A first principles calculation of the oxygen uptake in the human pulmonary acinus at maximal exercise

It has recently been shown that the acinus can have a reduced efficiency due to a "screening effect" governed by the ratio of oxygen diffusivity to membrane permeability, the gas flow velocity, as well as the size and configuration of the acinus. We present here a top to bottom calculation of the functioning of a machine acinus at exercise that takes this screening effect into account. It shows that, given the geometry and the breathing dynamics of real acini, respiration can be correlated to a single equivalent parameter that we call the integrative permeability. In particular we find that both V(O(2,max)) and PA(O(2)) depend on this permeability in a non-linear manner. Numerical solutions of dynamic convection-diffusion equations indicate that only a narrow range of permeability values is compatible with the experimental measurements of PA(O(2)) and V(O(2,max)). These permeability values are significantly smaller than those found in the literature. In a second step, we present a new type of evaluation of the diffusive permeability, yielding values compatible with the top to bottom approach, but smaller than the usual morphometric value.