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1.
Measurement of bone mineral density (BMD) by dual-energy X-ray absorptiometry (DXA) alone is only a moderate predictor of fracture risk. Finite element analysis (FEA) of bone mechanics, based on DXA images, may improve the prediction of fracture risk. We developed a method to estimate the 3D shape and density distribution of the proximal femur, using a 2D BMD image and a femur shape template. Proximal femurs of eighteen human cadavers were imaged using computed tomography and divided into two sets (N = 9 + 9). The template was created from the samples in first set by using 3D generalized Procrustes analysis and thin-plate splines. Subsequently, the template and 2D BMD image were utilized to estimate the shape and internal density distribution of the femurs in the second set. Finally, FEA was conducted based on the original and the estimated bone models to evaluate the effect of geometrical and density distributional errors on the mechanical strength. The volumetric errors induced by the estimation itself were low (<1.4%). In the estimation of bones in the second set, the mean distance difference between the estimated and the original bone surfaces was 0.80 ± 0.19 mm, suggesting feasible estimation of the femoral shape. The mean absolute error in voxel-by-voxel BMD was 120±8 mg cm?3. In FEA, the stiffness of the proximal femur differed by -7±16% between the original and estimated bones. The present method, in comparison with methods used in previous studies, improved the prediction of the geometry, the BMD distribution and the mechanical characteristics of the proximal femur. Potentially, the proposed method could ultimately improve the determination of bone fracture risk.  相似文献   

2.
Finite element (FE) modelling has been proposed as a tool for estimating fracture risk and patient-specific FE models are commonly based on computed tomography (CT). Here, we present a novel method to automatically create personalised 3D models from standard 2D hip radiographs. A set of geometrical parameters of the femur were determined from seven ap hip radiographs and compared to the 3D femoral shape obtained from CT as training material; the error in reconstructing the 3D model from the 2D radiographs was assessed. Using the geometry parameters as the input, the 3D shape of another 21 femora was built and meshed, separating a cortical and trabecular compartment. The material properties were derived from the homogeneity index assessed by texture analysis of the radiographs, with focus on the principal tensile and compressive trabecular systems. The ability of these FE models to predict failure load as determined by experimental biomechanical testing was evaluated and compared to the predictive ability of DXA. The average reconstruction error of the 3D models was 1.77 mm (±1.17 mm), with the error being smallest in the femoral head and neck, and greatest in the trochanter. The correlation of the FE predicted failure load with the experimental failure load was r2=64% for the reconstruction FE model, which was significantly better (p<0.05) than that for DXA (r2=24%). This novel method for automatically constructing a patient-specific 3D finite element model from standard 2D radiographs shows encouraging results in estimating patient-specific failure loads.  相似文献   

3.
Estimating the risk of osteoporotic fractures is an important diagnostic step that needs to be taken before medicinal treatment. Densitometry-based criteria are normally used in clinical practice for this purpose. However, densitometry-based techniques could not explain all low-energy fractures. As patient-specific finite element (FE) models allow for consideration of other parameters (e.g. load conditions) that are known to be associated with fracture, they are considered promising candidates for more accurate fracture risk estimation. Nevertheless, they are often time consuming, expensive, and complex to build and may need the type of expertise that is not normally available in clinical settings. In this study, we report the development of an automated platform for estimating proximal femur fracture loads using patient-specific 2D FE models generated using dual-energy x-ray absorptiometry (DXA) scans. First, a statistical shape and appearance model (SSAM) is built using DXA scans of patients screened for osteoporosis following a low energy fracture. SSAM is then used together with Active Appearance Models (AAM) for automated segmentation of the proximal femur from new unseen DXA scans. The mean point-to-curve error of the automated procedure, i.e. 1.2–1.4 mm, is shown to be only slightly larger than the intra-observer variability of manual segmentation, i.e. 1.0 mm. Moreover, the developed platform automatically meshes the segmented shape, assigns density-based mechanical properties, assigns loads and boundary conditions, submits the 2D FE model for solution, and performs post-processing of the 2D FE simulation data to determine fracture loads. The fracture loads predicted using the manually generated and automatically generated 2D FE models are shown to be very close with a mean difference of around 8.8%. Repeated measures ANOVA showed no significant differences between the fracture loads calculated using FE models manually generated by three independent observers and those calculated using the automatically generated FE models (p>0.05).  相似文献   

