Modelagem computacional de problemas de biotransferência de calor empregando transformações integrais, metamodelos e inferência Bayesiana

Abstract

This thesis addresses the process of heat transfer in biological tissues, modeled by the Pennes equation, with spatially variable parameters along the total thickness of the tissue. The main objective is to analyze the direct problem solution obtained by the Generalized Integral Transform Technique with a single-domain formulation and the pa- rameter estimation inverse problem using the Markov Chain Monte Carlo Method with the Metropolis-Hastings algorithm. In the solution of the direct problem, for a better convergence of the eigenfunction expansions, the eigenvalue problem is formulated including as much information as possible on the spatially variable properties. In the analysis of the inverse problem, to allow a faster sampling of posterior probability density, a metamodel, based on Radial Basis Functions, is employed. Considering applications aimed at identifying tumors, different theoretical cases involving problems with different levels of complexity were examined. Situations involving linear and non-linear problems were analyzed with the objective of showing the robustness and accuracy of the proposed methodologies. It was also evidenced the use of the perfusion term through a quadratic function as an alternative means to the use of the exponential model of local thermoregulation. The results obtained demonstrate that the use of the metamodel in the inverse problem can significantly reduce the computational time, in addition to accurate estimates acquired with the approach used.