An optimal bronchial tree may be dangerous

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 dissipation2,3,4. The bronchial tree of most mammalian lungs is a good example of an efficient distribution system with an approximate fractal structure5,6. 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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Figure 1: Geometry of a dichotomic and homothetic tree structure.
Figure 2: Homothety ratios for length and diameters of deep bronchi in the human lung (6 ≤ Z ≤ 16).
Figure 3: Dependence on the homothety ratio (h) of the resistance (R) and volume (V) of an 11-generation homothetic tree.
Figure 4: Dependence of tree resistance on bronchial constriction expressed as a percentage of reduction in diameter.

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Acknowledgements

The authors wish to thank J. M. Morel and M. Bernot for useful discussions.

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Correspondence to B. Sapoval.

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Mauroy, B., Filoche, M., Weibel, E. et al. An optimal bronchial tree may be dangerous. Nature 427, 633–636 (2004). https://doi.org/10.1038/nature02287

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