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J Appl Physiol (August 20, 2004). doi:10.1152/japplphysiol.00469.2004
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Submitted on May 4, 2004
Accepted on August 16, 2004

Diffusing Capacity Re-examined: relative roles of diffusion and chemical reaction in red cell uptake of O2, CO, CO2 and NO

Saikat Chakraborty1, Vemuri Balakotaiah2, and Akhil Bidani1*

1 Pulmonary, Critical Care and Sleep Medicine, Department of Internal Medicine, University of Texas HSC-Houston, Houston, TX, USA; Department of Chemical Engineering, University of Houston, Houston, TX, USA
2 Department of Chemical Engineering, University of Houston, Houston, TX, USA

* To whom correspondence should be addressed. E-mail: Akhil.Bidani{at}uth.tmc.edu.

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 oxygen 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 O2 and CO. Our results indicate that the discoidal shape of the human rbc with avearge dimensions of 1.6 µm thickness and 8 µm diameter is close to optimal design for oxygen 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.




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