Simulation of oxygen transport in capillaries

Abstract

A mathematical model is developed to predict oxygen transport from large capillaries. The model includes diffusion and convection in the plasma and rbc and the reaction in the rbcs. It also includes the radial distribution of red cells and flow velocities of red cells and plasma. The calculated oxygen saturations are in good agreement with the results from experiments in which artificial rubber capillaries are per- fused with red blood cell suspensions. It is found that in the large capillaries most of the resistance to Oxygen transport lies in the plasma. The Nusselt number for mass transfer is determined as a function of various parameters. The fluxes from large capillaries under various conditions can be easily predicted from these Nusselt numbers. The resistance to oxygen transport is found to be greater with rbc suspensions than with equivalent Hb solutions.

A mathematical model is developed for small capillaries. The effects of various parameters on oxygen transport are studied using this model. The physiological significance of these effects is discussed. The Nusselt number is calculated as a function of various parameters. It is found that a significant fraction of the transport resistance lies outside the tissue. The model is applied to certain physiological situations and is found to predict the observed behaviour.

The experimental methodology developed by Boland et al (13) is validated with the help of a well established mathematical model for haemoglobin solutions. The experimental system is characterized with the help of the model. The effects of physiological factors on oxygen transport from haemoglobin solutions is studied.