4.
doi: 10.1111/j.1741‐2358.2012.00625.x Comparison of mandibular bone mineral density in osteoporotic, osteopenic and normal elderly edentulous subjects measured by the dual‐energy X‐ray absorptiometry technique Objective: The aim of this study was to compare the mandibular body bone mineral density according to bone mineral density status of spine and femur measured by dual‐energy X‐ray absorptiometry (DXA) technique in elderly edentulous individuals. Background: One of the factors that affect the survival rate of implants is bone mineral density (BMD) of the jaws. Materials and methods: Fifty edentulous elderly patients’ (27 women and 23 men) spine, femur and the mandibular body BMDs were measured using DXA technique. BMD scans of the AP lumbar spine (L2–L3) and femur were classified using World Health Organisation criteria for bone mass. Results: There was a statistically significant difference between the normal femur group’s–osteoporosis group’s mandibular body BMD (p = 0.001) and femoral osteopaenia group’s–osteoporosis group’s mandibular body BMD (p < 0.001). The femoral osteoporosis group’s mandibular body BMDs were lower than those of both the normal femoral and the femoral osteopaenia group subjects’. Conclusion: Classification of edentulous mandibles according to low and high bone mineral densities is a problem in implant dentistry. The results of this study demonstrated that femoral bone mineral density status may be used to provide preliminary information about the bone mineral density of the mandibular body region in elderly edentulous subjects.  相似文献   

5.
Skeletal fractures associated with bone mass loss are a major clinical problem and economic burden, and lead to significant morbidity and mortality in the ageing population. Clinical image-based measures of bone mass show only moderate correlative strength with bone strength. However, engineering models derived from clinical image data predict bone strength with significantly greater accuracy. Currently, image-based finite element (FE) models are time consuming to construct and are non-parametric. The goal of this study was to develop a parametric proximal femur FE model based on a statistical shape and density model (SSDM) derived from clinical image data. A small number of independent SSDM parameters described the shape and bone density distribution of a set of cadaver femurs and captured the variability affecting proximal femur FE strength predictions. Finally, a three-dimensional FE model of an 'unknown' femur was reconstructed from the SSDM with an average spatial error of 0.016 mm and an average bone density error of 0.037 g/cm(3).  相似文献   

6.
Measurement of bone mineral density (BMD) by DXA (dual-energy X-ray absorptiometry) is generally considered to be the clinical golden standard technique to diagnose osteoporosis. However, BMD alone is only a moderate predictor of fracture risk. Finite element analyses of bone mechanics can contribute to a more accurate prediction of fracture risk. In this study, we applied a method to estimate the 3D geometrical shape of bone based on a 2D BMD image and a femur shape template. Proximal femurs of eighteen human cadavers were imaged with computed tomography (CT) and divided into two groups. Image data from the first group (N = 9) were applied to create a shape template by using the general Procrustes analysis and thin plate splines. This template was then applied to estimate the shape of the femurs in the second group (N = 9), using the 2D BMD image projected from the CT image, and the geometrical errors of the shape estimation method were evaluated. Finally, finite element analysis with stance loading condition was conducted based on the original CT and the estimated geometrical shape to evaluate the effect of the geometrical errors on the outcome of the simulations. The volumetric errors induced by the shape estimation method itself were low (<0.6%). Increasing the number of bone specimens used for the template decreased the geometrical errors. When nine bones were used for the template, the mean distance difference (±SD) between the estimated and the CT shape surfaces was 1.2 ± 0.3 mm, indicating that the method was feasible for estimating the shape of the proximal femur. Small errors in geometry led systematically to larger errors in the mechanical simulations. The method could provide more information of the mechanical characteristics of bone based on 2D BMD radiography and could ultimately lead to more sensitive diagnosis of osteoporosis.  相似文献   

7.
The decrease of bone mineral density (BMD) is a multifactorial bone pathology, commonly referred to as osteoporosis. The subsequent decline of the bone's micro-structural characteristics renders the human skeletal system, and especially the hip, susceptible to fragility fractures. This study represents a systematic attempt to correlate BMD spectrums to the mechanical strength characteristics of the femoral neck and determine a fracture risk indicator based on non-invasive imaging techniques. The BMD of 30 patients' femurs was measured in vivo by Dual-energy X-ray absorptiometry (DXA). As these patients were subjected to total hip replacement, the mechanical strength properties of their femurs' were determined ex-vivo using uniaxial compression experiments. FEA simulations facilitated the correlation of the DXA measurements to the apparent fracture risk, indicating critical strain values during complex loading scenarios.  相似文献   

