again around the level of the distal coating interface. A similar situation is evi

dent for the Epoch stem, although the proximal load transfer is probably due to

increased flexibility.

Using an anatomic finite element model, Keaveny and Bartel (1993a) analysed

the influence of the extent of porous coating for fully coated, partially coated (two

thirds), and uncoated AML stems. The interface was modelled with friction in the

region of coating, allowing for separation. Load transfer was influenced by surface

coating, with more transfer of axial loads related to reduced coating area. Using

the two-thirds coated implant, Keaveny and Bartel (1995) showed that ingrowth

substantially decreased proximal load transfer. Axial loading of the proximal bone

decreased from 68% with no ingrowth to 20% for ideal ingrowth. Skinner et al.

(1994b) investigated proximal, five-eigths and fully bonded AML implants with a

voxel-based model. With collar contact, the extent of porous coating had negligible

effect on bone stress proximal to the lesser trochanter, although the distal stress

concentration was reduced with the fully coated implant.


Experimental studies investigating the effect of porous coating area on load

transfer are scarce, most likely because strain gauge studies are not sufficiently

sensitive to detect differences. For instance, Gillies et al. (2002) found no significant

difference between cortical strains measured on a femur implanted with the Stability

hip with a the proximal surface smooth, with steps, or steps and porous coating.

Bone Density

Significant correlations were once again found between the percentage changes in

bone density in the Gruen zones predicted by the model and the 2 year clinical

data. The average difference between the bone density changes was 3.4%, with a

maximum of 7.4% for the Stability model, and 3.9%, with a maximum of 7.8%

for the Epoch. These results signify that one consistent theory is able to predict

bone adaptation around three dissimilar femoral prosthesis designs in three different

femora.

The predicted changes in BMD around the Stability and Epoch hip replacements

agreed extremely well with the clinical data. Resorption was underestimated by

the simulation to a small degree laterally for the Stability in zones 1 and 2, and

overestimated slightly in zone 5. With the Epoch, increased bone density was seen

in zones 1 and 2, rather than resorption as detected clinically, while bone loss was

underestimated in the medial Gruen zones. These results would all fall within

the range of clinical data, and differences could be attributed to inter-specimen

variation. Underestimation of bone resorption in the lateral zones could also be due

to the reasons described in relation to the Margron hip prosthesis.

Karrholm et al. (2002) have reported DEXA data for 20 cases of the Epoch stem,

although in this study the proximal two-thirds of the implant was hydroxyapatite

coated. Median, rather than mean changes in bone density are presented, as well as

a range of values. The simulated remodelling changes all fit within the range of data,

as do the results reported by Glassman et al. (2001). In fact Karrholm measured

a median decrease in BMD in zone 7 of 15%, compared with a mean change of


15.8% by Glassman. The Epoch DEXA data from Ki:irrholm et al. (2002) was also

compared with the titanium, one-third porous, two-thirds HA coated Anatomic hip

(Zimmer, Warsaw, IN, USA). Significantly less bone resorption took place in zones

1, 2, 6 and 7 with the Epoch at 2 years. No published clinical data is available for

the Margron or Stability hips.

The influence of implant stiffness on bone remodelling has been examined with

in vitro and in vivo studies. Huiskes et al. (1992) simulated remodelling around

110 GPa (titanium) and 20 GPa (isoelastic) stems. The isoelastic stem decreased

total bone loss from 23% to 9%. Weinans et al. (1992b) also found a reduction

in bone loss for more flexible implants when using a two-dimensional side-plate

finite element model and non-site-specific remodelling theory with cobalt-chrome

(210 GPa), titanium (110 GPa) and hypothetical isoelastic (20 GPa) implants. The

cobalt-chrome stem generated severe resorption in the calcar region (76%), com

pared with the titanium (54%) and isoelastic (7%) stems. Bone loss in the proximal

lateral region was also pronounced for the cobalt-chrome (45%) and titanium (38%)

stems.

As with the experimental strain gauge studies, the literature is inconclusive when

considering the in vivo effect of prosthesis flexibility. Engh et al. (1987) considered

stem diameter with the AML implant to be most important factor with respect to

stress shielding, and Engh and Bobyn (1988) noted that stem diameters~ 13.5 mm

led to 5 times the incidence of pronounced resorption sites around AML stems at

2 years, than smaller diameter implants. In a further study, Engh et al. (1990)

detected a statistically significant difference between the occurrence of moderate

and severe stress shielding for stem diameters larger than 13.5 mm.

Bobyn et al. (1990) compared cobalt-chrome and hollow titanium stems in a

bilateral canine study. Consistently increased resorption was found after 2 years

in situ on the stiff stem side, characterised by cortical thinning and reduction in

cortical cross-sectional area. They concluded that stem stiffness strongly influences

resorptive bone remodelling. Bobyn et al. (1992) examined longer term (3 year) data


and found larger differences between the femora. Differences obtained by DEXA

measurements were also larger than geometric changes. Sumner and Galante (1992)

reported similar results, with 50% less reduction in proximal cortical area and no

evidence of distal hypertrophy for dogs implanted with porous coated composite

stems for 6 months, compared with titanium alloy stems.

Not all studies have described a reduction in bone mineral content due to more

flexible implants. Initially with 11 (Sychterz and Engh, 1996), and later with 40

(Sychterz et al., 2001) autopsy-retrieved femora with unilateral AivfL implants, no

significant correlation could be found between stem stiffness parameters and bone

loss. It was thought that large variations in femoral bone mineral content between

subjects may have masked this effect. Hughes et al. (1995) compared cobalt-chrome

and titanium stems with similar geometry, and found little effect of stem modulus,

except at Gruen zone 7. Harvey et al. (1999) compared titanium and composite

implants with similar geometry. No clear decrease in stress shielding was associated

with the flexible stem, as determined by changes in cortical area and porosity.

Moreover, some researchers have proposed that there is little clinical advantage of

titanium over cobalt-chrome as an implant material (Jacobs et al., 1993; Jones and

Kelley, 2001; Mont and Hungerford, 1997).

One of the factors reported to contribute significantly to bone resorption sec

ondary to stress shielding is the ratio of implant-to-bone stiffness (Bobyn et al.,

1990; Huiskes et al., 1992; Jacobs et al., 1992; McGovern et al., 1994; Sumner and

Galante, 1992; Sychterz et al., 2001). This ratio applies to both axial and bending

stiffnesses. High stiffness ratios will be associated with low stiffness bone, which is

likely to undergo more bone loss than more rigid tissue implanted with the same

prosthesis. In fact a strong correlation has been identified between bone loss and

bone mineral content in the unoperated femur (Engh et al., 1994, 1992a; Sychterz

and Engh, 1996).

The implant-bone interface is important in load transfer, particularly with re

spect to experimental evaluation of stress shielding. Likewise, the extent of ingrowth


will effect the transfer of load to the bone. Remodelling simulations predict bone

density changes consistent with increased proximal load transfer with reduced coat

ing area. Weinans et al. (1994) predicted higher bone loss for a fully coated implant

compared with a reduced coating area, using a two-dimensional side-plate finite

element model, coupled with non-site-specific remodelling theory.

Huiskes and van Rietbergen (1995) investigated the effect of coating area with a

three-dimensional finite element model of a femur implanted with the Omniflex stem

(Osteonics, Allendale, NJ, USA). This was coupled with the remodelling theory from

Huiskes et al. (1992). Fully coated, one-third coated, stripe coated and uncoated

variations were analysed. The uncoated stem reduced bone loss dramatically, but

increased interface motions. The fully and proximally coated stems produced similar

levels of bone loss, although this may be related to the implant design, with a

tapered stem and larger distal tip to prevent toggling. In the fully coated case,

the coating on the distal part of the implant does not come into contact with

the diaphyseal cortex, and therefore this coating does not significantly alter load

transfer. The stripe coated implant produced improved bone retention, but was not

considered as a good clinical option.

Somewhat variable results have been reported in clinical studies when comparing

fully and partially coated implants, making it difficult to draw conclusions. Engh

and Bobyn (1988) examined the influence of extent of porous coating in 411 hip

replacements with the AML stem at 2 years. Radiographic evaluation showed 2~4

times the incidence of pronounced resorption (more than 5 sites) with two-thirds and

fully coated AML stems, compared with one-third coated. However, the number of

proximal resorption sites for the one-third coated stems was higher than for two

thirds, indicating that the gain in bone stock appears to occur in the uncoated

region. Further radiographic examination of 670 primary Al'viL stems (Engh et al.,

1990) showed that the level of porous coating had a significant effect on the incidence

and severity of stress shielding, with approximately three times the incidence of

moderate and severe stress shielding for extensively coated implants compared with


proximally coated. However, in a retrospective analysis of 507 unselected patients

with extensively coated AML stems, McAuley et al. (1998) asserted that proximal

bone loss secondary to stress shielding was not associated with a decrease in patient

function or satisfaction, nor related to thigh pain.

