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 02, C02, and HC03 -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 Poz, 02 saturation (S02), P02, 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 44 mmol l(RBC) -1 pH~ -1, so that the change in intracellular dissolved C02 caused by the Soz 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 0.3 s -• Torr 1, respectively. The Poz 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.Key words ; diffusion in red blood cell, Bohr effect, Haldane effect, overall gas exchange rate.Under physiological conditions in the pulmonary and peripheral capillaries, the 02 and C02 diffusions into and out of the red blood cells (RBC) are mutually influenced by the Bohr-and Haldane-effects. To estimate the overall gas exchange rate, the oxygenation and deoxygenation rates as well as the C02 and HC03 -diffusion rates in the RBC must be solved simultaneously. However, because of

Relationship between the transfer rate and the gap in partial pressure of gas molecules at a heterogeneous interface.

“…From the same numerical solution, we have recently derived the relationship between the contact time and gas exchange ratio during rebreathing by assuming ri(C02) at the RBC boundary to be 2.5 x 10-6 cm s -1 Torr -[1 1, 19,21]. Furthermore, SHIBUYA et al [29] demonstrated that the estimated contact time in a normal subject coincided well with the data thus far measured by other authors.…”

Configuration of the hemoglobin oxygen dissociation curve demystified: a basic mathematical proof for medical and biological sciences undergraduates

“…These include models that employed partial differential equations (15), hyperbolic trigonometrical functions based on known dynamic structural changes during oxygenation and deoxygenation (3,18), and the equations of Ackers and Halvorson (1). These include models that employed partial differential equations (15), hyperbolic trigonometrical functions based on known dynamic structural changes during oxygenation and deoxygenation (3,18), and the equations of Ackers and Halvorson (1).…”

A method for estimating contact time of red blood cells through lung capillary from O2 and CO2 concentrations in rebreathing air in man.

“…That is, the Haldane effect is included in the former curves, but not in the latter. In any event, the amount of C02 liberated out of the capillary blood plasma due to carbonic anhydrase in the capillary wall is estimated to be 0.3 to 0.4 vol%, as given by the difference in Cco2 between two time constants of 15 and 0.1 s. In the practical computation of the C02 diffusion (MOCHIzUKI and KAGAWA, 1986), however, the change in extracellular Pco2 was disregarded, assuming that the dehydration reaction is fairly slow compared with the C02 diffusion rate across the alveolar membrane. Although the change in extracellular Pco2 was neglected, the amount of C02 released out of the plasma by the extracellular dehydration reaction was implied in the computed diffusion quantity out of the RBC shown in Fig.…”

“…11, is one of the most important findings in this study. In our previous study (MOCHIZUKI and KAGAWA, 1986), we assumed that the time constant of extracellular HC03 -dehydration was 1.5s according to the experimental data of KLOCKE (1978). At that time, the requirement that t~ should be independent of the PA~o2 during the rebreathing, was not taken into account.…”