8.
Clinicians and patients would benefit if accurate methods of predicting and monitoring bone strength in-vivo were available. A group of 51 human femurs (age range 21-93; 23 females, 28 males) were evaluated for bone density and geometry using quantitative computed tomography (QCT) and dual energy X-ray absorptiometry (DXA). Regional bone density and dimensions obtained from QCT and DXA were used to develop statistical models to predict femoral strength ex vivo. The QCT data also formed the basis of a three-dimensional finite element (FE) models to predict structural stiffness. The femurs were separated into two groups; a model training set (n = 25) was used to develop statistical models to predict ultimate load, and a test set (n = 26) was used to validate these models. The main goal of this study was to test the ability of DXA, QCT and FE techniques to predict fracture load non-invasively, in a simple load configuration which produces predominantly femoral neck fractures. The load configuration simulated the single stance phase portion of normal gait; in 87% of the specimens, clinical appearing sub-capital fractures were produced. The training/test study design provided a tool to validate that the predictive models were reliable when used on specimens with "unknown" strength characteristics. The FE method explained at least 20% more of the variance in strength than the DXA models. Planned refinements of the FE technique are expected to further improve these results. Three-dimensional FE models are a promising method for predicting fracture load, and may be useful in monitoring strength changes in vivo.  相似文献   

9.
In women with osteoporosis, each 1% improvement in spine BMD (by DXA) is expected to reduce vertebral fracture risk by about 4%. However, randomized trials of antiresorptive agents show that 1 to 6% improvements in spine BMD reduce vertebral fracture risk by 35 to 50%. Less 20% of the decreased spine fracture risk produced by alendronate or raloxifene be explained by improvement in spine BMD. The discrepancy is even greater during the first year or two of treatment when 1 to 4% improvements in BMD are associated with 65-68% decreases in spine fracture risk. Bisphosphonates continue to increase BMD but the reduction in fracture risk wanes to 20 to 45%. DXA underestimates the change in bone density of spinal trabecular bone and this might explain part of the discrepancy between expected and observed reductions in spine fracture risk. Even more accurate measurement of BMD would not explain the rapid onset and later waning of effect despite gradually increasing BMD. The biomechanical effects inhibiting bone resorption could explain the early onset but not the waning effectiveness. The waning effectiveness of antiresorptives raises concerns that prolonged inhibition of remodeling may weaken bone by allowing microdamage to accumulate. The effect of drugs on nonspine fracture risk is more complex and cannot be predicted from changes in DXA BMD. For example, Beck showed that long-term users of estrogen increase section modulus vs. nonusers with a net increase in section modulus and predicted femoral neck strength despite losing about 0.4% per year in femoral neck BMD. PTH reduces spine fracture risk and this effect is more completely explained by improvement in spine BMD. This suggests that sustaining the increased BMD produced by PTH may maintain long-term reductions in fracture risk.  相似文献   

10.
Hip fractures are the most serious complication of osteoporosis and have been recognized as a major public health problem. In elderly persons, hip fractures occur as a result of increased fragility of the proximal femur due to osteoporosis. It is essential to precisely quantify the strength of the proximal femur in order to estimate the fracture risk and plan preventive interventions. CT-based finite element analysis could possibly achieve precise assessment of the strength of the proximal femur. The purpose of this study was to create a simulation model that could accurately predict the strength and surface strains of the proximal femur using a CT-based finite element method and to verify the accuracy of our model by load testing using fresh frozen cadaver specimens. Eleven right femora were collected. The axial CT scans of the proximal femora were obtained with a calibration phantom, from which the 3D finite element models were constructed. Materially nonlinear finite element analyses were performed. The yield and fracture loads were calculated, while the sites where elements failed and the distributions of the principal strains were determined. The strain gauges were attached to the proximal femoral surfaces. A quasi-static compression test of each femur was conducted. The yield loads, fracture loads and principal strains of the prediction significantly correlated with those measured (r=0.941, 0.979, 0.963). Finite element analysis showed that the solid elements and shell elements in undergoing compressive failure were at the same subcapital region as the experimental fracture site.  相似文献   

