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

Abstract

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 CO(2). 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 CO(2). 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,)(CO(2)) > Theta(t,)(O(2)) > Theta(t,CO).

Alveolar-Membrane Diffusing Capacity Improves in the Morbidly Obese after Bariatric Surgery

“…We have assumed, as most workers do, that ÈNO in vivo [5,9,[12][13][14][15], although not in vitro [16], is infinity. The likely reason for this discrepancy is facilitated diffusion and/or lack of a stagnant layer in vivo [17]. Therefore, the DLNO-to-DmCO ratios of 2.42 [5,14,15] and 1.97 [9,12,13,18,19] were calculated as the theoretical ratio of DLNO to DmCO during single-breath maneuvers because those ratios have both been used in the past.…”

Towards a virtual lung: multi-scale, multi-physics modelling of the pulmonary system

“…These studies demonstrate the importance of modelling small-scale structure; however, they do not easily extend to larger scales. In an effort to overcome this limitation, Chakraborty et al (2004) derived an analytic expression for the diffusing capacity of the 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 the RBC, and boundary layer, haematocrit and the slope of the dissociation curve. This is a particularly interesting and novel model, as it incorporates the size and the shape of the RBC within the analytic expression.…”

Multiscale model for pulmonary oxygen uptake and its application to quantify hypoxemia in hepatopulmonary syndrome

“…(14) is the mass transfer coefficient in the unstirred layer that quantifies the transfer resistance between the rbc and the plasma. An expression for Z in terms of measurable variables could be derived by solving the coupled CDR equation of the rbc with the unstirred (boundary) layer surrounding it and is obtained as (Chakraborty et al, 2004)…”

“…(21) numerically, we average it spatially over the volume of the rbc. The details of the spatial averaging process may be obtained from Chakraborty et al (2004) and we summarize the spatially averaged model below.…”

“…The spatially averaged model for the micro-scale (i.e. the rbc) has been derived by Chakraborty et al (2004), and here we summarize the results (from Chakraborty et al, 2004) and integrate the micro-scale model with the new models for meso-and macro-scales that we shall derive in the following sections. The spatially averaged models presented in this article, though low-dimensional in nature, retain all the important physics of the micro-and meso-scales.…”