Optimizing Accuracy of Proximal Femur Elastic Modulus Equations

Abstract

Quantitative computed tomography-based finite element analysis (QCT/FEA) is a promising tool to predict femoral properties. One of the modeling parameters required as input for QCT/FEA is the elastic modulus, which varies with the location-dependent bone mineral density (ash density). The aim of this study was to develop optimized equations for the femoral elastic modulus. An inverse QCT/FEA method was employed, using an optimization process to minimize the error between the predicted femoral stiffness values and experimental values. We determined optimal coefficients of an elastic modulus equation that was a function of ash density only, and also optimal coefficients for several other equations that included along with ash density combinations of the variables sex and age. All of the optimized models were found to be more accurate than models from the literature. It was found that the addition of the variables sex and age to ash density made very minor improvements in stiffness predictions compared to the model with ash density alone. Even though the addition of age did not remarkably improve the statistical metrics, the effect of age was reflected in the elastic modulus equations as a decline of about 9% over a 60year interval.

Cortical bone mapping improves finite element strain prediction accuracy at the proximal femur

“…We excluded the optimisation attempt requiring the development of individual relationships [25] because it lacks the generality to be prospectively applicable in vivo. The other two studies implemented radically different approaches (direct optimisation of the parameters of a power density-elasticity law on FE validation results [27] vs. extraction of median values from a stochastic analysis of raw data from previous mechanical tests aimed at defining density-elasticity laws [26]) but interestingly came to quite similar results, somehow providing a mutual corroboration. We chose to use the relationship by Rezaei et al [27], because it directly optimised FE results on a large set of femora (100).…”

“…The other two studies implemented radically different approaches (direct optimisation of the parameters of a power density-elasticity law on FE validation results [27] vs. extraction of median values from a stochastic analysis of raw data from previous mechanical tests aimed at defining density-elasticity laws [26]) but interestingly came to quite similar results, somehow providing a mutual corroboration. We chose to use the relationship by Rezaei et al [27], because it directly optimised FE results on a large set of femora (100). We thus implemented to the cortical compartment the relationship E = 11046*ρ ash 1.36 (both the trabecular and cortical thresholds above described were kept active), obtaining models that will be hereinafter called CBM-Opt models.…”

“…Interestingly, after 30 years since the first CT-based FE models, a lot of effort is still put in the choice of density elasticity relationships which best fit the modelling purpose, [46][47][48]. Focusing on the femur, there is evidence from three different approaches [25][26][27] that optimisation of the density-elasticity relationship can improve the accuracy of FE models of bones. We excluded the optimisation attempt requiring the development of individual relationships [25] because it lacks the generality to be prospectively applicable in vivo.…”

“…Our secondary hypothesis is that the density-elasticity relationship used to assign CT-based inhomogeneous Young's moduli in the previous reference study, derived from trabecular specimens only [24], might not be adequate when explicitly modelling the bone cortex. In addition, several recent studies supported for the femur the use of "optimised" density-elasticity relationships, either individual-based [25], stochastically derived [26], or tuned to large data samples [27]. Therefore, we tested whether the use of a cortical-specific or of an optimised densityelasticity relationship could improve the validation results of CBMaugmented FE models.…”

Risk modeling of femoral neck fracture based on geometric parameters of the proximal epiphysis

“…For this purpose, statistical shape models are employed to simultaneously assess the impact of risk factors and pathological changes in a variety of bone geometric phenotypes[ 29 ]. The analysis of the geometric and strength characteristics of cadaveric proximal femurs continues to be applied for more accurate construction of mathematical models[ 30 , 31 ].…”