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- J Bone Miner Res
- PMC2686919

# Prediction of Incident Hip Fracture Risk by Femur Geometry Variables Measured by Hip Structural Analysis in the Study of Osteoporotic Fractures

^{1}Thomas J Beck,

^{2}Jonathan Reeve,

^{1}Katie L Stone,

^{3}Teresa A Hillier,

^{4}Jane A Cauley,

^{5}and Steven R Cummings

^{6}

^{1}Departments of Medicine and Public Health and Primary Care, University of Cambridge, Strangeways Research Laboratory, Cambridge, United Kingdom

^{2}Department of Radiology, The Johns Hopkins University School of Medicine, Baltimore, Maryland, USA

^{3}California Pacific Medical Center, Research Institute, San Francisco, California, USA

^{4}Kaiser Permanente Center for Health Research Northwest and Hawaii, Portland, Oregon, USA

^{5}Department of Epidemiology, University of Pittsburgh, Pittsburgh, Pennsylvania, USA

^{6}California Pacific Medical Center, Research Institute, and Department of Epidemiology and Biostatistics, University of California, San Franicsco, California, USA

## Abstract

The role of bone tissue's geometric distribution in hip fracture risk requires full evaluation in large population-based datasets. We tested whether section modulus, a geometric index of bending strength, predicted hip fracture better than BMD. Among 7474 women from the Study of Osteoporotic Fractures (SOF) with hip DXA scans at baseline, there were 635 incident hip fractures recorded over 13 yr. Hip structural analysis software was used to derive variables from the DXA scans at the narrow neck (NN), intertrochanter (IT), and shaft (S) regions. Associations of derived structural variables with hip fracture were assessed using Cox proportional hazard modeling. Hip fracture prediction was assessed using the C-index concordance statistic. Incident hip fracture cases had larger neck-shaft angles, larger subperiosteal and estimated endosteal diameters, greater distances from lateral cortical margin to center of mass (lateral distance), and higher estimated buckling ratios (*p* < 0.0001 for each). Areal BMD, cross-sectional area, cross-sectional moment of inertia, section modulus, estimated cortical thickness, and centroid position were all lower in hip fracture cases (*p* < 0.044). In hip fracture prediction using NN region parameters, estimated cortical thickness, areal BMD, and estimated buckling ratio were equivalent (C-index = 0.72; 95% CI, 0.70, 0.74), but section modulus performed less well (C-index = 0.61; 95% CI, 0.58, 0.63; *p* < 0.0001 for difference). In multivariable models combining hip structural analysis variables and age, effects of bone dimensions (i.e., lateral distance, subperiosteal diameter, and estimated endosteal width) were interchangeable, whereas age and neck-shaft angle were independent predictors. Several parsimonious multivariable models that were prognostically equivalent for the NN region were obtained combining a measure of width, a measure of mass, age, and neck-shaft angle (BMD is a ratio of mass to width in the NN region; C-index = 0.77; 95% CI, 0.75, 0.79). Trochanteric fractures were best predicted by analysis of the IT region. Because section modulus failed to predict hip fracture risk as well as areal BMD, the thinner cortices and wider bones among those who fractured may imply that simple failure in bending is not the usual event in fracture. Fracture might require initiation (e.g., by localized crushing or buckling of the lateral cortex).

**Key words:**osteoporosis, hip fracture risk, bone geometry, BMD, section modulus, buckling ratio, structural instability

## INTRODUCTION

Complete fracture occurs when stress generated by an external load exceeds the capacity of a bone to absorb energy by the combined effects of elastic (reversible) and plastic (irreversible) deformation. The specific mechanisms responsible for most hip fractures remain controversial. Although conventional DXA BMD (reported in g/cm^{2}) predicts hip fractures quite well,(1) the reason is unclear. Because BMD is equivalent to the ratio of BMC to projected area of bone tissue, uncertainty persists concerning the respective roles of BMD's numerator and denominator in determining fracture resistance.

Aged non-osteomalacic bone tissue is probably more brittle (i.e., can absorb less energy after the stress level when plastic deformation becomes inevitable, called the yield stress). However, its yield stress is generally reported as being similar to younger bone.(2,3) Aging and osteoporosis each alter the distribution and the amount of bone tissue in the hip, and it seems likely that geometric effects underlie the better predictive ability of BMD than BMC. The hip structural analysis (HSA) method has been useful in exploring this issue, because the mineral data at a particular bone cross-section is thereby expressed in geometric terms.

