Multiscale analysis of thermoregulation in the human microvascular system

Abstract

SUMMARYThe bio-heat transfer equation is a macroscopic model for describing the heat transfer in microvascular tissue. So far the derivation of the Helmholtz term arising in the bio-heat transfer equation is not completely satisfactory. Here we use homogenization techniques to show that this term may be understood as asymptotic result of boundary value problems which provide a microscopic description for microvascular tissue. An appropriate scaling of so-called heat transfer coe cients in Robin boundary conditions on tissue-blood boundaries is seen to play the crucial role. In view of a future application of our new mathematical model for treatment planning in hyperthermia, we derive asymptotic estimates for the ÿrst-order corrector.

Cardiovascular mathematics

“…Pressure, velocity and vessel wall displacement will be functions of time and the spatial position. Accounting for temperature variation may be relevant in some particular context, for instance in the hyperthermia treatment, where some drugs are activated through an artificial localized increase in temperature (see [47], [28]). Temperature may also have a notable influence on blood properties, in particular on blood viscosity.…”

On the Thermoregulation in the Human Microvascular System

“…The formal derivation of correctors follows the standard approach in [2]. In view of a future application for treatment planning in hyperthermia we derived in [5,6] asymptotic estimates for the first order corrector under certain additional regularity assumptions.…”

Hierarchical decomposition of domains with fractures

“…The permeability k F within the fractures is usually some orders of magnitude larger than the permeability of the surrounding rock matrix, while their width F might be some orders of magnitude smaller than the overall computational domain. Similar problems occur in other applications: The heat transfer in the human body is dominated by the blood vessels which, depending on their size, are represented by effective parameters [7,8] or have to be incorporated directly. Another example concerns diffusion-induced drug permeation through stratum corneum [11,16].…”