Mathematical Description of Heat Transfer in Living Tissue

Lviv : VNTL Publishers, 1999.

Lubashevsky I., Gafiychuk V.

In the present monograph we formulate mathematical model for heat transfer in living tissue with self-regulation. Basing on the well known equivalence of the diffusion type process and random walks, we develop a certain regular procedure that enables us to average the mesoscopic equations describing heat transfer in living tissue practically over all scales of the hierarchical vascular network. The macroscopic governing equations obtained in this way describe living tissue in terms of an active medium with continuously distributed self-regulation.

Keywords: self-regulation, living tissue, active hierarchical systems, hierarchical control, tumor treatment, hyperthermia treatment