Finite Element Analysis of the Proximal Femur and Hip Fracture Risk in Older Men


  • Dr Keaveny has a financial interest in O.N. Diagnostics, and both he and the company may benefit from the results of this research. Dr Kopperdahl and Mr Hoffmann have equity interests in and are employees of O.N. Diagnostics. All other authors state that they have no conflicts of interest.


Low areal BMD (aBMD) is associated with increased risk of hip fracture, but many hip fractures occur in persons without low aBMD. Finite element (FE) analysis of QCT scans provides a measure of hip strength. We studied the association of FE measures with risk of hip fracture in older men. A prospective case-cohort study of all first hip fractures (n = 40) and a random sample (n = 210) of nonfracture cases from 3549 community-dwelling men ≥65 yr of age used baseline QCT scans of the hip (mean follow-up, 5.6 yr). Analyses included FE measures of strength and load-to-strength ratio and BMD by DXA. Hazard ratios (HRs) for hip fracture were estimated with proportional hazards regression. Both femoral strength (HR per SD change = 13.1; 95% CI: 3.9–43.5) and the load-to-strength ratio (HR = 4.0; 95% CI: 2.7–6.0) were strongly associated with hip fracture risk, as was aBMD as measured by DXA (HR = 5.1; 95% CI: 2.8–9.2). After adjusting for age, BMI, and study site, the associations remained significant (femoral strength HR = 6.5, 95% CI: 2.3–18.3; load-to-strength ratio HR = 4.3, 95% CI: 2.5–7.4; aBMD HR = 4.4, 95% CI: 2.1–9.1). When adjusted additionally for aBMD, the load-to-strength ratio remained significantly associated with fracture (HR = 3.1, 95% CI: 1.6–6.1). These results provide insight into hip fracture etiology and demonstrate the ability of FE-based biomechanical analysis of QCT scans to prospectively predict hip fractures in men.


Hip fracture is common in older persons and is an important cause of morbidity, disability, and mortality. The causation of hip fracture is multifactorial, but a major contributor is reduced strength of the proximal femur. Development of noninvasive measures of femoral strength could provide a better understanding of the causation of hip fracture and might improve clinical assessment of fracture risk.

Areal BMD (aBMD) as measured by DXA is highly associated with measured femoral strength in cadaver studiesmath image and clinical risk of hip fracture,math image but the majority of hip fractures occur in persons in whom hip aBMD is not severely reduced.math image This may be caused in part by the unexplained variance in bone strength related to such 3D structural factors as femoral bone geometry and spatial distribution of BMD, which are not specifically captured by aBMD. Moreover, because hip fractures occur only when the loads acting on the proximal femur exceed its structural capacity,math image a consideration of the in vivo loads that are applied to the bone during a fracturing event, such as a sideways fall, could allow improved estimates of fracture risk in an individual. In theory, a clinical tool integrating 3D mass distribution and structural data for accurate bone strength predictions, together with patient-specific estimates of in vivo loading, should be more successful than considering bone strength in isolation. This “load-to- strength ratio” approach has provided insight into age- and sex-specific fracture etiology.math image

Finite element (FE) analysis of QCT scans has been used for well over a decade in orthopedic research to study the mechanical behavior of such bones as the femur,math image skull,math image and vertebra.math image Conceptually, the technique biomechanically integrates the information in the QCT scan to produce a measure of whole bone strength. It has been well validated in cadaver studies for both the hip and spine.math image,math image Recently, FE analysis of the spine using the load-to-strength ratio approach was shown to differentiate those with prevalent vertebral fractures from those without, after accounting for age and aBMD.math image However, this general biomechanical approach incorporating FE analysis of QCT scans has yet to be evaluated in any prospective fracture outcome study.

To provide an initial evaluation of the ability of FE analysis of QCT scans to prospectively predict new hip fractures, we examined the association between FE-derived measures of femoral strength and the load-to-strength ratio with incident hip fracture in a population of older men (the Study of Osteoporotic Fractures in Men [MrOS]). We also tested whether these associations were independent of other factors associated with fracture, including aBMD as measured by DXA, age, and body mass index (BMI).