Yamaguchi et al. (2000) evaluated the cobalt-chrome Anatomical Hip Endopros

thesis (System Lubeck, S & G Implants, Lubeck, Germany) with full and partial

porous coatings in a total of 61 patients. BMD measurements were made by DEXA,

and significant differences were found in zones 3 and 6 only, with partially coated im

plants losing more bone distally. Results were similar in the proximal regions. This

is in contrast to the AML results, where the partially coated stems were associated

with increased distal bone stock (Engh and Bobyn, 1988).

Sumner and Galante (1992) performed fully and partially coated uncemented

hip arthroplasty in dogs. Proximally coated implants did not decrease cortical bone

loss proximally, and had only a negligible effect distally. At 6 months, proximally

coated stems were associated with less bone loss, however at later time points, bone

loss was similar. Fully coated stems may provoke accelerated bone loss, although

not to a greater extent in the long term.

The influence of hydroxyapatite coatings augmenting implant fixation is yet to

be fully assessed. Clinical success with HA coated implants has been reported by

many (e.g., D'Antonio et al., 1996; Skinner et al., 2003; Tanzer et al., 2001; Yee

et al., 1999). Low failure rates of modern uncemented implant designs will make

it difficult to establish the clinical benefits of HA coating (Mont and Hungerford,

1997), however it has been proposed that although clinical scores and stem sur

vivorship may not be significantly improved by HA coating (Tanzer et al., 2001;

Yee et al., 1999), it may provide a superior barrier to migration of debris particles

(D'Antonio et al., 1996; Skinner et al., 2003; Tanzer et al., 2001; Tonino et al.,

1999). HA coating may also speed up the process of ingrowth in the short term

after surgery, enhancing initial fixation.


Interestingly, Aebli et al. (2003) retrieved a proximally HA coated ABG stem

(Howmedica, Staines, UK) after 9.5 years in situ, and discovered that the HA

coating had completely degraded, with bone in direct contact with the titanium

surface in all areas that had been coated. This did not appear to have any negative

effect on ingrowth of the stem, and degradation did not adversely affect the long

term fixation. Tonino et al. (1999) retrieved 5 of the same ABG stems after 3.3-6.2

years in situ. Disintegration of the HA coated was observed again, and the greatest

amount of residual HA was found in the distal metaphyseal region. The coating

was lost proximally, in the region of greatest bone resorption, suggesting that HA

removal may be related to the remodelling process.

Strain-adaptive bone remodelling secondary to stress shielding is influenced by

the implant-bone interface characteristics (fit, bonding, coating area), implant stiff

ness (material and geometric properties) and initial bone stiffness. The differences

in bone density changes seen with the three implants analysed in this study, both

in the clinical and simulation results, can mostly be attributed to a combination of

these factors. Each implant design varied considerably, as did the extent of proximal

bone loss. Although proximal bone loss is a concern, lack of clinical data makes it

difficult to tell if this will influence implant stability in the long term.


Simulation of bone remodelling changes following hip replacement surgery are de

pendent on a variety of factors including implant stiffness, bone stiffness, interface

characteristics and the remodelling rule itself. The effects of these parameters have

been discussed in some detail already, although some of them are investigated fur

ther here. There are a number of other variables that can be examined, which are

not directly related to the implant design.



The three interface conditions that were examined produced very similar remod

elling simulation results. Proximally, the strain distributions were identical for the

three conditions, with all displaying the same degree of stress shielding. Distally, the

contact conditions produced quite different strain distributions, however they were

all within, or close to the dead zone threshold, and therefore very little remodelling

occurred here.

The lack of any significant difference between the contact conditions implies that

either of the three variants can be used for further investigation, and therefore the

choice should come down to other factors like computation time.

The effect of the extent of fixation area has been previously discussed above,

in terms of its effect on bone stress and also clinical outcome. Additional proxi

mal bone loss is reported for extensively coated implants, however proponents of

these prostheses argue that superior initial fixation distally, and lack of any clinical

implications associated with non-progressive bone resorption, make them suitable

(McAuley et al., 1998; Nourbash and Paprosky, 1998). Removal of the implant at

revision is a problem, particularly with well fixed, extensively coated implants.


Modular hip systems allow for selection of the optimum femoral head position in

cluding medial offset, vertical height and version angle, to restore normal joint

biomechanics and provide stability. The degree of variability depends on the sys

tem in question. Most hip systems allow offset and height to be altered together

by choosing a femoral head with the appropriate neck length. An increased offset

version of the stem is usually available, e.g., Taperloc (Biomet, Warsaw, IN, USA)

( Sakalkale et al., 2001), or in some cases a modular neck to select offset and version

angle, e.g., Margron and ANCA Fit (Cremascoli, Milano, Italy) (Sakai et al., 2002).

Head position can be chosen to modify soft tissue tension, joint stability and leg


length. Implant malposition, along with soft tissue imbalance, are the major factors

contributing to hip dislocation (Dorr and Wan, 1998).

In this study, version angle and neck length were varied to study their influence

on periprosthetic bone remodelling. Increased neck length was found to decrease

bone loss in the proximal Gruen zones, with little effect distally. Although the

greatest effect on medial bone strain was seen distally due to the increased moment

arm for bending in the coronal plane, the strains were still within the physiological

range represented by the dead zone, and therefore bone density in zones 3~5 was

unchanged.

Anteversion, relative to the physiological position, generally produced more bone

loss than retroversion. Gill et al. (2002) showed that decreasing the version angle

increases the moment arm (in the horizontal plane) for internally rotating torque.

The moment arm for bending in the coronal plane is also increased for lower version

angles, and is evident from the larger medial strains just after surgery. These larger

moments increase bone strains and lead to a reduction in bone resorption, as was

found in the current study.

The study by Gill et al. (2002) and the current investigation assumed that the

hip joint contact force is unchanged with femoral head position. However muscle

forces, and therefore the joint reaction force, are altered by the change in head

position. Using a biomechanical model, Johnston et al. (1979) showed that increased

neck length reduces the abductor moment arm, which decreases the joint contact

force, but increases the moment on the implant. With gait analysis, Heller et al.

(2001a) reported that the joint force and coronal plane bending moment increase

with increased anteversion after surgery. This was particularly evident for increases

over 20°, relative to the preoperative condition. With 30% of extra anteversion, the

hip contact force was up to 24% greater and the coronal plane bending moment

up to 14% greater in some cases. Decreasing the version angle by 5° was also

investigated, although this had little effect on the hip contact force and bending

moments.


Using an equilibrated muscle and joint force set representing 15% of the gait cy

cle, Kleemann et al. (2003) examined the influence of version angle and medial offset

on bone and cement strains using finite element modelling. Increasing prosthesis

anteversion by 20% caused higher muscle and joint contact forces, with surface bone

strains increased up to 16%. Greater offset of +4.8 mm reduced joint and muscle

forces, but increased bone strains by up to 5%, due to the longer moment arm.

The effects of neck length/offset, when the forces are re-calculated for equilib

rium, are essentially cancelled out, because the coronal plane moment arm and joint

reaction force are inversely related. Bone remodelling aspects of offset may be less

important than other clinical factors. Sakalkale et al. (2001) compared standard

and increased offset versions of an uncemented stem. They found that the greater

offset stem had half the polyethylene linear wear rate. The increased offset stem

in fact reproduced the preoperative offset better than the standard stem, which on

average had an smaller offset than the natural state. Increasing offset can tighten

soft tissue and increase stability, without altering leg length. Increased offset also

improves range of abduction and abduction strength (McGrory et al., 1995). Ab

duction strength is enhanced by an increased lever arm for the abductor muscles.

Version angle is also important for stability and range of motion at the hip joint.

Increased anteversion beyond the anatomical position may result in anterior sub

luxation of the femoral head with the hip in extension and external rotation, while

retroversion may cause posterior dislocation when the hip is internally rotation. Ori

entation of the femoral component is however, less critical than orientation of the

acetabular component (McCollum and Gray, 1990). D'Lima et al. (2000) showed

that too little anteversion of the femoral (or acetabular) component decreases the

range of motion in flexion, while too much anteversion reduces extension and ad

duction movements.

9.3 BONE REiviODELLING STUDY 251


The dead zone width controls the width of the physiological range of strains within

which there is no stimulus for bone adaptation. Altering the dead zone width

provokes a fairly predictable response: increasing the width increases the strain

threshold, meaning a greater deviation in strain away from the normal state to

provoke adaptation, and therefore less remodelling. Decreasing the dead zone width

has the opposite effect.

When the dead zone was altered for the Margron simulations, the changes in

density were proportional to the change in dead zone, for the range of widths ex

amined. This parameter was tuned to obtain the best fit of the simulations to the

clinical data. The dead zone width was also varied with the Epoch and Stability

simulations, to find a single value that matched all three models with their respec

tive clinical density changes. The most suitable quantity for the dead zone width

was s = 0.6, or ±60% of the natural strain. Further investigations with other im

plants and/or femora may reveal a slightly different value, say between 0.55 and

0.6.

