Multiscale mechanics and multiobjective optimization of cellular hip implants with variable stiffness

Bone resorption and bone-implant interface instability are two bottlenecks of current orthopaedic hip implant designs. Bone resorption is often triggered by mechanical bio-incompatibility of the implant with the surrounding bone. It has serious clinical consequences in both primary and revision surgery of hip replacements. After primary surgery, bone resorption can cause periprosthetic fractures, leading to implant loosening. For the revision surgery, the loss of bone stock compromises the ability of bone to adequately fix the implant. Interface instability, on the other hand, occurs as a result of excessive micromotion and stress at the bone-implant interface, which prevents implant fixation. As a result, the implant fails, and revision surgery is required.Many studies have been performed to design an implant minimizing both bone resorption and interface instability. However, the results have not been effective since minimizing one objective would penalize the other. As a result, among all designs available in the market, there is no implant that can concurrently minimize these two conflicting objectives. The goal of this thesis is to design an orthopaedic hip replacement implant that can simultaneously minimize bone resorption and implant instability. We propose a novel concept of a variable stiffness implant that is implemented through the use of graded lattice materials. A design methodology based on multiscale mechanics and multiobjective optimization is developed for the analysis and design of a fully porous implant with a lattice microstructure. The mechanical properties of the implant are locally optimized to minimize bone resorption and interface instability. Asymptotic homogenization (AH) theory is used to capture stress distribution for failure analysis throughout the implant and its lattice microstructure. For the implant lattice microstructure, a library of 2D cell topologies is developed, and their effective mechanical properties, including elastic moduli and yield strength, are computed using AH. Since orthopaedic hip implants are generally expected to support dynamic forces generated by human activities, they should be also designed against fatigue fracture to avoid progressive damage. A methodology for fatigue design of cellular materials is proposed and applied to a two dimensional implant, with Kagome and square cell topologies. A lattice implant with an optimum distribution of material properties is proved to considerably reduce the amount of bone resorption and interface shear stress compared to a fully dense titanium implant. The manufacturability of the lattice implants is demonstrated by fabricating a set of 2D proof-of-concept prototypes using Electron Beam Melting (EBM) with Ti6Al4V powder. Optical microscopy is used to measure the morphological parameters of the cellular microstructure. The numerical analysis and the manufacturability tests performed in this preliminary study suggest that the developed methodology can be used for the design and manufacturing of novel orthopaedic implants that can significantly contribute to reducing some clinical consequences of current implants.La résorption osseuse et l'instabilité de l'interface os-implant sont deux goulots d'étranglement de modèles actuels d'implants orthopédiques de hanche. La résorption osseuse est souvent déclenchée par une bio-incompatibilité mécanique de l'implant avec l'os environnant. Il en résulte de graves conséquences cliniques à la fois en chirurgie primaire et en chirurgie de révision des arthroplasties de la hanche. Après la chirurgie primaire, la résorption osseuse peut entraîner des fractures périprothétiques, conduisant au descellement de l'implant. Pour la chirurgie de révision, la perte de substance osseuse compromet la capacité de l'os à bien fixer l'implant. L'instabilité de l'interface, d'autre part, se produit à la suite d'un stress excessif et de micromouvements à l'interface os-implant, ce qui empêche la fixation des implants. De ce fait, l'implant échoue, et la chirurgie de révision est nécessaire.De nombreuses études ont été réalisées pour concevoir un implant qui minimise la résorption osseuse et l'instabilité de l'interface. Cependant, les résultats n'ont pas été efficaces, car minimiser un objectif pénaliserait l'autre. En conséquence, parmi tous les modèles disponibles sur le marché, il n'y a pas d'implant qui puisse en même temps réduire ces deux objectifs contradictoires. L'objectif de cette thèse est de concevoir une prothèse orthopédique de la hanche qui puisse simultanément réduire la résorption osseuse et l'instabilité de l'implant. Nous proposons un nouveau concept d'implant à raideur variable qui est mis en œuvre grâce à l'utilisation de matériaux assemblés en treillis.Une méthodologie de conception basée sur la mécanique multi-échelle et l'optimisation multiobjectif est développé pour l'analyse et la conception d'un implant totalement poreux avec une microstructure en treillis. Les propriétés mécaniques de l'implant sont localement optimisés pour minimiser la résorption osseuse et l'instabilité d'interface. La théorie de l'homogénéisation asymptotique (HA) est utilisée pour capturer la distribution des contraintes pour l'analyse des défaillances tout le long de l'implant et de sa microstructure en treillis. Concernant cette microstructure en treillis, une bibliothèque de topologies de cellules 2D est développée, et leurs propriétés mécaniques efficaces, y compris les modules d'élasticité et la limite d'élasticité, sont calculées en utilisant le théorie HA. Puisque les prothèses orthopédiques de hanche sont généralement censées soutenir les forces dynamiques générées par les activités humaines, elles doivent être également conçues contre les fractures de fatigue pour éviter des dommages progressifs. Une méthodologie pour la conception en fatigue des matériaux cellulaires est proposée et appliquée à un implant en deux dimensions, et aux topologies de cellules carrées et de Kagome. Il est prouvé qu'un implant en treillis avec une répartition optimale des propriétés des matériaux réduit considérablement la quantité de la résorption osseuse et la contrainte de cisaillement de l'interface par rapport à un implant en titane totalement dense. La fabricabilité des implants en treillis est démontrée par la fabrication d'un ensemble de concepts de prototypes utilisant la fusion par faisceau d'électronsde poudre Ti6Al4V. La microscopie optique est utilisée pour mesurer les paramètres morphologiques de la microstructure cellulaire. L'analyse numérique et les tests de fabricabilité effectués dans cette étude préliminaire suggèrent que la méthodologie développée peut être utilisée pour la conception et la fabrication d'implants orthopédiques innovants qui peuvent contribuer de manière significative à la réduction des conséquences cliniques des implants actuels