Study population

The MrOS study enrolled 5995 participants from March 2000 through April 2002 as previously described.math image,math image Briefly, recruitment occurred in Birmingham, AL; Minneapolis, MN; Palo Alto, CA; Pittsburgh, PA; Portland, OR; and San Diego, CA, and was accomplished primarily through targeted mailings based on motor vehicle registration, voter registration, and Veteran's Administration databases. Eligible participants were ≥65 yr of age, able to walk without assistance from another person, and had not had bilateral hip replacement surgery. Each study site enrolled ∼1000 men. Proportions of black, Asian, and Hispanic men enrolled at each study site were generally representative of those reflected in the local population of older men by U.S. Census data.math image,math image All participants gave written informed consent.

Baseline characteristics

Height (cm) was measured using a Harpenden stadiometer. Participants were weighed (kg) on balance beam or digital scales while wearing indoor clothing except shoes.

Scanning procedures

aBMD was obtained for the total hip and its subregions with fan-beam DXA (QDR 4500W; Hologic) at all study sites. Participants were scanned according to standardized procedures, scanners were cross-calibrated at baseline, and daily quality control scans showed no shifts in scanner performance at any site during the enrollment period.

Constraints on study resources limited the number of QCT scans that could be acquired. Thus, the MrOS study was designed such that approximately the first 650 men and all nonwhite men enrolled at each site were referred for QCT scans of the hip and lumbar spine as part of their baseline visit. Of 3786 men referred, 1 refused, and 122 were ineligible for a hip scan because of hip replacement. Ultimately, we obtained hip QCT scans on 3663 participants (61% of the MrOS cohort). Baseline characteristics of men referred and not referred for scans were comparable, except for a slightly greater proportion of nonwhite men among those referred.math image Details regarding acquisition of the baseline QCT scans have been described.math image Briefly, the pelvic region was scanned from just above the femoral head to 3.5 cm below the lesser trochanter at settings of 80 kVp, 280 mA, 3-mm slice thickness, and 512 × 512 matrix in spiral reconstruction mode.math image The effective radiation dose associated with this protocol is on the order of 1 mSv or less. A calibration phantom (Image Analysis, Columbia, KY, USA) containing known hydroxyapatite concentrations was included with the participant in every scan. Of the 3663 hip scans, 102 (2.8%) were lost or corrupted during transfer to the central processing site, leaving 3561 available for analysis.

Follow-up and case cohort selection

After enrollment, participants were observed for an average of 5.5 yr. We contacted participants every 4 mo through mailed questionnaires to ask about recent fractures. Follow-up for fractures was 99% complete. All reported hip fractures were validated by physician review of radiology reports or X-rays if no radiology report was available. Using a random selection procedure, we identified 225 men who had baseline hip CT scans, four of whom suffered hip fracture during follow-up. Differences in characteristics of the random sample and the entire cohort were compared using t-tests for continuous variables and χ2 tests for categorical variables. Overall, the age, height, weight, BMI, and aBMD characteristics were similar in this n = 225 group as in the full MrOS cohort (Table 1), confirming the validity of this randomized selection. Of those who suffered hip fracture during follow-up in the entire MrOS cohort (N = 82), 41 had available baseline CT scans. Image quality prevented FE analyses in 16 scans, leaving 250 included in this analysis (n = 40 cases; 210 controls).

Table Table 1.. Characteristics of Men in the Entire MrOS Cohort Compared With the Randomly Selected Sample of Nonfracture Controls
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Estimation of femoral strength

All FE analyses were performed blinded without knowledge of the fracture status of participants. Using custom code (O.N. Diagnostics, Berkeley, CA, USA), the QCT images were processed and converted into FE models using 1.5-mm-sided, cube-shaped, eight-noded brick elements (Fig. 1). A uniform threshold value was used to segment all images, and any discontinuous edges were semiautomatically filled by the analyst for masking purposes. Images were resampled at 1.5-mm isotropic resolution and registered to a reference coordinate system in a fall configuration (see below). In the remaining images, cortical bone and trabecular bone were defined on the basis of their calibrated density values (see below). Isotropic material properties were assigned to all elements by converting the calibrated density to material properties using empirical relations,math image with different assignments made to cortical versus trabecular bone. Cortical bone was defined as having an apparent density >1.0 g/cm3 (equivalent to a QCT calibrated mineral density of >693 mg/cm3). All bone material was assigned a higher strength in compression than tensionmath image,math image and was modeled using a von Mises type elastic-perfectly-plastic material with tension-compression strength asymmetry.math image Trabecular elastic and strength properties were adjusted by a factor of 1.28 to account for the inevitable side-artifact errors that occur during the biomechanical testing of cadaveric trabecular bone cores used to establish the empirical relations between density and mechanical properties.math image,math image

Figure Figure 1.

