Diffusing capacity reexamined:: relative roles of diffusion and chemical reaction in red cell uptake of O2, CO, CO2, and NO

This paper presents an analytical expression for the diffusing capacity (Theta(t)) of the red blood cell (RBC) for any reactive gas in terms of size and shape of the RBC, thickness of the unstirred plasma layer surrounding the RBC, diffusivities and solubilities of the gas in RBC and boundary layer, hematocrit, and the slope of the dissociation curve. The expression for Theta(t) has been derived by spatial averaging of the fundamental convection-diffusion-reaction equation for O-2 in the RBC and has been generalized to all cell shapes and for other reactive gases such as CO, NO, and CO2. The effects of size and shape of the RBC, thickness of the unstirred plasma layer, hemoglobin concentration, and hematocrit on Theta(t) have been analyzed, and the analytically obtained expression for Theta(t) has been validated by comparison with different sets of existing experimental data for O-2 and CO2. Our results indicate that the discoidal shape of the human RBC with average dimensions of 1.6-mum thickness and 8-mum diameter is close to optimal design for O-2 uptake and that the true reaction velocity in the RBC is suppressed significantly by the mass transfer resistance in the surrounding unstirred layer. In vitro measurements using rapid-mixing technique, which measures Theta(t) in the presence of artificially created large boundary layers, substantially underpredicts the in vivo diffusing capacity of the RBC in the diffusion-controlled regime. Depending on the conditions in the RBC, uptake of less reactive gases ( such as CO) undergoes transition from reaction-limited to diffusion-limited regime. For a constant set of morphological parameters, the theoretical expression for Theta(t) predicts that Theta(t,NO) > Theta(t,CO2) > Theta(t,O2) > Theta(t,CO).