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Journal of Biomechanics 38 (2005) 1229–1237

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Interrelationship of trabecular mechanical and microstructuralproperties in sheep trabecular bone

Erik Mittra, Clinton Rubin, Yi-Xian Qin�

Department of Biomedical Engineering, Stony Brook University, Psychology-A Building, 3rd Floor, Stony Brook, NY 11794-2580, USA

Accepted 28 June 2004

Abstract

The ability to evaluate fracture risk at an early time point is essential for improved prognostics as well as enhanced treatment in

cases of bone loss such as from osteoporosis. Improving the diagnostic ability is inherent upon both high-resolution non-invasive

imaging, and a thorough understanding of how the derived indices of structure and density relate to its true mechanical behavior.

Using sheep femoral trabecular bone with a range of strength, the interrelationship of mechanical and microstructural parameters

was analyzed using multi-directional mechanical testing and micro-computed tomography. Forty-five cubic trabecular bone samples

were harvested from 23 adult female sheep, some of whom had received hind-limb vibratory stimuli over the course of 2 years with

consequently enhanced mechanical properties. These samples were pooled into a low, medium, or high strength group for further

analysis.

The findings show that mCT indices that are structural in nature, e.g., structural model index (SMI) (r2 ¼ 0:85, po0:0001) is asgood as more density oriented indices like bone volume/total volume (BV/TV) (r2 ¼ 0:81, po0:0001) in predicting the ultimatestrength of a region of trabecular bone. Additionally, those indices more related to global changes in trabecular structure such as

connectivity density (ConnD) or degree of anisotropy (DA) are less able to predict the mechanical poperties of bone.

Interrelationships of trabecular indices such as trabecular number (TbN), thickness (TbTh), and spacing (TbSp) provide clues as to

how the trabecular bone will remodel to ultimately achieve differences in the apparent mechanical properties. For instance, the

analysis showed that a loss of bone primarily affects the connectedness and overall number of trabeculae, while increased strength

results in an increase of the overall thickness of trabeculae while not improving the connectedness.

Certainly, the mCT indices studied are able to predict the bulk mechanical properties of a trabecular ROI well, leaving

unaccounted only about 15–20% of its inherent variability. Diagnostically, this implies that future work on the early prediction of

fracture risk should continue to explore the role of bone quality as the key factors or as an adjuvant to bone quantity (e.g., apparent

density).

r 2004 Elsevier Ltd. All rights reserved.

Keywords: Micro-CT; Bone microstructure; Bone density; Bone strength; Osteoporosis; Bone remodeling

1. Introduction

The ability to accurately assess bone quality in vivo isessential for improving the diagnostic and therapeuticgoals for bone loss from such varied etiologies asosteoporosis, microgravity, bed rest, or stress-shielding

e front matter r 2004 Elsevier Ltd. All rights reserved.

iomech.2004.06.007

ing author. Tel.: +1-631-632-1481; fax: +1-631-632-

ess: yi-xian.qin@sunysb.edu (Y.-X. Qin).

from an implant. Early diagnostic ability is importantbecause the effectiveness of treatment diminishes withdisease progression, yet patients are rarely symptomaticbefore considerable bone loss has occurred—and some-times not until after the first fracture (Davidson, 2003;Homminga et al., 2004).Traditionally, the focus of clinical bone evaluation

has been apparent bone mineral density (BMD) asmeasured by dual energy X-ray absorptiometry orDEXA (Kanis et al., 2002; Brunader and Shelton,

ARTICLE IN PRESSE. Mittra et al. / Journal of Biomechanics 38 (2005) 1229–12371230