Typical FE model of the proximal femur, showing 3D (A) and 2D sectional (B) views. The color-coding shows the spatial variation of material strength assigned to the individual finite elements. A vertical force was applied through the center of the femoral head using a PMMA mold (shown in white). Bending moments and torque but no shear forces could be transmitted at the distal end, and shear forces could not be transmitted through the trochanter PMMA mold.

Similar to what has been used in a number of previous cadaver and FE studies,math image,math image,math image boundary conditions were applied to simulate a fall to the side of the hip, the diaphysis angled at 10° with respect to the ground with 15° of internal rotation. This represents a severe, unprotected, fall to the side of the hip, which is known to be associated with a high risk of fracture.math image,math image In the models, the bone was oriented appropriately using an automated registration scheme and shear-free loads were applied vertically using PMMA molds covering the femoral head and greater trochanter with moment and torque constraint applied distally (Fig. 1). The PMMA molds were used to simulate typical cadaver tests and to simplify application of boundary conditions (versus more complex loading of highly nonlinear articular cartilage and periosteal soft tissue). After creation of the FE models, the stress analyses were performed using our in-house FE solver. Strength was calculated from the resulting nonlinear force-deformation curve as the force at 4% deformation of the femoral head with respect to the greater trochanter. This overall technique has been shown to provide excellent predictions of femoral strength in cadaver laboratory studies (n = 51, r2 = 0.80, unpublished data on file).

Estimation of the load-to-strength ratio

We calculated the load-to-strength ratio for a simulated sideways fall and impact directly on the greater trochanter. The in vivo impact force on the side of the trochanter was estimated for each subject from biomechanical theory using patient-specific mass and height information. Specifically, we assumed a simple point-mass model of the body impacting the ground in which the potential energy associated with standing height was converted into kinetic energy at impactmath image and assumed also a linear relation between the maximum impact force and the soft tissue thickness at the greater trochanter.math image A uniform value of trochanteric soft tissue thickness of 25 mm was assumed for all subjects because patient-specific measures of soft tissue thickness were not measured from the QCT scans for this study. The resulting expression for the load-to-strength ratio was directly proportional to patient mass and the square root of patient height and was indirectly proportional to the FE-derived strength. To account for the very high rate of loading possible during a fall and the associated viscoelastic strengthening,math image the femoral strength value for the load-to-strength ratio calculation was increased by a factor 1.30.

Statistical analyses

Spearman correlation coefficients were calculated for the biomechanical parameters versus aBMD (total hip, by DXA), age, and weight to determine their associations with established predictors of hip fracture. The nonparametric correlation coefficient was chosen because biomechanical parameters were slightly right-skewed. Modeling of the time to incident hip fracture was performed using Cox proportional hazards regression with the Prentice weighting method and robust variance estimate necessitated by the case-cohort design.math image Each biomechanical parameter was included in a separate model of time to first hip fracture to estimate the relative increase in the hazard of fracture corresponding to a 1 SD change in the parameter. Covariates were added to the model sequentially (age, study site, BMI, and then aBMD) to assess their effect on the hazard ratio (HR) estimate. The distributions of strength, load-to-strength, and BMD by case status were explored by plotting the data using kernel density estimation (KDE) in Stata, Release 9.2 (Stata Corp., College Station, TX, USA). Whereas histograms are useful for discrete variables, smooth density functions better represent data from continuous distributions. KDE plots allowed us to examine the data for skewness and multimodality.math imageVariables included in the best fitting models were then included in a logistic regression model (with weights). Analysis of the receiver operating characteristics (ROC) curve was performed to calculate area under the curve (AUC), and partial AUC values were also calculated because these are more sensitive to diagnostic classification in the more clinically relevant high specificity regimen.math image,math image ROC curves were also calculated for unadjusted variables. Conventional cut-offs of hip fracture risk, specifically a total hip DXA T-score of T = − 2.5 (male reference) and the theoretical cut point of ϕ = 1.0 for the load-to-strength ratio, were also examined in ROC analyses.


