Mathematical circulation model for the blood-flow-heat-loss relationship in the rat tail

A mathematical model for the heat-loss-blood-flow relationship is developed for the rat tail. When supplied with experimental values of heat loss and blood flow, the model allows one to compute the distribution of flow in deep and cutaneous vessels as a function of body core and tail temperature and to determine the savings in heat loss that result from alterations in the pattern of circulation and from counter-current heat transfer. Blood flow in the cutaneous and deep lying veins of the tail is controlled by both central and local temperatures and increases fairly linearly with deep body temperature. However, the distribution of blood flow in the tail is controlled only by local tail temperature and is independent of deep body temperature. The change in venous distribution of flow has a great impact on the conservation of heat and can reduce the heat loss from the circulating blood by more than 50% when venous return is directed to deep lying veins. On the other hand, counter-current heat transfer is of only minor importance in the control of heat loss from the tail, resulting at most in a 10% saving of heat loss, and that only at the smallest rate of blood flow.