Identificação de parâmetros e funções via abordagem bayesiana para detecção de melanomas

Abstract

This work focuses on solving inverse problems in heat transfer, exploring their application in estimating parameters and functions for detecting melanoma skin tumors. Grounded in Bayesian methodologies, specifically Markov Chain Monte Carlo (MCMC), which has played a crucial role in advancing engineering, it opens new possibilities for tumor identification and treatment using the classical heat biotransfer equation. Heat transfer in living tissues, particularly in tumor detection, poses a multidisciplinary challenge. The classical Pennes model stands out, allowing for the estimation of distinctive thermal properties between healthy and unhealthy cells. However, the computational implementation of these models faces challenges due to their complexity, resulting in considerable computational costs. In response, this dissertation proposes a two-dimensional inverse problem for the thermal characterization of melanoma tumors. The focus is on considering realistic geometries and applying methodologies aimed at reducing computa tional costs. The use of Bayesian approaches is explored for their effective handling of uncertainties, providing a robust perspective for analysis. In conclusion, the relevance and consistency of the adopted approaches are highlighted, demonstrating the convergence of results obtained through different computational techniques, such as Wolfram Mathematica and COMSOL Multiphysics. The MCMC method proved consistent throughout the dissertation, successfully detecting tumor regions and providing information about the affected tissue’s geometry. Mesh refinement and uncertainty analysis proved essential for obtaining reliable estimates. The resulting distributions, mainly Gaussian and Gamma, offered valuable insights into parameters in healthy and tumor domains.