At the baseline visit the randomly selected nonfractured group (N = 210) was similar to the overall MrOS cohort, whereas the 40 men who experienced incident hip fracture were older and had lower height, weight, and BMI (Table 2). The correlations with known risk factors for fracture such as aBMD, age, and BMI were different between the two biomechanical parameters (Table 3). Femoral strength had a weak negative correlation with age and was strongly correlated with aBMD (Fig. 2A), and like the load-to-strength ratio, had a weak positive correlation with height, weight, and BMI. Unlike femoral strength, the load-to-strength ratio was negatively correlated with aBMD (Fig. 2B) and was not significantly correlated with age. As expected, femoral strength and the load-to-strength ratio were correlated and exhibited a nonlinear relationship (Fig. 2C).

Table Table 2.. Comparison of Mean Characteristics for the Nonfracture Controls (n = 210) vs. Fracture Cases (n = 40) Analyzed by FE Analysis
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Table Table 3.. Correlations Between the Various Predictors and Characteristics of Men in the Pooled Cohort (N = 250) Used in This Analysis
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Figure Figure 2.

Correlations between baseline measures of the hip. (A) Femoral strength vs. total hip aBMD. (B) Load-to-strength ratio vs. aBMD. (C) Load-to-strength ratio vs. femoral strength.

On average, biomechanical parameters were significantly different for the fracture cases compared with men who remained free from fracture (Table 2). The average value of femoral strength for the fracture cases was lower by 36% (p < 0.01), and the load-to-strength ratio load-to-strength ratio was higher (i.e., worse) by 51% (p < 0.01). aBMD was lower by 17% (p < 0.01). Fracture cases were older and had lower height, weight, and BMI, and because of this, they had lower values of estimated in vivo loads (p < 0.01). The frequency distributions showed appreciable overlap between fracture cases and noncases, although the shape of the distribution for femoral strength resembled more of a β distribution than a normal distribution (Fig. 3).

Figure Figure 3.

The distributions of the hip measurements at baseline using Kernel density estimate curves in men with subsequent hip fractures and nonfractured men. Kernel estimators can be regarded as nonparametric histogram smoothers and are used here to compare the distributions of baseline hip measures in the two groups. (A) Femoral strength. (B) Load-to-strength ratio. (C) Total hip aBMD by DXA.

Both femoral strength and the load-to-strength ratio were highly associated with hip fracture risk, as was aBMD (Table 4). These associations remained statistically significant after adjusting for age. When adjusted additionally for aBMD (and study site and BMI, which had only small effects), the HR for the load-to-strength ratio remained statistically significant, although the HR for femoral strength did not.

Table Table 4.. HR for Incident Hip Fracture per SD Change*
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Analysis of the individual fracture cases (Fig. 2) showed that men who experienced fracture clustered at the extreme ends of the ranges for each measure, and there was little evidence the measures provided complementary predictive information. For example, all subjects experienced a hip fracture with either a load-to-strength ratio value >1.5 or a femoral strength value <2900 N (n = 8 for load-to-strength ratio; n = 13 for femoral strength), suggesting that combining these criteria would not appreciably improve prognostic value. Similarly, of the nine subjects having a baseline aBMD T-score of less than −2.5, seven had an incident hip fracture, and all but one of those seven fracture cases had load-to-strength ratio >1.0, the theoretical biomechanical fracture threshold. However, four of the eight fracture cases having a load-to-strength ratio value >1.5 had aBMD T-scores greater than –2.5.

ROC analyses showed that AUC values for femoral strength and load-to-strength ratio were 0.83 and 0.79, respectively, and were similar to the value for aBMD (0.85) (Fig. 4). At the theoretical value of the fracture threshold for the load-to-strength ratio (ϕ = 1.0), sensitivity and specificity were 53% and 84%, respectively. The multivariate logistic regression model ROC analysis showed that, after accounting for age, BMI, and clinical center, AUC values were only slightly increased and were similar for femoral strength (0.87), load-to-strength ratio (0.88), and aBMD (0.88). The partial AUC values at false-positive rates of <20% were 0.12 for femoral strength and 0.09 for the strength-to-load ratio, which were not statistically different than the value of 0.10 for aBMD.


