Uso de Funções de Green no estudo da biotransferência de calor tridimensional considerando efeitos de perfusão sanguínea e metabolismo

Abstract

The present work rely on presenting analytical solutions for bioheat transfer problems using Green's Functions (GF). In the modeling process for an in vivo tissue, both metabolism and blood perfusion effects were considered. The first was taken as a heat source and, the other is modeled as proportional to the temperature difference between the body core and the tissue. The classic conduction equation when combined with those two assumptions is named Pennes' Bioheat transfer model. Using Green's function for obtaining the equation solution for this problem is justified for the possibility of its use in many different geometries and boundary conditions that could be both heterogeneous or time-spacing dependent. The problem solved is 3-D time-dependent, and, with GF it can be treated as three independent problems in each direction so the equation-solution would be simply the superposition for the correspondent GF in each direction, just multiplying each other. Also the theoretical bases of the technique, 1-D problems solution and verification and the 3-D transient problem in a domain corresponding a biological tissue, so as its intrinsic verification are presented. By using GF as the way for obtaining the analytical solution of heat conduction problems it can help in understanding the physical meaning of each term of the equation-solution and, once the exact solution is obtained, one can use it to build computational routines and codes in order to reduce the computational cost and improve accuracy.