The effect of dead zone width on bone loss reported in this study is similar to

that described elsewhere. The model developed by Huiskes et al. (1992) employed a

dead zone width of 0. 75, with strain energy density per unit mass as the remodelling

signal. In canines, a width of 0.35 gave better results (van Rietbergen et al., 1993;

Weinans et al., 1993). The effect of reducing the dead zone width from 0.75 to

0.35, with a human femur, increased total bone loss from 23% to 41% Huiskes et al.

(1992). In the proximal region, bone loss increased from 67% to over 80% for the

smaller dead zone width.


In previous bone remodelling simulations reported in the literature, it has always

been assumed that postoperative loading was identical to that experienced before

arthroplasty. It is likely that this is not the case, due to pain and difficulty of


movement before surgery, or the rehabilitation protocol after surgery. The effect

of reducing the postoperative loads experienced by the femur by 10% after surgery

was to produce additional bone loss in the proximal Gruen zones. The equivalent

strain values obtained along the medial cortex were reduced, with most differences

distally. At remodelling equilibrium, the strains adjacent to the proximal 40% of

the implant were the same as those with 100% of the preoperative loading, however

more bone loss was needed to get there.

This was a simple example to demonstrate the effects of postoperative activity

level on bone density changes in agreement with "Wolff's Law", and have not been

described before. More complex rehabilitation protocols, for example involving

gradually increasing loads during the months after surgery, could be examined in

this manner.


The effect of prosthesis stiffness was evaluated with the Epoch stem. The standard

Epoch was compared with two other models with identical geometry, but different

material properties. One model was a fully cobalt-chrome version of the Epoch

stem, and the other an isoelastic version with the elastic modulus of cortical bone.

Proximal stress shielding was most pronounced for the higher modulus stem. This

is due to greater load carrying by the more rigid implants, as predicted by simple

composite beam theory (Huiskes, 1996; Silva et al., 1999). Rigid implants were as

sociated with more extensive bone loss in the calcar region, which has been reported

in clinical and theoretical studies.

The influence of prosthesis stiffness on periprosthetic bone remodelling is dis

cussed in some detail above. The results here agree with these studies, indicating

more flexible implants retain more proximal bone. Finite element studies assume

ideal implant-bone interfaces, with fully bonded contact in most cases. In reality,

ingrowth of an uncemented femoral prosthesis depends on the initial stability of the

implant-bone interface. Too much movement at the interface leads to formation of


fibrous connective tissue, rather than ingrowth of bone (Callaghan, 1993; Kienapfel

et al., 1999). Micromotions of up to 40 Jtm reportedly allow bone ingrowth (Burke

et al., 1991).

The effect of the prosthesis stiffness on the immediately postoperative interface

stress was examined. The area of high stress was the most important difference,

with the largest area for the isoelastic material properties, and the lowest for the

cobalt-chrome. A distal shear stress concentration was also evident for the cobalt

chrome case. These results were in agreement with the literature, where increased

proximal interface stresses associated with reduced stiffness implants have been

reported in a number of finite element investigations (Cheal et al., 1992; Huiskes,

1990; Huiskes et al., 1992; Weinans et al., 1992b). Although Harrigan et al. (1988)

showed that continuum modelling of bone is not valid at implant interfaces for exact

values of stress, it is probably sufficient for comparisons. Huiskes (1990) found

that for a fully coated Omnifit stem (Osteonics, Allendale, NJ, USA), proximal

interface stress increased by 60% for a titanium stem compared with cobalt-chrome,

while distal interface stresses decreased by 8-21%. Similarly Cheal et al. (1992)

calculated interface stress for fully coated AML stems with cobalt-chrome, titanium

and composite properties. Again, proximal interface stresses increased with the

more flexible implants whilst distal interface stresses decreased.

High shear stress at the implant-bone interface increases the probability of inter

face failure, leading to fibrous tissue formation and accumulation of wear particles

due to abrasion (Huiskes, 1993a). Harvey et al. (1999) compared titanium and com

posite implants with similar geometry. No clear decrease in bone loss was observed,

however bone ingrowth was reduced for the composite implant with three times

more radiopaque lines, indicative of fibrous tissue formation. It is apparent that

stress shielding and interface stress represent conflicting design requirements that

are both dependent on the stem stiffness. Interface stress is also influenced by the

area available for bone ingrowth, however in this case, the area was not examined.


9.3.4 Limitations

Limitations with the remodelling simulations presented here can be classified into

those related to the finite element modelling and those related to the remodelling

theory. The results from any finite element analysis depend on the simplifying as

sumptions made. In this case, bone was assumed to be a linear elastic, isotropic

continuum. Cortical and cancellous bone were assumed to be the same material,

differing only by apparent density. Although the elastic modulus-apparent density

relationship may effect exact values, Weinans et al. (2000) showed that for subject

specific finite element models, the difference between subjects was essentially inde

pendent of the elastic modulus-density relationship. Other simplifications relate to

the removal of surface features on the implants and modelling of the implant-bone

interface.

The type of remodelling rule applied here is limited to studies of adaptation

from one equilibrium density distribution to another (Huiskes and Hollister, 1993).

It is not suitable for simulation of bone growth and development, or surface drifts

produced by modelling. The remodelling rule only accounts for internal remodelling,

and does not predict changes in geometry. This may be important when comparing

results with clinical data obtained from DEXA measurements.

Under complete disuse, this remodelling theory would eventually predict total

bone resorption, beyond a genetic baseline value. At the other end of the spectrum,

bone apposition proportional to loading is predicted. Realistically, there is a limit to

the rate at which lamellar bone can be created, with high strains leading to woven

bone formation. In pathalogical overload situations, bone resorption occurs. This

is possibly related to accumulation of fatigue damage leading to impaired cellular

inhibition of remodelling (Martin, 2000).

Prendergast (2002) proposed a remodelling rate curve that includes the effects

of strain and damage mediated remodelling (Figure 9.1). This is similar to the

piecewise linear curve employed in the current study for strains below the threshold

for damage accumulation, E'MDx-thresh, where the slope of the resorption part of the


dm dt

tMDx-thresh

! Em in

Figure 9.1: Nonlinear mechanoregulation rule including strain and damage mediated pathways. Adapted from Prendergast (2002).

curve is steeper than the deposition part. The damage threshold is reached when the

remodelling repair process is unable to keep up with the accumulation rate, in which

case bone resorption occurs. This curve represents less of a simplification, however

introduction of more parameters means that the number of assumptions would

rise. A remodelling rule including damage mediated adaptation would certainly

be necessary if a situation with large increases in strains after surgery were to be

simulated.

This theory only considers the mechanical aspects of bone adaptation. Other

metabolic and hormonal factors also influence bone remodelling, while osteolysis due

to wear particles can have a pronounced effect on periprosthestic bone density. It

has been suggested that bone remodelling secondary to stress shielding may actually

make the femur more prone to debris-induced osteolysis (Huiskes, 1993b). Further

modification to the model would be required to include these effects.

There is some degree of uncertainty involved with the finite element modelling

and the adaptation algorithm, due to simplifying assumptions and biological vari

ability. A approach to address these uncertainties would be to employ fuzzy logic.

This has previously been applied to simulation of fracture repair (Ament and Hofer,

2000) and prediction of cancellous bone structure (Luo et al., 2000). With fuzzy


rules, it is also possible to include multiple factors in a model. Nevertheless, the cur

rent model has been able to predict clinically relevant density changes in response

to a mechanical stimulus alone.

Chapter 10

Conclusions

This thesis examines the stress distribution and remodelling of a femur implanted

with the Margron hip prosthesis. The femoral stress distribution, pre- and post

operatively, was analysed using experimental strain gauge and finite element meth

ods. The finite element models were subsequently coupled with strain-adaptive

remodelling theory to predict bone density changes due to stress shielding. Density

changes were compared with radiographic data from clinical studies. Additional

finite element models with hip prostheses having different designs (Stability and

Epoch) were also created. Remodelling was simulated in the bone around the

stems, and compared with clinical studies. Some parameters associated with the

finite element models and the remodelling theory were then investigated.

The femoral strain distribution determined experimentally and by finite element

modelling showed severe stress shielding at the proximal-medial cortex for the femur

implanted with the Margron prosthesis. Finite element analysis of the Stability and

Epoch showed similar degrees of stress shielding towards the level of the osteotomy,

however strains distal to this level were observed to increase more quickly with these

two stems.

Remodelling with the l\ilargron prosthesis simulated bone density changes in the

seven Gruen zones that correlated with those found in a clinical DEXA study at 1,

2 and 3 years postoperatively. This has not been reported previously. Simulations

257

10. CONCLUSIONS 258

with the Epoch and Stability were compared with radiographic clinical data at 2

years, and both also correlated strongly and significantly across the Gruen zones.

Small differences between the simulated and clinical results may be attributable to

the choice of loading, representation of the implant-bone interface, bone geometry

changes, DEXA measurement errors, and preoperative bone mineral content. It is

important to remember that subject-specific models are being compared with the

average change in density for a population of patients. Therefore, the percentage

changes in bone mineral density at each Gruen zone should not necessarily be equal

to the mean of the population. Nevertheless, the trends predicted across the Gruen

zones were similar to those found clinically.