Sideways falls precipitate most elderly hip fractures, and the impact causes a combination of bending and axial compression in the proximal femur. Bending leads to axial compressive stresses superiorly and tensile stresses inferiorly (the reverse effect to that of stance). The maximum stress in a cross-section under bending is determined by the section modulus, and it has been hypothesized that this parameter should explain the predictive ability of BMD. In the Rotterdam study, section moduli were indeed significantly smaller in 106 female hip fracture patients before fracture than in controls,(4) but Rivadeneira et al.(4) found that predictive models worked better with BMD than with section modulus. Although the underlying reason is not mechanically obvious, this suggests that BMD is capturing a strength aspect that is not present in the section modulus. To be predictive of bending strength, the section modulus requires that integrity of the cross-section should be maintained as failure initiates, but this may not be the case in very thin-walled cross-sections. Only part of that cross-section needs to be crushed or otherwise destroyed (e.g., by local buckling through instability of one or other cortex) for a substantial shrinkage of the section modulus to occur and that could not be easily detected before fracture. The key to this paradox might be the opposing effects of periosteal expansion on BMD and on section modulus. Like other adult bones, the proximal femur gradually expands in diameter by subperiosteal apposition,(5–9) a process tending to preserve the section modulus while reducing BMD (because bone area is increased).

In an earlier radiographic analysis of the Study of Osteoporotic Fractures (SOF), Gluer et al.(10) showed that hip fracture cases had wider femoral necks, an observation borne out in several other studies.(4,11–13) The question is whether greater width improves fracture resistance consistent with its effect on section modulus or reduces it consistent with its effect on BMD. A given section modulus can be achieved with progressively less material as diameter is increased, but if carried too far, locally thin sections of cortex are prone to become unstable under compressive loads. Two mechanisms by which instability might occur have been proposed by Mayhew et al.,(14) who proposed a local buckling mechanism that is consistent with the BMD data, and Carpenter et al.,(15) who suggested that the initiating event in male hip fracture could be crushing of the same thin cortex, although with the relatively crude low resolution DXA technology they used, Yoshikawa et al.(16) could not find evidence for the latter in women.

A number of studies have used HSA to interpret DXA data, and these have mainly described age-related changes, sex/ethnic differences, and relationships with risk factors for osteoporosis.(9,11,12,17–21) Only a few studies have assessed the association of HSA variables with hip fracture.(4,12,22–25) The objective of this analysis was to provide a definitive assessment of the prediction of incident hip fracture risk using geometry variables measured by HSA in a substantially larger prospective cohort study. This provides better protection against confounding than the case-control design. HSA data from 7474 women in the prospective population-based SOF(17) were analyzed, during which 635 women suffered incident hip fractures in 13 yr of follow-up.

## MATERIALS AND METHODS

### Study population

The SOF is a large multicenter prospective study of nonblack postmenopausal women recruited from four areas in the United States.(26) Subjects were enrolled at 65 yr of age between September 1986 and October 1988. Between January 1989 and December 1990 (visit 2), each subject received a scan of the left hip using a Hologic QDR 1000 (Hologic, Waltham, MA, USA) DXA scanner. This study included 7474 women without hip fracture history before SOF visit 2 who then had DXA scans. Scan quality was generally adequate, and only a few were unusable because of a corrupted archive. Subjects were categorized as having incident hip fractures (incident hip Fx), other incident or prevalent fractures (other Fx), and fracture free (Fx-free). Hip fractures were confirmed radiologically and categorized as intracapsular (femoral neck) or extracapsular (trochanteric or subtrochanteric). Age, weight, and height at DXA scan were recorded, and whole body composition was measured by bioelectrical impedance, as described previously.(27)

### HSA

The HSA program uses the distribution of mineral mass in a line of pixels across the bone axis to measure geometric properties of cross-sections in cut planes traversing the bone at that location.(28,29) Current versions average measurements for five parallel mass profiles spaced ~1 mm apart along the bone axis, effectively corresponding to a 5-mm section thickness. Analysis locations were the narrow neck (NN) region across the narrowest point of the femoral neck, intertrochanter (IT) region across the bisector of the neck-shaft angle, and the shaft (S) region located 1.5 times minimum neck width distal to the intersection of the neck and shaft axes.

