Note: this is a post-print draft of the journal article:

Dickinson, A.S., Taylor, A.C., Browne, M. (2011) “Implant-Bone Interface Healing

and Adaptation in Resurfacing Hip Replacement”. Computer Methods in

Biomechanics and Biomedical Engineering iFirst (Online Ahead of Print)

The final, fully proofed and peer-reviewed journal article is available from the

publisher online, via the following link:

http://www.tandfonline.com/doi/abs/10.1080/10255842.2011.567269

Implant-Bone Interface Healing and Adaptation in Resurfacing Hip

Replacement

Alexander Dickinsona; Andrew Taylor

b; Martin Browne

a

a

Bioengineering Research Group, University of Southampton, Hampshire, UK b

Finsbury Development Ltd, Leatherhead, Surrey, UK

E-Mail: doctor@soton.ac.uk

Hip resurfacing demonstrates good survivorship as a treatment for young osteoarthritis

patients, but occasional implant loosening failures occur. On the femoral side there is

radiographic evidence suggesting that the implant stem bears load, which is thought to

lead to proximal stress shielding and adaptive bone remodelling. Previous attempts

aimed at reproducing clinically observed bone adaptations in response to the implant

have not recreated the full set of common radiographic changes, so a modified bone

adaptation algorithm was developed in an attempt to replicate more closely the effects of

the prosthesis on the host bone. The algorithm features combined implant-bone interface

healing and continuum bone remodelling. It was observed that remodelling simulations

which accounted for progressive gap filling at the implant-bone interface predicted the

closest periprosthetic bone density changes to clinical x-rays and DEXA data. This

model may contribute to improved understanding of clinical failure mechanisms with

traditional hip resurfacing designs, and enable more detailed pre-clinical analysis of new

designs.

Keywords: hip resurfacing; finite element analysis; remodelling; mechanobiology;

1. Introduction

Resurfacing hip replacement (RHR) is an established surgical treatment for the young

osteoarthritis patient. Hip resurfacing aims to replace degenerated articular cartilage

with a prosthetic bearing whilst offering improved femoral bone conservation,

reduced dislocation risk and shorter recovery time than total hip replacement (THR)

[1, 2]. The most comprehensive arthroplasty register data at the time of writing, from

the Australian Orthopaedic Association [3], indicated that hip resurfacing has a

similar revision rate to THR from 1-5 years, but more revisions in the first

postoperative year (1.8% vs. 1.2%). Considering young male patients, who typically

receive larger size implants, both the first year revision level (1.3%) and subsequent

revision rates were similar to results of THR for the same patient cohort (1.0%). More

natural joint biomechanics [2] and superior revision surgery outcomes are further

potential benefits over THR [3], but there is scope for improvement in the short and

medium term survivorship of resurfacing.

Mechanical failures in the first two postoperative years can be attributed

largely to fracture of the femoral neck. This is a multi-factorial failure mode, thought

to be linked to varus prosthesis positioning, notching of the neck cortex, inadequate

support bone quality or incorrect femoral prosthesis cementing, leading to incomplete

implant seating or thermal osteonecrosis on cement polymerisation [4-10]. In the

medium term, femoral failures tend to be restricted to sensitivity reactions to metal

ions released by Cobalt Chromium (CoCr) wear particles [11], and prosthesis

migration and loosening [12-16]. Loosening is also thought to be related to several

surgical, patient and implant design related factors. In particular, there is evidence to

suggest that altered pre- to postoperative biomechanics have considerable

involvement; bone density changes consistent with adaptive remodelling are observed

more frequently in loosening hips [12, 14]. Specifically, bone resorption occurs at the

superior femoral head-neck junction, known as ‘neck narrowing’ [15-17], and bone

densification is observed in the medial femoral neck and around the prosthesis

metaphyseal stem in so-called ‘pedestal lines’ [14, 17, 18]. Radiolucent lines are seen

more commonly around the stems of loosening implants [12], indicative of migration

and stem break-out [19]. The prosthesis stem is designed as a non load bearing

surgical alignment guide, but evidence indicates that the stem can bear load and

redirect the load transfer path away from the femoral head and into the medial femoral