The remodelling simulations were based on a purely mechanical stimulus that

was equivalent strain, equal to the magnitude of the strain tensor. The fact that

the simulations agree so well with the clinical data implies that stress shielding

is the major cause of proximal-medial bone loss, and that implant-dependent de

sign factors-such as material, geometric and surface treatment properties-are

extremely important in determining the extent of bone remodelling.

The Margron model was used to examine a number of parameters, with the

following results:

• Of the implant-bone interface contact conditions that were modelled, these

had little effect on the bone density predictions.

• Prosthetic femoral head position had a significant effect on density changes,

however a new equilibrium condition for all of the joint and muscle forces

should be re-calculated for the results to be clincally relevant.

• Dead zone width altered the sensitivity of the bone to the change in the me

chanical environment after surgery. Increasing the dead zone width increased

the range of strains for which no remodelling was stimulated, decreasing the

amount of bone resorption.

• Reducing the postoperative activity level, 1.e., the magnitude of the forces

after surgery, increases bone loss in the proximal Gruen zones.

10.1 RECOMMENDATIONS 259

The influence of prosthesis flexibility was examined with the Epoch femoral

prosthesis. Decreased stiffness enhanced bone retention postoperatively. However,

proximal interface stress was substantially increased for the isoelastic stem, which

could cause interface failure or fibrous tissue formation in vivo. A distal stress

concentration was evident for the cobalt-chrome stem.

The aim of this thesis was not to propose that one implant was superior to

the other. The choice of implant is dependent on many patient-specific factors

including age, bone quality and bone geometry, and therefore an implant that is

successful for one patient may not be appropriate for another. In the future, it

may be possible to predict which implant is better for the individual, in terms of

preserving long term bone stock, by running a number of simulations with different

implants in a patient-specific finite element model created from CT scans of the

subject. This relies to some extent on the continued development of fast automatic

mesh generation method, as this is currently the most labour intensive part of the

process. Although this technology currently requires considerably user input and

would therefore be expensive, it may help select the optimum femoral component for

a patient. Of course implant fixation must be assured and the acetabular component

must also perform for the surgery to be effective.

10.1 Recommendations

Further investigation is warranted for some aspects of the remodelling theory de

veloped in this study, including the reliability of the current method, investigation

of other parameters, and potential modifications to the theory. Aspects relating to

the reliability of the method include:

• Simulating remodelling with other femora containing the three implants ex

amined here. This ensure that the correct value of the dead zone width has

been selected.

10.1 RECOMMENDATIONS 260

• Simulating remodelling with other implants than have clinical DEXA data

available to assess the robustness of the theory.

• Closer examination of the remodelling time frame. In this study, it was com

pared with the radiographic clinical measurements at 1, 2 and 3 years for the

Margron model and 2 years with the others, however only to the nearest 10

remodelling increments. This will only have a small effect for the first few

years, but will become more significant at later time points.

Parameters that would be interesting to investigate further using the current theory

include:

• Examining the influence of rehabilitation protocols on bone adaptation. A

large proportion of bone loss occurs during the first 6 months after surgery.

Patient activity during this time may have a significant effect on bone remod

elling.

• Determining the effect of altered musculoskeletal loading after surgery. For

example, the lateral approach to the hip has the potential for damage to

the superior gluteal nerve, impairing function of the anterior third of gluteus

medius, tensor fasciae latae and gluteus minimus. This outcome could be

investigated using a remodelling simulation.

The remodelling theory could also be expanded to include other modulators of bone

adaptation, such as:

• The local effects of systemic influences including hormones, nutrition, age and

drugs. These factors might alter the dead zone width, the magnitude of the

reference strain (as perceived by the cells) or the remodelling rate.

• The cumulative effects of osteolysis and/ or fatigue microcracks.

These recommendations are beyond the scope and/ or time frame of the current

study.

This research indicates that the proposed bone remodelling theory may be appro

priate for predicting time-dependent, internal bone remodelling changes in subject

specific finite element models. This theory may also provide an implement for

10.1 RECOMl\fENDATIONS 261

pre-clinical assessment of new implant designs and modifications to existing prod

ucts.

Appendix A

Experimental Strain Gauge Data

The following tables contain the minimum and maximum principal strains and the

longitudinal strains for the four experimental femora. Preoperative and postopera-

tive strains are given for load cases 1 and 2. Average and standard deviations are

presented for each gauge location (1-16).

Table A.1: Preoperative minimum principal strains (Load case 1).

Gauge No Femur A Femur B Femur E Femur F Average Std Dev

1 -879.2 -576.4 -714.4 -794.6 -741.2 128.8 2 -632.9 -628.8 -216.2 -604.7 -520.7 203.3 3 -512.9 -578.4 -45.4 -545.8 -420.6 251.6 4 -369.2 -442.5 -456.9 -359.1 -406.9 49.9 5 -239.4 -243.1 -172.7 -176.7 -208.0 38.5 6 -40.5 -180.0 -50.4 -192.3 -115.8 81.5 7 -12.3 -47.4 -12.3 -11.1 -20.8 17.7 8 -27.8 -45.1 -71.1 -20.6 -41.1 22.5 9 -136.4 -172.8 -140.7 -210.9 -165.2 34.5 10 -200.5 -147.8 -147.2 -131.7 -156.8 30.1 11 -160.7 -126.3 -168.3 -97.9 -138.3 32.6 12 -103.1 -95.1 -138.8 -73.4 -102.6 27.2 13 -209.0 -112.7 -103.4 -104.0 -132.3 51.3 15 -231.4 -320.0 -116.3 -222.0 -222.4 83.4 16 -181.4 -374.1 -112.7 -298.5 -241.7 116.9

262

A. EXPERIMENTAL STRAIN GAUGE DATA 263

Table A.2: Preoperative minimum principal strains (Load case 2).


1 -850.0 -539.8 -617.0 -749.1 -689.0 137.8 2 -667.3 -689.6 -234.6 -563.8 -538.8 210.1 3 -532.4 -530.4 -56.6 -499.7 -404.8 232.6 4 -343.0 -288.8 -410.1 -293.9 -333.9 56.3 5 -288.3 -296.1 -204.5 -179.0 -242.0 59.0 6 -106.8 -150.1 -81.5 -450.7 -197.3 171.3 7 115.4 -180.5 -171.3 -171.1 -159.6 29.8 8 -154.1 -256.4 -186.9 -247.3 -211.2 49.0 9 -132.8 -131.9 -106.6 -183.3 -138.7 32.1 10 -192.4 -129.1 -119.7 -139.4 -145.2 32.5 11 -140.5 -149.8 -132.1 -126.9 -137.3 10.0 12 -126.8 -132.7 -166.9 -141.1 -141.9 17.7 13 -128.0 -88.8 -125.9 -112.4 -113.8 18.0 14 -410.8 -352.1 -396.8 -376.7 -384.1 25.5 15 -476.1 -779.6 -486.2 -587.1 -582.3 140.8 16 -484.6 -1038.7 -741.6 -798.4 -765.8 227.5

Table A.3: Preoperative maximum principal strains (Load case 1).


1 182.7 128.7 163.4 136.8 152.9 24.8 2 209.8 172.3 167.4 174.3 180.9 19.4 3 211.0 200.2 22.8 166.7 150.2 87.0 4 157.4 139.7 164.8 112.1 143.5 23.4 5 125.9 57.1 62.7 -34.2 52.9 65.9 6 80.3 63.7 33.5 93.7 67.8 25.9 7 28.9 37.8 14.5 24.6 26.4 9.7 8 49.2 98.2 49.0 50.7 61.8 24.3 9 377.2 324.8 308.6 265.0 318.9 46.3 10 564.0 494.1 341.9 355.9 439.0 108.0 11 437.0 450.2 349.9 323.5 390.1 62.9 12 300.1 257.8 259.8 194.8 253.1 43.5 13 254.2 164.0 203.4 157.6 194.8 44.5 14 73.0 40.3 83.0 39.5 58.9 22.4 15 98.5 112.9 53.6 109.5 93.6 27.4 16 95.0 143.7 52.2 126.4 104.3 40.2


Table A.4: Preoperative maximum principal strains (Load case 2).


1 150.0 90.3 133.3 131.8 126.4 25.4 2 250.4 344.2 203.9 178.5 244.2 73.0 3 233.1 220.5 34.5 156.6 161.2 90.8 4 183.5 139.7 193.4 106.8 155.8 40.2 5 216.4 276.0 219.8 -26.8 171.3 134.9 6 252.5 269.1 180.7 294.7 249.2 48.9 7 272.8 446.0 368.5 441.8 382.3 81.2 8 385.0 633.2 453.7 491.7 490.9 104.6 9 324.7 317.9 254.9 249.4 286.7 40.1 10 545.4 478.3 299.7 442.3 441.4 103.7 11 389.5 463.5 321.1 454.2 407.1 66.1 12 291.4 327.3 263.6 376.0 314.6 48.5 13 146.7 78.8 108.2 116.0 112.4 27.9 14 139.2 87.0 97.1 84.3 101.9 25.5 15 201.3 274.9 175.8 248.1 225.0 44.7 16 230.0 389.1 270.4 333.6 305.8 70.0

Table A.5: Preoperative longitudinal strains (Load case 1).


