Hydrodynamic analysis of the optimal design of fish gills and human lung

Abstract

It is generally assumed that shapes encountered in nature have evolved in a way as to maximize the robustness of a species. Nevertheless, given natures notoriously complex designs, it is often unclear what is being optimized. We here consider the optimization design principle in two respiratory systems: fish gills, and human lung.

The lamellar pattern of fish gills is one of the few cases in which optimization in nature can be well defined. We demonstrate that the lamellar pattern of fish gills has been optimized, such that fish display interlamellar spaces of similar dimension regardless of body mass or species, thereby revealing the primary evolutionary pressure on fish gills. This natural optimization strategy demonstrates how control of the channel arrangement in microfluidic devices enhances heat and mass transfer.

Lungs are natural microfluidic networks that transport oxygen from air into blood stream. The diameter reduction ratio of airways of lung determines the efficiency of physiological processes. An optimal diameter reduction ratio is thus expected. We here develop a mathematical model for diffusion transport of acinar airway and unveil the origin of the observed diameter reduction ratio of acinar airways: Minimizing the energy cost of acinar airways for a given amount of oxygen transport, suggesting a modified Murrays law for acinar airways.