Detecção de tumores cutâneos via inferência bayesiana com transformada integral das medidas de temperatura

Abstract

In this work, the analytical solution of a bioheat transfer problem considering a single layer of skin, described by a linear three-dimensional partial differential equation, was determined using the Classical Integral Transform Technique, considering a filtering approach to accelerate convergence. This solution was used to solve an inverse problem of identifying parameters present in the classical bioheat transfer equation, where the estimated parameter was the blood perfusion parameter. A Bayesian inference approach was applied to solve the inverse problem using the Markov chain Monte Carlo method implemented by the Metropolis-Hastings algorithm with different transition distributions. The computational codes were implemented on the Wolfram Mathematica platform and in the Python programming language. The results obtained considered simulated temperature measurements, as well as the integral transforms of these temperature measurements, and allowed an analysis under uncertainty of the inverse problem. Furthermore, they demonstrated the possibility of detection of tumors via non-invasive procedures with a low computational cost provided by the analytical solution of the associated direct problem and also by the use of measurements in the transformed field.