Modelagem computacional e estimativa de propriedade óptica via inferência Bayesiana com aplicações em processos que envolvam hipertermia e ablação térmica

Abstract

This work presents a computational analysis to estimate the effective attenuation coefficient of biological tissues. This coefficient is an optical property of materials and can vary from person to person in the same type of tissue and depending on the environmental conditions. Thus, an individualized knowledge of this property is important to adequately plan the thermal therapies when a laser is applied as heat source. Considering this relevance, this study used the classical bioheat transfer equation to model mathematically the bioheat transfer in a biological tissue heated by a continuous laser with a Gaussian beam. The direct problem was solved by the Generalized Integral Transform Technique with partial transformation scheme, and this solution was verified against the purely numerical solutions obtained with the software COMSOL Multiphysics® and by others methods. These solutions reveal an excellent graphical and numerical agreement. In the inverse analysis, the Bayesian inference is applied using the Markov chain Monte Carlo method performed with Metropolis-Hastings algorithm considering simulated temperature measurements to estimate the effective attenuation coefficient of the human prostate in simulated hyperthermia and ablation therapies. In all considered situations, the attenuation coefficient is accurately estimated and the uncertainties related to others parameters presented in the physical-mathematical model was quantified by applying the Bayesian framework.