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Keywords:

  • bone mechanics;
  • bone quality;
  • cancellous bone;
  • bone remodeling;
  • osteoporosis treatments

Abstract

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. REFERENCES

We evaluated the effects of resorption cavities on cancellous bone strength using computational methods. Adding cavities to cancellous bone caused reductions in strength and stiffness that were greater than expected from the associated changes in bone volume and more pronounced when cavities were targeted to regions of high tissue strain.

Introduction: The amount of bone turnover in the skeleton has recently been implicated as a factor influencing bone strength. One mechanism proposed to explain this effect is that resorption cavities reduce the effective thickness of trabeculae and modify local stress distributions leading to reduced mechanical performance of the entire structure. In this study, we tested the plausibility of this mechanism.

Materials and Methods: High-resolution finite element models were created from μCT images of 16 vertebral cancellous bone samples, as well as from images of the samples in which cavities had been added digitally—either at regions of high strain (targeted) or placed at random on the bone surface (nontargeted). The effect of resorption cavities on predicted bone strength and stiffness was evaluated by comparing the relationships between mechanical properties and bone volume fraction among the three groups (the original images, those with nontargeted cavities, and those with targeted cavities).

Results: Addition of resorption cavities modified the relationship between mechanical properties and bone volume fraction in the finite element models such that, for a given bone volume fraction, stiffness and yield strength were reduced compared with the original images (p < 0.05). The differences in yield strength–volume fraction relationships between the original models and those with targeted cavities were significantly greater than those between the original models and those with nontargeted cavities (p < 0.05). None of the differences in predicted mechanical properties per unit bone volume fraction could be accounted for by 3D measures of microarchitecture.

Conclusions: Resorption cavities may influence cancellous bone strength and stiffness independent of their effect on bone volume. The effects of cavities on bone mechanical performance relative to bone volume are greater when cavities are targeted to regions of high strain and cannot be predicted using standard microarchitecture measures.


INTRODUCTION

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. REFERENCES

Recent observations that reductions in fracture risk associated with antiresorptive therapies are greater than would be expected from changes in areal BMD (aBMD, g/cm2)(1,2) have led to increased interest in other determinants of bone strength. Observations that biochemical markers of bone remodeling can predict fracture risk independent of aBMD(3,4) have led to the suggestion that the amount of bone turnover influences bone mechanical performance.(5–7) Although bone turnover can regulate bone volume and the degree of mineralization,(8–10) cavities formed during the remodeling process (referred to here as resorption cavities) can influence bone microarchitecture by perforating and disconnecting individual trabeculae.(5–7) It has also been suggested that the very presence of a resorption cavity on a trabecula can influence bone strength by modifying local tissue strains and increasing the likelihood that the trabecula will buckle.(7,11,12) Because antiresorptive agents can fill and/or reduce the number of cavities but cannot replace disconnected trabeculae,(13) understanding the influence of cavities independent of perforation should provide insight into how these agents might alter bone strength.

Given the difficulty of isolating the microarchitectural effect of resorption cavities experimentally, our current understanding of their effects on bone mechanics is based on computational studies. Finite element analyses of individual trabeculae have shown that the presence of a resorption cavity can greatly increase local tissue strains,(14–16) supporting the idea that cavities may act as “stress risers.” In addition, in models of the entire cancellous bone structure, removal of bone tissue experiencing the greatest strains during loading caused large changes in the distribution of strain throughout the structure, suggesting that where a cavity is placed can be very important mechanically.(15) Because these studies used only elastic finite element analysis techniques, they did not address bone strength directly nor could they account for the large deformation and buckling failure mechanisms that have been proposed to explain the potential effects of cavities on cancellous bone strength.

The overall goal of this research was to improve understanding of the link between bone turnover and cancellous bone strength. Using μCT-based, nonlinear finite element models of vertebral cancellous bone, the objectives of this study were to (1) determine the biomechanical effects of adding resorption cavities that do not disconnect trabeculae, after accounting for differences in bone volume fraction, and (2) determine the degree to which preferential placement of cavities at highly strained regions influences any of the observed effects. Compared with related studies in this area, this study is novel in that it uses finite element methods that have been validated for prediction of cancellous bone strength and addresses the effects of resorption cavities independent of trabecular connectivity and bone volume fraction.

