Capillary-tissue arrangement in the skeletal muscle optimized for oxygen transport in all mammals

The aim of this computer simulation study is to evaluate the efficiency of capillary networks in the skeletal muscle for oxygen (O2) delivery to tissue for all mammals. This was performed by: (1) employing Krogh's cylinder model for the capillary-tissue system and the minimum volume model for the vascular system, (2) allometrically assessing the muscle blood flow and O2 consumption rate (the main input data) in the resting and exercising states as power functions of body weight from the data reported for several mammals, and (3) calculating the cost-performance of the system from the ratio (maximum O2 uptake of tissue)/(minimum energy expenditure of blood flow supply), as a function of number of capillaries. The results obtained for body weights ranging from 100 g to 1000 kg revealed that for each body weight and metabolic state, the efficiency curve attains a peak at a specific optimum capillary number, and that the calculated values of total muscle mass, capillary density, and capillary flow-rate by using the optimum capillary number and tissue radius during exercise agree remarkably well with those actually measured in various animals. These findings suggest the validity of a working hypothesis that in all mammals, the capillary arrangement in the skeletal muscle is optimized for O2 delivery to tissue during exercise.