neck. These biomechanical changes may be partially responsible for stress shielding

and bone resorption inside the femoral head. This area is obscured on clinical

radiographs but resorption has been observed in retrieval specimens [20, 21], and

would be consistent with prosthesis migration and loosening. It should be noted

however, firstly that the reported resorption within the resurfacing head could also

result from avascular necrosis (AVN) or wear particle reactions, and secondly that

radiographic changes also occur around well performing implants. Repeated

measurements over time have indicated that around well fixed implants the majority

of adaptation takes place over the first two to three postoperative years [15, 16], and

then stabilises. This implies that limited bone remodelling is not necessarily indicative

or predictive of clinical failure [15].

There have been several past attempts to predict or replicate bone adaptation

in the resurfaced hip joint in Finite Element (FE) analysis models. Most commonly,

these studies produced a static FE model of the intact and resurfaced joints, and used

the comparative mechanical strain or Strain Energy Density (SED) in the two

situations to predict the immediately post-operative remodelling stimulus [19, 22-28].

These studies have presented predictions of stress shielded bone within the femoral

head and the superior femoral neck, with bone densification around the prosthesis

stem. They allow the comparative performance of different surgical and implant

design variables to be predicted, such as prosthesis position [24, 26, 27] and sizing

[27], fixation methods [19, 25], stem diameter [23], stem length [28] and the extent of

stem-bone contact [23, 26]. However, these results only represent the driving force for

bone remodelling at one instant, and do not predict the progression or end point of the

nonlinear process. The immediate post-operative remodelling stimulus alone may not

indicate the long term performance of the implanted joint, so adaptive bone

remodelling simulation would be well suited to address this phenomenon. Simulation

of adaptive remodelling around THR implants is an established process [29-32], and

has more recently been applied to RHR implants. The first attempt to simulate the

progressive bone adaptation around a resurfacing head was produced by Gupta et al

[33], which has been followed by investigation of the influence of the contact

conditions at the cement-bone and stem-bone interfaces [34]. Both studies predicted

bone remodelling in qualitative agreement with clinical observations, with resorption

inside the femoral head and densification around the stem tip. However, previous

studies have not predicted the most commonly observed radiographic change,

narrowing of the femoral neck [15-17], and a goal of adaptive modelling should be to

achieve a quantitative correlation between predicted adaptive bone remodelling and

clinically measured bone mineral density (BMD) changes around hip resurfacing

implants.

All previous models have also been subject to simplification of the implant-

bone interfaces, in particular at the stem-bone interface. In surgery, a parallel bore is

drilled into which the stem fits [35], and a clear gap up to 5mm wide surrounds the tip

and tapering portion of the stem. In order for the previously reported radiographic

changes to occur, this gap must re-fill gradually with bone, in the months following

surgery. Therefore neither the assumption of a uniform, sustained gap around the

stem, nor of intimate stem-bone contact is representative of the clinical scenario.

This study tested the hypothesis that if a model is to capture fully the in-vivo

bone adaptation behaviour around hip resurfacing implants, the process of prosthesis-

bone interface defect healing should be simulated in parallel with bone remodelling.

The objective was to apply combined theories of implant-bone interface defect

healing and adaptive bone remodelling in a structural FE model of the resurfaced hip,

and to make a quantified comparison between the model’s predicted bone density

changes and clinical data.

2. Methods and Materials

2.1 Model Generation Process

An FE model of the geometry and materials properties of a proximal femur

was generated as described in a previous article [27], using a CT scan from a 63 year-

old male (height 1.77m, weight 85kgf) with no known orthopaedic disease. The CT

scan resolution was 0.781mm, with 2mm slice thickness. The geometry generation

process involved semi-automated CT-scan segmentation with Amira software

(Mercury Computer Systems Inc, USA), defining threshold values to identify the

external boundary of the cortical bone on each section. A solid model was created by

surface lofting and virtual implantation with SolidWorks 2007 software (SolidWorks

Corp, USA), and FE model meshing with ANSYS 12 FE analysis software (ANSYS

Inc., USA). Second order tetrahedral elements were used, with a maximum 1.5mm

side length at the implant-bone interface, up to 6mm side length in the femoral

diaphysis, away from the region of interest. The virtual implantation used a 52mm

