Finite element-based probabilistic analysis tool for orthopaedic applications

Abstract

Orthopaedic implants, as well as other physical systems, contain inherent variability in geometry, material properties, component alignment, and loading conditions. While complex, deterministic finite element (FE) models do not account for the potential impact of variability on performance, probabilistic studies have typically predicted behavior from simplified 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 uncertainty in the design variables on the performance of orthopaedic components under relevant conditions. Key aspects of the computational tool developed include parametric and automated 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.

Introduction

Inherent scatter exists in many variables in engineering design, for example, component geometry, loading conditions, 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 metrics. Each variable is typically represented as a distribution, and a distribution of performance is predicted. By understanding 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 probabilistic analysis and provide quantitative evaluation of the contribution of each design variable to the overall variation in performance.

Probabilistic modeling has been widely used in the automotive and aeronautical industries [1], [2], [3] and has recently been applied to orthopaedic applications. The most common applications are in structural reliability where distributions 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 with finite element analysis (FEA) in a study of a fixation plate represented as a cantilever beam. Ng and Teo [6] studied the influence of material moduli uncertainty in cervical spine components on biomechanical responses and disc annulus stress using a 3D FE model and Monte Carlo simulation methods.

The femoral stem component of a total hip replacement has been the subject of several probabilistic structural integrity studies [7], [8], [9], [10]. Nicolella et al. [7] developed a 3D model of an implanted cemented hip stem as the subject of a probabilistic study where variability in material properties and loading was considered in order to predict a probability of failure due to three separate cement failure modes. Bah and Browne [9] used an idealized cylindrical FE model to represent an implanted cemented hip stem in order to assess the most likely mode of failure and to identify which parameters had the largest contribution, where geometry, material properties and loading were considered random variables.

Studies to date have typically used a simplified finite element model, such as a cantilever beam or idealized cylindrical geometry, or a two-dimensional representation. Variability was commonly applied to material properties and loading conditions, while geometric uncertainty was only considered for idealized geometry. Typical results reported from these studies include a distribution of predicted stress, predicted probability of failure and/or sensitivity factors. The common objective of the previous studies was to demonstrate the applicability of probabilistic methods to orthopaedic components, and clinical or experimental verification was not reported.

In addition to structural integrity studies, probabilistic methods have also been used in orthopaedic applications to represent inherently random features such as numerical crack densities in bone [11] and porosity in bone cement [12]. This approach can account for the scatter seen experimentally in damage accumulation and fatigue life at a constant stress level.

The primary objective of this research was to develop a generalized computational tool to facilitate probabilistic analysis of orthopaedic components. The computational tool improves on previous probabilistic studies by including dimensional variability in a complex geometry and incorporating more realistic modeling conditions while maintaining computational efficiency. The secondary objective was to demonstrate the tool for two applications, one investigating the effect of geometry and material property variability on implant performance, the other the effect of component placement and experimental setup variability on the kinematics of a total knee replacement.

Traditionally, probabilistic analyses present several challenges, including potentially significant computational time due to the many trials required. This work utilizes an efficient reliability method coupled with calibrated rigid body analyses to deliver an efficient and accurate solution. Geometric perturbations are also typically difficult with FE-based analyses due to the impact of a dimensional change on the mesh. As a result, deterministic or simplified geometries are generally used. This work presents a fully automated computational tool to update parametrically defined 3D models by modifying geometries and meshes through custom programming with commercially available interfaces. Together, these techniques enable an efficient, versatile probabilistic analysis tool.