MATERIALS AND METHODS

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. REFERENCES

Sample preparation

Sixteen fresh frozen vertebral bodies (L4 or L5) were harvested from donors 54–90 years of age (seven men, 54–90 years, mean, 72.4 years; 9 women, 54–85 years, mean, 73.2 years) with no history of diseases known to influence bone metabolism. One cylindrical core was taken from each vertebral body in the superior–inferior direction. Each specimen was imaged at 22-μm resolution using μCT (μ-CT 40; SCANCO Medical, Basserdorf, Switzerland). The resulting image was thresholded using a mass-compensated hexahedral method,(17) and a cube (5 mm in each dimension) was removed from the center of the image for subsequent analysis. Bone volume fraction of the cubes ranged from 5.1% to 18.1% and was not significantly related to donor age or sex.

Addition of resorption cavities

Resorption cavities were added to the cancellous bone structure in the following manner (Fig. 1): a seed point was selected from surface voxels. Paths across the bone surface emanating from the seed point were labeled to define cavity length and width. Although resorption cavities are typically shown as hemispherical, existing evidence suggests that they are much longer than they are wide.(18) Cavity surface size was set to 500 μm long and 200 μm wide (22 voxels long by 9 voxels wide), matching the typical cavity surface size reported y Mosekilde.(19) Cavity depth was defined by labeling voxels within a specified radius of the surface so that cavity edges were gradual. Cavity depth was set in this manner to 44 μm (two voxels), a value approximating the median erosion depth found in the iliac crest of healthy postmenopausal females (49.1 μm)(20) and typical of erosion depth measured by others.(21) The process was repeated by adding additional cavities until a total of 6% of the original bone volume was labeled for removal. The value of 6% was based on estimates of the volume occupied by cavities in the lumbar spine of postmenopausal women.(8) Resorption cavities were allowed to overlap each other, but the seed point for each new cavity was required to be on a bone surface not yet associated with a cavity. After all cavities were placed, labeled voxels were removed from the model simultaneously. Any remaining bone voxels that were isolated from the cancellous bone structure (floating within the porous volume) were also removed. If the resulting bone volume was <93.9% of the original volume or if any trabeculae were disconnected, the resulting image was discarded and the entire process was repeated.

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Figure Figure 1. (A) Cavities were added to the image of each specimen using custom software that prevented the cavities from disconnecting any trabeculae. Colored regions represent resorption cavities added to the bone surface. (B) Three finite element models were generated for each sample, one of the original image, one with resorption cavities placed at random (nontargeted), and one with resorption cavities placed on surface tissues experiencing the greatest tissue strain (targeted).

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To isolate the independent effects of cavity existence and cavity location, a series of parameter studies was performed. Three cases were analyzed for each specimen: (1) the original image of the bone specimen without cavities added; (2) the same specimen with resorption cavities added to the bone surface at random (nontargeted); and (3) the same specimen with resorption cavities placed at regions of greatest magnitude maximum principal strain (targeted). Seed points for targeted simulations were selected in order of greatest absolute principal strain as observed in a linear elastic finite element analyses performed on the original image. To determine if trabecular microarchitecture differed between the three models, 3D measures of trabecular thickness (Tb.Th), trabecular number (Tb.N), trabecular separation (Tb.Sp), bone surface to volume ratio (BS/BV), degree of anisotropy (DA), and structure model index (SMI, a measure that describes the degree to which the structure is platelike or rodlike) were performed using 3D model-independent algorithms.(22,23)