1 -753.0 -564.8 -702.8 -778.9 -699.9 95.5 2 -613.8 -623.9 -155.1 -602.3 -498.8 229.3 3 -463.3 -568.1 -37.1 -540.3 -402.2 247.4 4 -366.9 -441.9 -451.3 -358.2 -404.6 48.8 5 -54.6 -117.3 -7.4 -160.0 -84.8 67.4 6 12.2 -156.9 -45.0 -172.7 -90.6 89.0 7 -2.8 -16.1 -9.8 8.3 -5.1 10.5 8 40.0 97.5 -39.4 46.3 36.1 56.6 9 366.9 321.8 308.3 263.0 315.0 42.8 10 560.1 471.2 323.5 355.8 427.7 108.7 11 430.8 442.5 337.0 320.5 382.7 62.9 12 298.7 257.7 239.0 192.0 246.8 44.3 13 35.0 25.1 16.1 58.5 33.7 18.3 14 -198.5 -103.9 -87.4 -100.6 -122.6 51.1 15 -213.0 -302.6 -106.2 -221.5 -210.8 80.6 16 -170.0 -364.8 -105.9 -294.9 -233.9 117.4


Table A.6: Preoperative longitudinal strains (Load case 2).


1 -791.7 -538.8 -612.5 -739.9 -670.7 115.8 2 -612.3 -603.4 -129.2 -557.7 -475.6 232.2 3 -457.8 -498.2 -41.0 -487.4 -371.1 220.7 4 -322.0 -254.1 -390.1 -284.6 -312.7 58.6 5 -26.6 54.9 133.3 -165.0 -0.9 127.4 6 175.4 185.6 125.0 -145.2 85.2 155.9 7 252.8 445.2 354.6 385.4 359.5 80.5 8 376.1 627.7 453.2 466.5 480.9 105.7 9 298.2 317.9 253.9 249.1 279.8 33.7 10 545.4 467.0 293.7 439.4 436.4 105.2 11 373.0 463.5 320.9 427.2 396.1 62.4 12 264.9 316.2 262.5 361.3 301.2 47.1 13 -9.2 -87.1 -120.1 -84.3 -75.2 46.9 14 -353.1 -304.0 -360.5 -367.4 -346.3 28.8 15 -434.9 -738.6 -441.0 -587.1 -550.4 143.9 16 -466.6 -1017.4 -730.4 -783.0 -749.3 226.0

Table A.7: Postoperative minimum principal strains (Load case 1).


1 -34.9 -36.2 -20.2 -39.2 -32.6 8.5 2 -194.0 -210.5 -63.4 -187.7 -163.9 67.7 3 -252.7 -430.1 -15.0 -424.5 -280.6 195.3 4 -180.2 -472.1 -445.1 -343.5 -360.2 132.2 5 -32.1 -127.6 -78.9 -80.9 -79.9 39.0 6 -104.6 -63.3 -37.7 -150.8 -89.1 49.5 7 -52.1 -86.1 -54.1 -67.9 -65.1 15.7 8 -73.0 -127.0 -65.0 -81.0 -86.5 27.8 9 -51.9 -90.5 -43.1 -72.0 -64.4 21.2 10 -75.1 -46.0 -38.8 -41.1 -50.2 16.8 11 -72.0 -104.5 -109.7 -60.6 -86.7 24.1 12 -63.4 -24.4 -127.8 2.0 -53.4 56.4 13 -74.8 -80.3 -42.5 -47.6 -61.3 19.0 14 -71.2 -97.3 -127.0 -72.0 -91.8 26.4 15 -234.4 -398.1 -164.2 -246.0 -260.7 98.5 16 -236.2 -562.9 -316.8 -412.1 -382.0 140.4


Table A.8: Postoperative minimum principal strains (Load case 2).


1 -73.1 -52.9 -14.0 -100.3 -60.1 36.3 2 -245.0 -263.0 -72.9 -243.2 -206.1 89.2 3 -349.4 -479.2 -22.4 -619.6 -367.6 255.2 4 -262.2 -465.4 -493.1 -552.7 -443.3 126.1 5 -27.0 -180.0 -107.5 -116.1 -107.7 62.8 6 -122.7 -78.1 -53.6 -262.7 -129.3 93.4 7 -223.1 -202.1 -128.8 -205.5 -189.9 41.7 8 -346.9 -304.5 -213.0 -277.1 -285.4 56.1 9 -49.1 -100.1 -44.8 -82.4 -69.1 26.6 10 -81.6 -46.4 -35.3 -53.9 -54.3 19.8 11 -67.3 -128.5 -110.8 -79.7 -96.6 28.0 12 -137.1 -61.7 -153.4 -69.4 -105.4 46.6 13 -117.3 -121.1 -56.3 -61.4 -89.0 34.9 14 -189.7 -151.3 -191.0 -108.8 -160.2 38.9 15 -596.4 -722.8 -338.5 -507.0 -541.2 161.5 16 -680.0 -1153.1 -742.8 -873.6 -862.4 209.9

Table A.9: Postoperative maximum principal strains (Load case 1).


1 13.0 17.3 25.5 -4.6 12.8 12.7 2 64.4 27.5 54.7 59.6 51.6 16.5 3 98.4 163.3 12.6 163.3 109.4 71.4 4 101.9 162.9 175.5 127.8 142.0 33.5 5 15.4 55.1 50.2 63.3 46.0 21.1 6 172.4 101.7 60.3 83.9 104.6 48.3 7 90.5 158.1 121.8 143.4 128.4 29.4 8 151.2 289.5 157.9 135.8 183.6 71.2 9 48.7 58.2 42.1 27.7 44.2 12.8 10 212.1 223.9 135.0 159.3 182.6 42.4 11 199.5 349.8 260.5 218.1 257.0 67.0 12 135.6 371.7 310.0 155.3 243.1 115.9 13 54.5 66.3 54.5 57.6 58.2 5.6 14 28.7 46.7 81.2 32.4 47.2 23.9 15 79.5 171.5 69.7 110.0 107.7 45.9 16 108.9 204.2 113.7 150.5 144.3 44.0


Table A.10: Postoperative maximum principal strains (Load case 2).


1 17.0 8.4 0.1 6.8 8.1 6.9 2 90.4 89.2 66.7 114.8 90.2 19.6 3 143.2 236.0 22.8 288.4 172.6 116.5 4 218.2 166.5 215.9 250.2 212.7 34.6 5 23.9 19.2 122.0 99.9 66.2 52.4 6 358.0 187.7 80.9 175.2 200.5 115.4 7 474.5 455.4 275.4 432.0 409.3 90.9 8 774.3 812.6 476.3 432.1 623.8 197.3 9 48.3 60.9 39.8 34.9 46.0 11.4 10 218.1 240.6 134.3 199.5 198.1 45.7 11 192.6 425.3 269.4 312.7 300.0 97.2 12 266.1 484.5 353.7 315.3 354.9 93.5 13 107.7 122.0 68.8 82.6 95.3 24.0 14 88.5 69.0 77.9 37.9 68.3 21.8 15 227.3 312.4 135.6 216.2 222.9 72.3 16 311.3 455.5 259.4 346.8 343.2 83.0

Table A.11: Postoperative longitudinal strains (Load case 1).


1 5.9 -0.8 -12.9 -4.7 -3.1 7.9 2 -183.8 -197.8 -43.1 -178.8 -150.9 72.3 3 -208.8 -425.9 -7.8 -407.5 -262.5 196.2 4 -179.9 -471.3 -444.8 -335.8 -358.0 132.4 5 -10.8 -37.7 -3.3 -53.4 -26.3 23.3 6 94.2 66.9 33.4 8.9 50.9 37.4 7 74.9 140.3 113.9 105.0 108.5 26.9 8 150.6 287.9 157.7 134.4 182.6 70.8 9 48.7 40.5 37.0 26.5 38.2 9.2 10 211.7 217.6 134.5 157.7 180.4 40.8 11 198.5 343.3 254.7 216.1 253.1 64.5 12 111.5 371.2 275.0 136.8 223.6 121.8 13 -42.1 -76.7 -22.9 -5.3 -36.8 30.6 14 -70.6 -84.5 -108.8 -19.8 -70.9 37.6 15 -232.1 -391.8 -163.1 -241.6 -257.2 96.3 16 -234.3 -552.6 -316.0 -405.6 -377.1 136.3


Table A.12: Postoperative longitudinal strains (Load case 2).


