Simulation Capabilities for Challenging Medical Imaging and Treatment Planning Problems

Author: Beni, Catherine Elizabeth

Year: 2011

Degree: Dissertation (Ph.D.)

Advisor: Bruno, Oscar P.

Committee Members: Bruno, Oscar P.; Desbrun, Mathieu; Owhadi, Houman; Pullin, Dale Ian

Option: Applied And Computational Mathematics

DOI: 10.7907/8PBA-RN43

Abstract

Advanced numerical solvers and associated simulation tools, such as, for example, numerical algorithms based on novel spectral methods, efficient time-stepping and domain meshing techniques for solution of Partial Differential Equations (PDEs) (enabling, in particular, effective resolution of extremely steep boundary layers in short computing times), can have a significant impact in the design of medical procedures. In this thesis we present three recently introduced numerical algorithms for medical problems whose performance improves significantly over those of earlier counterparts, and which can thereby provide solutions to a range of challenging computational problems for planning and design of medical treatments.

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