Mechanical properties and evaluation of bone strength

Each image was converted into a high-resolution finite element model made up of eight-noded brick elements. Linear elastic high-resolution finite element models have long been capable of predicting cancellous bone elastic modulus.(24) Recent advancements have also accounted for tissue and geometric nonlinearities (buckling and large deformation), important for the prediction of cancellous bone strength.(25–27) The inclusion of such details is necessary for this study, because buckling has been proposed as a potential mechanism behind the unique effect of resorption cavities.(7,11,12) The finite element model of bone tissue used in this study accounts for these details using a finite plasticity model modified to include tension-compression asymmetry through pseudo-kinematic hardening.(28) Tissue-level yield was based on von Mises yielding, resulting in tissue yield strains of 0.81% and 0.33% in compression and tension, respectfully, matching those determined in calibration studies.(29) The model was validated in another study using 54 fresh frozen cancellous bone cadaver specimens that had undergone μCT imaging as well as mechanical testing (22 tested in compression and 32 in tension).(27) Differences in elastic modulus, yield strain, and yield strength between experimental measures and those obtained using this finite element formulation were not significantly different from zero (p > 0.13).(27) Thus, these models provide realistic predictions of elastic modulus and yield strength of cancellous bone specimens. In this study, a specimen-specific tissue elastic modulus was assigned using a combined experimental–computational analysis.(24)

Each model (16 original images, 16 with nontargeted cavities, 16 with targeted cavities) was loaded to 1% apparent strain in compression along the primary loading direction (superior–inferior) to generate predictions of the yield strength, yield strain, and elastic modulus. The finite element models contained between 0.56 and 2.12 million elements and were solved on the IBM Datastar supercomputer (National Partnership for Advanced Computational Infrastructure, San Diego Supercomputer Center, San Diego, CA, USA). The 48 simulations performed for this study used ∼1800 supercomputer processor hours.

Simulations with resorption cavities had less bone volume and therefore were expected to show reduced strength and stiffness compared with the original sample. To determine if the reduction in strength and/or stiffness was greater than would be expected from the imposed 6% reduction in bone volume, the relationships (regression lines) between these mechanical properties and bone volume fraction were compared between the three model types. In this way, we accounted statistically for effects of cavity presence independent of variation in bone volume fraction. As a secondary evaluation, the average strength:bone volume fraction and elastic modulus:bone volume fraction ratios were compared between the three model types.(30) A difference in the yield strength–bone volume fraction or modulus–bone volume fraction characteristics between the original images and those with cavities indicated a change strength or stiffness per unit bone volume. Comparison of the relationships between mechanical properties (strength or elastic modulus) and bone volume fraction were performed using repeated-measures ANCOVA (version 11.0.3; SPSS, Chicago, IL, USA). Repeated-measures techniques were used because the computational analysis produced outcome parameters for all cases on each specimen. Differences in the yield strain, yield strength:bone volume fraction, and elastic modulus:bone volume fraction ratios between models were compared using repeated-measures ANOVA and confirmed through matched pairs comparisons. Repeated-measures ANCOVA was also used to determine if there were differences in trabecular microarchitecture measures between model types after accounting for the effect of bone volume fraction. Additional analyses were performed to determine if accounting for variations in trabecular microarchitecture measures could explain any observed differences between the three model types. Multiple comparisons were performed using the Holm test.

RESULTS

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. REFERENCES

The addition of resorption cavities changed the relationships between all predicted compressive mechanical properties and bone volume fraction (Fig. 2). Percent reductions in yield strength for a 6% bone loss in the form of targeted cavities (41.68 ± 8.54 [SD]) were significantly greater than those predicted for nontargeted cavities (17.45 ± 2.75). In contrast, in the original data set, a 6% decrease in bone volume across specimens was associated with only a 6–7% decrease in yield strength and elastic modulus. Percent reductions in yield strength and elastic modulus caused by cavities were greatest in specimens having lower initial bone volume (Fig. 3). Percent reductions in yield strength were significantly greater than the reductions in elastic modulus (p < 0.01). The slopes of the linear strength–bone volume fraction and modulus–bone volume fraction relationships differed significantly among model types (p < 0.05 for all possible comparisons; Table 1). The repeated-measures statistical tests were found to be highly sensitive to differences among groups, allowing for the detection of differences that were very subtle (Fig. 2, slopes for original and nontargeted groups). The slope of the strength–bone volume fraction relation in models having targeted cavities was 25% lower than that for models without cavities. The ratios of yield strength to bone volume fraction and of elastic modulus to bone volume fraction for models with targeted cavities were 36% and 25% lower than those observed for the original images. Significant differences in these ratios were observed between each of the three model types (p < 0.01; Table 1). Minor but significant differences in yield strain were observed among the three model types (p < 0.001 for each comparison). Donor age and sex did not significantly contribute to the slopes of the yield strength–bone volume fraction or elastic modulus–bone volume fraction relationships.

