Development of Maximized Total Capillary Surface: the quarter power scaling law from developmental biology perspective

摘要

Quarter-power scaling of biological features with body mass is commonly observed in a variety of organisms and is considered a universal law in biology. The origin of the quarter-power scaling law has been proposed to be a universal requirement of a maximized hierarchical network for distributing materials (e.g., oxygen and nutrients) in any organism. We propose a mathematical model for the development of a maximized total capillary surface. This model quantitatively demonstrates how body mass is related to the biological information controlling development of capillaries under the condition that the maximization of total capillary surface area is subject to the minimization of the informational complexity.