Abstract
A theoretical model is developed to investigate the role played by the particulate (two-phase) nature of blood on oxygen (O2) release in capillary-size vessels. Red cells flowing in single-file suspension through capillaries are modelled as evenly spaced, hemoglobin (Hb)-containing circular particles in a rectangular channel (two-dimensional case) or axisymmetric spheres in a circular tube (three-dimensional case). The model includes the free and Hb-facilitated transport of O2 and Hb-O2 kinetics inside the particles, diffusion of free O2 in the suspending phase, and a specified O2 tension at the capillary wall that drives the release of O2 from the particles as they traverse the capillary. The results are expressed in the form of a capillary mass transfer coefficient, an inverse resistance, that relates the spatial average flux of O2 out of the capillary to a driving force for O2 release. The results indicate that this coefficient depends significantly on particle spacing and clearance (channel size relative to particle size) but not significantly on the O2 tension at the capillary wall nor the eccentricity of the particles in the channel. It is also found that the capillary mass transfer coefficient can be several times smaller (more resistance) than that for a continuous Hb solution releasing O2. As a physiological application of the coefficients obtained, they are combined with a Krogh-type model for tissue, and the resulting analysis suggests that the fraction of total O2 transport resistance that resides inside the capillary is influenced significantly by the discrete nature of blood and can account for 30 to 70% of the total resistance to O2 transport from blood to tissue.