1 -4.5 2.5 -4.4 0.3 -1.5 3.5 2 -205.0 -201.6 -41.7 -206.6 -163.7 81.4 3 -267.1 -410.2 -7.4 -545.2 -307.5 230.1 4 -184.1 -437.5 -480.6 -502.3 -401.1 147.2 5 5.3 -62.6 55.4 -81.0 -20.7 62.9 6 306.8 164.6 64.7 88.8 156.2 109.0 7 456.8 445.1 263.3 347.4 378.1 90.9 8 750.8 798.6 472.5 403.5 606.3 197.4 9 47.6 37.0 29.6 26.2 35.1 9.5 10 217.4 233.6 133.9 196.8 195.4 43.7 11 178.7 423.5 268.2 304.0 293.6 101.4 12 190.8 479.1 329.5 273.7 318.3 121.4 13 -116.9 -120.5 -54.2 -45.4 -84.3 40.0 14 -176.5 -149.4 -186.7 -74.4 -146.8 50.8 15 -583.6 -695.8 -327.7 -503.2 -527.6 154.9 16 -677.7 -1128.4 -738.9 -850.3 -848.8 199.6

Table A.13: P-values showing the statistically significant difference between the strains before and after surgery for each load case (bold indicates p < 0.05).

Minimum Principal Maximum Principal Longitudinal Gauge No Case 1 Case 2 Case 1 Case 2 Case1 Case 2

1 0.0016 0.0018 0.0013 0.0024 0.0007 0.0013 2 0.0136 0.0127 0.0007 0.0298 0.0215 0.0261 3 0.0596 0.5915 0.2018 0.8199 0.0561 0.3081 4 0.4068 0.2303 0.9414 0.1444 0.4033 0.3502

5 0.0175 0.0545 0.8816 0.2990 0.0783 0.7004 6 0.5267 0.2188 0.1790 0.4176 0.0302 0.3744 7 0.0019 0.3977 0.0051 0.6933 0.0069 0.7915 8 0.0940 0.1593 0.0142 0.2712 0.0131 0.2831

9 0.0046 0.0186 0.0007 0.0006 0.0005 0.0004 10 0.0007 0.0009 0.0056 0.0052 0.0066 0.0060 11 0.0377 0.0464 0.0318 0.0658 0.0331 0.0637 12 0.0465 0.1764 0.8790 0.4832 0.7430 0.7945

13 0.0056 0.3542 0.0109 0.4573 0.0126 0.8311 14 0.3255 0.0007 0.3741 0.0306 0.2148 0.0080 15 0.0985 0.5241 0.4573 0.9199 0.0701 0.7245 16 0.0272 0.0972 0.0477 0.1838 0.0241 0.1024


Table A.14: Postoperative strains as a percentage of preoperative strains (maximum and minimum principal strains and their corresponding errors).

Gauge Minimum Principal Strain Maximum Principal Strain No Case 1 Error Case 2 Error Case 1 Error Case 2 Error

1 4.4% 1.4% 8.7% 5.6% 8.4% 8.4% 6.4% 5.6% 2 31.5% 17.9% 38.2% 22.3% 28.5% 9.6% 36.9% 13.7% 3 66.7% 61.2% 90.8% 81.8% 72.9% 63.6% 107.1% 94.2% 4 88.5% 34.2% 132.8% 43.9% 99.0% 28.4% 136.5% 41.6% 5 38.4% 20.1% 44.5% 28.1% 87.0% 115.5% 38.7% 43.2% 6 77.0% 69.0% 65.5% 74.0% 154.2% 92.5% 80.4% 48.9% 7 313.1% 277.6% 119.0% 34.3% 485.9% 209.9% 107.1% 32.9% 8 210.2% 133.2% 135.1% 41.1% 297.4% 164.3% 127.1% 48.5% 9 39.0% 15.2% 49.9% 22.4% 13.9% 4.5% 16.0% 4.6% 10 32.0% 12.4% 37.4% 16.0% 41.6% 14.1% 44.9% 14.8% 11 62.7% 22.8% 70.3% 21.1% 65.9% 20.2% 73.7% 26.7% 12 52.0% 56.7% 74.3% 34.1% 96.0% 48.7% 112.8% 34.5% 13 36.3% 14.1% 78.3% 33.1% 29.9% 7.4% 84.7% 30.0% 14 69.4% 33.5% 41.7% 10.5% 80.2% 50.7% 67.0% 27.2% 15 117.2% 62.4% 92.9% 35.7% 115.0% 59.4% 99.0% 37.7% 16 158.1% 96.0% 112.6% 43.2% 138.3% 67.9% 112.3% 37.4%

Table A.15: Postoperative strains as a percentage of preoperative strains (longitudinal strains and their corresponding errors).

Longitudinal Strain Gauge No Load Case 1 Error Load Case 2 Error

1 0.4% 1.1% 0.2% 0.5% 2 30.3% 20.1% 34.4% 24.0% 3 65.3% 63.2% 82.9% 79.2% 4 88.5% 34.4% 128.3% 52.9% 5 31.0% 36.9% 2382.6% 349096.8% 6 -56.1% -68.9% 183.4% 359.1% 7 -2117.4% -4352.0% 105.2% 34.6% 8 506.0% 816.7% 126.1% 49.5% 9 12.1% 3.3% 12.6% 3.7% 10 42.2% 14.3% 44.8% 14.7% 11 66.1% 20.1% 74.1% 28.1% 12 90.6% 52.0% 105.7% 43.6% 13 -109.1% -108.3% 112.1% 87.8% 14 57.9% 39.0% 42.4% 15.1% 15 122.0% 65.3% 95.9% 37.7% 16 161.2% 99.7% 113.3% 43.3%

Appendix B

Strain Distributions

EE, Min . Principal (Ave. Crit . : 75%)

+6.332e-04 +O.OOOe+OO -2.500e-04 -s . oooe-04 -7 . 500e-04 -l.OOOe-03 -1.250e-03 -l . SOOe-03 -1.750e-03 -2 . 000e-03 -2 . 250e-03 -2 . 500e-03 -5 . 006e-02

(a) Intact femur (b) Postoperative (c) Remodelled

Figure B.l: Minimum principal strain distribution (Stability, anteromedial view).

270

B. STRAIN DISTRIBUTIONS

UVARM3 (Ave . Crit . : 75%)

+4.924e - 02 +S . OOOe-03 +4 . 500e- 03 +4 . 000e-03 +3 . 500e-03 +3 . 000e-03 +2 . 500e-03 +2 . 000e-03 +l . SOOe - 03 +l . OOOe-03 +S . OOOe-04 +O . OOOe+OO -1 . 676e-02

(a) Intact femur

271


Figure B.2: Equivalent strain distribution (Stability, anteromedial view) .

B. STRAIN DISTRIB UTIONS

EE, Min. Principal (Ave. Crit .: 75%)

+1.029e-03 +O.OOOe+OO - 2.500e-04 -s . oooe-04 -7 . 500e-04 - l . OOOe-03 -1 . 250e - 03 -1. SOOe-03 -1.750e - 03 -2.000e-03 -2.250e-03 -2.500e-03 -3.754e- 02

(a) Intact femur

272


Figure B.3: Minimum principal strain distribution (Epoch , anteromedial view).

B. STRAIN DISTRIBUTIONS

UVARM3 (Ave . Crit .: 75%)

+3 . 833e-02 +5 . 000e-03 +4 . 500e-03 +4 . 000e-03 +3 . 500e-03 +3.000e- 03 +2.500e-03 +2 . 000e-03 +1.500e-03 +l.OOOe-03 +5.000e-04 +O.OOOe+OO -1.14le-02

(a) Intact femur

273


Figure B.4: Equivalent strain distribution (Epoch, anteromedial view) .

Appendix C

Density Changes and

Distributions

C .l M argron

Table C.1: Predicted bone density changes in the Gruen zones for the Margron model (dead zone 0.6 , no distal contact, version angle 0°, neck length +4 mm).

Increment Zone 1 Zone 2 Zone 3 Zone 4 Zone 5 Zone 6 Zone 7

10 2.4% -2.6% 0.0% 0.0% 0.3% -8.9% -16.6% 20 1.4% -4.5% 0.0% 0.0% 0.4% -16.7% -26.2% 40 0.5% - 6.7% 0.0% 0.0% 0.5% -22.7% -29 .7% 60 0.3% -7.7% 0.0% 0.0% 0.5% -24.7% -30.3% 80 0.2% -8.1% 0.0% 0.0% 0.5% -25.7% - 30.5% 100 0.1% -8.4% 0.0% 0.0% 0.5% -26.2% -30.6% 120 0.1% - 8.5% 0.0% 0.0% 0.5% -26.5% -30.6%

274

C .2 COMPARISON WITH OTHER I MPLANTS 275

C.2 Comparison with Other Implants

Table C.2: Predicted bone density changes in the Gruen zones for the Stability model.


