Incorporating uncertainty in mechanical properties for finite element-based evaluation of bone mechanics

https://doi.org/10.1016/j.jbiomech.2007.03.013Get rights and content

Abstract

Finite element (FE) models of bone, developed from computed tomography (CT) scan data, are used to evaluate stresses and strains, load transfer and fixation of implants, and potential for fracture. The experimentally derived relationships used to transform CT scan data in Hounsfield unit to modulus and strength contain substantial scatter. The scatter in these relationships has potential to impact the results and conclusions of bone studies. The objectives of this study were to develop a computationally efficient probabilistic FE-based platform capable of incorporating uncertainty in bone property relationships, and to apply the model to a representative analysis; variability in stresses and fracture risk was predicted in five proximal femurs under stance loading conditions. Based on published variability in strength and modulus relationships derived in the proximal femur, the probabilistic analysis predicted the distributions of stress and risk. For the five femurs analyzed, the 1 and 99 percentile bounds varied by an average of 17.3 MPa for stress and by 0.28 for risk. In each femur, the predicted variability in risk was greater than 50% of the mean risk calculated, with obvious implications for clinical assessment. Results using the advanced mean value (AMV) method required only seven analysis trials (1 h) and differed by less than 2% when compared to a 1000-trial Monte-Carlo simulation (400 h). The probabilistic modeling platform developed has broad applicability to bone studies and can be similarly implemented to investigate other loading conditions, structures, sources of uncertainty, or output measures of interest.

Introduction

Finite element (FE) models developed from computed tomography (CT) scans have become an important tool to evaluate mechanical stresses and strains in bone (Taddei et al., 2004; Hernandez and Keaveny, 2006; Bevill et al., 2006), load transfer related to implant fixation and repair (Taylor, 2006; Haider et al., 2006), bone–cement interface mechanics (Mann et al., 2001; Mann and Damron, 2002), and fracture risk (Perillo-Marcone et al., 2003; Keyak and Falkinstein, 2003; Keyak et al., 2001). Bone fracture continues to be an important issue affecting aging populations and patients with bone diseases, and an understanding of the local bone quality and properties is important in making assessments of fracture potential or implant performance.

These FE models utilize CT intensity in Hounsfield unit (HU) to determine the material properties in a specific finite element or voxel. Numerous studies have sought to define relationships between HU and density, density and Young's modulus, and density and bone strength (e.g. Carter and Hayes, 1977; Bentzen et al., 1987; Hvid et al., 1989; Snyder and Schneider, 1991; Keller, 1994; Rho et al., 1995; Hernandez et al., 2001; Morgan et al., 2003) for various bones, with average relationships fit to the experimental data. In all of these references, large amounts of scatter are present in the experimental data. For example, Keller (1994) reported differences from the mean commonly around 100% (and up to 400%) for modulus and strength. The scatter in these relationships has potential to impact the results and conclusions of bone studies. Mupparapu et al. (2006) examined the effects of using different HU–modulus relationships on predicted stress in a proximal tibia with a unicondylar implant and found large differences in modulus assignment and resulting displacements and strains predicted. Using Monte-Carlo simulation, Taddei et al. (2006a) found that bone stresses and strains in the proximal femur were more sensitive to uncertainties in the geometric representation than material properties.

The objectives of the current study were to develop a probabilistic FE-based platform to incorporate uncertainty in bone property estimation for prediction of bone mechanics and fracture risk, and to apply the model to evaluate resulting stresses and risk in the proximal femur under stance loading conditions. In addition, this study evaluated the use of efficient probabilistic methods, as an alternative to the computationally intensive Monte-Carlo method, in making accurate predictions of bone mechanics. The probabilistic model predicts the level of performance (stress or fracture risk) and its likelihood, which provides a more comprehensive evaluation of the physical system and may impact bone study findings as well as clinical assessment.

Section snippets

Methods

An automated probabilistic platform was developed that linked probabilistic modeling software (Nessus, SWRI, San Antonio, TX), bone material property assignment (Bonemat, Instituti Ortopedici Rizzoli, Bologna, Italy), and FE analysis (Abaqus, Inc., Providence, RI) to predict the distributions of stresses and risk (Fig. 1). Probabilistic analyses were performed on FE models of five human proximal femurs extracted from CT scans. The CT scans were from three cadavers with an average age of 50.

Results

The model predicted the modulus, strength, stress, and risk for every element in each femur (Fig. 3). The results of the mesh convergence study (Fig. 4) exhibited convergence for the 4.5 mm mesh with differences less than 1% for maximum stress and 1.2% for predicted risk compared to the 3 mm mesh. Results presented for all femurs were based on the 3 mm results.

Modulus was higher in elements in cortical regions of the bone and stresses were highest in the femoral neck region (Fig. 3). Based on the

Discussion

A probabilistic analysis platform was developed to quantitatively assess the effects of variability in relationships between CT and bone mechanical properties on outputs of stress and risk. While the model was applied to hip fracture risk incorporating variability in the conversion of CT data to bone material properties, other loading conditions, bones, sources of uncertainty, or output metrics could be similarly evaluated. The substantial differences in reported relationships for modulus and

Conflict of interest

The authors have nothing to disclose.

Acknowledgment

This research was supported in part by DePuy, a Johnson & Johnson Company.

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