11.
Dual energy X-ray absorptiometry (DXA) is the standard for assessing fragility fracture risk using areal bone mineral density (aBMD), but only explains 60–70% of the variation in bone strength. High-resolution peripheral quantitative computed tomography (HR-pQCT) provides 3D-measures of bone microarchitecture and volumetric bone mineral density (vBMD), but only at the wrist and ankle. Finite element (FE) models can estimate bone strength with 86–95% precision. The purpose of this study is to determine how well vBMD and FE bone strength at the wrist and ankle relate to fracture strength at the hip and spine, and to compare these relationships with DXA measured directly at those axial sites. Cadaveric samples (radius, tibia, femur and L4 vertebra) were compared within the same body. The radius and tibia specimens were assessed using HR-pQCT to determine vBMD and FE failure load. aBMD from DXA was measured at the femur and L4 vertebra. The femur and L4 vertebra specimens were biomechanically tested to determine failure load. aBMD measures of the axial skeletal sites strongly correlated with the biomechanical strength for the L4 vertebra (r = 0.77) and proximal femur (r = 0.89). The radius correlated significantly with biomechanical strength of the L4 vertebra for vBMD (r = 0.85) and FE-derived strength (r = 0.72), but not with femur strength. vBMD at the tibia correlated significantly with femoral biomechanical strength (r = 0.74) and FE-estimated strength (r = 0.83), and vertebral biomechanical strength for vBMD (r = 0.97) and FE-estimated strength (r = 0.91). The higher correlations at the tibia compared to radius are likely due to the tibia’s weight-bearing function.  相似文献   

12.
Patient specific quantitative CT (QCT) imaging data together with the finite element (FE) method may provide an accurate prediction of a patient's femoral strength and fracture risk. Although numerous FE models investigating femoral fracture strength have been published, there is little consent on the effect of boundary conditions, dynamic loading and hydraulic strengthening due to intra-medullary pressure on the predicted fracture strength. We developed a QCT-derived FE model of a proximal femur that included node-specific modulus assigned based on the local bone density. The effect of three commonly used boundary conditions published in literature were investigated by comparing the resulting strain field due to an applied fracture load. The models were also augmented with viscoelastic material properties and subject to a realistic impact load profile to determine the effect of dynamic loads on the strain field. Finally, the effect of hydraulic strengthening was investigated by including node specific permeability and performing a coupled pore diffusion and stress analysis of the FE model. Results showed that all boundary conditions yield the same strain field patterns, but peak strains were 22% lower and fracture load was 18% higher when loaded at the greater trochanter than when loaded at the femoral head. Comparison of the dynamic models showed that material viscoelasticity was important, but inertial effects (vibration and shock) were not. Finally, pore pressure changes did not cause significant hydraulic strengthening of bone under fall impact loading.  相似文献   

13.
With the prevalent use of DXA-measured BMD to assess pathologic hip fractures and its recently reported lack of reliability to predict fracture or account for efficacy of anti-resorptive therapy, it is reasonable to assess whether variations in the primary and secondary tensile and compressive trabecular microstructure can account for variations in proximal femur strength in comparison to DXA-measured BMD. To that end, microstructural and densitometric measures of trabecular bone specimens, from discrete sites within the proximal femur, were correlated with their mechanical properties. We hypothesize that accounting for regional variations in trabecular microstructure will improve predictions of proximal femur strength and stiffness compared to bone density measured by DXA. Forty-seven samples (seven donors) from seven distinct sites of human proximal femur underwent DXA and muCT imaging and mechanical testing. The results revealed significant variations in BMC, morphometric indices and mechanical properties within the proximal femur. This work has demonstrated that the mechanical performance of each sub-region is highly dependent on the corresponding trabecular microstructure. BMD measured by DXA at standard regions of interest cannot resolve the variations in trabecular density and microstructure that govern the mechanical behavior of the proximal femur. This work suggests that a quantitative Singh index that uses high resolution QCT to monitor the trabecular microstructure at specific sub-regions of the proximal femur may allow better predictions of hip fracture risk in individual patients and an improved assessment of changing bone structure in response to pharmacological interventions.  相似文献   

