Eventos Anais de eventos
COBEM 2023
27th International Congress of Mechanical Engineering
Parameter identification in bioheat transfer models using the transitional Markov Chain Monte Carlo method
Submission Author:
Eduardo Cunha Classe , RJ
Co-Authors:
Eduardo Cunha Classe, Luiz A. S. Abreu, Diego Knupp, Leonardo Stutz, Lucas Asth
Presenter: Eduardo Cunha Classe
doi://10.26678/ABCM.COBEM2023.COB2023-0635
Abstract
Accurately estimating the unknown parameters in bioheat transfer is essential for numerous biomedical applications such as hyperthermia treatment, thermal imaging, and cryopreservation. In this work, the Transition Markov Chain Monte Carlo method (TMCMC) was applied for estimating the posterior distributions of certain parameters that can inform whether a region is healthy or likely to have tumor cells within the bioheat transfer. The TMCMC algorithm is a more recent approach that utilizes a series of transition kernels applied to the probability density function in steps. This results in better convergence and a higher likelihood of finding global minima. Furthermore, it is capable of evaluating the model evidence as a by-product, unlike the Markov Chains Monte Carlo method (MCMC), already well known in the literature. In this research, a non-linear bioheat transfer model will be used for the blood perfusion term (quadratically dependent on temperature) to simulate the measurement data of the direct problem. From these data, the posterior distributions of the unknown parameters will be estimated using the TMCMC, but now simpler models will be analyzed, including a constante model and a linear model with the perfusion term linearly dependent on temperature. The results obtained for the linear model have much less model evidence than for the model with the constant perfusion term, although in both models it is possible to identify (or not) the presence of tumors.
Keywords
Bayesian methods, bioheat transfer, Inverse problem, Transitional Markov Chain Monte Carlo, Metropolis-Hastings
