A Tool for Studying the Mechanical Behavior of the Bone–Endoprosthesis System Based on Multi-scale Simulation

Abstract

The chapter presents recent advances in developing numerical models for multiscale simulation of the femur–endoprosthesis system for the case of hip resurfacing arthroplasty. The models are based on the movable cellular automaton method, which is a representative of the discrete element approach in solid mechanics and allows correctly simulating mechanical behavior of a variety of elastoplastic materials including fracture and mass mixing. At the lowest scale, the model describes sliding friction between two rough surfaces of TiN coatings, which correspond to different parts of the friction pair of hip resurfacing endoprosthesis. At this scale, such parameters of the contacting surfaces as the thickness, roughness, and mechanical properties are considered explicitly. The next scale of the model corresponds to a resurfacing cap for the femur head rotating in the artificial acetabulum insert. Here, sliding friction is explicitly computed based on the effective coefficient of friction obtained at the previous scale. At the macroscale, the proximal part of the femur with a resurfacing cap is simulated at different loads. The bone is considered as a composite consisting of outer cortical and inner cancellous tissues, which are simulated within two approaches: the first implies their linear elastic behavior, the second considers these tissues as Boit’s poroelastic bodies. The later allows revealing the role of the interstitial biological fluid in the mechanical behavior of the bone. Based on the analysis of the obtained results, the plan for future works is proposed.

Development of a Computational Model of the Mechanical Behavior of the L4–L5 Lumbar Spine: Application to Disc Degeneration

“…In the last decades, movable cellular automata have been successfully used for modeling heterogeneous materials, including bone tissues at the macroscale and mesoscale [ 38 , 39 , 40 , 41 ]. In this method, the material is considered an ensemble of discrete elements of the same finite size (movable cellular automata) that interact with each other according to certain rules, which due to many-body interaction forces, describe the deformation behavior of the material as an isotropic elastoplastic body.…”