Assessment of a fictitious domain method for patient-specific biomechanical modelling of press-fit orthopaedic implantation

Abstract

In this article, we discuss an application of a fictitious domain method to the numerical simulation of the mechanical process induced by press-fitting cementless femoral implants in total hip replacement surgeries. Here, the primary goal is to demonstrate the feasibility of the method and its advantages over competing numerical methods for a wide range of applications for which the primary input originates from computed tomography-, magnetic resonance imaging- or other regular-grid medical imaging data. For this class of problems, the fictitious domain method is a natural choice, because it avoids the segmentation, surface reconstruction and meshing phases required by unstructured geometry-conforming simulation methods. We consider the implantation of a press-fit femoral artificial prosthesis as a prototype problem for sketching the application path of the methodology. Of concern is the assessment of the robustness and speed of the methodology, for both factors are critical if one were to consider patient-specific modelling. To this end, we report numerical results that exhibit optimal convergence rates and thus shed a favourable light on the approach.

Keywords:

• fictitious domain method
• regular and geometry-conforming finite element methods
• press-fit implant
• linear elasticity
• CT- or MRI-scan
• medical imaging

Acknowledgement

We are grateful for the partial support for the research reported herein provided by the National Science Foundation under grant awards IIS-9422734 and ATM-0326449.

Notes

^1. Bone typically regenerates and in many cases will grow into the porous surface of an implant; such long-term post-operative bone ‘remodelling’ processes are not taken into account in the analysis of the short-term intra-surgical processes presented herein.

^2. The cortical bone's behaviour is closer to an orthotropic material; here we opted for isotropic linear elastic behaviour for simplicity, even though the presented methodology is not limited by the particular form of the constitutive relation.

^3. We will henceforth refer to traction jump as the Lagrange multipliers.

^4. For the bilinear-constant pair, we use the term optimal to refer to rates.

^5. The expressions for the constants are quite lengthy and are thus not included here; however, they can be readily obtained using any symbolic computation software package.