Associations Among Hip Structure, Bone Mineral Density, and Strength Vary With External Bone Size in White Women

ABSTRACT Bone mineral density (BMD) is heavily relied upon to reflect structural changes affecting hip strength and fracture risk. Strong correlations between BMD and strength are needed to provide confidence that structural changes are reflected in BMD and, in turn, strength. This study investigated how variation in bone structure gives rise to variation in BMD and strength and tested whether these associations differ with external bone size. Cadaveric proximal femurs (n = 30, White women, 36–89+ years) were imaged using nanocomputed tomography (nano‐CT) and loaded in a sideways fall configuration to assess bone strength and brittleness. Bone voxels within the nano‐CT images were projected onto a plane to create pseudo dual‐energy X‐ray absorptiometry (pseudo‐DXA) images consistent with a clinical DXA scan. A validation study using 19 samples confirmed pseudo‐DXA measures correlated significantly with those measured from a commercially available DXA system, including bone mineral content (BMC) (R 2 = 0.95), area (R 2 = 0.58), and BMD (R 2 = 0.92). BMD–strength associations were conducted using multivariate linear regression analyses with the samples divided into narrow and wide groups by pseudo‐DXA area. Nearly 80% of the variation in strength was explained by age, body weight, and pseudo‐DXA BMD for the narrow subgroup. Including additional structural or density distribution information in regression models only modestly improved the correlations. In contrast, age, body weight, and pseudo‐DXA BMD explained only half of the variation in strength for the wide subgroup. Including bone density distribution or structural details did not improve the correlations, but including post‐yield deflection (PYD), a measure of bone material brittleness, did increase the coefficient of determination to more than 70% for the wide subgroup. This outcome suggested material level effects play an important role in the strength of wide femoral necks. Thus, the associations among structure, BMD, and strength differed with external bone size, providing evidence that structure–function relationships may be improved by judiciously sorting study cohorts into subgroups. © 2022 The Authors. JBMR Plus published by Wiley Periodicals LLC on behalf of American Society for Bone and Mineral Research.

Introduction the osteoporosis threshold criterion (T-score ≤ À2.5) identifies only half of the individuals who fracture, (11)(12)(13)(14) resulting in large numbers of individuals who may have benefited from fracture-reducing treatments. Better understanding of the association between BMD and bone strength may help refine the clinical use of this technology in identifying individuals at high risk of fracturing.
Clinically, BMD is used to monitor bone strength decline with the assumption that a reduction in BMD reflects structural changes that compromise strength. However, the structural variations that give rise to the variation in DXA parameters (ie, bone mineral content [BMC], area, BMD) and strength are not fully understood. Prior work has related bone structure with BMD at the image resolution of clinical CT or MRI, (15)(16)(17) consistent with the use of these technologies on living humans. Only a few studies related BMD to measures of trabecular architecture (18)(19)(20) ; these studies were conducted on cadaveric tissue to enable image acquisition at the higher resolutions required for microstructural quantification. Thus, despite the prevalent use of DXA BMD, we do not have a full understanding of how variation in bone structure contributes to BMD and, in turn, whole bone strength.
Hip BMD is calculated as the ratio of BMC to bone area for a standardized FN region of interest (ROI). Bone area provides a measure proportional to outer bone size, whereas BMC provides a measure proportional to the amount of bone tissue. (21) Studies investigating how DXA parameters relate to bone structure focused primarily on the association between BMC and the proportion of cortical and trabecular bone. FN BMC is thought to reflect a fixed 60:40 ratio for cortical/trabecular mass. (22)(23)(24) However, the femoral neck is constructed with multiple, interacting trabecular arcades traversing the FN ROI (25,26) and varying proportions of cortical and trabecular bone along the length (22,27) and around the circumference (28,29) (Fig. 1A). The proportion of cortical and trabecular bone also varies among individuals depending on outer bone size, with wider femoral necks showing greater cortical area on an absolute basis but lower area on a relative basis compared with narrower femoral necks. (30) Critically, BMD did not differ between the narrow and wide groups, suggesting different bone structures give rise to similar BMD values. These studies suggested BMD is not uniquely related to bone structure, which has the potential to complicate the association between BMD and strength.