RHR implant representing the ADEPT prosthesis (Finsbury Orthopaedics, UK),

which was positioned according to current operative techniques. The implant was

oriented by aligning its metaphyseal stem 10° valgus with respect to the femoral neck

axis. Then, comparing the diameters of the prosthesis shell opening and the femoral

neck, its final position was set at the highest point possible along the femoral neck

without notching the neck cortex. The prosthesis shell was modelled as bonded to the

bone via a 2mm-thick bone cement layer, and contact was defined between the stem

and the bone, with a coefficient of friction of 0.3.

Heterogeneous, linear elastic, isotropic bone materials properties were applied

to the model using Bonemat freeware (Rizzoli Institute, Italy). The rule of mixtures

was used to calculate a weighted average bone density in each element from the

greyscale units of its corresponding voxels in the CT scan. This was calibrated by

taking a point in the mid-shaft cortex to represent 100% dense bone and a point in the

intermedullary canal to represent 100% marrow. Then a Young’s Modulus (E) value

was assigned to each element according to its density (ρ) using the relationship

E=6850ρ1.49

[36]. The model was loaded with generalised 2500N joint contact and

833N abductor muscle forces representing the heel strike instant in gait [23]. Figure 1

shows the FE meshes in the intact and implanted femur models, along with a cross

section of the model showing the implant and over drilled stem bore. In order to

simulate the biomechanical processes of adaptive bone remodelling and defect

healing, the following algorithms were employed as post-processing code,

augmenting the structural FE solution:

Figure 1: The Finite Element Mesh in the Intact (left) and Implanted Femur (centre), and a

Cross Section of the Implant (A), Bone (B), Cement (C) and Stem Bore Defect (D) Geometry

(right).

2.2 Adaptive Bone Remodelling

Bone remodelling was simulated on the functional adaptation principal [37] using a

Strain Energy Density (SED) stimulus. On a site-specific approach, the adaptation of

each element’s mechanical properties was considered independently [30]. The SED

was read for each element in both the intact (Sref) and implanted bone (S) cases, and

the remodelling stimulus was calculated as the percentage change. If this stimulus was

less than a threshold level (s) of 75% [31], no bone adaptation occurred. Bone density

increased if the implanted SED was over 75% above the intact SED, and bone was

resorbed if the implanted SED was over 75% below the intact level. Forwards Euler

integration was used to calculate each element’s explicit bone density change

iteratively, with the whole process summarised by the following set of three

equations. For each iteration and in each element:

(1)

where ρn is the density before the time step, and ρn+1 is the density after the time step.

a(ρ) is a surface area density function promoting bone resorption or deposition only

where the internal surface area for osteoclast and osteoblast activity is high [38]. τ is a

rate constant of 130g2mm

-2J

-1 per month [31], and Δt is the time step size for the

forwards integration. The density of each element was limited to 1.73g/cc or 0.05g/cc,

representing 100% theoretical density cortical bone and complete resorption

respectively. Adaptation was calculated in fixed one day time increments, and once

the largest bone density change in the model reached 0.173g/cc, a new structural FE

solution was run with the updated materials properties, giving updated stimulus

levels. This limit was used to ensure numerical stability, and the 0.173g/cc value

represents 10% of the density of cortical bone, a value reported in the literature to

give a balance between numerical convergence and reasonable solution time [39]. A

maximum limit of the bone remodelling rate was applied for each element, calculated

using a maximum lamellar bone deposition rate of 5.5μm/day [40], the element’s

density and Martin’s surface area density function a(ρ) [38]. A schematic plot of the

remodelling stimulus function and the surface area density function is shown in

Figure 2.

Figure 2: Schematic of the Bone Remodelling Algorithm (left) and Martin’s Surface Area Density

Function [38] (right).

