A NEW FUNDAMENTAL BIOHEAT EQUATION FOR MUSCLE-TISSUE .1. BLOOD PERFUSION TERM

A new model for muscle tissue heat transfer has been developed using M yrhage and Eriksson's [23] description of a muscle tissue cylinder sur rounding secondary (s) vessels as the basic heat transfer unit. This m odel provides a rational theory for the venous return temperature for the perfusion source term in a modified Pennes bioheat equation, and g reatly simplifies the anatomical description of the microvascular arch itecture required in the Weinbaum-Jiji bioheat equation. An easy-to-us e closed-form analytic expression has been derived for the difference between the inlet artery and venous return temperatures using a model for the countercurrent heat exchange in the individual muscle tissue c ylinders. The perfusion source term calculated from this model is foun d to be similar in form to the Pennes's source term except that there is a correction factor or efficiency multiplying the Pennes term, whic h rigorously accounts for the thermal equilibration of the returning v ein. This coefficient is a function of the vascular cross-sectional ge ometry of the muscle tissue cylinder, but independent of the Peclet nu mber in contrast to the recent results in Brinck and Werner [8]. The v alue of this coefficient varies between 0.6 and 0.7 for most muscle ti ssues. In part II of this study a theory will be presented for determi ning the local arterial supply temperature at the inlet to the muscle tissue cylinder.