Numerical Solution of Partial Differential Equations Describing the Simultaneous O2 and Co2 Diffusions in the Red Blood Cell

Abstract

To describe the overall gas exchange rates in red blood cells (RBC), a computer program for solving the diffusion equations for O2, CO2, and HCO3- that accompany the chemical reactions of Bohr- and Haldane-effects was developed. Three diffusion equations were solved alternatively and repeatedly in an increment time of 2 ms. After solving the diffusion equations the PO2, O2 saturation (SO2), PCO2, pH, and HCO3- content were corrected by using the Henderson-Hasselbalch equation, where the buffer value was newly derived from the C02 dissociation curve. In computing the Haldane effect, the buffer value was taken to be 44mmol.l(RBC)-1.pHc-1, so that the change in intracellular dissolved CO2 caused by the SO2 change was fully compensated by the subsequent C02 diffusion. The oxygenation and deoxygenation rate factors of hemoglobin were assumed to be 2.09.(1 -S)2.02 and 0.3s′1 Torr-1, respectively. The PQl change due to the Bohr-shift was computed from Hill's equation, in which the K value was given by a function of the intracellular pH. When the parameter values thus far measured were used, the computed Bohr- and Haldane-effects coincided well with the experimental data, supporting the validity of the equations. The overall gas exchange profiles calculated in the pulmonary capillary model showed that the C02 equilibration time was significantly longer than the oxygenation time. © 1986, PHYSIOLOGICAL SOCIETY OF JAPAN. All rights reserved.