2002). DEXA provides an effective way to measureBMD in a specific region of interest (ROI) and is themost widely used diagnostic modality for assessingosteoporosis and osteopenia. However, because itprovides only a 2-D image of apparent density, itsability to assess early fracture risk is limited. Whiledensity (quantity) does positively correlate with strength(Keaveny et al., 2001), about 30% of the variability inbone strength remains unexplained (National Institutesof Health, 2000; Hans et al., 1997). DEXA also suffersfrom an inability to differentiate trabecular fromcortical bone. This is unfortunate since the effects ofbone loss are more prevalent in trabecular bone due toits much higher surface area, and because the greateramount of bone mineral content in cortical bone canconceal small changes in trabecular bone (Brismar et al.,2001). In general, the evaluation of bone status isdifficult because the bone changes are initially quitesmall, may not be highly related to apparent density,and is effectively localized to region (i.e., one femoralhead but not the other) and type of bone (i.e., trabecularbut not cortical bone).Increasingly, evidence shows that bone quality is

important for the evaluation of bone status (Grimm andWilliams, 1997; Pothuaud et al., 2002), but while theidea of quality has been widely accepted, it remains anambiguous term in practice. In essence, quality refers toa combination of bone apparent modulus and strengthas well as some quantified measure of the trabeculargeometry, stereology, micro-damage, material (tissue)and chemical properties of the bone (Judex et al., 2003).Unfortunately many other currently available diag-

nostic modalities (e.g., peripheral DEXA, single energyx-ray absorptiometry, radiographic absorptiometry, andsingle and dual photon absorptiometry) suffer from thesame shortcomings as DEXA since they are relient onthe same underlying technology. Other modalities suchas quantitative computed tomography (QCT) candifferentiate between cortical and trabecular bone, but,because of its resolution, still cannot provide verydetailed microstructural information (Brismar et al.,2001). The broadband ultrasound attenuation (BUA)and ultrasound velocity (UV) coefficients of quantitativeultrasound (QUS) have been significantly correlated toboth density and bulk mechanical properties, respec-tively, but the current technique does not directlyprovide structural or quantity measures. Rather, QUSserves as an useful screening tool (Faulkner, 2001;Nichols et al., 2000).In fact, none have the necessary precision to evaluate

both the quantity and quality of trabecular bone equallywell, except perhaps the newest generation of high-resolution scanners (Genant et al., 1999). These systemsfall into two broad categories—those that are based oncomputed tomography (CT) versus those that aremagnetic resonance imaging (MRI) based. Some of

these are in use clinically, while others are only used inresearch. In general, the clinical scanners have lowerradiation and shorter scan times than their researchcounterparts, but also suffer from lower resolution. TheCT-based scanners includes peripheral QCT (pQCT)(clinical) and micro CT (mCT) (research), while the MRbased modalities includes general MRI scanners (clin-ical) and high resolution MRI (hrMRI) (research).Considering only the higher-resolution research scan-ners, the CT-based machines have better resolution (e.g.,20� 20� 20 mm3 voxel size for mCT), but are limited forhuman use by their high radiation dose and smallallowable sample size. MR-based scanners, on the otherhand, have lower resolution (156� 156� 300 mm3 voxelsize for hrMRI), but are not irradiating and couldtherefore more easily be used in vivo (Brismar et al.,2001).

mCT, which has a limit of approximately 10 mm,provides the best resolution short of using a synchrotronlight source (which has a limit of 1 mm) and has thereforebecome the imaging modality of choice in research overthe past decade. While its use is not novel in research,mCT has recently been adapted for in vivo use in humansas well (Kohlbrenner and Ruegsegger, 2001). Thistechnique is not yet clinically available, but thetechnology is clearly advancing toward that goal.Therefore, understanding the clinical applicability ofthese very high-resolution mCT images would be ofvalue.The objective of this study is to understand the

relative effects of bone quantity and structure onapparent mechanical properties, i.e., elastic modulus,yield strength, and ultimate strength. The following twoaims are pursued. First, a comprehensive analysis of allthe mCT indices is undertaken to understand whichindices best predict the anisotropic qualities of trabe-cular bone strength. Secondly, the mechanical implica-tions of architecture versus quantity provided by theseindices is considered in terms of their clinical impor-tance.

2. Methods

The trabecular bone samples for this study wereobtained from adult female sheep that had previouslyundergone 2 years of vibratory mechanical stimulationas part of an unrelated research study (Rubin et al.,2002), with the treatments resulting in a certain degreeof variation in bone strength and structural properties inthe samples. Of these animals, 18 were part of theexperimental group, and five were part of the controlgroup. As the goals of the current study are simply tocharacterize the ability of microstructural indices topredict apparent mechanical behavior, the samples werenot separated with respect to experimental or control

ARTICLE IN PRESSE. Mittra et al. / Journal of Biomechanics 38 (2005) 1229–1237 1231

groups from the previous study but rather sorted withrespect to ultimate strength and then separated equallyinto high, medium, and low strength groups. In thisway, not only can regression analysis be done betweenthe structural and strength properties, but the micro-structural indices can also be compared between thegroups to see if significant differences would be foundbetween groups with significantly different apparentmechanical properties.

