A mathematical model for gas exchange in the fish gill based on non-linear blood gas equilibrium curves

Abstract

A mathematical model for gas exchange in fish gills is presented, which makes allowance for the non-linear nature of the oxygen and carbon dioxide equilibrium curves of blood, for the uneven distribution of diffusion conductance along the secondary lamellae, and for coupling of oxygen and carbon dioxide exchange through the Bohr and Haldane effects. The model demonstrates that for oxygen loading in the gill the sigmoid equilibrium curve us superior to a linear one, whereas the non-linearity of the carbon dioxide equilibrium curve does not significantly effect carbon dioxide exchange and that the Bohr and Haldane effects have importance obly for carbon dioxide exchange. It is shown also shown that the arterial and expired gas tensions and concentrations are unaffected by whether the bulk of the diffusion conductance is at either the afferent of the afferent end of the individual lamellae, provided that the total conductance is unchanged.