2.3 Cancellous Bone Defect Healing

Many structures in the body are believed to be developed and healed through

sequential, mechanoregulatory tissue differentiation of Mesenchymal Stem Cells

(MSCs). This process is thought to contribute to bone fracture healing [41],

osteochondral defect repair [42] and implant-bone interface adaptation. MSCs are

unspecialised cells which maintain an ‘undifferentiated phenotype until they are

exposed to the appropriate signals’ [43], at which point they can differentiate into

connective tissue. Defects will be populated by granulation tissue containing MSCs,

deriving from the bone marrow and migrating towards an injury site to perform tissue

repair. In this study, the gradual refilling of the over-drilled stem bore (a cancellous

bone defect) was simulated using a diffusive cell migration and mechanobiological

tissue differentiation process. This was based on the principles of models developed

to simulate implant-bone fixation interface adaptation [44, 45] which have since been

used in such applications as bone fracture healing [46-48] and osteochondral defect

repair [49].

In this model, the defect around the implant stem was filled initially with

granulation tissue which is infiltrated by mesenchymal stem cells by diffusion [47],

representing the combined effects of cell migration and proliferation. The diffusion of

stem cells was modelled using Equation 2, where ‘[c]’ is the cell concentration,

initially zero throughout the defect. Diffusion was driven by the percentage cell

concentration in the mature bone at the cut surface, and a zero diffusion boundary

condition was imposed on the surface of the implant. ‘D’ represents the diffusion

coefficient (2.37mm2/day [46]).

(2)

The differentiation and maturation of these cells was then modelled using a

smoothed mechanical stimulation process [47]. The differentiation of the stem cells

into a target phenotype (fibroblasts, chondroblasts or osteoblasts) according to

mechanical conditions was controlled using dilatational hydrostatic pressure and

deviatoric equivalent strain stimuli (Table 1), assuming good vascularity [50]. These

cells were then allowed to mature to form fibrous tissue, cartilage or bone. At each

iteration, the stimulated phenotype was identified for each element and its new target

modulus ‘En+1’ was calculated with Equation 3, by a rule of mixtures using the

fractional cell concentration ([c]/[c]max

), the target tissue modulus ‘Etissue’ and the

granulation tissue modulus ‘Egranulation’:

(3)

The Etissue values are given in Table 1 [48]. The temporal smoothing of the formed

tissue’s modulus to give its final value ‘En+1,smoothed’, was achieved by averaging the

target value with the modulus values from the 9 preceding days, as in Equation 4:

(4)

and this value was used to update the structural model’s mechanical properties.

Tissue Phenotype Young’s

Modulus /MPa

Strain

Stimulus /

%

Hydrostatic

Pressure

Stimulus / MPa

Granulation Tissue 1 - -

Fibrous Tissue 2

-

>5

<-5

and

and

>0.15

>-0.15

>-0.15

Cartilage 10 >15

<-15 and <-0.15

Bone (Endochondral

Ossification) 1000 (Immature)

6000 (Mature)

-15 to 15 and <-0.15

Bone

(Intramembranous

Ossification)

-5 to 5 and -0.15 to 0.15

Table 1: Healing Defect Tissue Phenotype Properties and Stimulus Levels [48, 50]

2.4 The Combined Bone Remodelling / Defect Healing Algorithm

To simulate the adaptive bone remodelling process in combination with the gradual

healing of the defect around the implant stem, the two processes were combined into a

single algorithm on a similar basis to Liu and Niebur’s model of implant-bone

interface adaptation [51]. This allowed the following processes to be captured by the

model:

differentiation of stem cells in granulation tissue in the defect into mature tissue,

modelling of immature bone in the defect and

remodelling of mature bone.

Figure 3: The Combined Bone Modelling / Remodelling / Tissue Differentiation Algorithm.

The process is illustrated by the flow chart in Figure 3. First, a structural FE analysis

of the intact bone was solved to obtain reference stimulus values for each element.

