The Model Analysis of the Efficiency of the Mammalian Circulation System for Oxygen Supply to Tissue

The efficiency of the vascular-tissue system of mammals for oxygen supply to body tissue was estimated employing the spherical model for the capillary-tissue arrangement. In this model,a whole body consists of uniform tissue spheres with a sigle capillary in each center, The tissue mass of each sphere was calculated as the region of positive O₂ tension. Total tissue mass was determined as the function of the capillary number (n) with parameters of total blood flow (F₀) and tissue O₂ consumption rate (q_O2). The energy cost to maintain the vascular system with n terminals (capillaries) was assessed with the minimum volume model proposed by Kamiya and Togawa(1972). The efficiency of the entire system was defined as the ratio of (total tissue mass) or (total O₂ consumption)/(the energy cost). Using physiological data of F₀ and q_O2 in various mammals with body weights from 200 g to a ton, the efficiency was calculated to determine the optimum capillary numbers and density in each animal. The results indicated that the total tissue mass corresponding to the optimum capillary number during exercise well agreed with the actual body mass in every animal and that the efficiency and the capillary blood flow (F_c) in such a state are almost invariable, irrespective of difference in species. From these results, it was suspected that there must exist a common design principle in mammals supported with a biological mechanism constructing and regulating the capillary-tissue system so that F_c during exercise might be maintained at the optimum level.