The primary goal of this study was to determine how variation in bone structure correlates with FN DXA parameters (BMC, area, BMD) and whole bone strength. We tested the hypothesis that associations between DXA parameters and strength depend on outer bone size. To accomplish these goals, bone mineral distribution maps, or "pseudo-DXA" images, were generated from high-resolution nano-computed tomography (nano-CT) images of cadaveric proximal femurs corresponding to the region assessed during a routine hip DXA scan. The pseudo-DXA images provided full access to the bone mineral distributions, which allowed us to study the associations among DXA parameters and the interindividual variation in bone structure and strength.

Samples
Unfixed cadaveric proximal femurs (n = 30) from White female donors (36-89+ years of age) with no known musculoskeletal pathologies were obtained from the University of Michigan Anatomical Donations program (Ann Arbor, MI, USA), Science Care (Phoenix, AZ, USA), and Anatomy Gifts Registry (Hanover, MD, USA). Human tissue use and handling procedures were approved by the University of Michigan Institutional Biosafety Committee (IBC), and this study was declared exempt by the Institutional Review Board (IRB). Femurs were cut transversely 16.5 cm distal to the superior aspect of the femoral head. The femoral shaft was embedded in a 5-cm-square aluminum channel filled with acrylic resin (Ortho-Jet BCA, Lang Dental, Wheeling, IL, USA) using a custom alignment fixture so the femoral neck was oriented at 15 degrees of internal rotation relative to the embedding block faces. The embedding block thus allowed for consistent sample orientation.
Dual-energy X-ray absorptiometry A total of 19 of the samples were used as a pseudo-DXA image validation subgroup and prepared for DXA scanning. The proximal femurs with embedding blocks were placed within two clear plastic, sealable bags. Biosafety level 2 (BSL2) safety protocols necessitated minimizing the potential for fluid leaks; as such, the samples could not be imaged while immersed in water. Instead, each sample was scanned while covered with approximately 2 inches of rice to simulate muscle. (31) The samples were held in place by the embedding blocks using a custom-built fixture that allowed scanning to be conducted at any angle. All scanning angles were confirmed using a digital inclinometer with a resolution of 0.1 degrees. DXA images of the potted proximal femurs were acquired on a QDR Discovery A Bone Densitometer (Hologic Inc., Marlborough, MA, USA) using a standard clinical protocol. Sagittal images were acquired for each sample with the femoral neck internally rotated 15 degrees, consistent with clinical imaging practices. FN BMC, area, and BMD were calculated using the manufacturer's software.
Dragonfly software (version 2021.1.0.977; Object Research Systems Inc, Montreal, Canada) was used to create a FN volume of interest (VOI) corresponding to a standard DXA ROI from each nano-CT volume. The nano-CT volumes were rotated 15 degrees to remove the anteversion, thereby aligning the FN axis in parallel with the x-y plane of the nano-CT scanner. A 15-mm-thick VOI perpendicular to the FN axis was extracted, with one corner placed at the inflection point between the femoral neck and the greater trochanter on the superior side of the bone consistent with the ROI placement used by the Hologic scanner. A repeatability study was performed to confirm consistent VOI extraction by a single individual performing this method three times each on five samples. The intraclass correlation coefficient (ICC 3,1) and the 95% confidence intervals (CI) were calculated based on a single rater, consistency, two-way mixed effects model. Reliability was determined based on the 95% CI of the ICC estimate, where values grouped by less than 0.5, 0.5-0.75, 0.75-0.9, and greater than 0.9 indicate poor, moderate, good, and excellent reliability, respectively. Reliability was excellent for area ICC = 0.9997 (95% CI 0.9987-0.9999) and BMC ICC = 0.988 (95% CI 0.9433-0.9987). A validated fully convolutional neural network (FCNN) was used to segment bone from background (DICE coefficient = 0.983 AE 0.016). A second validated FCNN was used to segment cortical from trabecular bone (Dice coefficient = 0.977 AE 0.023) to generate cortical and trabecular subvolumes for structural quantification. The boundary between cortical and trabecular bone was defined in accordance with prior studies (28,29) ; examples are shown in Fig. 1B. The segmented image files were evaluated for thresholding quality and cortical-trabecular segmentation. Erroneously identified voxels were manually corrected. The structural measures assessed from the 3D nano-CT volumes included trabecular volume fraction (BV/TV), trabecular thickness (Tb.Th), average cortical thickness (Ct.Th), total cross-sectional area (Tt.Ar), and cortical area (Ct.Ar).