2.1. Bone harvesting

Forty-six bone cubes (10mm in each axis) wereharvested from the center of both the medial and lateralcondyles of the left distal femur of 23 adult sheep using alow-speed diamond blade saw (Microslice, MetalsResearch Limited, Cambridge, England) with contin-uous water irrigation (Fig. 1a). One bone cube wasirreversably damaged during the initial bulk mechanicaltesting such that the final sample size came to 45.Prior to cutting, the femoral shaft was placed at a 451

angle to the blade such that the axes of the resultantcube corresponded to the physiologic superior–inferior(SI; presumed greatest weight bearing), anteroposterior(AP), and mediolateral (ML) directions (Fig. 1a).

Fig. 1. (a) shows the orientation of a bone cube in vivo; (b) is a

schematic close-up of the bone cube placement within the MTS

machine, showing the nail head (black) above the bone; (c) is a sample

image of a sheep trabecular bone cube from the Scanco mCT-20.

Femoral rotation was furthermore standardized bypositioning the bone such that the inferior surfaces ofboth condyles were equally in contact with the cuttingsurface. All the harvesting was performed by one personand standard visual guidelines were used for all femoralcuts (e.g., inferior-most transverse section made justproximal to intercondylar fossa) to ensure that the cubeswere harvested from the same relative location fromeach femur.After harvesting, the cubes were stored in equal

amounts normal saline and 70% ethanol at 4 1C. Thisstorage method was chosen based upon the previouswork of Ashman and colleagues in which they harvestedcancellous bone specimens for mechanical testing andultrasound studies (Ashman et al., 1984, 1985, 1987,1989). Moreover, they had performed specific experi-ments in which they demonstrated that this solutionpreserved the elastic behavior of the ex vivo bonespecimens for several months at room temperature(Ashman et al., 1984). Our own studies, however, showthat after 12 months of storage in this solution at 4 1C,an average 30% reduction in modulus and strength isobserved. For this experiment, the time from the firstbone harvested to the last bone mechanically tested wasapproximately 4 months, with a mean time betweenharvesting and materials testing of only about 1 monthper bone—well within the time frame analyzed byAshman et al. The leaching of mineral over time thatultimately results in this loss of bone strength, however,would not affect the geometry of the samples asvisualized by mCT.

2.2. Materials testing

Direct force–displacement testing was used to deter-mine the Young’s (elastic) modulus and strength of thebulk specimens. Using a mechanical testing machine(MTS Systems Corporation, PA), the bone cubes wereuniaxially loaded in compression using displacementcontrol. To overcome slight deviations from surfaceparallelism, a smoothly curved nail head was placedabove the bone cube such that the force would bedistributed evenly to the bone (Fig. 1b). An upper limitof 300N of force—determined by prior loading of non-experimental but otherwise identical bone cubes—wasestablished to prevent the plastic yielding of anyspecimens. The loading rate was approximately1000 me/s. Prior to data collection, several precondition-ing cycles of 1% strain was used to overcome edgeeffects from the harvesting process. This precondition-ing consisted of at least five cycles, and was stoppedonce the preload stabilized at around 10N or reachedeight cycles (whichever came first). Subsequently, threeexperimental compressions of 1% strain were done andthe final result was taken to be the average of these threevalues.

ARTICLE IN PRESSE. Mittra et al. / Journal of Biomechanics 38 (2005) 1229–12371232

Both displacement and force was digitized using MTSBasicTestware software. Force–displacement was con-verted to an analogous stress–strain curve by dividingforce by the cross-sectional area, and displacement bylength (each cube was measured independently to reducethe geometrical error inherent in harvesting). Afterscanning in the mCT, the bones were tested to failure inthe SI direction. The material properties studied includemodulus, yield strength (calculated using the 0.2%strain offset method), and ultimate strength.

