Hierarchical topology optimization of the intervertebral fusion cage with microstructure design control

A spine fusion procedure should be performed upon patients from whom a ruptured or herniated intervertebral disc is removed. In its place a bone graft can be inserted in order to promote fusion between adjacent vertebrae. Grafts must combine spine support and excellent osteoconductive environment. As an alternative to traditional bone grafts, artificial bone substitutes (scaffolds) have been developed [1]. They must exhibit a fine balance between two conflicting requirements, mechanical efficiency for load bearing (high stiffness) and biological function related with bone ingrowth (high porosity). The focus of the present work is on scaffold design using structural optimization techniques in order to find a desirable balance between the above mentioned conflicting criteria. The proposed approach applies hierarchical topology optimization that can be defined as the problem of finding optimal material distributions at different but interconnected structural length scales. This paper follows the approach presented in [2] which considers two scales, macro and micro-scales, identified with the design domains of the structure and its material (cellular or composite material), respectively. Structure and material evolve concurrently for their optimal lay-outs as a result of updating the density based design variables such that the global compliance is minimized (stiffness maximized) and a global resource volume constraint is satisfied (global volume fraction). Here the class of cellular or composite materials, is restricted to single scale periodic materials, with the microstructure topology locally optimised for the given objective function and constraints. The model uses the asymptotic homogenization model to compute equivalent material properties for the specific microstructures designed using a SIMP model. Regarding material microstructure design constraints one applies orthotropic permeability control and as a result an interconnected network of pores is obtained to comply with the scaffold biological function [3]. The results shown here involve a Yucatan minipig lumbar spine. A CT scanner was used to obtain initially a 3D geometric model that was subsequently converted to a finite element model. The resulting model comprises intervertebral discs, facet joints, vertebrae, cage design domain and ligaments. The applied loads simulate compression, lateral bending, extension and flexion. Several scaffold design solutions are shown and discussed.