Table Table 1.. Parameter Estimates (SE) for the Strength, Bone Volume Fraction, and Elastic Modulus
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Figure Figure 2. The relationships between sample bone volume fraction and (A) yield strength and (B) elastic modulus are shown. The three types of models differed from each other in terms of regression slopes (p < 0.05). The sensitivity of repeated-measures techniques allowed the detection of small differences in slope between the original and nontargeted models.

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Figure Figure 3. The percent reductions in (A) yield strength and (B) elastic modulus from that measured in the original models were negatively correlated with original bone volume fraction.

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Small differences in microarchitecture parameters were observed among groups (Table 2). With the exception of DA, all the measured microarchitecture parameters were correlated with bone volume fraction within each group (p < 0.01, magnitude of Pearson's r ranged from 0.65 to 0.88). Yield strength and elastic modulus were significantly correlated with all of the microarchitecture measures except DA (p < 0.05 within each group; Table 3). After accounting for the effects of bone volume fraction, many of the correlations between microarchitecture and mechanical properties were no longer significant (Table 4).

Table Table 2.. Average (SD) of Measured Microarchitecture Indices
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Table Table 3.. Pearson Correlation Coefficients Between Microarchitecture Measures and Mechanical Properties Within Each Group
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Table Table 4.. Partial Correlations Accounting for Effect of BV/TV Within Each Group
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Microarchitecture measures were not able to explain the observed differences in biomechanics–bone volume fraction characteristics among the groups. None of the measured microarchitecture indices contributed to the slope of the elastic modulus–bone volume fraction relation (p > 0.09). Trabecular thickness and mean intercept length both showed significant contributions to the slope of the yield strength–bone volume fraction relation (p < 0.05) but could not explain the observed differences among model types (p < 0.05). The strength:bone volume fraction ratio was significantly correlated with trabecular number, trabecular separation, and SMI within each group (p < 0.05, magnitude of Pearson's r ranged from 0.53 to 0.77). The elastic modulus:bone volume fraction ratio was significantly correlated to trabecular separation and SMI in the models with cavities (p < 0.05, r ranged from −0.67 to −0.51) and marginally correlated in the original images (p < 0.10, r = −0.46 in both cases). Differences in strength:bone volume fraction and elastic modulus:bone volume fraction ratios among groups (original, nontargeted, targeted) were maintained even after accounting for the variation in measured microarchitecture indices. Trabecular number and SMI both showed significant correlations to yield strain (p < 0.05), but could not account for differences among model types.

DISCUSSION

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. REFERENCES

Using a validated, high-resolution nonlinear finite element method, we sought to determine if the addition of resorption cavities that do not disconnect trabeculae can influence cancellous bone yield strength and elastic modulus more than would be expected from the associated change in bone volume fraction and whether such effects depended on the location of the cavities. We found that typically sized resorption cavities can modify the slope of the relationship between bone strength and bone volume fraction by as much as 25%. In addition, we found that the effect of cavities on the slope of the strength–bone volume fraction relationships can be much greater if cavities are targeted to regions of high strain, suggesting that such cavity placement can be important biomechanically. Taken together, these findings provide evidence that resorption cavities can indeed influence the mechanical behavior of cancellous bone, particularly if the cavities are placed in regions of high tissue strain.