2.3. Micro computed tomography

After the initial materials testing, the bones werescanned in a mCT machine (mCT-20, Scanco Corp.) witha voxel resolution of 34 mm in all axes. A sample imagefrom the mCT machine is shown in Fig. 1c. The mCTproperties analyzed (using built-in code) include bonevolume over total volume (BV/TV; or bone volumefraction (BVF)), degree of anisotropy (DA), structuralmodel index (SMI), trabecular spacing (TbS), trabecularnumber (TbN), trabecular thickness (TbTh), and con-nectivity density (ConnD). In addition, the meanintercept length (MIL) function ultimately gives theanisotropy tensor from which the principal trabecularaxis (the highest ranked eigenvalue) can be derived(Cowin, 1985). The complete explanation of the variousmCT indices and their respective derivation/calculationis found in several sources (Fajardo and Muller, 2001;Hildebrand et al., 1999; Hildebrand and Ruegsegger,1997a, b) and so is not repeated here.

Table 1

Average7SD for mCT and mechanical indices studied

Overall Low strength Medium strengt

n 45 15 15

SI E (MPa) 542778 462751 551734

AP E (MPa) 4547108 358791 455755

ML E (MPa) 3597104 256769 361749

Bulk E (MPa) 452791 359759 455740

Yield s (MPa) 1777 1072 1672

Ult. s (MPa) 1977 1272 1872

BV/TV 0.2870.07 0.2270.02 0.2770.03

ConnD 4.9470.93 5.1270.70 5.4070.90

SMI 0.1270.69 0.7970.28 0.1970.28

TbN 1.7070.13 1.5970.07 1.7470.10

TbTh 0.1970.05 0.1670.02 0.1870.01

TbSp 0.5370.05 0.5870.03 0.5270.03

DA 1.9070.18 1.8070.15 1.9070.17

The given p-values are the results of a one-way ANOVA comparing the mecha

medium, and high). ConnD, TbN, TbTh, and DA were the only indices not

column indicates which of the three strength groups were significantly diffe

inferior modulus; AP E=antero-posterior modulus; ML E=medio-lateral

directions); Yield s=yield strength; Ultimate s=ultimate strength; B

SMI=structural model index; TbN=trabecular number; TbTh=trabecular

2.4. Statistics

The data was analyzed using Analyze-it version 1.67.Comparisons of like indices (such as the orthogonalmodulus in sheep) was analyzed with a one-wayANOVA with Tukey posthoc pairwise comparisons.Un-related indices (like the different mCT indices) werecompared with multiple linear regression and Pearson’sproduct moment correlation coefficient. In all cases, thesignificance level was set at po0:05.

3. Results

3.1. Distribution of bulk mechanical properties

The average values for all the mechanical andmicrostructural parameters tested are shown inTable 1. The range of values is consistent with theliterature (Keaveny et al., 2001). The overall elasticmodulus in the SI direction (542778MPa) is greaterthan the AP direction (4547108MPa), which is stillgreater than the ML direction (3597104MPa). Thesedifferences are all significantly different from oneanother both overall as well as in the low, medium,and high strength groups (all have po0:0001).Comparing across the three strength groups, each of

the mechanical properties—elastic modulus (in anyof the orthogonal directions), yield strength, andultimate strength—were significantly different fromone another (po0:0001) (Table 1). The comparison of

h High strength ANOVA p-value Significant pairs

15 — —

612757 o0.0001 All

549778 o0.0001 All

461767 o0.0001 All

541757 o0.0001 All

2476 o0.0001 All

2675 o0.0001 All

0.3670.05 o0.0001 All

4.3570.91 0.0098 M vs. H

�0.6170.52 o0.0001 All

1.7870.14 0.0002 L v. M

L v. H

0.2370.07 0.0026 L v. H

M v. H

0.4870.04 o0.0001 All

1.9970.16 0.0204 L vs. H

nical or microstructural indices between the three strength groups (low,

significantly different between all three indices. The ‘‘Significant Pairs’’

rent using Tukey posthoc pairwise comparisons.Key: SI E=superior-

modulus; Bulk E=bulk modulus (average of the three orthogonal

V/TV=bone volume/total volume; ConnD=connectivity density;

thickness; TbSp=trabecular spacing; DA=degree of anisotropy.

