Análise Computacional da Produção de Próteses via Otimização Topológica

Abstract

One of the great challenges faced by regenerative orthopedic medicine is the production of prostheses and implants seeking to achieve a behavior close to that of damaged or lost bones. The complexity of the task is due to the organic composition of bones and their continuous, but finite, capacity for biological renewal and, consequently, the limitation of regeneration. With this, the damage to the bone structure can reach two situations: it comes at a low level and the bone is able to regenerate, and the opposite case. When the first case occurs, the bone is able to regenerate itself with an external aid (splints and plaster). In the second case, there are three possible approaches: 1) performing an autograft with the patient's own biological material, 2) performing a graft with bone materials from another person, and 3) inserting a prosthesis. The latter is the context in which this work is developed. The use of Topological Optimization is considered in the design of prostheses in order to obtain more efficient solutions from the point of view of material distribution and internal efforts. Computational tests were carried out evaluating three solution methods: Optimality Criterion, Alternating Minimization, and Interior Points, respectively seeking to explore the elastic mechanical characteristics of four life stages of bones. Two formulations of the Minimum Compliance problem were implemented in the FEniCS environment. Two filters are used to handle pseudo-densities and mesh dependence in the material distribution proposed by Andreassen and Lazarov, respectively. Numerical examples are presented to verify the generality of the proposed methods. The results indicated that: (i) the life stage in which the bone tissue is directly affected by its mechanical properties and (ii) the exact methods with the density filter proposed by Lazarov enable the manufacture of the geometries generated through the Topology Optimization technique.