Pseudo-DXA images
A 2D bone density mapping was generated for each nano-CT VOI (n = 30) by projecting all bone voxels onto a planar FN ROI. The anatomical location, orientation, and width of the FN ROI were consistent with the Hologic DXA scanner used for the validation study. The 2D mapping was called the pseudo-DXA image (Fig. 1C). This analysis focused exclusively on the number of bone voxels, since the X-ray attenuation giving rise to BMC and the associated image reflects primarily the mineral component. (33) The contributions of marrow and X-ray scattering to the pseudo-DXA image were not assessed, as this initial study focused on the relative contributions of cortical and trabecular tissues to the DXA parameters.
The parameters calculated from the pseudo-DXA images included the ROI area (pseudo-DXA area), number of cortical bone voxels, number of trabecular bone voxels, total number of bone voxels (pseudo-DXA BMC), and total number of bone voxels/area (pseudo-DXA BMD). The numbers of cortical and trabecular bone voxels above (superior) and below (inferior) the FN ROI midline were also calculated. The average FN width and minimum FN width were measured directly from the pseudo-DXA image. All terms preceded by pseudo-DXA designate traits defined from the projected nano-CT images, whereas terms preceded by DXA refer to traits determined by the DXA system.

Mechanical testing
Proximal femurs (n = 30) were loaded to failure on an Instron 8511 (Instron, Inc., Norwood, MA, USA) in a fall-to-the-side configuration to collect measures of bone strength, as previously described. (34) Samples were oriented so the shaft was 10 degrees relative to a horizontal plane and the femoral neck axis was internally rotated 15 degrees, consistent with the loading configuration experienced during a sideways fall and with prior studies. (35) The load was applied through a metal acetabular cup that was custom fitted to the sample based on the femoral head diameter. A custom polyester putty-filled (Bondo, 3M, Inc., St. Paul, MN, USA) pad was used to distribute load to the greater trochanter. Bones were preloaded to 100 N to ensure proper seating of the sample and fixtures and then loaded to failure at a displacement rate of 100 mm/s. Maximum load (N), stiffness (N/mm), yield load (N), and post-yield displacement (PYD, mm) were calculated from the load-displacement curves. The yield point was defined as the location where a 10% reduction in the stiffness regression crossed the load-displacement curve. A validation study determined the deflection attributable to the load cell and Bondo pads was 0.04 mm (0.02-0.1 mm), which accounted for 0.96% (0.56%-2.2%) of the total displacement of the fractured femurs. For simplicity, maximum load was used synonymously with whole bone strength. An error in data acquisition prevented the collection of strength data for 1 sample.

Statistical analysis
For clarification of the sample size, the DXA validation study was conducted on a subset of the sample cohort; the validation sample size was limited based on the availability of the system, which was actively being used to acquire bone density data on living humans for numerous independently funded studies. Data are expressed as mean AE standard deviation, unless otherwise indicated. Variables were tested for normality (Shapiro-Wilk test, p < 0.05) and transformed using log or square root, if necessary. Three primary analyses were conducted. First, linear regression analysis was used to examine the relationship between the pseudo-DXA parameters and standard DXA parameters. We also determined the extent to which variation in pseudo-DXA BMC arose from the proportion of cortical and trabecular bone in the superior and inferior halves and how these individual contributors correlated with age. Second, we tested if the proportion of cortical and trabecular bone varied with external bone size. Samples were sorted into narrow (n = 15) and wide (n = 15) subgroups using pseudo-DXA area. This sorting was conducted without height adjustment because height information was not available for all donors. Linear regression analysis was used to relate pseudo-DXA BMC and the number of cortical bone voxels, the number of trabecular bone voxels, and the proportion of cortical bone voxels. ANCOVA was used to test whether the slope and y-intercepts differed between narrow and wide subgroups.
