The respiratory system of mammals is made of two successive trees. The first is the bronchial tree terminated with around 30 000 transitional respiratory bronchioles in the case of humans. Each of these bronchioles is feeding a diffusion-reaction tree with a complex geometry called an acinus. The role of the bronchial tree is to distribute air to the 30 000 acini inside which oxygen if transferred by diffusion to blood cells. The bronchial tree in humans is found to be close to a “magic tree”. It will be shown that such a magic tree has redundant optimal properties such as space filling character, minimal viscous dissipation for the tree volume, optimal transport time for pulsatile respiration. The diffusion reaction in the acinar tree will be shown to be robust against various physiological perturbations linked to diseases.
The redundancy properties of these systems will be briefly discussed from the point of view of evolution.