Then, the model was implanted and a series of iterative analyses were completed. At

the beginning of each FE iterative loop, a structural analysis was solved to obtain

implanted stimulus values for each element. This was followed by a diffusion FE

analysis (Equation 2) in the healing defect to obtain target cell concentrations. Next, a

bone adaptation process was applied to each element phenotype:

in mature bone, a remodelling step was completed (Equation 1), to obtain the

element’s remodelled modulus,

in soft tissue, a healing step was completed, to obtain the element’s target tissue

phenotype and modulus (Table 1), and

in immature bone, target moduli from both modelling and healing processes were

obtained, and the larger value was selected. This ensured that the element’s

density evolved by the modelling process initially, when its density ρ and surface

area density a(ρ) were low, and that remodelling became dominant as ρ and a(ρ)

increased, with a smooth transition between the processes. The immature bone

modelling process was identical to the mature bone remodelling process, except

that a single reference strain value of 2000µε was used, with a threshold stimulus

value of s=±33% [40, 52].

In soft tissue and immature bone elements, the modulus was smoothed

(Equation 4). Finally, as explained earlier for numerical convergence, each element’s

new modulus value was compared to its value at the last structural solution. Repeated

adaptation calculations were performed until the largest element modulus change in

the model reached 0.173g/cc, at which point a new FE iterative loop was begun, with

a new structural solution.

2.5 Model Outputs

Two results interpretation methods were used, in an attempt to link the models’

predictions to clinical observations. First, virtual X-Rays were generated from the FE

model [53] for qualitative analysis (Figure 4 left) with comparison to clinical

radiographs from the literature. Nodal and elemental bone density values and

locations in a coordinate system orthogonal to the prosthesis were exported from the

FE programme. This data was imported into MATLAB (The MathWorks Inc., MA,

USA) and overlaid with a grid of pixels, and the elements overlapped by each pixel

were selected. For each pixel, the fractional transmitted intensity ‘I/I0’ value was

calculated using a discretised version of the X-Ray equation:

(4)

where ‘µi’ is the linear attenuation of each of the ‘N’ elements, based on its density,

and ‘xi’ is its tetrahedral half-depth. These virtual X-Rays allowed the distribution of

bone density adaptations to be observed. They are more informative than plots of

bone density adaptations on a single plane through the FE model, as they illustrate the

adaptation throughout the bone’s thickness.

Figure 4: Results Interpreted using Virtual X-Rays (left) and Virtual DEXA Scans of Femoral

Neck Zones (right)

Second, virtual DEXA (Dual Energy X-Ray Absorptiometry) scans were

carried out for quantitative analysis, measuring the areal Bone Mineral Density

(BMD) associated with defined regions in the medial and lateral femoral neck (Figure

4, right). To corroborate the model’s predictions, the percentage change in BMD from

preoperative levels was compared to clinical measurements of percentage BMD

changes in each of the zones obtained from DEXA scans, reported in the literature at

3, 6, 12 and 24 postoperative months [54-56].

2.6 Study Design

Three models were solved, with no stem-bone contact (with the bore empty), perfect

stem-bone contact (with the bore filled with natural density bone) and gradually

established stem-bone contact (with the bore re-filling through simulated healing).

The first two models employed an algorithm with adaptation through bone

remodelling alone, and are representative of previous approaches used in the literature

[33, 34]. The third model added the healing process to the bone adaptation algorithm.

3. Results

Figure 5: Virtual X-Rays at 0, 3, 12 and 24 Months Follow-Up for a Permanent Stem-Bone Gap

(left), Full Stem-Bone Contact (centre) and a Healing Stem-Bone Gap (right).

Figure 6: Details of Virtual X-Rays for a Healing Stem-Bone Gap.

Figure 7: Charts showing Postoperative BMD Changes in the Six Femoral Neck DEXA Scan

Zones for a Permanent Stem-Bone Gap (top), Full Stem-Bone Contact (middle) and a Healing

Stem-Bone Gap (bottom).

For the two extreme, pure remodelling situations and the healing situation,

bone density variations over the first two postoperative years were predicted and

virtual X-Rays were generated. The postoperative, 3, 12 and 24-Month follow-up

virtual X-Rays (Figure 5) show the predicted bone adaptation around the prosthesis.

