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 offish respiration | biomechanics | biofluiddynamics F ish gills have evolved exclusively in aquatic creatures to extract aqueous oxygen. Because oxygen has considerably low solubility and diffusivity in water, the efficiency of respiration is critical (1). Gills consist of plate-like structures called filaments that are covered by an array of lamellae enclosing a capillary blood network, as shown in Fig. 1 (1, 2). Oxygen-rich water passes through the narrow channels formed by the lamellar layers, where oxygen diffuses into the capillaries. The densely packed lamellar structure is advantageous because it provides a large surface area for oxygen transfer; however, it also generates considerable viscous resistance. This resistance is overcome by pumping. Fish typically adopt one of the following two pumping mechanisms: branchial pumping and ram ventilation. Most teleost fish, members of the diverse group of ray-finned fish, use branchial pumping, and muscular compression in the pharynx enables water flow through the gills. In ram ventilation, which is used by many pelagic fish, the dynamic pressure generated by their swimming drives water flow into the gills (3).Most previous studies on the structure of fish gills have focused on the dependence of the total surface area of the gill upon the body size and species of fish (1, 4, 5). We consider the convective oxygen transfer that occurs in fish gills. As water passes through the narrow lamellar channels, increased viscous resistance impedes water flow at a given pumping pressure, which is limited by muscle power or swimming speeds; this leads to a lowering of the oxygen transfer rate. Hence, the flow rate within the gaps of the lamellae and the extended surface area play important roles in determining the oxygen transfer rate. The number of lamellae per unit length of gill filament determines both the surface area for diffusion and the size of the water channels. Therefore, we investigate the relationship between lamellar distance and oxygen transfer rate, an aspect that previously has seldom been explored.
ResultsTheoretical Analysis. W...