Homogenization results for dynamical heat transfer problems in heterogeneous biological tissues

Abstract

The effective behavior of the solution of a dynamical boundary-value problem modeling the bio-heat transfer in heterogeneous microvascular tissues is analyzed. We consider an "ε-periodic structure Ω, consisting of two parts: a solid tissue part and small regions of the blood of a certain temperature. In this domain, we consider a heat equation, with a dynamical condition imposed on the boundaries of the blood zones. The limit equation, as ε", the small parameter related to the characteristic size of the blood regions, tends to zero, is a new heat equation, with extra-terms coming from the influence of the nonhomogeneous dynamical boundary condition.