Much like real X-Rays, some of the changes were subtle so they are best visualised in

the detail views shown in Figure 6, and on charts of Bone Mineral Density (BMD)

changes from the virtual DEXA scans (Figure 7). The first case, with a permanent gap

around the prosthesis stem and pure remodelling bone adaptation (Figure 5, left)

predicted a slight, progressive increase in BMD in the medial femoral neck (zone

M2). A slight reduction in BMD around the tip of the stem (M3 and L3) was also

predicted, due to the presence of the stem bore, with a reduction in BMD at the

superior head-neck junction (L1) representative of femoral neck narrowing. This was

visible on the virtual x-rays (Figure 5) as a reduction in density at the superior head-

neck junction. Finally, the BMD losses in regions M3 and L1 were both predicted to

recover by 24 months, and the bore remained visible radiographically.

The second case, with full stem-bone contact and pure bone remodelling

(Figure 5, centre) predicted considerable BMD increases in the medial neck, further

down the stem (M2 and M3), in a focussed line between the stem and medial calcar.

Increased BMD was also predicted at the stem tip similar to a ‘pedestal’ line

indicating a stem neo-cortex (L3), with a sustained reduction in BMD at the superior

head-neck junction (L1) indicating femoral neck narrowing.

The third case, with the healing stem-bone gap through combined bone

remodelling and interface healing (Figure 5, right and Figure 6) predicted more

gradual and diffuse BMD increases in the medial neck (M2 and M3) and around the

stem tip (L3), along with sustained narrowing of the femoral neck at its superior edge

(L1). This is best visualised in the close-up image (Figure 6).

The presence of these radiographic changes and their time of appearance are

summarised in Table 2.

Radiographic Change

Scenario

Superior

Head

Resorption

Femoral

Neck

Narrowing

Stem Tip

Pedestal

Line

Medial Neck

Densification

Permanent

Stem-Bone Gap Yes (3mo)

Slight (3mo)

Recovers No Slight (12mo)

Full

Stem-Bone Contact Yes (3mo) Slight (3mo) Yes (3mo) Yes (3mo)

Healing

Stem-Bone Gap Yes (3mo) Yes (3mo) Yes (12mo) Yes (12mo)

Table 2: Presence (and Time of Appearance) of Radiographic Changes in the Three Scenarios

4. Discussion

This study set out to test an algorithm for FE modelling of bone adaptation around hip

resurfacing implants. The hypothesis was that combined simulations of bone

remodelling and implant-bone interface gap healing would predict the distribution of

bone density changes following implantation more closely than remodelling alone.

The simulation of gradual stem-bone interface healing with the new algorithm was

compared to two extreme stem-bone contact situations, with a pure remodelling

algorithm.

The results indicate that neither extreme stem-bone contact situation, with

pure remodelling, produced a complete set of clinically representative bone

adaptations. Without stem-bone contact, radiographic changes in the femoral neck

were incomplete (Table 2), and those changes which were observed were only slight

(Figure 5 left, Figure 7 top). Conversely, stem-bone contact does not exist

immediately postoperatively, so this situation is not realistic and although this model

produced the full set of radiographic changes, they appeared unrealistically fast

(Figure 5 centre, Figure 7, middle). Furthermore, medial trabecular densification was

very focussed in a line tangential to the medial cortex, whereas more diffuse

densification is observed clinically. With the gradually established stem-bone contact

produced by stem-bone interface healing, the results lay between the two extreme,

pure remodelling cases (Figure 5 right). Superior femoral head resorption was similar

to the previous two cases, but femoral neck changes were more consistent with

clinical observations because they occurred more progressively than in the full contact

case (Figure 7, bottom). Bone densification was also more evenly distributed (Figure

6).

This study quantified predictions of postoperative BMD changes in the

femoral neck which could be compared to clinical measurements. Literature data [54-

56] shows a general trend of a BMD drop in the first 3-6 postoperative months which

recovers up to 24 months, reaching approximately 115-125% of the preoperative

level. Greater BMD increases are seen in the medial femoral neck than on the lateral

side. However, a slight increase in BMD in the contralateral hip was reported [56],

consistent with increased postoperative activity. Furthermore, similar magnitude

BMD changes were measured in the operated femur remote from the prosthesis [55],

indicating reduced activity or loading of the operated leg immediately

postoperatively, and later increased activity level or favouring of the treated leg.

