Automating the Image-to-Analysis Pipeline in Biomechanics

Omar Hafez, University of California, Davis

Polyhedral finite element methods constitute a class of approximation methods that retain most of the favorable properties of conventional finite element methods, but without finite-element-like restrictions on the element geometry and topology. Such schemes offer the promise of greatly simplified automatic mesh generation, even on extremely complex and/or evolving domains. Fully realizing this promise, however, hinges on success in two areas: the element formulation must be tolerant of geometric pathologies; and the mesh-generation approach must handle geometric near-degeneracies in a robust way. Both of these elements present some interesting challenges. With regard to the former, a new approach, the "partitioned element method," will be described, in which the shape functions are defined only discretely, as piecewise-linear functions over a cellular partition of the element. The cells also serve to define the quadrature rule on the element.

The computational geometry challenges associated with polyhedral mesh generation also will be discussed. A key issue here is the need to avoid geometric features of the mesh − edges and facets − that are smaller than a prescribed tolerance. 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 are typical. In biomechanics problems, the problem domain usually comes from a CT or MRI scan, in the form of voxel density data. A tool to reconstruct surfaces from 3-D point data from medical images will be described. Once the boundary representation is defined, automatic polyhedral mesh generation can be performed, followed by solution via the partitioned element method. Thus, a pipeline is set to solve computational biomechanics problems beginning from medical imaging and ending in patient-specific simulation of mechanical processes.

Abstract Author(s): Omar Hafez, Mark Rashid