14.
15.
PurposeTo experimentally validate a non-linear finite element analysis (FEA) modeling approach assessing in-vitro fracture risk at the proximal femur and to transfer the method to standard in-vivo multi-detector computed tomography (MDCT) data of the hip aiming to predict additional hip fracture risk in subjects with and without osteoporosis associated vertebral fractures using bone mineral density (BMD) measurements as gold standard.MethodsOne fresh-frozen human femur specimen was mechanically tested and fractured simulating stance and clinically relevant fall loading configurations to the hip. After experimental in-vitro validation, the FEA simulation protocol was transferred to standard contrast-enhanced in-vivo MDCT images to calculate individual hip fracture risk each for 4 subjects with and without a history of osteoporotic vertebral fractures matched by age and gender. In addition, FEA based risk factor calculations were compared to manual femoral BMD measurements of all subjects.ResultsIn-vitro simulations showed good correlation with the experimentally measured strains both in stance (R2 = 0.963) and fall configuration (R2 = 0.976). The simulated maximum stress overestimated the experimental failure load (4743 N) by 14.7% (5440 N) while the simulated maximum strain overestimated by 4.7% (4968 N). The simulated failed elements coincided precisely with the experimentally determined fracture locations. BMD measurements in subjects with a history of osteoporotic vertebral fractures did not differ significantly from subjects without fragility fractures (femoral head: p = 0.989; femoral neck: p = 0.366), but showed higher FEA based risk factors for additional incident hip fractures (p = 0.028).ConclusionFEA simulations were successfully validated by elastic and destructive in-vitro experiments. In the subsequent in-vivo analyses, MDCT based FEA based risk factor differences for additional hip fractures were not mirrored by according BMD measurements. Our data suggests, that MDCT derived FEA models may assess bone strength more accurately than BMD measurements alone, providing a valuable in-vivo fracture risk assessment tool.  相似文献   

16.
It has been recently suggested that mechanical loads applied at frequencies close to the natural frequencies of bone could enhance bone apposition due to the resonance phenomenon. Other applications of bone modal analysis are also suggested. For the above-mentioned applications, it is important to understand how patient-specific bone shape and density distribution influence the natural frequencies of bones. We used finite element models to study the effects of bone shape and density distribution on the natural frequencies of the femur in free boundary conditions. A statistical shape and appearance model that describes shape and density distribution independently was created, based on a training set of 27 femora. The natural frequencies were then calculated for different shape modes varied around the mean shape while keeping the mean density distribution, for different appearance modes around the mean density distribution while keeping the mean bone shape, and for the 27 training femora. Single shape or appearance modes could cause up to 15% variations in the natural frequencies with certain modes having the greatest impact. For the actual femora, shape and density distribution changed the natural frequencies by up to 38%. First appearance mode that describes the general cortical bone thickness and trabecular bone density had one of the strongest impacts. The first appearance mode could therefore provide a sensitive measure of general bone health and disease progression. Since shape and density could cause large variations in the calculated natural frequencies, patient-specific FE models are needed for accurate estimation of bone natural frequencies.  相似文献   

17.
Concept and development of an orthotropic FE model of the proximal femur   总被引:2,自引:0,他引:2  
PURPOSE: In contrast to many isotropic finite-element (FE) models of the femur in literature, it was the object of our study to develop an orthotropic FE "model femur" to realistically simulate three-dimensional bone remodelling. METHODS: The three-dimensional geometry of the proximal femur was reconstructed by CT scans of a pair of cadaveric femurs at equal distances of 2mm. These three-dimensional CT models were implemented into an FE simulation tool. Well-known "density-determined" bony material properties (Young's modulus; Poisson's ratio; ultimate strength in pressure, tension and torsion; shear modulus) were assigned to each FE of the same "CT-density-characterized" volumetric group.In order to fix the principal directions of stiffness in FE areas with the same "density characterization", the cadaveric femurs were cut in 2mm slices in frontal (left femur) and sagittal plane (right femur). Each femoral slice was scanned into a computer-based image processing system. On these images, the principal directions of stiffness of cancellous and cortical bone were determined manually using the orientation of the trabecular structures and the Haversian system. Finally, these geometric data were matched with the "CT-density characterized" three-dimensional femur model. In addition, the time and density-dependent adaptive behaviour of bone remodelling was taken into account by implementation of Carter's criterion. RESULTS: In the constructed "model femur", each FE is characterized by the principal directions of the stiffness and the "CT-density-determined" material properties of cortical and cancellous bone. Thus, on the basis of anatomic data a three-dimensional FE simulation reference model of the proximal femur was realized considering orthotropic conditions of bone behaviour. CONCLUSIONS: With the orthotropic "model femur", the fundamental basis has been formed to realize realistic simulations of the dynamical processes of bone remodelling under different loading conditions or operative procedures (osteotomies, total hip replacements, etc).  相似文献   