These BMD changes are similar in magnitude to those around the prosthesis, and the

reported range of measurement variability was up to approximately ±25% [54]. The

implication is that quantitative comparison with the models may be attempted for the

time scale, but is precluded for BMD change magnitudes due to the high inherent

variability of the clinical data. It was concluded that this data should be interpreted

qualitatively, in conjunction with the reported X-Ray observations.

On that basis, according to the combined model’s predictions, the remodelling

process dominated in the first three months and appeared to account well for the

distributions of femoral head and head-neck junction resorption. After three months,

the stem bore healed sufficiently for the stem to bear load and stimulate remodelling.

For the remainder of the time period, similar BMD change trends were predicted

including a mean increase in the femoral neck, particularly medially.

In comparison to past FE modelling studies, the results obtained with the

modified algorithm show a closer fit to the clinical observations. The results were in

agreement with static models predicting the postoperative remodelling stimulus for

varying extents of stem-bone contact [23, 26]. Pal et al’s adaptive remodelling study

[34] predicted resorption inside the femoral head, with densification where there was

stem-bone contact which led to partial qualitative predictions of clinically observed

radiographic changes. The present work has shown that by incorporating progressive

healing of the surgically introduced defect around the stem, a closer, partially

quantified comparison between these computational predictions and clinical DEXA

data was achieved. This study also produced predictions of the full set of radiographic

changes which are observed clinically around resurfacing implants, including femoral

neck narrowing. In previous work [27], neck narrowing was predicted to be linked to

a shortened horizontal femoral offset in resurfaced hips in comparison to healthy

joints [57], and the present study aimed to achieve such clinically representative

prosthesis positioning and biomechanical measurements. The present study predicted

a BMD reduction at the superior head-neck junction with an internal-remodelling

algorithm, which would be indicative of additional external remodelling of the neck

cortex, which is thin in this region. The study employed virtual X-Rays for

visualisation of adaptations throughout the bone FE model’s full thickness, in an

attempt to obtain more evidence than is visible by observing results on a single plane

through the model. This approach may have made these adaptations more visible.

There were two discrepancies between the model data and clinical

measurements. First, the bone adaptations were predicted to occur artificially fast,

with adaptations largely stabilising in the first 12 months on the virtual X-Rays

(Figure 5), and between 12 and 24 months according to the virtual BMD data (Figure

7). Clinical adaptations are reported to stabilise after 2-3 years [15, 16]. This indicates

that the use of literature values for the healing process parameters (‘D’, the diffusion

coefficient and the ten day smoothing period) may not be optimal for this cancellous

bone defect healing application. This may also explain the second discrepancy, the

development of a focussed dense line of load transfer from the stem to the medial

cortex (Figure 6). More gradual healing of the tapering defect would lead to a

progressive distal shift of the load path along the prosthesis stem, producing a more

diffuse, clinically representative pattern of medial neck bone densification [14]. There

is therefore scope for further research into the selection of bone adaptation process

parameters which yield closer predictions to clinical evidence.

The study was subject to some limitations, as a result of modelling

assumptions and simplifications. In the modelling process, standard model

verification tests were conducted, followed by corroborative comparisons of the basic

model predictions with other modelling and clinical data [27]. The major

simplifications were that a single femur model was used, and that a single load case

was used representing the peak joint contact force instant in the gait cycle. A main

reason for these simplifications was the computational expense of the simulations;

since the goal of the study was the detailed reproduction of a biomechanical process,

accuracy was favoured over short solution time. For a multi-femur analysis attempting

to capture a range of clinical and loading variability, minimal solution time would be

favoured, and with the available computer hardware, solution accuracy would have

been inadequate. Multi femur analysis would also be precluded by the multiple

solution iterative approach, so to minimise the effects of these limitations, an ideal

candidate, orthopaedic disease-free patient, ideal implant position and single load case

were chosen with care.

The limitation of the use of a single femur model is highlighted because

radiographic changes are not observed in all patients. Some extent of femoral neck

narrowing is observed in the majority (up to 90%) of patients [13, 15-18]. Sclerotic

lines around the stem are also common, and radiographically clear lines have been

observed around 60-75% of implants [14, 18]. However, medial trabecular

densification is less usual, observable in only 50% of these patients [14]. This may

explain the subtle nature of some of the adaptations, and illustrates that the study

would benefit from further analyses of different clinical cases.

