The important of surface area/volume ratio to the rate of oxygen uptake by red cells

Dear Sir: Holland and Forster (1966) demonstrated experimentally that velocity constants for initial rates of oxygen uptake by fully reduced erythrocytes (k~) are inversely related to mean corpuscular volume (MCV) (Table I). They based k" upon measurements of the rate of hemoglobin saturation with oxygen, so that the entire process included oxygen diffusion through the cell membrane, diffusion through the cell interior, and the chemical reaction of oxygen with hemoglobin. Cell thickness was considered the most obvious factor to account for decrease in k~ as cell volume increases. However, when they used an infinite sheet as a cell model, they did not establish a clear relationship between k~ and thickness. An inverse relationship was demonstrated between k~ and the radius (r) of a hypothetical sphere used as a cell model. Related material has been reviewed by Forster (1964). The present analysis is based upon the data in Table I. Average diameters (d) of sheep, rabbit, and human cells in plasma were taken from Ponder (1948); the other diameters are of dried cells (Altman and Ditmer, 1971) multiplied by 1.08 to correct for cell shrinkage. Red cell shape is considered to be that of a cylindrical disc, which differs little from a prolate spheroid and is easier to work with mathematically; thickness is taken as mean corpuscular thickness (MCT) as calculated by Wintrobe (1967). Surface area (S) and surface to volume ratio (S/V) are calculated as for a disc. All pairings between variables in Table I yield highly significant (P < 0.001) correlation coefficients, indicating that all of these characteristics are closely interrelated. If the calculations of M C T in Table I are accepted, then the increase of ~50% in cell thickness appears inadequate to account for a major portion of the 34-fold increase in cell volume, or the decrease in k~ to one-eighth of the maximal value. From Table I, we can see that increase in cell diameter is primarily responsible for the increase in MCV. The correlation coefficients which involve k" show that its best correlation is with S /V (r ~ 0.92), followed by d (r --0.83), M C T (r --0 .76) , S (r --0.76) , and M C V (r --0.73). For these experiments, we believe that decreasing S / V has the critical role in limiting rate of oxygen uptake as cell size increases. Apparently the rate of hemoglobin saturation is limited primarily by the surface area through which oxygen can diffuse in relation to the cell volume (and hemoglobin content), which must become saturated, rather