ARTICLE IN PRESSE. Mittra et al. / Journal of Biomechanics 38 (2005) 1229–1237 1233

microstructural indices across these three groups,however, was not as clear. Three of the indices, bonevolume/total volume (BV/TV), structural model index(SMI), and trabecular spacing (TbSp) were, in fact,different between all three groups. Trabecular number(TbN) (p ¼ 0:0002) and trabecular thickness (TbTh)(p ¼ 0:0026) were significantly different between twopairs each (TbN: low vs. medium and low vs. high;TbTh: low vs. high and medium vs. high), whileconnectivity density (ConnD) (p ¼ 0:0098) and degreeof anisotropy (DA) (p ¼ 0:0204) were only significantlydifferent between one pair each (ConnD: medium vs.high; DA: low vs. high).

3.2. Interrelationship of mechanical and microstructural

properties

Table 2 is a complete listing of the coefficients ofdetermination between all the variables studied for thesheep bones and it reveals several notable outcomes. Forease of reading here and in the table, please note thatwhere p-values are not given, po0:0001. Firstly, theelastic modulus (E) correlates well with both yield stress(sy) (r2 ¼ 0:69) and ultimate stress (su) (r2 ¼ 0:74).Expectedly, sy and su correlate very well together(r2 ¼ 0:98). There were no clear differences between

Table 2

r2 values between all mechanical and microstructural indices studied

SI E AP E ML E Bulk E SI YS SI US BV/TV

SI E 1.00 0.64 0.58 0.85 0.58 0.61 0.40

p

AP E 1.00 0.71 0.87 0.61 0.64 0.49

p

ML E 1.00 0.86 0.64 0.67 0.58

p

Bulk E 1.00 0.69 0.74 0.54

p

sI YS 1.00 0.98 0.79

p

SI US 1.00 0.81

p

BV/TV 1.00

p

ConnD

p

SMI

p

TbN

p

TbTh

p

TbSp

p

DA

p

Note: r2 values without associated p-values indicate po0:0001. Values in ita

the individual directional E in sheep with respect to howwell they correlated with either the yield or ultimatestrength or the microstructural parameters. For in-stance, su correlated about equally well with SI E

(r2 ¼ 0:61), AP E (r2 ¼ 0:64), and ML E (r2 ¼ 0:67),although there was a trend for the ML value toconsistently correlate better than the AP value, whichcorrelated better still than the SI value.BV/TV correlated with su (r2¼0:81) about the same as

with sy (r2¼0:79) and better than with E (r2¼0:54).However, SMI actually correlates slightly betterwith su (r2¼0:85) than BV/TV does (Fig. 2).Not surprisingly then, SMI and BV/TV correlated verywell together (r2¼0:94). Considering the other structuralindices, TbN correlated well with TbSp (r2¼0:88),but not significantly with TbTh (r2¼0:02, p ¼ 0:3168).ConnD and DA correlated the least well withother parameters. ConnD was not significantly corre-lated with any of the orthogonal moduli or thebulk modulus (r2¼0:03, p ¼ 0:2302), nor with TbSp(r2¼0:01, p ¼ 0:3609). DA did not significantly correlatewith two of the three orthogonal moduli (AP andML) and neither with TbN or TbTh. The only otherlack of correlation in between the structural indicesthemselves was between TbTh and TbN (r2¼0:02,p ¼ 0:3168).

ConnD SMI TbN TbTh TbSp DA

0.03 0.36 0.14 0.19 0.25 0.15 SI E

0.2012 0.0051 0.0008 0.0042 p

0.06 0.46 0.12 0.25 0.27 0.06 AP E

0.0741 0.0081 0.0796 p

0.02 0.05 0.30 0.26 0.46 0.04 ML E

0.3492 0.1206 p

0.03 0.49 0.23 0.26 0.37 0.10 Bulk E

0.2302 0.0003 0.0157 p

0.14 0.85 0.40 0.19 0.66 0.27 SI YS

0.0204 0.0062 p

0.12 0.87 0.42 0.20 0.69 0.25 SI US

0.0319 0.0053 p

0.16 0.94 0.35 0.59 0.62 0.14 BV/TV

0.0024 0.0037 p

1.00 0.20 0.14 0.26 0.01 0.23 ConnD

0.0005 0.0048 0.3609 0.0002 p

1.00 0.31 0.46 0.55 0.16 SMI

0.0026 p

1.00 0.02 0.88 0.04 TbN

0.3168 0.1252 p

1.00 0.14 0.03 TbTh

0.0057 0.1997 p

1.00 0.08 TbSp

0.0325 p

1.00 DA

p

lics indicate p40:05.