The justification for gait as the loading scenario was that, as explained by

Frost [40], modelling and remodelling are stimulated most by ‘a time averaged value

of repeated peak strains’ whereas occasional high magnitude strain events have little

influence, provided they do not cause damage. Furthermore, the single peak instant in

the gait cycle was used instead of a number of time averaged instants in the cycle

because low magnitude strains ‘below a minimum effective strain’ of perhaps 2000µε

do not evoke an osteocyte reaction. Finally, the loading conditions were unchanged

between the pre- and post-operative cases, thus neglecting changes in pre- to

postoperative activity levels and biomechanics. The combined effects of these load

case simplifications are minimised by the comparative remodelling stimulus, which

considers only the percentage change in the bone strain field as a result of

implantation. The use of a single load case may have contributed to the formation of

some of the bone adaptations, notably the focussed band of densification between the

implant stem and the medial neck cortex (Figure 6). Use of a variety of load cases to

produce an averaged stimulus would lead to a more diffuse bone density distribution.

However, the band was observed to align tangential to the neck cortex, and not with

the load vector (13° to vertical), so its formation may also be related to the implant-

bone geometry and artificially fast healing, as discussed above. With additional

computer resources, this aspect of the algorithm’s use could be improved, testing its

predictive capabilities more thoroughly.

Similarly, the choices of stimuli for bone healing, modelling and remodelling

are likely to be simplifications of the in-vivo transduction process. It is likely that a

combination of mechanical and biological processes drive remodelling and healing,

but mechanical stimuli alone have been used assuming that they induce a biological

response. Bone modelling and healing may be, at least initially, entirely biologically

driven processes which are influenced by mechanical factors as they progress. The

results show the importance of a defect filling process, regardless of the stimulus.

Although they arise from single studies [50, 58], the strain energy density, equivalent

strain and hydrostatic pressure stimuli have been used repeatedly in the literature,

establishing their suitability through corroboration. The biomechanical behaviour

predicted by models employing these stimuli is in good agreement with clinical

observations, so they can be considered as acceptable analogies to the in-vivo stimuli.

This study aimed to extend their use and combine two biomechanical processes, so

given the assumption that mechanical stimuli drive these processes, it was logical to

base the methods upon established approaches.

There is scope to improve the stimuli employed in the model. Bone

remodelling using a combination of strain and damage stimuli has been reported in

the literature [39, 59], and permits resorption through microdamage accumulation at

high strain levels. The volume of bone at strains likely to stimulate damage resorption

according to the cited studies was typically very low in these models, featuring

correctly oriented prostheses, which indicates that the strain stimulus would dominate.

However, inclusion of damage stimulated bone resorption at high strains may improve

the models’ agreement with clinical observations. As noted previously, there is also

scope to improve the healing process model’s application to cancellous bone defect

refilling. However, the stimuli employed were able to produce predictions of the

patterns of postoperative bone adaptation in overall agreement with clinical

observations, which suggests that they are suitable for comparative investigations.

Finally, although the various algorithm parameters were based on existing published

models, a sensitivity analysis to assess the effects of parameter variability should be

the subject of further research.

5 Conclusions

The results of this study indicated that a combined remodelling and implant-bone

interface healing algorithm produced predictions of bone adaptation around hip

resurfacing prostheses that were closer to clinical data than a remodelling

algorithm alone.

The combined algorithm predicted the appearance of the full set of clinically

observed characteristic radiographic changes, including superior femoral head

resorption, the formation of sclerotic lines around the prosthesis stem, and

narrowing of the femoral neck.

It is accepted that the combined stimulus model tested in this study is a

simplification of the physiology of postoperative adaptation to hip resurfacing.

However, the model has value as a tool for the biomechanical analysis of

traditional resurfacing prosthesis designs, and the potential to contribute to the

pre-clinical analysis of new designs.

The authors would like to acknowledge funding from the EPSRC and the European Union Seventh

Framework Programme. None of the authors has any conflict of interest arising from the research

presented in this article.

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