BMD, bone cross-sectional area (CSA; i.e., surface area of bone in the cross-section excluding soft tissue voids, equivalent to an estimate of BMC), bone outer diameter (subperiosteal width), and cross-sectional moment of inertia (CSMI) were measured directly from mineral mass distributions using algorithms described previously.(29) Section modulus was calculated as CSMI divided by the greater of the measured distances from the center of mass to the medial or lateral surface. Because it has been suggested that the shift in the center of mass itself might be useful in fracture discrimination,(14,16,30,31) we recorded: (1) measured distance in centimeters from the lateral cortical margin to the center of mass (lateral distance, d_{lat}) and (2) the relative centroid position calculated as measured distance from the center of mass to the medial cortical margin, divided by measured bone diameter.

Assumptions of cross-sectional shape are needed for estimates of average cortical thickness and buckling ratio, an approximate index of cortical instability.(17) Buckling ratios were calculated as the ratio of maximum distance from the center of mass to the outer cortical margin divided by the mean cortical thickness. As in previous studies, cortices of the NN and S regions were modeled as circular annuli with 60% and 100% of the measured mass in the cortex, respectively.(29) The IT estimate assumes an elliptical annulus with 70% of the measured bone mass in the cortex, and the anteroposterior diameter is assumed to be the subperiosteal diameter of the shaft region. The HSA program also measures the femur neck length and the neck-shaft angle, which influence the effective bending moment in a fall. CVs measured for geometric properties on a similar QDR1000 scanner ranged from 0.8% to 4.7%, averaging 2.2% in a study by Nelson et al.,(19) and from 1.8% to 7.2% in a study by Khoo et al.(32) that included osteoporotic women only.

### Statistical analysis of associations with hip fracture

To determine whether any HSA-based model could help explain the predictive value of BMD and whether the models are consistent with the hypotheses of Mayhew et al.(14) or Carpenter et al.,(15) Cox proportional hazard regression models were fitted to assess association between HSA variables and risk of incident hip fracture. Ascertainment included follow-up time since the visit 2 DXA exam until their first hip fracture, death, or study censoring date (spring 2002). Hazard ratios (HRs) corresponding to a 1 SD change in the HSA variables were estimated from the Cox models. Initially, age-adjusted univariate models for each structural parameter measured in the three HSA regions of interest were fitted. More parsimonious multivariable models combining HSA variables not highly correlated with one another were selected on the basis of the significance of the independent effect entered into the model. The appropriateness of choosing linear associations between HSA variables and hip fracture risk was assessed by the statistical significance of fractional polynomial terms in the Cox models.(33)

The Cox model estimates the most likely values of statistical parameters describing disease-risk factor associations by maximizing a log-likelihood function. More positive log-likelihood values indicate better model fit, and statistics based on log-likelihood are used to compare the fit of different models. The quantity 2 × (max log-likelihood of fitted model − log-likelihood of restricted model) has a χ^{2} distribution with degrees of freedom equal to the number of extra statistical parameters estimated in the fitted model. We defined the restricted model as one without HSA parameters and age, and the significance of adding a combination of HSA variables and age as predictors of incident hip fracture was evaluated. The Akaike information criterion (AIC), defined as −2 × max log-likelihood + 2 × number of estimated statistical parameters, was used for comparing non-nested models. Smaller values of AIC are desirable because the AIC favors more parsimonious models. The fit of different models was also assessed using the *r*
^{2} statistic,(34) representing the proportion of variation in time to hip fracture explained by the HSA variables.

### Predicting hip fracture

Predictive abilities of different models were compared using the C-index statistic, a concordance measure for survival data analogous to the area under a receiver operating characteristic (ROC) curve (AUC), that takes into account censored observations over time in its calculation (rather than treating them as observed nonoccurrence of the event as would be the case in direct calculation of AUC using a binary outcome variable). Discriminative ability was also assessed using the D statistic,(35,36) interpreted as the average separation of survival curves (i.e., difference in log HR) for two independent prognostic groups in the top versus bottom half of the distribution of a prognostic index derived from a Cox model. Higher values of the C-index and D statistics indicate better discrimination. All statistical analyses were done using Stata version 9 statistical software (StataCorp).

