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1Pulmonary, Critical Care and Sleep Medicine, Department of Internal Medicine, The University of Texas Medical School, Houston 77030, and 2Department of Chemical Engineering, University of Houston, Houston, Texas 77204-4004
Submitted 4 May 2004 ; accepted in final form 16 August 2004
This paper presents an analytical expression for the diffusing capacity (
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
t has been derived by spatial averaging of the fundamental convection-diffusion-reaction equation for O2 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
t have been analyzed, and the analytically obtained expression for
t has been validated by comparison with different sets of existing experimental data for O2 and CO2. Our results indicate that the discoidal shape of the human RBC with average dimensions of 1.6-µm thickness and 8-µm diameter is close to optimal design for O2 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
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
t predicts that
t,NO >
t,CO2 >
t,O2 >
t,CO.
red blood cells; diffusing capacity; hemoglobin; oxygen; carbon monoxide; nitric oxide; carbon dioxide
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