Author's personal copy Journal of Biomechanics 40 (2007) 2831–2836 Incorporating uncertainty in mechanical properties for finite element-based evaluation of bone mechanics Peter J. Laz a,Ã , Joshua Q. Stowe a , Mark A. Baldwin a , Anthony J. Petrella b , Paul J. Rullkoetter a a Computational Biomechanics Laboratory, University of Denver, 2390 S. York Street, Denver, CO 80208, USA b DePuy, A Johnson & Johnson Company, Warsaw, IN, USA Accepted 14 March 2007 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. r 2007 Elsevier Ltd. All rights reserved. Keywords: Bone mechanics; CT scan; Probabilistic; Mechanical properties; Fracture 1. 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 ARTICLE IN PRESS www.elsevier.com/locate/jbiomech www.JBiomech.com 0021-9290/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2007.03.013 Ã Corresponding author. Tel.: +1 303 871 3614; fax: +1 303 871 4450. E-mail address: plaz@du.edu (P.J. Laz).