Subject-specific finite element models can accurately predict strain levels in long bones

Abstract

The prediction of the stress-state and fracture risk induced in bones by various loading conditions in individual patients using subject-specific finite element models still represents a challenge in orthopaedic biomechanics. The accuracy of the strain predictions reported in the literature is variable and generally not satisfactory. The aim of the present study was to evaluate if a proper choice of the density–elasticity relationship can lead to accurate strain predictions in the frame of an automatic subject-specific model generation strategy. To this aim, a combined numerical–experimental study was performed comparing finite element predicted strains with strain-gauges measurements obtained on eight cadaver proximal femurs, each instrumented with 15 rosettes mostly concentrated in the bone metaphyses, tested non-destructively in vitro under six different loading scenarios. Three different density–elasticity power relationships were selected from the literature and implemented in the finite element models derived from computed tomography data. The results of the present study confirm the great influence of the density–elasticity relationship used on the accuracy of numerical predictions. One of the tested constitutive laws provided a very good agreement (R²=0.91, RMSE lower than 10% of the maximum measured value) between numerical calculations and experimental measurements. The presented results show, in addition, that the adoption of a single density–elasticity relationship over the whole bone density range is adequate to obtain an accuracy that is already suitable for many applications.

Introduction

Subject-specific finite element models of bones derived from computed tomography (CT) data are a promising tool to non-invasively assess the stress-state and fracture risk of bones in individual patients, but still represent a challenge. Their fields of application span from the design and optimisation of prosthetic devices, to the evaluation of skeletal reconstructions, or the definition of fracture risk for bone segments (Anderson et al., 2005; Barker et al., 2005; Bitsakos et al., 2005; Cody et al., 1999; Couteau et al., 2001; Crawford et al., 2003; Dalstra et al., 1995; Ford et al., 1996; Gardiner and Weiss, 2003; Gupta et al., 2004; Keyak et al., 1993; Keyak et al., 2005; Lotz et al., 1991; Maurel et al., 2005; Oden et al., 1999; Ota et al., 1999; Perillo-Marcone et al., 2004; Schmitz et al., 2004; Taddei et al., 2003; Taylor, 2006; Vazquez et al., 2003; Viceconti et al., 2004; Wagner et al., 2002; Weinans et al., 2000; Wong et al., 2005). A high level of automation is needed (Viceconti et al., 2004) and an evaluation of the obtainable numerical accuracy is mandatory (Viceconti et al., 2005) for the use of subject-specific FE models in the clinical practice. In particular a high accuracy in strain prediction is required to investigate bone limit conditions and eventually define fracture risk factors, given the growing consensus on the adoption of strain-based yield and failure criteria for bone tissue (Bayraktar et al., 2004a, Bayraktar et al., 2004b; Cowin and He, 2005; Currey, 2004; Kopperdahl and Keaveny, 1998).

A very limited number of studies have been dedicated to the systematic validation of subject-specific finite element models of bones against experimental measurements. A good accuracy (R²>0.8) in the prediction of strain levels was reported only in three recent works (Anderson et al., 2005; Barker et al., 2005; Gupta et al., 2004) that present, however, a limited degree of generality and automation of the modelling procedures. All of them require high manual effort for tissue type distinction and rely on the assumption of a priori data for the mechanical properties of bone. To the authors’ knowledge the validation studies implementing general and automatic model generation procedures reported low correlations (R²<0.7) between predicted and experimental strains (Keyak et al., 1993; Ota et al., 1999). A very good accuracy (R²>0.9) was reported in the prediction of stresses using an automated and general modelling procedure in Taddei et al. (2006a). However, when the same model was used to compare with the strain-gauges measurements, a lower degree of accuracy was found (R²<0.8) (Taddei et al., 2006a). This might have been due to the density–Young's modulus relationship adopted (Keller, 1994).

In fact, it has been demonstrated that the density–elasticity relationship influences subject-specific FE results (Weinans et al., 2000) but still a consensus on the constitutive law to be used has not been reached. This is indeed supported by the existence of a huge spread in the experimentally derived density–elasticity laws reported in the literature (Linde et al., 1992) and by the difficulty in judging which are the most accurate among them. In fact the experimental testing methods evolved through the last decade (Keaveny et al., 1997; Linde et al., 1992) and are still a matter of discussion (Un et al., 2006). To the authors’ knowledge only one study (Barker et al., 2005) investigated the influence of the density–elasticity law within a validation study. The resulting accuracy was dependent on the assignment of the material properties but no final conclusion can be derived from the presented results on the best law to adopt, since the predicted accuracy was highly dependent on the applied load case.

The aim of the present study is to verify which density–elasticity relationship, among three selected from the literature, leads to the most accurate strain predictions within an automated subject-specific finite element modelling strategy. To this aim, a combined numerical–experimental study was performed comparing FE predicted strains with strain-gauges measurements obtained on eight cadaver proximal femurs tested non-destructively in vitro under different loading scenarios.