1. Centre de Mathématiques et de leurs Applications, Ecole Normale Supérieure de Cachan, 94235 Cachan, France
2. Laboratoire de Physique de la Matière Condensée, CNRS Ecole Polytechnique, 91128 Palaiseau, France
3. Department of Anatomy, University of Bern, CH-3000 Bern, Switzerland

Correspondence to: B. Sapoval^1,2 Email: Bernard.Sapoval@polytechnique.fr

Abstract

The geometry and dimensions of branched structures such as blood vessels or airways are important factors in determining the efficiency of physiological processes. It has been shown that fractal trees can be space filling¹ and can ensure minimal dissipation^{2, 3, 4}. The bronchial tree of most mammalian lungs is a good example of an efficient distribution system with an approximate fractal structure^{5, 6}. Here we present a study of the compatibility between physical optimization and physiological robustness in the design of the human bronchial tree. We show that this physical optimization is critical in the sense that small variations in the geometry can induce very large variations in the net air flux. Maximum physical efficiency therefore cannot be a sufficient criterion for the physiological design of bronchial trees. Rather, the design of bronchial trees must be provided with a safety factor and the capacity for regulating airway calibre. Paradoxically, our results suggest that bronchial malfunction related to asthma is a necessary consequence of the optimized efficiency of the tree structure.

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