Modeling Laser-Induced Thermotherapy in Biological Tissue
Master of Arts
This thesis studies simulations of laser-induced thermotherapy (LITT), a minimally-invasive procedure which ablates cancerous tissue using laser heating. In order to predict this procedure, mathematical models are used to assist in treatment. By simulating the laser heating of tissue, surgeons may estimate regions of tissue exceeding a thermal damage threshold. One important component of the LITT model is laser simulation, which is typically characterized by the radiative transfer equation (RTE). The RTE is a time-dependent integro-differential equation with variables in both angular and physical spaces. In this thesis, we conduct numerical experiments using both discrete ordinate and Galerkin methods. The former discretizes a finite number of directions using finite difference methods, while the latter employs continuous functions for both angular and spatial discretizations. Numerical results indicate that the numerical errors in both methods are dominated by the error in the less restricted space. In addition, the discrete ordinate method suffers from the ray effect, in which isotropic scattering is violated, whereas in the Galerkin method, the ray effect is not observed.
Laser-Induced Thermal Therapy; Radiative Transfer Equation; High Performance Computing