A new bioheat equation and its application to peripheral tissue and whole limb heat transfer

Much of the mathematical modeling of heat transfer in perfused tissue over the past three decades has been based on the Pennes bioheat equation. This equation assumes that blood at the local arterial supply temperature reaches the capillaries where the primary thermal equilibration occurs because of the large surface area available for heat exchange. While this argument is correct for gas, water and solute transport, recent theoretical and experimental studies have shown that virtually no heat exchange occurs in vessels under 100 μm and that the primary mechanism for microvascular heat exchange is the imperfect heat exchange between the larger paired countercurrent microvessels that occur 3 to 6 generations prior to the capillaries. A new fundamental bioheat equations has been derived to describe this heat transfer mechanism. This equation contains a basic new expression for the thermal conductivity of perfused tissue which depends on the geometry and flow in the largest microvessels of the local tissue element and the direction of the vessels relative to the local tissue temperature gradient. Although the new equation appears to be complicated, it is shown that it can be applied with relative ease to a host of problems previously treated by the Pennes equation