Mathematical modelling of oxygen transport in the microcirculation

Many mathematical models of the transport of oxygen in the microcirculation have been proposed. It is the aim of the present study to examine the validity of some of the many simplifying assumptions that have been used. Due to the many experimental difficulties,mathematical modeling has proved most useful in elucidating the effect of the physical and chemical processes on. the oxygen trasport of the microcirculation. The validity of using the simpler variable rate coefficient kinetic model compared to the complicated but realistic Adair model is studied. It is found that the variable rate coefficient model is adequate for the normal physiological range of fluxes. The choice of which kinetic models to use only becomes important at high fluxes i.e. in the reaction kinetics rate-limiting regime. The neglect of oxyhemoglobin diffusion in aiding the oxygen transport is found to be valid only at high fluxes where again the rate-limiting step is the chemical kinetics. For physiological range of fluxes, the neglect of oxyhemoglobin diffusion introduces substantial errors in the estimation of the resistance to oxygen transport in the capillary. The simpler mathematical model incorporating the simplifying assumption of local chemical equilibrium and no hemoglobin diffusion predicted the capillary wall oxygen concentration within an error of 16% but gave large errors in predicting the resistance to oxygen transport in the capillary. The mixed-mean and space-averaged oxyhemoglobin concentrations for a hemoglobin solution flowing through the capillary are compared and found to be significantly different. Solutions for the simulation of oxygen transport from a hemoglobin solution flowing through the capillary in a parabolic velocity profile is presented in the form of the Nusselt number against the Graetz number. The Nusselt number from an in-vitro experimental capillary is compared to that calculated from a model simulating the experimental and is found to agree very closely