A biomechanically derived minimum work model of the fish gill lamellar system exhibits its exquisite morphological arrangement and perfusate regulation for oxygen uptake from water.
To evaluate the efficiency of oxygen (O2) uptake from water through the fish gill lamellar system, a cost function (CF) representing mechanical power expenditure for water ventilation and blood circulation through the gill was formulated, by applying steady-state fluid mechanics to a homogeneous lamellar-channel model. This approach allowed us to express CF as the function of inter-lamellar water channel width (w) and to derive an analytical solution of the width (wmin) at the minimum CF. Morphometric and physiological data for rainbow trout in the literature were referred to calculate CF(w) curves and their wmin values at five intensity stages of swimming exercise. Obtained wmin values were evenly distributed around the standard measure of the width (ws = 24 μm) in this fish. Individual levels of CF(wmin) were also fairly close to the corresponding CF(ws) values within a 10% deviation, suggesting the reliability of approximating [CF(wmin) = CF(ws)]. The cost-performance of O2 uptake through the gill (ηg) was then assessed from reported data of total O2 uptake/CF(ws) at each intensity stage. The ηg levels at any swimming stage exceeded 95% of the theoretical maximum value, implying that O2 uptake is nearly optimally performed in the lamellar-channel system at all swimming speeds. Further analyses of O2 transport in this fresh water fish revealed that the water ventilation by the buccal/opercular pumping evokes a critical limit of swimming velocity, due to confined O2 supply to the peripheral skeletal muscles, which is avoided in ram ventilators such as tuna.