ARTICLE IN PRESS

High Med LowExperimental

loadingaxis

Long axisof sheep femora

Average

Fig. 3. Demonstration of calculated principal trabecular axes (PTA)

overlying a sample trabecular bone cube for ease of visualization. The

experimental loading axis, at 901, and the long axis of the sheep, at 451,

form the outer boundaries of the derived PTA’s. The PTA of the low,

medium, and high strength groups lie 261, 141, and 121, respectively,

away from the experimental loading axis, with a trend toward

approaching the experimental loading axis as the mean ultimate

strength of the bone increases. The average of all strength groups was

181 and is shown as the central line. A one-way ANOVA showed

significant differences overall (po0:0001) with post hoc analysis

demonstrating that the PTA of the low strength group was

significantly different than both the medium and high strength groups,

but with no significant differences between the PTA’s of the medium

and high strength groups.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SMI BV/TV TbS TbN DA TbTh ConnD MILmicro-CT index

r2 val

ue(

wit

h u

ltim

ate

stre

ng

th)

Fig. 2. Relative r2 values of various mCT indices versus ultimate

strength (US).

E. Mittra et al. / Journal of Biomechanics 38 (2005) 1229–12371234

3.3. Derivation of principal trabecular orientation

The direction of the principal trabecular axis (PTA) inrelation to the SI axis (the presumed direction ofprincipal loading) in the overall sheep data is shown inFig. 3. The PTA was calculated as the directionassociated with the largest eigenvalue of the fabrictensor, which is in turn derived from a 3-D mean

intercept length (MIL) analysis of the mCT image. Dueto methodological limitations, this vector could only becalculated with respect to the Z-axis. The mean PTA ofall 3 strength groups lies 181 off the principal loadingaxis (equivalent to the superior–inferior (SI) axis and thez-axis). The mean PTA of the low, medium, and highstrength groups lies 261, 141, and 121 off the prinicipalloading axis. The trend is clearly that the PTAapproaches the principal loading axis as the meanstrength of the group increases. A one-way ANOVA ofthese PTAs showed significant differences overall(po0:0001) with post hoc analysis demonstrating thatthe PTA of the low strength group was significantlydifferent than both the medium and high strengthgroups, but with no significant differences between thePTAs of the medium and high strength groups.

4. Discussion

The interrelationship of trabecular mechanical andmicrostructural properties is important for two principalreasons for better understanding consequences oftrabecular remodeling, and for the potential improve-ment of diagnostic measures for bone loss. The results ofthis study are able to shed some lights on both of theseissues.The significantly different elastic moduli in the three

orthogonal directions tested for the sheep cubes under-lines the highly anisotropic nature of trabecular bone.More specifically, the fact that the modulus was rankedsuch that SI4AP4ML (from high value to low value)supports the notion that the trabecular bone willorganize itself to withstand the greatest force in thedirection of maximal loading. This anisotropic patternwas maintained regardless of which strength group wasanalyzed, indicating this is a very basic feature oftrabecular bone which does not change with overallbone status. This idea is further characterized throughthe principal trabecular axis (PTA) analysis. Theaverage PTA for all the sheep lies 181 off the SI axis,presumably because the trabeculae have orientedthemselves essentially halfway between the 451 of thelong-axis of the sheep femur, and the 901 of theexperimental loading axis (i.e., the SI axis itself) (Fig.3). However, as the ultimate strength of the boneincreases, this PTA trends toward the SI axis. Thisprovides more evidence, then, for trabecular reorganiza-tion toward the principal loading axis to increase itsability to withstand greater forces. Homminga andcolleagues (Homminga et al., 2004) recently reportedvery similar findings in that osteoporotic vertebraltrabeculae, imaged by mCT, were more oriented in thelongitudinal direction than normal controls. Moreoever,mFEM analysis of these samples found that undernormal loading conditions, both osteoporotic and