A number of characteristics of the study lend support to our conclusions. First, our finite element methodology is one of the most realistic available, accounting for material nonlinearities including tension–compression asymmetries in bone tissue strength as well as geometric nonlinearities (large deformations and buckling). The methodology has been shown to give accurate predictions of cancellous bone elastic modulus and yield strength as measured experimentally.(27) Second, the size of resorption cavities added to the bone surface was typical of that observed histologically (including the surface length and width). Last, this study used statistical methods to detect differences in mechanical properties after taking into account differences in bone volume fraction. As a result, our analysis was able to separate the mechanical effects of the addition of resorption cavities from those associated with reductions in bone volume.

The results of the study should be interpreted with regard to limitations of the mechanical modeling and the simulation of resorption cavities. Because finite element modeling involves the conversion of a structure into individual elements, insights gleaned from the models will be limited by their discretized nature. The magnitude of this effect will be related to the element shape and size and can limit the ability of the model to simulate stress riser effects. In this study, the resolution of the finite element mesh (22 μm) was comparable in size to the depth of resorption cavities (44 μm), a fact that may effect local strain concentrations, possibly influencing the absolute differences in bone strength and modulus between models with and without cavities. The use of a nonlinear model in this study is expected to minimize this effect on apparent mechanical properties because, unlike linear models, the tangent modulus of each element is greatly reduced after it yields, limiting the effect of local stress concentrations on neighboring tissue. For these reasons, the results of this study do not represent all possible biomechanical effects of stress risers associated with cavities but instead describe only the gross changes in structure associated with the presence of cavities. In addition, the overall resolution of the models, expressed as the ratio of average trabecular thickness to element size, was 3.8–4.0 at the smallest, a resolution sufficient to predict the stiffness of cancellous bone.(31,32) Second, because this study sought to isolate the structural effects of cavities from any other effects, the finite element models used homogeneous (but specimen-specific) tissue properties. Localized variations in tissue properties can influence cancellous bone mechanics(33–35) and may therefore modulate the effects of cavities in vivo. These limitations in mechanical modeling may influence absolute values of strength and stiffness, but because they are consistent in all three groups of this study, they are not expected to influence the relative differences between groups, especially the comparisons made between models having targeted and nontargeted cavities.

Although simulation of resorption cavities was performed based on existing evidence, variations in some characteristics between individuals and groups may influence our findings. For example, the volume of bone removed in the form of cavities will have an important effect on net changes in strength and stiffness. The prescribed bone loss in this study was set to 6% of the original volume, matching estimates of the volume occupied by cavities in the lumbar spine of postmenopausal women.(8) As a result, the addition of cavities in this study may represent as much as a doubling of bone turnover—a large change, yet one that is similar to what is observed around the time of menopause.(36) In addition, the placement of cavities relative to local microarchitecture may also have an effect on strength and stiffness. Because no disconnections of trabeculae were allowed, it is possible that cavity placement might have been biased to thicker trabeculae. Whereas this restriction was necessary to separate the role of cavities from that of disconnections, because disconnections themselves are known to modify bone stiffness relative to volume fraction,(37,38) lifting this restriction would most likely increase the observed differences between groups. In addition, because it was not feasible to identify pre-existing cavities on the original bone surface, it is possible that some cavities in the simulations were added on top of natural cavities, essentially doubling the cavity depth. A supplementary analysis using a cavity depth twice as large (88 μm) as that used in this study(39) found that doubling of cavity depth did indeed modify the magnitude of the changes in strength and stiffness, but did not change the relative differences between groups, supporting our conclusions.

In addition, there are aspects of resorption cavities that are not yet well understood, yet may modulate their mechanical effects on cancellous bone. For example, it is not known if the surface size (length and width) and/or the number of cavities can influence cancellous bone mechanics independent of bone volume. Information regarding cavity surface size and number is extremely limited because such measures cannot be performed in 2D sections, and precise 3D techniques for making such measures have not yet been developed. Because cavity size was consistent in nontargeted and targeted models, it is unlikely that variations in cavity size would affect the statistical significance of the differences between groups.