Third, predictors of bone strength were identified using multivariate linear regression analysis. The analysis was conducted using the full data set and with the data divided into narrow and wide subgroups. Regression models started with predictors that are available clinically (model 1: age, body weight, BMD), then proceeded to replace general predictors with parameters that provide progressively more refined information. For example, in model 2, pseudo-DXA BMD was replaced with its constituents' pseudo-DXA area and pseudo-DXA BMC. In model 3, pseudo-DXA BMC was replaced with the amount of bone in the superior and inferior halves of the FN. In model 4, the amount of bone (ie, number of voxels) in the superior and inferior halves was segmented into the number of cortical and trabecular bone voxels in the superior and inferior halves of the FN. Finally, model 5 included PYD, a measure reflecting material-level brittleness, to the regression analysis, based on prior work showing the dependence of whole bone strength on PYD. (34,36) Although samples were sorted based on pseudo-DXA area, pseudo-DXA area was included in models 2 to 5 to generate consistent regression models across the groupings (ie, all samples, narrow, wide) and because this measure remains a continuous variable despite the sorting. The log of body weight was used in the regression analyses because body weight failed the Shapiro-Wilk normality test. The square root of PYD was used in the regression analysis because PYD failed the normality test. Variance inflation factors (VIF) were calculated for each model. For models showing one or more variables with VIF >10, the multiple variable regression analysis was repeated with the variable having the maximum VIF removed. This process resulted in VIF <10 for all variables. All bivariate linear regression analyses were conducted using GraphPad Prism (v. 9.1.0; GraphPad Software, La Jolla, CA, USA). Linear regression modeling was conducted using SPSS (IBM SPSS Statistics, v. 27, Armonk, NY, USA).
Because actual DXA images were acquired for only 19 samples and pseudo-DXA images were generated for 30 samples, it was not possible to test the impact of discordance in the assignment to narrow versus wide subgroups when rank-ordering the samples using DXA area versus pseudo-DXA area. When sorting the 19 samples used in the validation study by actual DXA area, there was some discordance between assignment to the narrow versus wide subgroup, and most of the discordant assignments were near the boundary dividing the rank-ordered samples into narrow and wide subgroups. Because the validation cohort was too small to repeat the analyses while removing discordant samples, we conducted a sensitivity analysis that removed a progressively larger number of samples from the middle of the pseudo-DXA area rank-ordered samples. This sensitivity analysis tested whether the major outcomes depended on assignment to the narrow or wide subgroup by removing the middle 4 (2 narrow and 2 wide excluded), middle 8 (4 narrow and 4 wide excluded), and middle 12 (6 narrow and 6 wide excluded) samples. We repeated the analysis of the association between pseudo-BMC and the proportion of cortical and trabecular bone and the multivariate regression analysis.

Results
Correlations between pseudo-DXA and DXA parameters Linear regression analyses were conducted to assess the relationship between pseudo-DXA parameters and standard DXA parameters for the 19 proximal femurs scanned on both the nano-CT and Hologic DXA systems (Fig. 2). Significant correlations were found between pseudo-DXA BMC (total number of bone voxels) and DXA BMC (R 2 = 0.947, p = 0.0001), pseudo-DXA area and DXA area (R 2 = 0.581, p = 0.0001), and pseudo-DXA BMD (total number of bone voxels normalized by the pseudo-DXA area) and DXA BMD (R 2 = 0.919, p = 0.0001). The slope of the pseudo-DXA area -DXA area regression was 0.90 (95% CI 0.51-1.29), but the y-intercept was 0.78 (95% CI À1.03-2.58), indicating the pseudo-DXA area underestimated the area determined from the DXA system. These significant correlations demonstrated high correspondence between the pseudo-DXA  Abbreviations: Min FN width = width at the minimum femoral neck location; Tt.Ar = cross-sectional total area averaged over region of interest; Ct.Ar = cross-sectional cortical area averaged over region of interest; Ct.Th = average cortical thickness; BV/TV = bone volume fraction (bone volume divided by total volume contained with the subendosteal boundary); BMC = bone mineral content; BMD = bone mineral density. and standard DXA parameters, confirming the rigor of our methodology. A preliminary study comparing DXA parameters with 1 inch versus 2 inches of rice confirmed the amount of rice had no impact on the outcome parameters (FN area, p = 0.348; FN BMC, p = 0.499, FN BMD, p = 0.302; paired t tests).

