Constructal theory of flow architecture of the lungs

Abstract

Here we explain the reasons why we have a bronchial tree with 23 levels of bifurcation. Based on Bejan's Constructal Principle we found that the best oxygen access to the alveolar tissues as well as carbon dioxide removal is provided by a flow structure composed of ducts with 23 levels of bifurcation (bronchial tree) that ends with spaces (alveolar sacs) from where oxygen diffuses into the tissues. The model delivers the dimensions of the alveolar sac, the total length of the airways, the total alveolar surface area, and the total resistance to oxygen transport in the respiratory tree. A constructal law also emerges: the length defined by the ratio of the square of the airway diameter to its length is constant for all individuals of the same species and is related to the characteristics of the space allocated to the respiratory process and determines univocally the branching level of the respiratory tree.