ARTICLE IN PRESSE. Mittra et al. / Journal of Biomechanics 38 (2005) 1229–1237 1235

normal bone had similar load distributions, while undercollateral loads, the osteoporotic cancellous bone had agreater percentage of highly loaded trabeculae. That is,the trabeculae, while losing mass, retains the necessaryorientation to maximize load distribution along theprincipal loading axis.Of the mechanical parameters analyzed, su is the most

clinically relavent since it signifies when fractures willtruly occur (at least for the ROI comprised by the cubicbone sample). In the sheep bone, su was correlated mosthighly with SMI (r2¼0:87) followed by BV/TV(r2 ¼ 0:81). That BV/TV (a 3-D substitute for apparentbone density) performed well is not particularlysurprising, but the fact that SMI (a purely architecturalindex) performed equally well is. Specifically, this is ofdiagnostic interest since it implies that not only canarchitecture be considered an adjuvant to density for theevaluation of bone status, but may even be a viablealterantive to it. At the very least, the combined use ofboth density and architecture should be emphasized inthe future development of modalities for assessingfracture risk. In fact, as yet unpublished work by ourown group as well as work by Homminga and others(Homminga et al., 2003) show that using only micro-structural information in a linear elastic mFE model ofcancellous bone (with static, homogeneous materialproperties) can accurately predict the apparent levelmechanical properties very well. The great benefit ofsuch methods is that it directly computes the mechanicalproperties of the skeletal volume of interest rather thanrelying on an indirect relationship between density andstrength.The strong correlation between BV/TV and SMI

(r2¼0:94) implies some real connection between theseindices but does not necessarily suggest that they aresampling the same feature of the bone. Most clearly, itsuggests that the shape of individual trabeculae issensitive to the amount of bone present, while SMIrepresents the ratio of plate- and rod-like structures. Inother words, a loss of bone causes trabeculae to becomerod-like while a net increase in bone volume causes themto become quite plate-like. It should also be consideredhowever, that the algorithm for SMI is perhaps verysensitive to BV/TV such that it is better able to calculatethis index for trabeculae when the bone volume is highwhile it may miss thinner plate-like trabeculae when theoverall bone volume fraction is low. This confirms thenotion that remodeling of trabecular bone will alter thesize and shape of individual trabeculae, but will notcause large perturbations in the overall geometry ormicrostructure of the bone.An analysis of the other microstructural indices gives

further credence to this theory. The two microstructuralindices that best capture the overall picture of thetrabecular geometry (or, in other words, are leastsensitive to changes only in individual trabeculae) in

any given ROI is the connectivity density and degree ofanisotropy. In fact, these two indices were the least wellcorrelated with both the apparent mechanical propertiesand even several of the other microstructural indices(e.g., TbN, TbTh, and TbSp). For instance, ConnDcorrelated poorly with TbN (r2s ¼ 0:14, p ¼ 0:0048) andTbS (r2s ¼ 0:01, p ¼ 0:3609), but slightly better withTbTh (r2s ¼ 0:26). Taken together, this implies that anincrease in bone through therapeutics results in athickening of existing trabeculae, but does not increasethe number of trabeculae.This is furthered by the fact that both SMI and BV/

TV correlated very highly with TbTh and TbS, and lessso with TbN and ConnD. Mechanistically, this indicatesthat an increase in bone volume results in an increase intrabecular diameter (and a concurrent decrease in thespace between trabeculae) but does not cause anincrease in trabecular number or connectivity. In short,mechanical countermeasures for bone loss can increasethe size of existing trabeculae but does not lead to theformation of new trabeculae. However, ultimatestrength is correlated better with TbN (r2 ¼ 0:42) thanwith TbTh (r2 ¼ 0:20) suggesting that the maintenanceof trabeculae is more important for the strength of thebone than is a subsequent increase in the thickness ofremaining trabeculae.

