Optimized FE mesh generation based on medical imaging and on a user-defined spatial refinement gradient. Application to a motion segment

Abstract

In general, the starting point for the 3D geometrical modelling by finite elements of an anatomical structure is the generation of a 3D voxel-based geometrical model, obtained after denoising, smoothing and segmentation of a set of 2D medical images. The accuracy of the FE computation increases if the geometry of model resembles, for instance, the natural smoothness of real anatomical structure. Usually, the lack of detailed data in conventional imaging techniques causes further problems in the IVD finite element mesh generation and analysis. Difficulties arise mainly due to the complexity and the dimension of the IVD constituent structures and the lower resolution of medical imaging. After the 3D voxelized model has been defined, a specific isotropic tetrahedral FE meshing procedure is applied and, generally, a too dense and highly refined FE mesh is obtained. Therefore, it is necessary to decrease its size by diminishing the total number of nodes and elements while maintaining both geometrical accuracy and a physically compatible FE mesh refinement. Generally, after this procedure, the smaller elements are located at the internal and external boundaries, while larger elements are located inside the FE mesh. However, this is not always acceptable. There may be situations where this accuracy may be required simultaneously in structures outside and inside the FE mesh. In a motion segment, the FE mesh should be more refined at the IVD and coarser at the vertebrae (nearly incompressible medium). On the other hand, since the annulus fibrosus (AF) is a stiff ring-shaped structure made up of concentric lamellae [1], an optimized FE mesh should be more refined at the annulus fibrosus than at the nucleus pulposus (NP)The aims of this study are: - to study the impact of medical imaging resolution in the FE mesh accuracy; - to develop a refinement gradient, where in this case the elements should be smaller in the outer annulus (where lamellae are denser and combined) than the ones in the inner annulus (less dense lamellae).