invited editorial Invited Editorial on ‘‘A finite-element model of oxygen diffusion in the pulmonary capillaries’’ ALEKSANDER S. POPEL Department of Biomedical Engineering, School of Medicine, Johns Hopkins University, Baltimore, Maryland 21205 THE TOTAL AMOUNT of oxygen transferred in the lung from the gas phase in the alveoli to the blood is of critical importance to the function of the organism as a whole as well as to its every organ and cell. This amount is proportional to the difference in the oxygen tension in the alveoli and the mean oxygen tension in the pulmonary capillary; the coefficient of proportional- ity is called the overall pulmonary diffusing capacity (DL). An analogous relationship is considered for other organs where oxygen is transferred from the blood to the tissue. The value of the organ diffusing capacity is a function of the blood-gas barrier morphology (e.g., thickness) in the lung, capillary-parenchymal cell mor- phology in other organs, and blood hematocrit in all organs. Experiments to establish the determinants of organ diffusing capacity for lung and other organs and the corresponding mathematical modeling have been carried out in parallel, with fruitful interchange of concepts and ideas developed for the pulmonary and systemic circulations (13, 16). Mathematical modeling of oxygen transport has become an important and powerful tool in investigating biophysical and physi- ological mechanisms of organ function (8, 10). It is instructive to follow the progress in the modeling developments leading to the work of Frank et al. (5) published in this issue of the Journal of Applied Physiology (p. 2036). The inverse of the diffusing capacity characterizes the resistance to oxygen transport. In a landmark paper, Roughton and Forster (11) expressed the total transport pulmonary resistance to oxygen as the sum of in-series resistances of the membrane element (Dm) and of the red blood cells (RBCs) element. Therefore, they recognized that a fraction of the resistance to oxygen transport may be intracapillary. Two decades later, Hellums (7) formulated a mathematical model of oxygen transport from systemic capillaries with dis- crete RBCs represented in the model as cylindrical slugs; he showed that at a capillary hematocrit of 50% about one-half of the total resistance is intracapillary. Contribution of the plasma gaps between the RBCs was neglected. An elegant analysis of Clark et al. (2) pro- vided a simple analytic expression for the intra-RBC portion of the transport resistance in terms of hemoglo- bin concentration, hemoglobin-oxygen reaction rate, PO 2 at 50% oxyhemoglobin saturation, and other perti- nent parameters. Federspiel and Popel (4) extended the analysis of intracapillary transport by considering spherical RBCs and taking into account diffusion in the plasma gaps. They calculated the capillary mass trans- fer coefficient (a characteristic similar to the organ diffusing capacity but applied to a single capillary) as a function of hematocrit and predicted significant varia- tion of the mass transfer coefficient with hematocrit. Wang and Popel (14) carried this analysis further by considering parachute-shaped RBCs. Groebe and Thews (6) found that taking into account the effect of RBC velocity leads to a mild increase of the predicted mass transfer coefficient. A comparative theoretical study of transport resistances along the pathway from the RBC to the mitochondrion in a group of skeletal muscles, diaphragms, and myocardia in different animals (adap- tive species) based on a large body of physiological data confirms earlier predictions that a very large fraction of the total transport resistance, as much as 50%, is intracapillary (12). The first mathematical model of pulmonary capillary oxygen transport with discrete RBCs was formulated by Federspiel (3), who considered spherical RBCs in a cylindrical capillary. He predicted that a significant portion of the membrane transport resistance, Dm 21 , resides in the blood plasma gaps between the cells and, thus, is affected by inter-RBC distance or capillary hematocrit. This theoretical analysis prompted a mor- phological study in which Dm was estimated from micrographs using a measure of distance between RBC surface and alveolar surface, a morphometric method (15). Hsia et al. (9) considered a two-dimensional geometry with cylindrical RBCs positioned symmetri- cally between two planes representing the membrane and performed detailed calculations for DL and Dm as functions of capillary hematocrit; they also compared the predictions for Dm with the results of the morpho- metric method. The results were in good agreement for hematocrits .30% but diverged at smaller hemato- crits. The mathematical modeling study of Frank et al. (5) combines most of the features of the previous models; it 0161-7567/97 $5.00 Copyright r 1997 the American Physiological Society 1717 http://www.jap.org Downloaded from journals.physiology.org/journal/jappl (054.172.162.159) on June 17, 2022.