computer methods and programs in biomedicine 85 ( 2 0 0 7 ) 32–40 journal homepage: www.intl.elsevierhealth.com/journals/cmpb Finite element-based probabilistic analysis tool for orthopaedic applications Sarah K. Easley a , Saikat Pal a , Paul R. Tomaszewski b , Anthony J. Petrella b , Paul J. Rullkoetter a , Peter J. Laz a,* a University of Denver, Computational Biomechanics Lab, 2390 S. York, Denver, CO 80208, United States b DePuy, a Johnson & Johnson Company, 700 Orthopaedic Dr., Warsaw, IN 46581, United States article info Article history: Received 2 August 2005 Received in revised form 4 September 2006 Accepted 17 September 2006 Keywords: Probabilistic modeling Reliability Sensitivity Variability Orthopaedic implants Finite element modeling abstract Orthopaedic implants, as well as other physical systems, contain inherent variability in geometry, material properties, component alignment, and loading conditions. While com- plex, deterministic finite element (FE) models do not account for the potential impact of variability on performance, probabilistic studies have typically predicted behavior from sim- plified FE models to achieve practical solution times. The objective of this research was to develop an efficient and versatile probabilistic FE tool to quantify the effect of uncer- tainty in the design variables on the performance of orthopaedic components under relevant conditions. Key aspects of the computational tool developed include parametric and auto- mated FE model creation for changes in dimensional variables, efficient solution using the advanced mean-value (AMV) reliability method, and identification of the most significant design variables. Two orthopaedic applications are presented to demonstrate the ability of the computational tool to efficiently and accurately represent component performance. © 2006 Elsevier Ireland Ltd. All rights reserved. 1. Introduction Inherent scatter exists in many variables in engineering design, for example, component geometry, loading condi- tions, and material strength and fatigue properties. The combined effects of variability in individual parameters can dramatically affect component performance. Probabilistic modeling provides an approach to quantitatively determine the impact of multiple variables on specific performance met- rics. Each variable is typically represented as a distribution, and a distribution of performance is predicted. By understand- ing the distribution of performance, evaluations of quality (e.g. design for six sigma) and risk assessment can be performed. Sensitivity factors are also determined as a result of prob- abilistic analysis and provide quantitative evaluation of the ∗ Corresponding author at: Computational Biomechanics Lab, University of Denver, 2390 S. York St., Denver, CO 80208, United States. Tel.: +1 303 871 3614; fax: +1 303 871 4450. E-mail address: plaz@du.edu (P.J. Laz). contribution of each design variable to the overall variation in performance. Probabilistic modeling has been widely used in the auto- motive and aeronautical industries [1–3] and has recently been applied to orthopaedic applications. The most com- mon applications are in structural reliability where distri- butions of stress are compared to distributions of material strength. Recently, studies have taken a probabilistic approach to assessing the structural integrity of orthopaedic implants. Browne et al. [4] applied reliability theory to aid in fracture mechanics-based life prediction procedures for a tibial tray component represented as a cantilever beam subjected to constant amplitude loading. Dar et al. [5] demonstrated how Taguchi and probabilistic methods could complement each other to account for uncertainties when predicting stresses 0169-2607/$ – see front matter © 2006 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.cmpb.2006.09.013