In this prospective, case-cohort study of incident hip fracture in older men, FE-derived biomechanical measures from baseline CT scans were strongly associated with fracture risk, both alone and after adjustments for age, BMI, and clinical site. Although this study, with only 40 fracture cases, was not highly powered to compare the FE outcomes against aBMD by DXA in terms of predictive ability, after further adjustment for aBMD, the load-to-strength ratio-an index that includes both femoral strength and the force estimated to occur in a sideways fall-remained predictive of fracture. This is the first prospective evaluation of the application of FE analyses for the prediction of hip fracture. Additional and larger studies are needed to determine whether the same trends can be shown and whether further improvements can be gained by refining the biomechanical analyses.

We have previously shown that several measures of proximal femoral mass and structure, including femoral neck cortical thickness, trabecular density, and integral volume, are associated with incident hip fracture risk in men.math image Whereas those findings and results from other cadaver and clinical studiesmath image,math image can provide information concerning how individual structural components of the proximal femur contribute to femoral strength and fracture risk, FE analysis of QCT scans provides an integrated estimate of whole bone biomechanical strength. In fact, studies of proximal femoral breaking strength in vitro confirm that FE estimates are closely related to actual measures of fracture resistance,math image,math image and there has been considerable interest in the potential that FE analysis of QCT scans might add value to existing clinical measures.

Our findings showed that femoral strength and load-to-strength ratio are highly predictive of incident hip fractures in men. Although we provide preliminary comparisons of the FE measures with aBMD by DXA, with only 40 fracture cases, the statistical power available for the evaluation was suboptimal. In that context, there was not a significant difference in fracture predictive ability of aBMD and FE, but a number of trends in the data suggest that the FE approach, which biomechanically integrates 3D geometry and density distribution, may have merits over aBMD for fracture prediction. First, despite the large and overlapping CIs between femoral strength and aBMD, the very high HR for femoral strength compared with aBMD is unlikely to be a statistical artifact. Second, the sensitivity at high specificity was greater for femoral strength than aBMD, and there was separation of the frequency distributions between fracture and no-fracture cases at low strength, which was not as evident for aBMD. For instance, all subjects having strength values of <2900 N fractured, accounting for almost one in three fracture cases. Finally, the load-to-strength ratio, which is easily combined with femoral strength, was strongly related to fracture risk even after adjusting for aBMD, age, and BMI. Future studies are needed to confirm and extend these findings in different and larger fracture cohorts.

From an etiological perspective, these results establish that accounting for the strength of the femur in the context of the loading expected to apply to the femur during a fall-which in theory should be a more powerful predictor of fracture than accounting for bone strength alonemath image—does indeed represent a risk factor for hip fracture that is independent of aBMD. Similar findings have been reported recently in women for hipmath image and spinemath image fractures, indicating that this phenomenon is not limited to hip fracture or to men. Indeed, the effect observed here was quite large: an individual having a load-to-strength ratio value of 2 SD above the mean should have an ∼9-fold increased risk of fracture-after accounting for aBMD, age, and BMI. However, our results did not show any obvious trend by which the load-to-strength ratio can be combined with femoral strength to improve predictive value, in part because all subjects having very low bone strength also had very high values of the load-to-strength ratio. A possible reason for this was that our strategy of assessing the load-to-strength ratio using just a single load case (fall to the side) may be inherently limited. Improvements might be forthcoming if multiple load cases could be accounted for. Furthermore, we did not include a patient-specific measure of trochanteric soft tissue thickness, which may play an important role in load attenuation during a sideways impact of the hip.math image,math image It remains to be seen if including such detail alters the gradient of risk for the load-to-strength ratio reported here or its interaction with femoral strength. We did not explore calculation of a load-to-strength ratio using aBMD as a surrogate for femoral strengthmath image,math image because our focus was on assessment of the FE-derived parameters. Any possible clinical advantage of adding a load-to-strength ratio parameter to aBMD remains to be explored for this cohort.

