On the relationship between blood perfusion, metabolism and temperature in biological tissue heat balance

A general, one-dimensional steady-state analysis of the thermal behavior of biological tissues is presented. The three major geometries, i.e., rectangular, cylindrical and spherical, are considered along with boundary conditions of the general type. It is shown that transport of heat inside the tissue may be dominated by conduction, convection by blood perfusion, metabolism or a combination thereof. The role of each of these mechanisms is presented by suitable dimensionless parameters expressed in terms of tissue physical properties. The order of magnitude of these parameters indicates the relative importance of the various mechanisms on the transport of heat inside the tissue. It is further shown that in areas where convection by blood perfusion is dominant, tissue temperatures are almost uniform except for narrow regions near the boundaries. The occurrence of maximum temperatures inside the tissue is also studied along with the combinations of blood perfusion and heating rates which would insure that certain predetermined values are not exceeded. This work also demonstrates that the amount of heat which may be convected into the tissue by the circulatory system depends on the heating rate and the boundary conditions, as well as the blood perfusion rate. This quantity is shown to reach a finite limit as the blood perfusion rate becomes very high.