18.
Finite element (FE) models are often used to model bone failure. However, no failure theory for bone has been validated at this time. In this study, we examined the performance of nine stress- and strain-based failure theories, six of which could account for differences in tensile and compressive material strengths. The distortion energy, Hoffman and a strain-based Hoffman analog, maximum normal stress, maximum normal strain, maximum shear strain, maximum shear stress (tau(max)), Coulomb-Mohr, and modified Mohr failure theories were evaluated using automatically generated, computed tomographic scan-based FE models of the femur. Eighteen matched pairs of proximal femora were examined in two load configurations, one approximating joint loading during single-limb stance and one simulating impact from a fall. Mechanical testing was performed to assess model and failure theory performance in the context of predicting femoral fracture load. Measured and FE-computed fracture load were significantly correlated for both loading conditions and all failure criteria (p < or = 0.001). The distortion energy and tau(max) failure theories were the most robust of those examined, providing the most consistently strong FE model performance for two very different loading conditions. The more complex failure theories and the strain-based theories examined did not improve performance over the simpler distortion energy and tau(max) theories, and often degraded performance, even when differences between tensile and compressive failure properties were represented. The relatively strong performance of the distortion energy and tau(max) theories supports the hypothesis that shear/distortion is an important failure mode during femoral fracture.  相似文献   

19.
目的建立LISS-DF治疗股骨远端骨折近端螺钉不同单双皮质固定的三维有限元模型,并进行初步生物力学分析。方法提取CT图片相关数据,利用自行编写程序生成命令流文件,建立完整股骨以及16个不同LISS-DF治疗股骨远端AO分型33-A3型骨折的实体模型(钢板和股骨不接触、螺钉分别固定于钢板和股骨),进行网格划分。分析不同载荷作用下完整股骨和LISS钢板近端螺钉全双皮质固定治疗骨折的模型受力状况。结果建立了相关的有限元模型。不同载荷作用下,LISS钢板近端螺钉全双皮质固定模型和完整股骨的应力集中均位于股骨颈内侧和股骨干外侧中下1/3处。相同载荷作用下,LISS钢板近端螺钉全双皮质固定模型的股骨颈部最大等效应力值略减小,股骨干最大等效应力值明显减小。结论研究建立的三维有限元模型,为应用LISS治疗股骨骨折的生物力学分析提供了良好的实验平台和基础。从生物力学角度而言,LISS-DF近端螺钉全双皮质固定为治疗股骨远端复杂骨折的有效方法。  相似文献   

20.

Physical exercise induces spatially heterogeneous adaptation in bone. However, it remains unclear where the changes in BMD and geometry have the greatest impact on femoral neck strength. The aim of this study was to determine the principal BMD-and-geometry changes induced by exercise that have the greatest effect on femoral neck strength. Pre- and post-exercise 3D-DXA images of the proximal femur were collected of male participants from the LIFTMOR-M exercise intervention trial. Meshes with element-by-element correspondence were generated by morphing a template mesh to each bone to calculate changes in BMD and geometry. Finite element (FE) models predicted femoral neck strength changes under single-leg stance and sideways fall load. Partial least squares regression (PLSR) models were developed with BMD-only, geometry-only, and BMD-and-geometry changes to determine the principal modes that explained the greatest variation in neck strength changes. The PLSR models explained over 90% of the strength variation with 3 PLS components using BMD-only (R2 > 0.92, RMSE < 0.06 N) and 8 PLS components with geometry-only (R2 > 0.93, RMSE < 0.06 N). Changes in the superior neck and distal cortex were most important during single-leg stance while the superior neck, medial head, and lateral trochanter were most important during a sideways fall. Local changes in femoral neck and head geometry could differentiate the exercise groups from the control group. Exercise interventions may target BMD changes in the superior neck, inferior neck, and greater trochanter for improved femoral neck strength in single-leg stance and sideways fall.

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