Contributions of regional bone density to BMC
The number of cortical and trabecular voxels were calculated for the superior and inferior halves of the FN ROI and related to pseudo-DXA BMC to quantify the extent to which the   (Fig. 3). For the superior half, 20.1 AE 3.8% and 18.7 AE 4.3% of the total voxels were attributed to cortical and trabecular bone, respectively. For the inferior half, 36.3 AE 6.7% and 24.8 AE 6.4% of the total voxels were attributed to cortical and trabecular bone, respectively. Only the trabecular bone in the superior (R 2 = 0.546, p = 0.0001) and inferior (R 2 = 0.304, p = 0.002) halves showed significant correlations between the number of bone voxels and age (Fig. 3C).
Associations between the amount of bone and age differ between narrow and wide femoral necks Samples were sorted into narrow (n = 15) and wide (n = 15) subgroups by pseudo-DXA area. Neither age nor body weight differed between the narrow and wide subgroups ( Table 2). Linear regression analyses compared the associations between the number of bone voxels (total, cortical, trabecular) and age for the narrow and wide subgroups (Fig. 4). The wide subgroup showed a significant negative correlation between the total number of bone voxels and age (R 2 = 0.628, p = 0.004), but the narrow subgroup did not (R 2 = 0.118, p = 0.209). The y-intercepts were significantly different (p = 0.019, ANCOVA), suggesting the FN ROI was composed of a larger amount of bone tissue for the wide compared with the narrow subgroup at the younger ages of our cohort. The age associations for the cortical (Fig. 4B) and trabecular (Fig. 4C) tissues were generally consistent with that of the total amount of bone (Fig. 4A) with a few exceptions. The wide subgroup showed a significant negative correlation with age for trabecular bone (p = 0.001) and borderline significant negative correlation for cortical bone (p = 0.057), which explain how the decline in the total amount of bone arose from age-related declines in both tissue types. In contrast, the narrow subgroup showed a significant negative correlation with age for the trabecular bone only, which may explain why the negative association between total bone voxels and age was not significant. A comparison of the linear regressions between the narrow and wide subgroups showed nonsignificant differences in the y-intercepts; the significance of both the cortical and trabecular regressions were borderline (p = 0.065-0.073), suggesting the two tissue types combined accounted for the y-intercept difference in the total amount of bone.
