The first few steps in the pipeline of patient-specific modeling involve segmenting a medical image such as an MRI or CT, followed by producing an analysis-ready mesh of the tissues of interest. Current approaches require a significant degree of manual effort in image segmentation and/or mesh generation. Polyhedral finite element methods constitute a class of approximation methods that offers the promise of a more automated process.
Fully realizing this promise requires that an explicit, facetized boundary representation (b-rep) of the analysis domain be automatically produced and fed into the meshing/analysis framework. Medical imaging does not provide this geometric product directly. Even in the presence of a robust polyhedral FEM, extracting the necessary b-rep from MRI/CT stands in the way of extensive clinical use of physics-based simulation. Efforts toward producing this product will be discussed.
Automatically producing an acceptable polyhedral mesh from the b-rep also presents some interesting challenges. Polyhedral finite element methods retain most of the favorable properties of conventional finite element methods, but without the same restrictions on element geometry and topology. Such schemes are amenable to greatly simplified automatic mesh generation, even on complex and/or evolving domains. An automatic analysis-ready mesh is realized through a novel element formulation – the partitioned element method – that is tolerant of geometric pathologies and a mesh-generation approach that handles geometric near-degeneracies in a robust way.
The ability of the partitioned element method to handle complex domains makes it a natural fit to solve mechanics problems of the human body, in which complex three-dimensional geometries and material heterogeneity are typical. From medical image to explicit facetized boundary representation to automatic polyhedral mesh generation to solution via the partitioned element method, a pipeline is set to solve computational biomechanics problems beginning from medical imaging and ending in patient-specific simulation of mechanical processes.
