Optimality Analysis of Vascular-tissue System in Mammals for Oxygen Transport

The efficiency of the vascular-tissue system in mammals for oxygen (O2) transport to tissue was evaluated by employing the following simulation models; (i) the spherical tissue model for assessing the maximum tissue mass for which a certain number of capillaries located in the center of each sphere can deliver sufficient O2; (ii) the minimum volume model of the multi-terminal vascular system for estimating the energy cost of blood flow supply to that number of capillaries; and (iii), the efficiency evaluation of the whole system by the ratio (the maximum O2 uptake)/(the energy cost). The computer simulation was carried out by inputting the physiological estimates of tissue O2 consumption rate and cardiac output of mammals in the resting and exercising states, which were calculated from the statistically determined power functions of body weight (the allometric relationship) in the range of 10 g to 500 kg. The results obtained from the data during exercise revealed that the optimum capillary number attaining the maximum efficiency alters nearly in proportion to the body weight and that the total tissue mass corresponding to the optimum capillary number agrees well with the actual tissue mass for virtually all the mammals, while their maximum efficiency remains constant. From these results, it is concluded that any mammal is provided with an equally efficient mass transport system, which is optimized for O2 transport to tissue under the highest metabolic activity, regardless of body weight variation. This may suggest one of the reasons why so many species of mammals with greatly different sizes can exist on the earth.