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ENCIT 2020
18th Brazilian Congress of Thermal Sciences and Engineering
DIRECT AND INVERSE ANALYSIS OF THE BIOHEAT EQUATION EMPLOYING INTEGRAL TRANSFORMS AND SURROGATE MODELS
Submission Author:
Taciano Barros , RJ
Co-Authors:
Taciano Barros, Gisele Moraes Marinho, Luiz A. S. Abreu, Diego Knupp
Presenter: Taciano Barros
doi://10.26678/ABCM.ENCIT2020.CIT20-0519
Abstract
This paper addresses the heat transfer process within living tissues, as modeled by Pennes’ equation, with spatially variable parameters across the tissue thickness to account for different tissues: epidermis, dermis, subcutaneous and inner tissue. The solution of this problem may be of major relevance in applications such as clinical diagnostics employing infrared thermography, burn injuries evaluation and hyperthermia cancer treatments, but it requires the accurate knowledge of the thermophysical properties and blood perfusion rates, which are generally obtained with the solution of the corresponding inverse heat conduction problems. Hence, the main goal of this research is performing the direct and inverse analysis of this bioheat model by combining the Generalized Integral Transform Technique with single domain formulation and Bayesian inference. In the direct problem solution, to allow faster convergence of the eigenfunction expansions, the eigenvalue problem is formulated including as much information as possible, with all the spatially variable properties included. In the inverse problem analysis, to allow for faster sampling of the sought posterior probability densities, a surrogate model based on Radial Basis Functions is employed for the prediction of temperature distributions. The Bayesian approximation error approach is then employed to compensate for the discrepancy of the surrogate model. The good results obtained demonstrate the feasibility of the proposed approaches.
Keywords
bioheat transfer, Integral Transform, Metamodel, Bayesian inference
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