Mechanical properties of lattice materials via asymptotic homogenization and comparison with alternative homogenization methods

Several homogenization schemes exist in literature to characterize the mechanics of cellular materials. Each one has its own assumptions, advantages, and limitations that control the level of accuracy a method can provide. There is often the need in heavy multiscale analyses of lattice materials to find the method that can provide the best trade-off between accuracy and computational cost.In this paper, asymptotic homogenization (AH) is used as a benchmark to test the accuracy of alternative schemes of homogenization applied to lattice materials. AH is first applied to determine the effective elastic moduli and yield strength of six lattice topologies for the whole range of relative density. Yield surfaces are also obtained under multiaxial loading for square, hexagonal, and Kagome lattices, and closed-form expressions of the yield loci are provided for a convenient use in multiscale material problems. With respect to the relative density, the results are then compared to those obtained with other methods available in literature. [...

Multiscale Design and Multiobjective Optimization of Orthopaedic Hip Implants with Functionally Graded Cellular Material

Revision surgeries of total hip arthroplasty are often caused by a deficient structural compatibility of the implant. Two main culprits, among others, are bone-implant interface instability and bone resorption. To address these issues, in this paper we propose a novel type of implant, which, in contrast to current hip replacement implants made of either a fully solid or a foam material, consists of a lattice microstructure with nonhomogeneous distribution of material properties. A methodology based on multiscale mechanics and design optimization is introduced to synthesize a graded cellular implant that can minimize concurrently bone resorption and implant interface failure. The procedure is applied to the design of a 2D left implanted femur with optimized gradients of relative density. To assess the manufacturability of the graded cellular microstructure, a proof-of-concept is fabricated by using rapid prototyping. The results from the analysis are used to compare the optimized cellular implant with a fully dense titanium implant and a homogeneous foam implant with a relative density of 50%. The bone resorption and the maximum value of interface stress of the cellular implant are found to be over 70% and 50% less than the titanium implant while being 53% and 65% less than the foam implant

Fatigue design of lattice materials via computational mechanics: Application to lattices with smooth transitions in cell geometry

A numerical method based on asymptotic homogenization theory is presented for the design of lattice materials against fatigue failure. The method is applied to study the effect of unit cell shape on the fatigue strength of hexagonal and square lattices. Cell shapes with regular and optimized geometry are examined. A unit cell is considered to possess a regular shape if the geometric primitives defining its inner boundaries are joined with an arc fillet, whose radius is 1% of the cell length. An optimized cell shape, on the other hand, is obtained by minimizing the curvature of its interior borders, which are conceived as continuous in curvature to smooth stress localizatio

High-Strength Porous Biomaterials for Bone Replacement: a strategy to assess the interplay between cell morphology, mechanical properties, bone ingrowth and manufacturing constraints

High-strength fully porous biomaterials built with additive manufacturing provide an exciting opportunity for load-bearing orthopaedic applications. While factors controlling their mechanical and biological response have recently been the subject of intense research, the interplay between mechanical properties, bone ingrowth requirements,and manufacturing constraints, is still unclear. In this paper, we present two high-strength stretch-dominated topologies, the Tetrahedron and the Octet truss, as well as an intuitive visualization method to understand the relationship of cell topology, pore size, porosity with constraints imposed by bone ingrowth requirements and additive manufacturing. [...] This research is the first to demonstrate the occurrence of bone ingrowth into high-strength porous biomaterials which have higher structural efficiency than current porous biomaterials in the market