Mathematical description of heat transfer in living tissue (Q2740479)

The present monograph states the bioheat transfer problem, which, from the authors' point of view, describes the main properties of transport phenomena peculiar to such media. The following three inalienable characteristics of living tissue, namely ``hierarchically organized'', ``active'' and ``heterogeneous'', are the essence of the bioheat transfer problem in its own right. A simple model for heat transfer in living tissues with self-regulation is formulated. The initial point of the model is the governing equations describing heat transfer in living tissues at the mesoscopic level, i.e., considering different vessels individually. Then, basing on the well-known equivalence of diffusion type processes and random walks, a certain regular procedure that enables to average these mesoscopic equations practically over all scales of the hierarchical vascular network, is developed.NEWLINENEWLINENEWLINEThe microscopic governing equations obtained in this way describe living tissues in terms of an active medium with continuously distributed self-regulation. One of the interesting results obtained is that there can be the phenomenon of ideal self-regulation in large active hierarchical systems. The characteristics of such systems occuring in nature are discussed from the standpoint of regulation problems.