Last, the biomechanical analyses in this study were limited to compressive yield strength and elastic modulus in the primary loading direction. It is possible that the magnitude of observed effects could differ under other loading conditions (shear, fatigue, creep) or in other directions (transverse or multiaxial as opposed to longitudinal) or if other mechanical properties were used as analysis endpoints (toughness, postyield deflection). It is unclear at this juncture if any of these other loading conditions/mechanical endpoints would be more closely related to vertebral fracture risk than those measured in this study.

Our finding that variation in microarchitecture measures could not explain the observed differences in strength–bone volume fraction characteristics was surprising because the differences between model types were entirely microarchitectural. However, most of these microarchitecture measures express averages over the entire specimen (particularly trabecular thickness, number, and separation) and may therefore be insensitive variations in surface morphology caused by resorption cavities when measured at this resolution. Additional microarchitecture measures (such as SD of trabecular thickness or separation, direct measures of trabecular thickness or orientation, etc.) that may be more sensitive to variations caused by cavities have been proposed,(40,41) but are not yet regularly used.

This study builds on that presented by van der Linden et al.(15) Using linear finite element models, they showed that removal of bone tissue experiencing the greatest strain resulted in much larger changes in strain distribution throughout the structure than were observed when bone was lost at random. This study showed that changes in apparent yield strength can occur when bone is removed in the form of cavities and when no trabeculae are disconnected. Furthermore, our study showed that cavities targeted to regions of high strain can have greater effects on cancellous bone strength from those that are placed randomly on the bone surface. Our findings that the percent changes in cancellous bone strength were greater than those in elastic modulus suggest that cavities can have an effect on bone strength different from the effect on modulus, supporting the idea of a “stress riser” effect.

It has been suggested that resorption cavities, even when they do not disconnect trabeculae, may influence cancellous bone strength.(12) The current analysis supports this theory—but suggests that the location of the resorption cavity can be a critical factor. This is important in that regions of cancellous bone experiencing the greatest tissue strain are the most likely to sustain tissue damage. Microscopic tissue damage in the form of diffuse damage and microcracks have been found to be spatially and temporally related to the initiation of new bone resorption events in cortical bone.(42,43) This study therefore supports the idea that remodeling targeted to regions of tissue damage may be the most detrimental to bone strength.(44) Remodeling associated with tissue damage is commonly referred to as “targeted remodeling,” whereas “nontargeted remodeling” identifies bone cell activity that is not associated with tissue damage (it is placed randomly or initiated by other factors).(44) It is not yet known what proportion of remodeling in cancellous bone is targeted remodeling. Although no direct measurements have been made, it has been suggested that as much as 30% of remodeling in cortical bone is targeted.(45)

Although intended to study the biomechanical effects of resorption cavities, the results of this study can provide insights into the effects of antiresorptive therapy. By viewing models with cavities as a pretreatment condition and models without cavities as a post-treatment condition (in which the resorption cavities have been filled), this study can be viewed as a simulation of antiresorptive therapy. In this light, this study suggests that improvements in bone strength caused by the filling of existing resorption cavities may be much greater when remodeling targeted to regions experiencing high strain is affected rather than remodeling that is not specifically targeted to regions of high strain. Concerns regarding the long-term effects of antiresorptive therapy on the removal of tissue damage have led some to suggest that an ideal antiresorptive therapy would inhibit nontargeted remodeling without disrupting remodeling targeted to regions of tissue damage.(45–47) This analysis suggests that, with regard to the effects of cavities on strength and stiffness, such an antiresorptive therapy may not be as effective as a therapy that inhibits both targeted and nontargeted remodeling.

Acknowledgements

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. REFERENCES

The authors thank Sreenu Konda and Harold Haller at the Case Statistical Consulting Center for help with data analysis. This work was supported by NIH/NIAMS AR49570, AR43784, and AR049828 and Case Western Reserve University. Computational support was provided in part by the National Science Foundation through the San Diego Supercomputer Center NPACI Grant UCB 256. Structure model index measures were performed using 3D Calculator (Erasmus Orthopaedic Research Laboratory and Skyscan).

REFERENCES

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. REFERENCES