FORMULATION OF A STATISTICAL-MODEL OF HEAT-TRANSFER IN PERFUSED TISSUE

A new model of steady-state heat transport in perfused tissue is prese nted. The key elements of the model are as follows: (1) a physiologica lly-base algorithm for simulating the geometry of a realistic vascular tree containing all thermally significant vessels in a tissue; (2) a means of solving the conjugate heat transfer problem of convection by the blood coupled to three-dimensional conduction in the extravascular tissue, and (3) a statistical interpretation of the calculated temper ature field. This formulation is radically different from The widely u sed Pennes and Weinbaum-Jiji bio-heat transfer equations that predict a loosely defined local average tissue temperature from tr local perfu sion rate and a minimal representation of the vascular geometry. Inste ad, a probability density function for the tissue temperature is predi cted, which carries information on the most probable temperature at a point and uncertainty in that temperature due to the proximity of ther mally significant blood vessels. A sample implementation illustrates t he dependence of the temperature distribution on the flow rate of the blood and the vascular geometry. The results show that the Pennes form ulation of the bio-heat transfer equation accurately predicts the mean tissue temperature except when the arteries and veins are in closely spaced pairs. The model is useful for fundamental studies of tissue he ar transport, and should extend readily to other forms of tissue trans port including oxygen, nutrient, and drug transport.