## RESULTS

### Participant characteristics

Table 1 shows characteristics of the study participants and their HSA analyzed DXA data. In total, 7474 women without prior hip fracture at SOF visit 2 were followed (mean, 10.0 yr; SD, 2.9 yr), contributing a total of 78,090 person-years. Incident first hip fractures numbered 635, giving an incidence rate of 8.14 per 1000 person-years (95% CI, 7.54, 8.80). Incident cases were significantly older, were shorter, weighed less, and had lower fat mass and percent fat mass (all *p* < 0.008 by *t*-test).

Incident hip fracture cases had significantly more obtuse (larger) neck shaft angles, wider subperiosteal and estimated endosteal diameters, greater lateral distances, and higher estimated buckling ratios (*p* < 0.0001 for all parameters in all three regions). The structural parameters that were significantly lower in hip fracture cases were areal BMD, CSA (as a surrogate for BMC), CSMI, section modulus, estimated average cortical thickness, and centroid position (*p* < 0.0001 for all parameters in all three regions, except for IT and S centroid positions for which *p* < 0.044).

### Comparison of HSA variables by fracture group

Twenty-nine percent (2138 women) remained free of any type of fragility or traumatic fracture through spring 2002 (Fx-free group), whereas 4701 (63%) had fragility fractures at sites other than at the hip (other Fx group). The Fx-free, incident hip Fx, and other Fx groups were contrasted.

Table 2 shows the age-, weight-, and height-adjusted mean values of HSA variables measured at the NN region. With the sole exception of neck length and centroid position in other Fx, all cross-sectional properties in the incident hip Fx and other Fx groups differed significantly from the Fx-free group, with greater differences evident for incident hip Fx than for other Fx. As expected, the two Fx groups had lower indices related to bone mass (BMD, CSA, CSMI, section modulus, thinner cortices), as well as broader outer diameters and higher buckling ratios. The incident hip Fx group also had more medial centroids, indicating preferential loss of lateral bone mass. With regard to estimators of compression and bending strength, the two fracture groups showed lower values than the Fx-free group in CSA and section modulus, respectively, but the greatest structural differences were in indices of cortical stability (buckling ratio higher by 0.78 SDs, cortical thickness lower by 0.73 SDs, and CSA lower by 0.61 SDs in incident hip Fx group).

### Association between HSA variables and incident hip fracture risk

Tests based on fractional polynomial terms in the Cox models suggested that a linear association with hip fracture risk was appropriate for all HSA parameters. Figure 1 shows age-adjusted univariate HRs for incident hip fracture associated with a 1 SD change in each HSA variable. Risk of hip fracture increased by 1.11- to 1.16-fold per year of age, which was adjusted for in Fig. 1. The only variable that showed no significant association was neck length (RR = 0.93; 95% CI, 0.86, 1.00; *p* = 0.056); otherwise, 95% CIs for all other parameters excluded unity. Adjustment for weight and height did not materially change the HRs in Fig. 1.

### Combining HSA variables contributing independently to risk

We built multivariable models combining HSA parameters that were associated with hip fracture but not highly correlated with one another. The highly associated parameters were first grouped, and one from each group chosen: (1) BMD versus CSA plus subperiosteal diameter; (2) section modulus versus CSMI; and (3) estimated buckling ratio versus estimated cortical thickness plus lateral distance.

To make the point that no model is uniquely predictive, Table 3 shows 13 multivariable models combining independent associations with hip fracture for HSA variables measured at the NN region. Neck-shaft angle consistently entered all models as an independent predictor, with HRs ranging from 1.11 to 1.15 per 1 SD increase. Effects of lateral distance were interchangeable with those of centroid position plus either subperiosteal or endosteal diameter. This was expected because the Pearson correlation between lateral distance and both subperiosteal and endosteal diameters was 0.94 and that between subperiosteal and endosteal diameter was 0.99.

In models 1–3, average cortical thickness decrease and section modulus decrease were each independently associated with increased risk of incident hip fracture (Table 3). Additionally, lateral distance increased risk by 1.48 per 1 SD decrease (in model 1). Models 1–3 gave exactly the same maximized log-likelihood value of −4814. Model 1 with five parameters gave the smallest AIC value of 9638 and was preferred as being most parsimonious.

Models 4–6 contained the effect of CSA (analogous to BMC), replacing cortical thickness and section modulus. The Pearson correlation between CSA and cortical thickness was 0.84 and with section modulus was 0.89. A decrease in CSA increased risk of incident hip fracture by 1.80–1.93 per 1 SD depending on whether the model contained an additional independent effect of lateral distance (model 4), centroid position and subperiosteal diameter (model 5), or centroid position and endosteal diameter (model 6). These three models gave a maximized log-likelihood value of −4817 and slightly higher AICs than for models 1–3.

