The optimal branching asymmetry of a bidirectional distribution tree

Several transportation networks in living systems are pulsatile branching trees. Due to the alternating character of the flow, these trees have to simultaneously satisfy two constraints: they have to deliver the carried products in a limited time and they must exhibit a satisfactory hydrodynamic performance in both directions of the flow. We report here that introducing a systematic branching asymmetry into a distribution tree improves performance and robustness, both at inhalation and exhalation. Moreover, optimizing the asymmetry level for both phases leads to a value very close to the one measured in the human lung.