This study has several important strengths. It takes advantage of a large observational study of older men to perform the first evaluation of the association of FE-based biomechanical measures with hip fracture risk. A major advantage is the prospective design of the study that avoids the limitations of cross-sectional evaluations. Moreover, the FE analyses were performed in a blinded fashion, and the case-cohort approach provided adequate power to detect meaningful associations between the proximal femoral measures and fracture risk. The study participants were carefully characterized at baseline, including measures of hip aBMD by DXA and proximal femoral CT scans. The biomechanical analysis provided outcomes of not just FE estimates of femoral strength for a clinically relevant type of fall, but also the load-to-strength ratio, which accounts for patient-specific estimates of the force at impact. This study was performed without any calibration of the modeling parameters, so the study provided a fully prospective test of the risk association for these biomechanical parameters, providing a strong degree of external validity to the results.

The study also has limitations. As noted above, despite the large number of men who had CT scans at the baseline evaluation (>3600), the number of hip fractures in this analysis (n = 40) was small. Indeed, the small size of the fracture cohort prevented us from comparing the predictive abilities of the FE-derived parameters against aBMD with any appreciable level of statistical power. Similarly, this initial study of the association of FE measures with fracture risk does not yield sufficient data to make recommendations concerning the role of FE analyses in clinical settings. Further analyses will be possible in MrOS to address this limitation as additional hip fractures occur during continued follow-up, and other studies will similarly contribute to the field. Age-related changes in the femur that set the stage for reduced bone strength and increase hip fracture risk in men (loss of trabecular bone mass, cortical thinning) are slightly different than those that occur in women.math image Whereas such differences are inherently incorporated in the FE analyses, there may be sex-related differences in fall biomechanics, including soft tissue characteristics, which could affect associations with fracture risk. Thus, the results of these studies in men may not be representative of comparable analyses in women. Similarly, although the MrOS population includes nonwhite men, there were few fractures in those cohorts and whether these results are applicable in nonwhite populations is uncertain. Our estimates of femoral loads were based on models of falling to the side, but we have not included information concerning the circumstances of the trauma that resulted in hip fracture in the participants included in this study, nor did we include any patient-specific measures of soft tissue thickness or muscle function. The FE models themselves, although highly detailed, did not include such effects as material anisotropy or explicit modeling of the thin cortex. Further advances in the technology that address these issues, both in the FE model and in the in vivo load estimates, may lead to more refined estimates of the outcome parameters. Finally, although the FEs were 1.5 mm per side, the CT images themselves had voxels reconstructed at 3 mm, which provides limited detail of the thin cortex and bone curvature in such regions as the femoral neck. Although the scans themselves were not adjusted for intersite differences in acquisition parameters, CT machines, or calibration errors, we included study site in our statistical models as a way of adjusting for site differences. It remains to be seen if use of higher resolution and/or more standardized imaging protocols lead to improved predictions of hip fracture risk.

In summary, we found that femoral strength and the load-to-strength ratio, as measured from FE biomechanical analysis of QCT scans of the proximal femur, are strongly associated with risk of hip fracture, alone and after accounting for age and BMI. When aBMD as measured by DXA for the total hip was accounted for, the load-to-strength ratio remained a highly significant risk factor. These results provide insight into hip fracture etiology and show the ability of FE-based biomechanical analysis of quantitative CT scans to prospectively predict hip fractures in men.

Figure Figure 4.

ROC curves for hip fracture prediction using the three baseline hip measures. Conventional cut-offs of hip fracture risk, a total hip DXA T-score of T = − 2.5 (male reference), and the theoretical cut point of ϕ = 1.0 for the load-to-strength ratio, are indicated.


The MrOS Study is supported by National Institutes of Health funding. The following institutes provide support: the National Institute of Arthritis and Musculoskeletal and Skin Diseases (NIAMS), the National Institute on Aging (NIA), the National Center for Research Resources (NCRR), and NIH Roadmap for Medical Research under the following grant numbers: U01 AR45580, U01 AR45614, U01 AR45632, U01 AR45647, U01 AR45654, U01 AR45583, U01 AR052234, U01 AG18197, U01-AG027810, and UL1 RR024140. Additional support for these analyses was provided by Merck& Co., Eli Lilly, and Amgen and by NIH Grant AR049828.