Models 7–9 contained the effect of areal BMD instead of CSA and average cortical thickness. The Pearson correlation between BMD and CSA was 0.86 and between BMD and cortical thickness was 0.99. A 1 SD decrease in BMD increased the risk of incident hip fracture by 1.44–1.52 depending on which other covariates were in the model. An independent effect of section modulus increased risk by 1.36–1.41 per 1 SD decrease. The other independent effects in these models were the same distance parameters as in models 1–3. The maximized log-likelihood value in these three models with BMD was −4814, being exactly the same as for models 1–3. Thus, models 1–3 were statistically equivalent to models 7–9.

Models 10–12 show that per 1 SD increase in average buckling ratio, the risk of incident hip fracture increased by 1.28–1.63 times, independently of age, neck-shaft angle, and section modulus (model 10), CSA (model 11), or areal BMD (model 12).

### Predicting hip fracture

Table 4 shows the C-index statistics (AUC for survival data) depicting the practical ability of HSA variables to predict cases of incident hip fracture. The C-index for areal BMD is shown as a comparator. The three most impressive parameters were areal BMD, cortical thickness, and average buckling ratio, all with C-indexes of 0.72 at the NN region, either 0.71 or 0.72 at the IT region, and 0.68 at the S (all differences between predictors not significant).

Figure 2 shows that the ROC curves for estimated cortical thickness and buckling ratio were superimposable over that for BMD across the whole range of sensitivities and specificities. The ROC curve for CSA was slightly lower than that for BMD. Section modulus performed less well than these three parameters in discriminating incident hip fracture cases from noncases.

*n*= 635) vs. those without hip fracture (

*n*= 6839) in comparison

**...**

The C-index statistics were calculated separately for incident femoral neck (intracapsular) fractures (*n* = 340) and trochanteric (extracapsular) fractures (*n* = 286). Figure 3 shows a summary of the resulting C-index values for HSA parameters. The IT region HSA parameters were consistently better at identifying trochanteric fractures than femoral neck fractures, whereas NN region parameters were not clearly better at identifying femoral neck fractures than trochanteric fractures.

All 13 multivariable models in Table 3 for the NN region gave the same C-index value of 0.77 (95% CI: 0.75, 0.79). Additionally, the *r*
^{2} measure of explained variation suggested that the 13 models were all comparable in terms of proportion of variation in time to hip fracture explained by each model, the *r*
^{2} being either 42% or 43%. The D statistic suggested that there was no difference in the discriminating ability of these models, all giving D statistic values between 1.74 and 1.77 (Table 3). When age was excluded from the models, the C-index decreased to 0.74 (0.72, 0.76) in models 1–10, 0.73 (0.71, 0.75) in models 11 and 12, and 0.72 (0.70, 0.75) in model 13, suggesting that the geometric variables retained much of the predictive ability associated with age, whose C-index as a single predictor was 0.71 (0.69, 0.74).

### Extracapsular HSA and fractures

The results for multivariable models combining independent effects of intertrochanter HSA variables showed that the most parsimonious models combined effects of age, neck-shaft angle, areal BMD or CSA, and one of the dimension variables and gave a C-index value of 0.78 (95% CI, 0.76, 0.80), *r*
^{2} value of 43% (39%, 47%), and D statistic of 1.74 or 1.79.

When these calculations were repeated so that the NN region results were used to predict intracapsular fractures and the IT results were used to predict extracapsular fractures, the C-index values for the NN region parameters predicting femoral neck fractures ranged from 0.75 to 0.78, whereas the C-index values for IT region parameters predicting trochanteric fractures were larger, ranging from 0.81 to 0.83. The *r*
^{2} and D statistics also suggested better predictive ability for IT region parameters in predicting trochanteric fractures, the *r*
^{2} values ranging from 49% to 54% and D statistic values ranging from 2.00 to 2.20; this compared with *r*
^{2} values ranging from 38%to 43% and D statistic values ranging from 1.62 to 1.77 for NN region parameters in predicting femoral neck fractures.