Associations between pseudo-DXA BMC and the proportion of cortical and trabecular bone differ between narrow and wide femoral necks Pseudo-DXA BMC (p = 0.134) and pseudo-DXA BMD (p = 0.601) did not differ between narrow and wide subgroups (Table 2). Further, the fraction of bone voxels within the FN ROI attributed to cortical bone did not differ between the narrow (0.539 AE 0.112, mean AE SD) and wide (0.587 AE 0.068) subgroups (p = 0.177). However, when segmenting total bone voxels into cortical and trabecular voxels (Fig. 5), the narrow subgroup showed significant correlations between pseudo-DXA BMC and the number of cortical bone voxels (R 2 = 0.842, p < 0.0001) but a weaker association with trabecular bone voxels (R 2 = 0.239, p = 0.064). In contrast, the wide subgroup showed significant associations between pseudo-DXA BMC and the number of cortical (R 2 = 0.709, p = 0.001) and trabecular (R 2 = 0.688, p = 0.0001) bone voxels. When the number of cortical voxels was expressed as a fraction of total bone voxels, a significant positive correlation was observed between pseudo-DXA BMC and the fraction of cortical bone voxels for the narrow (R 2 = 0.406, p = 0.011) but not the wide (R 2 = 0.033, p = 0.518) subgroups (ANCOVA, slope p = 0.013). The wide subgroup showed a

BMD-strength associations depend on external bone size
The fall-to-the-side loading direction resulted in similar distributions of femoral neck and trochanteric fractures for the narrow (3 femoral neck, 11 trochanteric) and wide (4 femoral neck, 11 trochanteric) subgroups. The multivariate linear regression analyses were conducted to identify strength predictors and to determine if the significant predictors differed between narrow and wide subgroups (Table 3). Model 1 predictors included basic information such as age, body weight (BW), and pseudo-DXA BMD. The adjusted R 2 was 0.579 when all samples were included in the analysis. When the analyses were conducted by subgroup, adjusted R 2 values increased to 0.788 for the narrow subgroup but remained relatively modest at 0.491 for the wide subgroup.
Replacing pseudo-DXA BMD with pseudo-DXA area and pseudo-DXA BMC (model 2) improved the adjusted R 2 for both the narrow (adj. R 2 = 0.892) and wide (adj. R 2 = 0.537) subgroups. Replacing pseudo-DXA BMC with the amount of bone in the superior and inferior halves did not appreciably affect the adjusted R 2 values for either subgroup (model 3). Likewise, breaking the total amount of bone in the superior and inferior halves into cortical and trabecular bone also did not appreciably affect the adjusted R 2 values for either subgroup (model 4) but did reveal subregions contributing significantly (trabecular bone inferior half) or borderline significantly (cortical bonesuperior and inferior halves) to whole bone strength for the narrow subgroup. Adding PYD, a measure of material brittleness, as a predictor in the regression analyses (model 5) resulted in a large increase in the adjusted R 2 to 0.706 for the wide subgroup but not the narrow subgroup. The variance inflation factors were generally less than 10 and the models remained significant when individual terms having VIF >10 were removed (data not shown). The variables identified as contributing significantly to the prediction of strength differed between the narrow and wide subgroups. Body weight was a consistently strong predictor for the narrow subgroup, as was the number of cortical voxels in the superior and inferior halves and the number of trabecular voxels in the inferior half. For the wide subgroup, significant predictors included the number of cortical voxels in the superior half and PYD.

Sensitivity analysis
The outcomes of the sensitivity analysis are shown in Supplemental Fig. S1 and Supplemental Table S1. The associations Note: Data shown include the standardized beta coefficients (p value). Bold indicates significant relationships, and bold/italics indicates borderline significance.
between the number of bone voxels and the number of trabecular voxels and pseudo-DXA BMC (total number of bone voxels) were consistent when using all data and when excluding the middle 4, 8, and 12 samples (Supplemental Fig. S1). Likewise, the multivariate regression analyses also showed consistent adjusted R-squared values for the five models, albeit there were changes in the significance of these associations, which was expected as the sample sizes became progressively smaller.

Discussion
The goals of this study were to understand how variation in bone structure gives rise to variation in BMD and strength and to test whether these associations differ with external bone size. BMD is relied upon clinically to reflect bone structure changes affecting strength and fracture risk. (37,38) Although BMD correlates significantly with experimentally determined strength, a critical evaluation of these associations shows a two-to threefold variation in strength for a given BMD value. (15,31,39) Because half of the individuals who fracture have hip BMD values above the osteoporosis threshold, (11)(12)(13)(14) there is a need to better understand how projecting a three-dimensional structure onto a plane and reducing the bone mineral distribution map within a specified boundary to scalar variables ( Fig. 1) affect the association between BMD and strength. (37,38) High-resolution 2D bone mineral distribution maps (pseudo-DXA images) of the FN ROI were generated from 3D nano-CT images of unfixed cadaveric proximal femurs to investigate and partition the underlying structure with sufficient resolution to quantify cortical and trabecular architecture. The pseudo-DXA output parameters correlated significantly with the corresponding parameters measured from a DXA system (Fig. 2). The DXA parameters, the age associations of the pseudo-DXA parameters, and the BMD-strength association reported herein were consistent with prior studies. (30,31,40) Thus, we demonstrated a clinically relevant research tool to investigate the structural determinants of BMD and strength by defining pseudo-DXA images from 3D nano-CT volumes of proximal femurs experimentally tested to assess strength.