5 -0.6% 0.1% -2.4% - 2.6% -2.5% -2.6% -15.4% 10 -0.5% -0.1 % -2.9% -3.1% - 2.9% -3.2% -18.2% 20 -1.3% -0.8% -3.6% - 3.9% -3.7% -4.1% - 20.4% 30 -1.7% -1.1% - 3.9% -4.2% - 4.1% -4.5% -21.2% 40 -1.9% -1.2% -4.0% - 4.3% -4.2% -4.7% -21.6% 50 -2.0% -1.2% -4.1% -4.4% -4.3% -4.8% -21.7% 60 -2.1% -1.3% -4.1% -4.4% -4.4% -4.9% -21.8%

Table C.3: Predicted bone density changes in the Gruen zones for the Epoch model.


5 1.8% 1.0% 0.0% 0.5% 0.1% 0.1% -5.1% 10 2.0% 1.5% 0.0% 0.6% 0.1 % 0. 1% - 8. 1% 20 2.1 % 1.9% 0.0% 0.8% 0.1% 0.1% -9.7% 30 2.1 % 2.0% 0.1% 0.9% 0.1 % 0.1% - 10.2% 40 2.1 % 2.1% 0.1 % 1.0% 0.1 % 0.1% -10.4% 50 2.2% 2. 1% 0.1% 1.1% 0.2% 0.1 % -10.5% 60 2.2% 2.2% 0.1% 1.1% 0.2% 0.1 % -10.5%

C .2 COMPARISON WITH OTHER IMPLANTS

SDV2 (Ave. Crit. : 75%)

+5.028e+03 +2.800e+03 +2 . 500e+03 +2.200e+03 +1.900e+03 +1 . 600e+03 +1.300e+03 +1.000e+03 +7.000e+02 +4.000e+02 +1.000e+02 -2 . 000e+02 -3.007e+03


t •

( (


276

Figure C.l: Density distribution (Hounsfield units) of the immediately postoperative Stability femur.

C.2 COMPARISON WITH OTHER IMPLANTS

SDV2 (Ave . Crit .: 75%)

I +5 . 028e+03 +2 . 800e+03 +2 . 500e+03

- +2 . 200e+03 ::': +1 . 900e +03

+1 .600e+03 +1. 300e+03 +1.000e+03 +7.000e+02 +4 .000e+02 +1.0 00e+02 -2 . 000e +02 -3 . 089 e +03


t I

' ••

277


Figure C.2: Density distribution (Hounsfield units) of the remodelled Stability femur.

C.2 COMPARISON WITH OTHER IMPLANTS 278


Figure C.3: Simulated DEXA images during remodelling of the Stability femur.


SDV2 (Ave. Crit.: 75%)

+5.397e+03 +2.800e+03 +2.500e+03 +2.200e+03 +1.900e+03 +1.600e+03 +1. 300e+03 +l . OOOe+03 +7 . 000e+02 +4 . 000e+02 +1.000e+02 -2.000e+02 -3 .1 71e+03


279

••

)


Figure C.4: Density distribution (Hounsfield units) of the immediately postoperative Epoch femur.


SDV2 (Ave. Crit . : 75%)

+5.425e+03 +2.800e+03 +2.500e+03 +2.200e+03 +1.900e+03 +1.600e+03 +1 . 300e+03 +1 . 000e+03 +7.000e+02 +4.000e+02 +1.000e+02 -2.000e+02 -3. 1 71e+03


280

'.

·'

)


Figure C.5: Density distribution (Hounsfield units) of the remodelled Epoch femur.

C.2 COMPARISON WITH OTHER IMPLANTS 281


Figure C.6: Simulated DEXA images during remodelling of the Epoch femur.

C.3 INVESTIGATION OF PARAMETERS 282

C.3 Investigation of Parameters

C.3.1 Effect of Interface Conditions

Table C.4: Predicted bone density changes in the Gruen zones for the Margron model (fully bonded contact).


10 2.4% -2.6% 0.2% 0.0% 0.4% -9.4% -16.6% 20 1.4% -4.5% 0.3% 0.0% 0.5% -17.6% -26.3% 40 0.5% -6.7% 0.5% 0.1% 0.6% -24.2% -29.8% 60 0.3% -7.6% 0.6% 0.1% 0.7% -26.4% -30.4% 80 0.2% -8.0% 0.6% 0.1% 0.7% -27.4% -30.6% 100 0.1% -8.3% 0.7% 0.1% 0.6% -28.0% -30.7% 120 0.1% -8.4% 0.7% 0.1% 0.6% -28.4% -30.7%

Table C.5: Predicted bone density changes in the Gruen zones for the Margron model (distal sliding contact).


10 2.4% -2.6% 0.1% 0.0% 0.0% -9.2% -16.6% 20 1.4% -4.5% 0.2% 0.0% 0.0% -17.2% -26.3% 40 0.5% -6.8% 0.3% 0.0% 0.1% -23.3% -29.7% 60 0.3% -7.8% 0.3% 0.0% 0.1% -25.3% -30.4% 80 0.2% -8.2% 0.4% 0.0% 0.1% -26.2% -30.6% 100 0.1% -8.5% 0.4% 0.0% 0.1% -26.6% -30.7% 120 0.1% -8.6% 0.4% 0.0% 0.1% -26.9% -30.7%

C.3.2 Effect of Femoral Head Position

Table C.6: Predicted bone density changes in the Gruen zones for the Margron model (version angle 0°, neck length -4 mm).


10 2.2% -3.8% 0.0% 0.0% 0.2% -11.3% -18.0% 20 1.1% -7.2% 0.0% 0.0% 0.2% -21.6% -28.0% 40 0.2% -11.1% 0.0% 0.1% 0.3% -29.8% -31.4% 60 -0.2% -12.6% -0.1% 0.1% 0.3% -32.6% -32.1% 80 -0.3% -13.3% -0.1% 0.1% 0.3% -33.9% -32.3% 100 -0.3% -13.6% -0.1% 0.1% 0.3% -34.7% -32.3% 120 -0.3% -13.8% -0.2% 0.1% 0.3% -35.1% -32.4%


Table C.7: Predicted bone density changes in the Gruen zones for the Margron model (version angle 0°, neck length 0 mm).


10 2.3% -3.0% 0.0% 0.0% 0.2% -9.8% -17.2% 20 1.3% -5.5% 0.0% 0.0% 0.3% -18.7% -27.0% 40 0.4% -8.3% 0.0% 0.0% 0.4% -25.5% -30.4% 60 0.1% -9.5% 0.0% 0.0% 0.4% -27.8% -31.1% 80 0.0% -10.0% 0.0% 0.0% 0.4% -28.9% -31.3% 100 0.0% -10.3% 0.0% 0.0% 0.5% -29.6% -31.4% 120 -0.1% -10.4% 0.0% 0.0% 0.5% -29.9% -31.4%

Table C.8: Predicted bone density changes in the Gruen zones for the Margron model (version angle 0°, neck length +4 mm).


10 3.3% -2.2% 0.9% 1.3% 0.9% -5.8% -11.0% 20 2.7% -4.3% 1.2% 2.0% 1.2% -11.1% -19.4% 40 2.1% -6.8% 1.6% 3.1% 1.4% -15.4% -23.1% 60 1.6% -8.1% 1.4% 3.4% 1.2% -17.4% -24.1% 80 1.2% -8.8% 1.2% 3.5% 0.9% -18.4% -24.5% 100 0.9% -9.2% 1.1% 3.6% 0.8% -18.9% -24.8% 120 0.7% -9.5% 1.0% 3.6% 0.6% -19.3% -24.9%

Table C.9: Predicted bone density changes in the Gruen zones for the Margron model (version angle 0°, neck length +7 mm).


10 2.7% -1.8% 0.0% 0.0% 0.3% -7.1% -15.3% 20 1.7% -3.0% 0.0% 0.0% 0.5% -13.2% -24.5% 40 1.0% -4.4% 0.1% 0.0% 0.6% -17.8% -28.0% 60 0.7% -5.0% 0.1% 0.0% 0.6% -19.3% -28.6% 80 0.6% -5.3% 0.1% 0.0% 0.7% -19.9% -28.8% 100 0.6% -5.5% 0.1% 0.0% 0.7% -20.3% -28.9% 120 0.6% -5.6% 0.1% 0.0% 0.7% -20.5% -28.9%

Table C.10: Predicted bone density changes in the Gruen zones for the Margron model (version angle -20°, neck length +4 mm).


10 3.3% -2.2% 0.9% 1.3% 0.9% -5.8% -11.0% 20 2.7% -4.3% 1.2% 2.0% 1.2% -11.1% -19.4% 40 2.1% -6.8% 1.6% 3.1% 1.4% -15.4% -23.1% 60 1.6% -8.1% 1.4% 3.4% 1.2% -17.4% -24.1% 80 1.2% -8.8% 1.2% 3.5% 0.9% -18.4% -24.5% 100 0.9% -9.2% 1.1% 3.6% 0.8% -18.9% -24.8% 120 0.7% -9.5% 1.0% 3.6% 0.6% -19.3% -24.9%


Table C.ll: Predicted bone density changes in the Gruen zones for the Margron model (version angle -10°, neck length +4 mm).