## DISCUSSION

This cohort study allowed the analysis of six times as many female hip fracture cases as the next largest(4) and allowed us to contrast with much enhanced precision the predictive ability for future hip fracture of DXA-derived femur geometry parameters including BMD. An important aspect of this study is that the predictive ability of different quantities derived mathematically from the same mineral mass data in a region could be compared, including key dimensions incorporating the mineral distribution projected in two dimensions within the proximal femur. A critical finding is that hip fracture cases and controls significantly differ geometrically in several mechanically important ways that can be measured from DXA data. We confirm the finding of Rivadeneira et al.(4) that section modulus (an estimate of bending strength in the plane of the DXA scan) is inferior to BMD in predicting hip fracture in women. However, BMD as a single index or ratio is difficult to interpret mechanically. By expressing the data in ways that are mechanically more interpretable using HSA, the geometric differences that underlie the prognostic value of BMD measurements provided critical insights into fragility mechanisms. In particular, our study highlights the important role of the gradual widening of the bony envelope with adult aging that lowers BMD independently of lost bone tissue (because BMD is equivalent to the ratio of bone mass to projected area, which is determined by bone width in the proximal femur). This aging phenomenon was first described four decades ago by Garn et al.(37) and Richmond Smith(38) and specifically confirmed for the intracapsular femoral neck by Heaney et al.,(6) Beck et al.,(17) Kaptoge et al.,(9) and Power et al.(39)

Engineering simulations of loads on the proximal femur in both normal activities and in falls likely to cause fragility fractures show that bending is dominant at most cross-sections. For constant material properties, loss of bending strength in an intact cross-section should be evident as a reduced section modulus. However, Yoshikawa et al.,(16) Carpenter et al.,(15) and the high-resolution finite element study of Verhulp(40) showed that the stresses in a sideways fall are maximal in the supero-lateral cortex. This becomes preferentially thinned(41) and relatively poorly supported by internal trabeculae(42) in osteoporosis. If the cross-section does not remain intact (through being crushed or suffering local instability leading to buckling), the section modulus would overestimate strength under fall loads. Calculations by Yoshikawa et al.(16) suggested that falling sideways from standing height would not generate sufficient stress to fracture femoral necks in elderly women in a pure bending (intact cross-section) mode unless the tissue material strength were degraded or if local flaws in the thin lateral cortex of the femoral neck concentrated stress more than expected. Tissue yield stress does not seem to be degraded in cases of hip fracture(42,43) and in aging in general,(2,3) although there is good evidence that bone tissue is more brittle and fails more abruptly when it does fracture.(2,3) Several studies have considered that structural failure in the femoral neck might begin locally(15,16) by elastic instability.(14) If the superior cortex buckles in a fall mode the section modulus would quickly diminish and its prefracture section modulus would not predict failure well. The necessary geometry can only be crudely estimated from DXA data in the buckling ratio. The predictive ability of buckling ratio in this study is consistent with, but not proof of, the idea that osteoporosis degrades strength by reducing cortical stability. It also provides a target in population genetic studies of fracture.

In this study, bone mass differences alone (CSA) did not predict hip fractures as well as BMD alone, but when CSA was combined with subperiosteal diameter, the C-index value equaled that of BMD (Table 4; Fig. 2). As previously noted, expansion has opposing effects on BMD and on section modulus, and it seems that the processes that adapt section moduli to prevalent mechanical loads in aging bones(4,9,17,21,29) might actually increase fracture risk in the elderly. This implication was supported by the significantly lower C-index for section modulus than for CSA (which represents BMC), not just for BMD. Expansion seems to have progressed further in fracture cases in this study, consistent with previous observations in female fracture cases.(4,10,12) Thus, it would seem that the mechanical effect of periosteal expansion in fracture cases is deleterious consistent with the effect on BMD, rather than advantageous as the section modulus effect would infer.

Alterations in the distribution of bone within femur cross-sections may be relevant to hip fragility. As shown by Mayhew et al.,(14) the preservation of the infero-medial femoral neck cortex with preferential loss in the supero-lateral cortex may serve the limited mechanical demands of middle and old age, but a fall on the greater trochanter puts the most thinned cortex in maximum compression. It is relevant that we observed a greater infero-medial shift in the center of mass in those suffering fragility fractures in this study (Table 2), with a significant association with incident hip fracture risk independent of age and other HSA variables (Table 3). This effect was theoretically modeled by Fox and Keaveny,(44) showing that the shift should have a protective effect under physiologic stance loads, but conversely, during bending in a fall mode, it should reduce strength.

