Constructal theory and flow architectures in living systems

Abstract

We apply Constructal theory to the study of the flow structure of the human respiratory tree. We show that the flow architecture that would perform oxygenation of the blood and removal of carbon dioxide best, i. e. with lowest resistance, would be composed of a channel system with 23 bifurcation with a diffusive zone (alveolus) at the end. As this tree matches the human respiratory tree we conclude that nature has optimized it in time. Two constructal relationships also emerge: (1) the length l, defined by the ratio of the square of the air way diameter to its length, is constant for all individuals of the same species, and (2) the length l is related to the volume of the space allocated to the respiratory process, to the length of the respiratory tree and to the area of the alveoli, and determines univocally the branching level of the respiratory tree.