The non-linear partial differential equation for O
2 diffusion was solved numerically in the three-dimensional red cell model by using the alternating-direction implicit method. The oxygenation rate factor of hemoglobin (
Fs) was assumed to decrease as the O
2 saturation (
SO
2) increases, as given by
Fs=2.1 ×(1-
S)
2 (sec
-1·(mmHg)
-1). The result obtained was compared with the solutions of the equations derived by Thews and Moll and also with those obtained from the sheet model. The oxygenation rate of the red cell largely depended on the diffusivity across the diffusion barrier around the red cell (η). When
η=2.5 × 10
-8 cm · sec
-1·(mmHg)
-1 was inserted into the present equation, the numerical solution showed a good correlation with the experimental data. When the sheet model was applied, the η value obtained from the same experimental data was about twice as great as that obtained in the disc model.
One of the characteristic features of the
SO
2-time curves of the red cell was the decrease in steepness at a high
SO
2 range, which has been thought to occur due to the decrease in the oxygenation rate of hemoglobin. Therefore, the difference of the actual
PO
2 in the red cell from the fictitious, so-called “back-pressure” which is evaluated from the O
2 dissociation curve through the actual
SO
2 has been expected to become greater as the S
O2 increases. The result obtained from the present equation revealed that the above
PO
2 difference became as great as 20 mmHg at the maximum point. In the solutions obtained from Thews' and Moll's equations, however, the slope of the S
O2-time curve was not significantly reduced at a high
SO
2 range.
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