### Limitations

There are methodological limitations to our measurements.(17,29) Our conclusions depend on dimensional characterization of femur cross-sections, which can only be partially specified from a single projection. With the limited information available from the DXA-based HSA method, alternative explanations for our observations must be considered. The poorer predictive value of section modulus than BMD might be because failure loads are consistently out of the scan plane. Indeed, most 3D engineering models load the proximal femur in the fall mode with 20–30° of rotation out of the frontal (scan) plane, but this cannot be done with single plane image data. Femoral neck strength may be ~20% weaker when bent out of the frontal plane because of cross-section asymmetry.(15,45) To change our conclusions, the asymmetry in this property would have to be greater in fracture cases than controls, which seems unlikely but not impossible. We remain to be convinced that lower stress resistance is largely caused by diminished tissue yield stress in most patients with osteoporosis, although one might suspect this from literature using QCT methods to derive finite element (FEA) models. In FEA models, reduced volume fraction from thinned cortices and trabeculae are simulated using empirical density/elastic modulus relationships and not actual measurements of tissue properties. It remains possible that local variations in tissue properties contribute to failure in fracture cases but are not measurable clinically. Estimates of cortical thickness, buckling ratio, and endosteal diameter (but not section modulus or the other dimensions) depend on a simplistic model of cross-sectional geometry that uses elementary geometric shapes, uniform cortices, and fixed proportions of bone mass between the cortex and trabecular bone(41,46,47) that might alter with aging. Data from Bell et al.(41) suggest that the cortical proportion of femoral neck bone is reduced in femoral neck fracture cases; this will distort the predictive ability of the buckling ratio as we currently define it. The buckling ratio is (as previously discussed) a simplification, derived from the study of uniform tubular structures and is only indirectly related to the concept of local buckling(48) that may be more relevant to hip fracture. Local buckling susceptibility depends in part on surface curvature,(14) which will require some form of 3D imaging such as CT for its measurement. The effects of internal trabecular support on the cortex remained undefined but are likely to decline if aging reduces trabecular more than cortical BMD. Although we showed important geometric differences between femurs of hip fracture cases and controls in this large study, 2D DXA scans of 3D bones provide modest precision for measuring quantities other than BMD in the clinical setting.

We conclude that proximal femurs of elderly women with hip fracture have lower bending (section modulus) and axial (CSA) strengths, with thinner more asymmetric cortices, and are wider in diameter than those of fracture-free women. Their neck-shaft angle is also more obtuse, increasing the bending moment in a fall to the side. In this large study, given all the limitations noted, the superiority of BMD over section modulus for hip fracture prediction suggest that the simple bending failure model of hip fracture is unlikely and emphasizes the potential role of expansion of outer femoral neck diameter and cortical thinning that occurs with aging. It seems likely that expansion by subperiosteal bone formation is more than offset by endosteal resorption that accelerates after menopause(49) in the elderly female. Indeed, Kaptoge et al.(50) have found that, in postmenopausal women, the velocity of growth in bone width is inversely related to estimated free estradiol levels.

This large well-characterized study has high statistical power in showing that geometry measured from DXA data by HSA is prognostically equivalent but not superior to BMD in hip fracture prediction. However, by expressing the data in ways that are mechanically interpretable, HSA provided critical insights into fragility mechanisms and underlying dimensional effects that will now refocus the search for reversible age-related changes in the elderly hip. HSA in a more anatomically accurate 3D form might help interpret future clinical studies of hip fragility and its prevention.

## ACKNOWLEDGMENTS

This work was supported by Research Grant AR44655 from the National Institute of Arthritis and Musculoskeletal and Skin Diseases, National Institutes of Health; Research Grants AG05407, AR35582, AG05394, AR35584, and AR35583 from Public Health Services, National Institutes of Health; and EU NEMO Contract QLK6-CT-2002-00491. The authors thank Gabrielle Milani and Tu Duong for assistance in data management and HSA analysis and Lisa Pennels, Ian White, and Angela Wood for input in discussions on methods for assessing predictive ability of survival models.

## Footnotes

Dr Cauley states that she has research grants from Merck & Co., Eli Lilly & Co., Pfizer Pharmaceuticals, and Novartis Pharmaceuticals. All other authors state that they have no conflicts of interest.

## REFERENCES

**American Society for Bone and Mineral Research**

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