Diffusion Reaction of Carbon Monoxide in the Human Lung

The capture of CO, a standard lung function test, results from diffusion-reaction processes of CO with hemoglobin inside red blood cells (RBCs). In its current understanding, suggested by Roughton and Forster in 1957, the capture is represented by two independent resistances in series, one for diffusion from the gas to the RBC periphery, the second for internal diffusion reaction. Numerical studies in 3D model structures described here contradict the independence hypothesis. This results from two different theoretical reasons: (i) The RBC peripheries are not equi-concentrations; (ii) diffusion times in series are not additive.

Figure 1

The system where the gas is captured. (a) The capillary bed in the human lung. One can observe a few red blood cells out of capillaries (figure from E. Weibel with permission). (b) Schematic representation of the capture process. The gas concentration $C_g$ drops through extremely rapid dissolution to $\alpha C_g$ on the internal face of the alveolar-capillary interface. Then the molecules starting from any point on the interface follow individual Brownian paths through the membrane and plasma and into the RBC cytoplasm to reach the Hb molecules and finally react. See, for example, the blue and green trajectories.

Figure 2

Example of heterogeneous alveolar-capillary membrane in the lung. (a) The inherent heterogeneity is intensified with accumulated water (edema) inside or outside the membranes $C=\text{capillaries}$; $\mathrm{AE}=\text{alveolar}$ edema; $\mathrm{IE}=\text{interstitial}$ edema. Note that no RBC is visible in the capillaries (figure adapted from Ref. [8] and used with permission). (b) Idealized model of heterogeneous membrane with schematic RBCs in a capillary. (c) The simplified artificial model considered in this study is made of equidistant biconcave RBCs at the center of a cylindrical capillary. (d) Two membrane thicknesses—0.2 and $3\mu \mathrm{m}$—are arbitrarily chosen in this study to describe the heterogeneity with their combination. The figure represents one-half of an axial planar cross section of biconcave RBCs in the cylindrical capillary of Fig. 2 with RBC volume of $100\mu {\mathrm{m}}^3$ and a hematocrit of 40%.

Figure 3

Dependence of (a) the total resistance and (b) the blood resistance on the reaction time for several cases of membrane thickness heterogeneity. Each curve represents various membrane configurations. Resistance values are given in physiological units. (a) The ordinates at origin represents $R_{\mathrm{CO}}(\tau =0)$ and are naturally different for different membrane configurations. (b) The difference between $R_B$ curves is in contradiction to the Roughton and Forster hypothesis [5], which would call for a single curve. This is true whatever the value of reaction time of CO with hemoglobin. The inset exhibits larger differences for short reaction times.

Figure 4

Spatial distribution of the CO concentration in the thick (top) and thin (bottom) regions for two values of $\tau$. The concentration on the top thick line is normalized to 1. In these figures the local flux is proportional to the inverse of the distance between isoconcentration lines.