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Automated Meshing of Complex 3-D Domaind From Classified Images

Schimpf P.H., D.R. Haynor and Y. Kim

Proceedings, 4th International Meshing Roundtable, Sandia National Laboratories, pp.193-204, October 1995

INTERNATIONAL
MESHING
ROUNTABLE

Abstract
Traditional methods for generating finite element meshes presuppose parametric or discretized descriptions of the boundaries between subdomains with dissimilar properties. The boundary descriptions are difficult to obtain for the complex 3-D domains encountered in many bio-medical applications. In this paper we describe an adaptive finite element algorithm that automates the modeling of these domains by eliminating the requirement for such explicit boundary descriptions. The algorithm uses images of the tissue class to build non-uniform irregular meshes of rectangular parallelepiped elements with potentially heterogeneous domains corresponding to a variable number of input image voxels. The principal difficulty with this approach is limiting the number of irregular nodes and enforcing continuity. Local h-adaptation is based on an approximation of the Zienkiewicz-Zhu method for estimating the local flux area, modified for application in a heterogeneous domain. The algorithm was tested on the cardiac defibrillation problem using classified, X-ray computed tomography images. The adapted solutions were compared to those obtained from a uniform mesh of elements at the input image resolution. The uniform mesh approach was previously validated against experimentally observed data in pigs. Using linear basis functions, the voltage gradient solution in the ventricles of the heart converged to within 5% of the uniform mesh solution using less than 8% of the memory and processing time required by the uniform mesh approach, which has been the only practical alternative for subject-specific modeling. An additional advantage over the uniform mesh approach, is that the solution accuracy is controlled separately from the input image resolution.

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