Optimal branching asymmetry of hydrodynamic pulsatile trees

TL;DR

This study demonstrates that systematic branching asymmetry in pulsatile flow networks, like the human respiratory system, optimizes delivery time and robustness, aligning with observed lung structures.

Contribution

It introduces the concept that controlled asymmetry in branching improves delivery efficiency and matches biological observations in the human lung.

Findings

Asymmetry reduces average delivery time.

Asymmetry enhances robustness against size variability.

Human lung asymmetry is near a critical threshold.

Abstract

Most of the studies on optimal transport are done for steady state regime conditions. Yet, there exists numerous examples in living systems where supply tree networks have to deliver products in a limited time due to the pulsatile character of the flow. This is the case for mammals respiration for which air has to reach the gas exchange units before the start of expiration. We report here that introducing a systematic branching asymmetry allows to reduce the average delivery time of the products. It simultaneously increases its robustness against the unevitable variability of sizes related to morphogenesis. We then apply this approach to the human tracheobronchial tree. We show that in this case all extremities are supplied with fresh air, provided that the asymmetry is smaller than a critical threshold which happens to fit with the asymmetry measured in the human lung. This could indicate that the structure is adjusted at the maximum asymmetry level that allows to feed all terminal units with fresh air.