Study of the Bioheat Equation Using Monte Carlo Simulations for Local Magnetic Hyperthermia

Abstract

Hyperthermia is a type of cancer treatment in which cancer cells are exposed to high temperatures (up to 44–45°C). Research has shown that high temperatures can damage and kill cancer cells, by a localized and concentrated heating source. By killing cancer cells and damaging proteins and structures within cells, hyperthermia may shrink tumors, with minimal injury to normal tissues. Penne’s bio-heat equation is used to model a heat diffusion process inside a tumor, modeled as a spherical domain with magnetic nanoparticles distributed within the diseased tissue. These magnetic particles are considered as point heat sources. Heat is generated as the result of magnetic relaxation mechanisms (Brownian and Neel relaxation) by the application of alternating magnetic fields. The Bio-Heat equation is solved using Monte Carlo techniques. Monte Carlo simulations are based on departing random walkers from the point where temperature is going to be determined. The probability in each step of the random walk is given by the coefficients of the nodal temperatures after a Finite Difference Discretization of the Penne’s bio-heat diffusion equation. The main advantage of Monte Carlo simulations versus classical numerical methods lies in the possibility of solving the temperature in a specific point without solving for all the points within the domain. This feature and the fact that each random walk is independent from each other results in an easy parallelization of the computer code. Parametric studies of the temperature profiles are carried out to study the effect of different parameters like the heat generation rate, perfusion rate and diameter of the point source on the maximum temperature and on the temperature profile.