A major outcome of the current study was finding pseudo-DXA BMD did not predict strength uniformly across the study cohort. The multivariate regression analysis showed strength was better predicted by dividing the study cohort into subgroups based on external size, allowing for different structurefunction associations. Study cohorts are often treated as homogeneous, assuming a single structure-function relationship will identify structural features that predict strength for an entire cohort. (41) Many prior studies seeking to identify structural features that differ between subgroups sorted cohorts by fracture status, (42)(43)(44)(45) fracture location, (46) bone turnover, (47) sex, (48,49) and race/ethnicity (50) ; in general, these studies assumed a single structure-function relationship existed for each subgroup and that a comparison between subgroups would identify a trait capable of explaining fracture risk for a population. The current study deviated from this approach by testing for more than one structure-function relationship within the cohort. In some prior studies, sorting individuals based on fracture location has successfully identified different structural determinants of fracture risk and bone strength. (51)(52)(53) Our current work builds on these studies by showing different structure-function relationships based on external bone size. Investigating the effects of heterogeneity in relation to bone structure and strength may provide the means for defining multiple biomechanical pathways leading to fracture and moving toward optimal treatment strategies for subgroups based on bone structure. The significant predictors of strength differed for the narrow and wide subgroups (Table 3). Nearly 80% of the variation in strength of the narrow subgroup was explained by age, body weight, and pseudo-DXA BMD. Including additional structural or density distribution information in regression models 2 to 5 modestly improved the adjusted R-squared values, explaining more than 90% of the variation in strength. Thus, simply knowing the amount of bone present was sufficient to predict strength for the narrow subgroup. In contrast, age, body weight, and pseudo-DXA BMD explained only half the variation in strength for the wide subgroup. Including variables providing greater insight into bone mineral distribution (model 3) or segmentation into cortical and trabecular tissues (model 4) did not improve the adjusted R-squared values for the wide subgroup. Including PYD, a measure of bone brittleness, in model 5 increased the adjusted R-squared to a value more than 70% for the wide subgroup but did not improve the strength prediction for the narrow subgroup. This outcome suggests materiallevel effects may play an important role in the strength of wide femoral necks but not narrow. Thus, unlike the narrow subgroup, measures of the amount of bone may correlate with strength but have limited ability to explain the variation in strength, suggesting proximal femurs in the wide subgroup may undergo a different failure mechanism when overloaded. As such, the wide subgroup appears to depend on structural and material traits differently from the narrow. (41,54) DXA parameters have generally been related to bone structure with the intent of understanding the limitations of estimating morphology (48,(55)(56)(57)(58)(59) and strength. (19,60) Only a few studies investigated the structural features responsible for the variation in BMD. (15,19,20,27,61) Structural variation within the inferior half of the FN was associated with more than 60% of the variation in pseudo-DXA BMC (Fig. 3), consistent with prior work, (61) and most of the BMC variation was attributed to the inferior cortex. This distribution was expected, given the greater thickness of the inferior cortex and the greater density of the compressive trabecular arcade compared with those features within the superior half. The amount of cortical bone comprising the inferior and superior cortices showed nonsignificant (borderline significant for the wide subgroup) associations with age (Fig. 3C). Only the amount of trabecular bone showed significant associations with age, whether sorted into superior and inferior halves (Fig. 3C) or narrow and wide subgroups (Fig. 4B, C). The amount of trabecular bone accounted for less than half of the variation in pseudo-DXA BMC, which may explain in part why age-related changes in BMD tend to be relatively small. (62)  The proportion of cortical to trabecular bone varied within the narrow subgroup (Fig. 5A). The ratio of cortical to trabecular bone varies along the length (22,27) and around the circumference (28,29) of the femoral neck. However, femoral neck morphology has been estimated from hip DXA assuming this ratio is fixed