Numerical analysis of heat transfer in countercurrent blood flow and biological tissue

Bioheat transfer in biological tissue is described by the Pennes equation, while the change of blood temperature along the artery and vein is described by ordinary differential equations, at the same time the countercurrent blood flow is taken into account. The coupling of these equations results from the boundary conditions given by the blood vessel walls. There are two methods used here in order to calculate the temperatures along the blood vessels and across biological tissue. To solve the Pennes equation, the Multiple Reciprocity Boundary Element Method (MRBEM) is applied. It should be pointed out that this method does not require discretisation of the interior of the domain. The second method used in this paper is the Finite Difference Method (FDM) and it is applied to calculate the temperatures along the blood vessels, and it complements the previous one. It is important to note that the diameter of an artery is smaller than of a vein, which results from the physiological characteristics of these blood vessels. In the final part of the paper, the results of the computations are shown and conclusions are formulated.