Influence of aging on mechanical properties of the femoral neck using an inverse method

Abstract

Today, we are facing rapid aging of the world population, which increases the incidence of hip fractures. The gold standard of bone strength assessment in the laboratory is micro-computed finite element analysis (μFEA) based on micro-computed tomography (μCT) images. In clinics, the standard method to assess bone fracture risk is based on areal bone mineral density (aBMD), measured by dual-energy X-ray absorptiometry (DXA). In addition, homogenized finite element analysis (hFEA) constructed from quantitative computed tomography reconstructions (QCT) predicts clinical bone strength more accurately than DXA. Despite considerable evidence of degradation of bone material properties with age, in the past fifty years of finite element analysis to predict bone strength, bone material parameters remained independent of age. This study aims to assess the influence of age on apparent modulus, yield stress, and strength predictions of the human femoral neck made by laboratory-available bone volume fraction (BV/TV) and μFEA; and by clinically available DXA and hFEA. Using an inverse method, we test the hypothesis that FEA material parameters are independent of age. Eighty-six human femora were scanned with DXA (aBMD) and with QCT. The femoral necks were extracted and scanned at 16 μm resolution with μCT. The grayscale images were downscaled to 32 μm and 65 μm for linear and non-linear analyses, respectively, and segmented. The μFE solver ParOSolNL (non-linear) and a standard hFEA method were applied to the neck sections with the same material properties for all samples to compute apparent modulus, yield stress, and strength. Laboratory-available BV/TV was a good predictor of apparent modulus (R² = 0.76), almost as good as μFEA (R² = 0.79). However, yield stress and strength were better predicted by μFEA (R² = 0.92, R² = 0.86, resp.) than BV/TV (R² = 0.76, R² = 0.76, resp.). For clinically available variables, prediction of apparent modulus was better with hFEA than aBMD (R² = 0.67, R² = 0.58, resp.). hFEA outperformed aBMD for predictions of yield stress (R² = 0.63 vs R² = 0.34 for female and R² = 0.55 for male) and strength (R² = 0.48 vs R² = 0.33 for female and R² = 0.15 for male). The inclusion of age did not improve the multiple linear models for apparent modulus, yield stress, and strength. The resolution of the μFE meshes seems to account for most morphological changes induced by aging. The errors between the simulation and the experiment for apparent modulus, yield stress, and strength were age-independent, suggesting no rationale for correcting tissue material parameters in the current FE analysis of the aging femoral neck.

Keywords: Bone aging; Bone mechanical properties; Bone strength prediction; DXA; Femoral neck; Homogenized finite element; Micro finite element.

Fig. 1

a) Proximal femur b) cut of the neck section c) 10 mm thick parallel cut d) lapping e) template for positioning f) template placement g) sample ready for testing h) global compression setup.

Fig. 2

Age dependence of the a) areal bone mineral density (aBMD) b) bone volume fraction (BV/TV), c) tissue mineral density (TMD) d) experimental apparent elastic modulus e) experimental yield stress and f) experimental ultimate strength g) μFEA apparent elastic modulus h) μFEA yield stress i) μFEA strength.

Fig. 3

Left column: apparent elastic prediction, middle column: yield stress prediction, right column: strength prediction, top row: bone volume fraction predictors, middle-high row: micro finite element predictors, middle-low row: DXA aBMD predictors, bottom row: homogenized finite element predictors. F is for female, M for male, and N/A for not available.

Fig. 4

Residuals. Left column: elastic modulus prediction, middle column: yield stress prediction, right column: strength prediction. Rows a), b), and c): DXA aBMD predictor; d), e), f): BV/TV predictor; g), h) i): hFE predictor; j), k), l): μFE predictor. None of the residuals is age-dependent.