Simulações numéricas de queimaduras em tecidos via modelo não linear de biotransferência de calor

Abstract

This paper aims at performing a sensitivity analysis of blood perfusion and thermal conductivity when simulating skin burning process due to an external heat source, considering different boundary conditions and using the finite element method (FEM) to discretize Pennes’s equation. The 2D model employed here considers a biological tissue formed by epidermis, dermis and subcutaneous layers, and also considers nonlinear functions for blood perfusion and thermal conductivity. The nonlinear assumption is explained by the fact that for the blood perfusion it is observed an increase followed by a decrease greater than the specific temperatures resulting from damage induced by temperature increase in blood capillaries, and also that the thermal conductivity varies linearly with temperature growth. The system of nonlinear ordinary differential equations arising from the discretization by FEM is solved by employing the implicit Euler method in conjunction with the method of Picard. Once the distribution of temperature is determined, the Arrhenius model is used to calculate the thermal damage and classify the burn degree (i.e., first, second or third degree).