Optimal lamellar arrangement in fish gills

Fish respire through gills, which have evolved to extract aqueous oxygen. Fish gills consist of filaments with well-ordered lamellar structures, which play a role in maximizing oxygen diffusion. It is interesting that when we anatomically observe the gills of various fish species, gill interlamellar distances (d) vary little among them, despite large variations in body mass (M-b). Noting that the small channels formed by densely packed lamellae cause significant viscous resistance to water flow, we construct and test a model of oxygen transfer rate as a function of the lamellar dimensions and pumping pressure, which allows us to predict the optimal interlamellar distance that maximizes the oxygen transfer rate in the gill. Comparing our theory with biological data supports the hypothesis that fish gills have evolved to form the optimal interlamellar distances for maximizing oxygen transfer. This explains the weak scaling dependence of d on M-b: d similar to M-b(1/6).