at 0.60. (22)(23)(24)63) This ratio was 0.59 AE 0.07 for the wide subgroup, consistent with these prior studies. However, the narrow subgroup showed a significant association between the cortical/trabecular bone ratio and pseudo-DXA BMC with individuals having lower pseudo-DXA BMC showing a lower ratio compared with those at higher pseudo-DXA BMC. Thus, the proportion of cortical to trabecular bone was not uniform across the study cohort. Assuming DXA images reflect a fixed proportion of cortical and trabecular bone may affect estimates of morphology and strength. In contrast to the wide subgroup, which maintained a consistent proportion of cortical and trabecular bone across pseudo-DXA BMC values, the narrow subgroup showed a proportionally greater amount of cortical bone at higher pseudo-DXA BMC values. These associations suggest that narrow and wide femoral necks contribute to strength with different combinations of femoral neck traits. (64) This study has several important limitations. The proximal femurs were imaged with DXA using rice to simulate soft tissue, rather than water, because of safety considerations. Although the DXA parameters were not affected by the amount of rice, additional studies are warranted to study the impact of these scanning parameters on DXA BMC and area. The current study focused on the number of bone voxels, deferring the effects of beam scattering and soft tissues, air, and marrow on the pseudo-DXA image to future studies. Even without consideration of these imaging effects, the association between the number of bone voxels and DXA BMC showed a coefficient of determination of 0.947 ( Fig. 2A). This strong correlation suggested the variation in DXA BMC primarily reflects the amount of bone present and including more nuanced imaging effects may contribute relatively little to pseudo-DXA BMC variation. Although pseudo-DXA area correlated significantly with DXA area, the coefficient of determination (Fig. 2B) was lower than those for BMC (Fig. 2C) and BMD ( Fig. 2A). Further, pseudo-DXA area consistently underestimated the actual DXA area. This discrepancy may be attributed to the fine resolution of the pseudo-DXA image, which, unlike the actual DXA image, creates well-defined boundaries between bone and background. Differences in resolution and boundary detection may contribute to the discrepancy between pseudo-DXA area and DXA area. Anatomical positioning and 3D orientation of the nano-CT volume were highly repeatable but may contribute additional error. These errors were considered negligible, given the strong correlation between pseudo-DXA BMD and DXA BMD, and the outcome of the sensitivity analysis, which confirmed subgroup assignment did not meaningfully affect the major outcomes and suggested the overall results of this study are robust. The cadaveric samples were composed of White female donors. Additional studies are needed to test if similar structure-function relationships hold for men and other races/ethnicities. The sample size was sufficient to address the major questions of this study, but additional samples are needed to test how the associations between cortical and trabecular voxels in different regions (superior, inferior) vary with external bone size. Lack of power for these latter analyses may explain the borderline significant differences for the age regressions for cortical (Fig. 4B) and trabecular (Fig. 4C) bone. There are limitations in the extent to which the age associations shown for cadaveric tests reflect how age-related changes in bone structure would be reflected in BMD and strength. Examination of longitudinally acquired DXA images are needed to confirm the associations reported herein.
In conclusion, our data suggested BMD is not uniquely related to the underlying bone structure, and similar BMD values can give rise to substantially different values of bone strength. As illustrated in Fig. 6 and Supplemental Table S2 and Supplemental Fig. S2, varying combinations of cortical and trabecular structures gave rise to relatively similar BMD values, which were, in turn, associated with a twofold variation in strength. This relatively simple consideration of bone heterogeneity demonstrates that associations between bone structure, BMD, and strength vary, leading to significant differences in bone strength in association with bone structure. Basic information available clinically (BMD, BMC, area) appears sufficient to predict strength for the narrow subgroup. However, this limited set of variables did not predict strength accurately for the wide subgroup. Additional studies are needed with larger sample sizes to better understand how variation in structural and material properties leads to variation in the strength of wide proximal femurs.