10 2.9% -2.1% 0.3% 0.3% 0.5% -7.1% -13.7% 20 2.1% -3.7% 0.5% 0.5% 0.8% -13.1% -22.8% 40 1.5% -5.8% 0.6% 0.7% 1.0% -18.0% -26.2% 60 1.2% -6.7% 0.7% 0.9% 1.1% -19.9% -26.9% 80 1.1% -7.2% 0.8% 1.1% 1.1% -20.8% -27.1% 100 1.1% -7.4% 0.8% 1.2% 1.1% -21.2% -27.2% 120 1.1% -7.6% 0.9% 1.3% 1.2% -21.5% -27.2%

Table C.12: Predicted bone density changes in the Gruen zones for the Margron model (version angle + 10°, neck length +4 mm).


10 2.0% -4.7% -0.2% 0.0% -0.5% -10.5% -19.8% 20 0.8% -9.9% -0.8% -0.3% -1.9% -20.2% -29.8% 40 0.0% -17.6% -2.9% -1.3% -4.8% -27.5% -33.0% 60 -0.3% -21.8% -4.6% -2.1% -6.4% -30.2% -33.6% 80 -0.4% -24.2% -5.7% -2.6% -7.3% -31.5% -33.8% 100 -0.4% -25.7% -6.4% -2.8% -7.8% -32.2% -33.9% 120 -0.4% -26.7% -6.9% -3.0% -8.1% -32.6% -34.0%

Table C.13: Predicted bone density changes in the Gruen zones for the Margron model (version angle +20°, neck length +4 mm).


10 1.8% -6.8% 0.7% 1.4% 0.3% -9.3% -23.2% 20 0.7% -15.0% 0.9% 2.1% 0.3% -17.1% -33.6% 40 -0.1% -25.2% 0.9% 2.9% 0.2% -22.3% -37.1% 60 -0.3% -30.0% 0.9% 3.4% 0.2% -24.1% -37.7% 80 -0.3% -32.5% 0.8% 3.9% 0.1% -24.9% -38.0% 100 -0.3% -33.9% 0.8% 4.2% 0.1% -25.3% -38.0% 120 -0.4% -34.7% 0.8% 4.5% 0.1% -25.5% -38.1%


C.3.3 Effect of Dead Zone Width

Table C.14: Predicted bone density changes in the Gruen zones for the Margron model ( vdead zone 0.55).


10 1.3% -4.3% 0.0% 0.0% 0.3% -12.2% -21.2% 20 -0.1% -7.7% 0.0% 0.0% 0.4% -21.8% -30.5% 40 -1.1% -10.9% 0.0% 0.0% 0.5% -28.5% -33.3% 60 -1.4% -12.0% 0.0% 0.0% 0.5% -30.7% -33.8% 80 -1.4% -12.4% 0.0% 0.0% 0.6% -31.7% -33.9% 100 -1.5% -12.6% 0.0% 0.0% 0.6% -32.2% -34.0% 120 -1.5% -12.8% 0.0% 0.0% 0.6% -32.6% -34.0%

Table C.15: Predicted bone density changes in the Gruen zones for the Margron model (vdead zone 0.65).


10 3.4% -1.3% 0.0% 0.0% 0.2% -6.0% -12.2% 20 2.7% -2.2% 0.0% 0.0% 0.3% -11.9% -21.5% 40 2.0% -3.4% 0.0% 0.0% 0.4% -17.0% -25.6% 60 1.9% -4.0% 0.0% 0.0% 0.5% -18.8% -26.4% 80 1.8% -4.4% 0.0% 0.0% 0.5% -19.6% -26.7% 100 1.7% -4.6% 0.0% 0.0% 0.5% -20.1% -26.9% 120 1.7% -4.7% 0.0% 0.0% 0.5% -20.4% -26.9%

C.3.4 Effect of Activity Level

Table C.16: Predicted bone density changes in the Gruen zones for the Margron model (90% activity level).


10 0.2% -3.5% 0.0% 0.0% 0.2% -10.7% -19.0% 20 -1.0% -6.3% 0.0% 0.0% 0.3% -20.1% -29.3% 40 -2.0% -9.4% 0.0% 0.0% 0.4% -27.4% -32.8% 60 -2.3% -10.6% 0.0% 0.0% 0.4% -29.7% -33.4% 80 -2.0% -11.1% 0.0% 0.0% 0.4% -30.8% -33.6% 100 -2.5% -11.4% 0.0% 0.0% 0.4% -31.5% -33.7% 120 -2.5% -11.6% 0.0% 0.0% 0.4% -31.8% -33.8%

C.3.5 Effect of Prosthesis Stiffness


Table C.17: Predicted bone density changes in the Gruen zones for the Epoch model ( isoelastic properties).


5 1.9% 0.6% 0.0% 0.4% 0.0% 0.0% 2.2% 10 2.1% 0.8% 0.0% 0.5% 0.1% 0.0% 1.4% 20 2.2% 1.0% 0.0% 0.6% 0.1% 0.0% 0.9% 30 2.2% 1.1% 0.0% 0.7% 0.1% 0.0% 0.8% 40 2.3% 1.1% 0.0% 0.7% 0.1% 0.1% 0.8% 50 2.3% 1.2% 0.0% 0.8% 0.1% 0.1% 0.7% 60 2.3% 1.2% 0.0% 0.8% 0.1% 0.1% 0.7%

Table C.18: Predicted bone density changes in the Gruen zones for the Epoch model (cobalt-chrome properties).


5 1.5% 0.5% 0.1% 0.9% 0.2% -2.2% -19.9% 10 1.4% 0.9% 0.1% 1.4% 0.3% -3.6% -28.8% 20 1.8% 1.3% 0.2% 2.2% 0.5% -4.6% -33.3% 30 1.9% 1.4% 0.3% 2.6% 0.6% -5.1% -34.5% 40 1.9% 1.5% 0.3% 2.8% 0.6% -5.3% -35.0% 50 1.8% 1.5% 0.3% 3.0% 0.6% -5.5% -35.3% 60 1.8% 1.6% 0.3% 3.1% 0.6% -5.6% -35.4%

Appendix D

Bone Density Correlations

6

0

-6

c 0

~ -12 "S E

U5 -18

-24 0

-30 -30

Clinical vs. Simulation DEXA Data (Margron, 1 Year)

SIM = 2.6054 + .93938 * CLIN

Correlation: r = .89701

/ /~oo

0

-24 -18 -12 -6 0

Clinical

6

'R._ Regression 95% confid.

Figure D.l: Correlation between simulated and clinical BMD changes (Margron, 1 year postop).

287

D. BONE DENSITY CORRELATIONS 288

c 0

~ "S E

U5

5

0

-5

-10

-15

-20

-25

-30

Clinical vs. Simulation DEXA Data (Margron, 2 Years)

SIM = 1.3144 + .86789 *GUN


-35 '------~~----"~-~~~~~~~~~~-~-~-~----' ~ Regression -35 -30 -25 -20 -15 -1 o -5 o 5 95% confid.

Clinical

Figure D.2: Correlation between simulated and clinical BMD changes (Margron, 2 years postop).

5

0

-5

-10 c 0

~ -15 "S E

U5 -20

-25

-30

-35 -40 -35

Clinical vs. Simulation DEXA Data (Margron, 3 Years)

SIM = 3.9598 + .89638 * GUN

Correlation: r= .81868

0

0

-30 -25 -20 -15 -10 -5

Clinical

0

0 5

-,~ Regression 95% confid.

Figure D.3: Correlation between simulated and clinical BMD changes (Margron, 3 years postop).

D. BONE DENSITY CORRELATIONS

2

-2

-6

c 0

~ -10 :::J E

U5 -14

-18

-22 -26

0

Clinical vs. Simulation DEXA Data (Stability, 2 Years)

Sim = 1 .0708 + .83698 * Clin


-22 -18 -14 -10 -6

Clinical

289

~- Regression

-2 2 95% confid.

Figure D.4: Correlation between simulated and clinical BMD changes (Stability, 2 years postop).

c 0 -~

'S E

U5

-10 0

Clinical vs. Simulation DEXA Data (Epoch, 2 Years)

SIM = 1.8451 + .59313 * CLIN


-12L-~--~~~~--~--~~~--------~------~~----~

-18 -14 -10 -6 -2 2 6

Clinical

'-c..___ Regression 95% confid.

Figure D.5: Correlation between simulated and clinical BMD changes (Epoch, 2 years postop).

D. BONE DENSITY CORRELATIONS 290

c 0

~ "S E

U5

5

0

-5

-10

-15

-20

-25

-30

Clinical vs. Simulation DEXA Data (All Data)

SIM = 1.5129 + .88797 * CLIN

Correlation: r = .85202, p < 0.000000

-35 "----~-~-~---------~---------_j ~ Regression -35 -30 -25 -20 -15 -10 -5 o 5 95% confid.

Clinical

Figure D.6: Correlation between simulated and clinical BMD changes (all data).

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