4.1. Limitations

Even though the bone cubes were mechanically tested,on average, within one month of being harvested, sincewe did observe a 30% reduction in elastic modulus at 12months post harvesting, we further analyzed oursamples to confirm that our storage methods did notresult in unexplained errors in our analysis by compar-ing the elastic modulus values obtained after initialharvesting versus those obtained 12 months later. The30% reduction in modulus was found on a subset ofbones (n ¼ 6) tested at the same strain rate as at theinitial timepoint. However, when all the bones wereretested at the 12 month timepoint, they were unin-tentionally tested at a higher strain rate. Interestingly,the increase in stiffness from the higher strain rate seemsto have cancelled the decrease in stiffness from mineralloss over time as the average elastic modulus at 12months (5247150MPa) was very similar to themodulus at the initial timepoint (5207106MPa).Moreoever, the correlation between these two sets ofdata was also significant (r2 ¼ 0:65, po0:0001). Lastly,the elastic modulus values at 12 months was used toreanalyze the correlations to the mCT derived structuralindices done with the initial testing (and found in thefirst line of Table 2). The r2 and p values for the re-evaluation of these correlations are as follows: BV/TV=0.79, po0:01; ConnD=0.10, po0:06; SMI=0.81,po0:01; TbN=0.43, po0:01; TbTh=0.20, p ¼ 0:01;

ARTICLE IN PRESSE. Mittra et al. / Journal of Biomechanics 38 (2005) 1229–12371236

TbSp=0.70, po0:01, DA=0.24, po0:01. The correla-tion coefficients either went up or stayed the same, butthe net relationships (whether significant or not) stayedthe same. Based on these analyses of the initial and 12month timepoint moduli, we feel confident that thechosen storage method preserved the elastic behavior ofthe bone samples during the few months in which theywere tested, similar to the finding by Ashman et al.(1984).With regard to other limitations, this study did not

include a direct comparison of the microstructuralindices with the current clinical densitometry techniquessuch as bone mineral density derived from DXAscanning. This shortcoming is currently being addressedin a related study. Still, these results are obviouslydifficult to relate clinically. Additionally, while the bonesamples studied did have a fairly large range of ultimatestrength (7–37MPa, mean of 1977MPa), they were allderived from healthy adult sheep, and so does notinclude the very low range of trabecular bone strengthpossible in, say, diseased human bone. Again, this isbeing addressed in our current research, but limits theresults from this study somewhat. Despite these issues,the results are quite strong and clearly indicate thedirection for future research in the non-invasive assess-ment of trabecular bone status.

5. Conclusion

The traditional dogma for the evalution of bonestatus has consistently been dependent upon bonequantity or bone density. More recently, it is becomingmore clear that bone quality is also quite important inthe assessment of bone status. As advances in imagingresolution continue to allow more and more detailedviews of the bony microstructure of trabecular bone, it isimportant to understand which of the myriad architec-tural indices are truly useful for the prediction offracture risk. Using a sheep model, this study directlyanalyzed the relative usefulness of seven differentarchitectural indices in the prediction of elastic modulus,and yield and ultimate strengths. The results show twoprinicipal findings.Firstly it was shown that purely architectural indices

such as structural model index (SMI) could predict theultimate strength of bone as well as the more densitybased index of bone volume/total volume (BV/TV).Therefore, it is clear that a limited focus on density isnot valid. Additionally, an analysis of the variousstructural indices showed that those parameters bestable to pick up subtle changes in the shape of trabeculaeare better able to predict the mechanical properties ofbone than those that provide a value for overallconnectedness or degree of anisotropy. This is alsosupported by the fact that the relative orthogonal

moduli does not change in relation to changing strength.This data is completely in accord with previous researchsuggesting that bone remodeling (whether to add or losebone) will alter mainly the surface topography ofindividual trabeculae, while leaving the general shapeintact (though not the alignment of the trabeculae asevidenced by the altered PTAs between the threestrength groups).Future work is needed to validate these results to

more clinical indices such as bone mineral density (fromDXA) and with the inclusion of bone that is on the lowend of the bone density spectrum, such as bone fromhumans with osteoporosis.

Acknowledgment

This work is kindly supported by the National SpaceBiomedical Research Institute (TD00207, Qin) throughNASA Cooperative Agreement NCC 9-58.

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