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描述红细胞中氧气和二氧化碳同时扩散的偏微分方程的数值解。

Numerical solution of partial differential equations describing the simultaneous O2 and CO2 diffusions in the red blood cell.

作者信息

Mochizuki M, Kagawa T

出版信息

Jpn J Physiol. 1986;36(1):43-63. doi: 10.2170/jjphysiol.36.43.

DOI:10.2170/jjphysiol.36.43
PMID:3088308
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 CO2 dissociation curve. In computing the Haldane effect, the buffer value was taken to be 44mmol X l(RBC)-1 X pHc-1, so that the change in intracellular dissolved CO2 caused by the So2 change was fully compensated by the subsequent CO2 diffusion. The oxygenation and deoxygenation rate factors of hemoglobin were assumed to be 2.09 X (1-S)2.02 and 0.3s-1 X Torr-1, respectively. The Po2 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 CO2 equilibration time was significantly longer than the oxygenation time.

摘要

为了描述红细胞(RBC)中的整体气体交换率,开发了一个计算机程序,用于求解与玻尔效应和哈代效应化学反应相伴的氧气、二氧化碳和碳酸氢根的扩散方程。以2毫秒的增量时间交替且重复地求解三个扩散方程。求解扩散方程后,使用亨德森-哈塞尔巴尔赫方程校正氧分压(Po2)、氧饱和度(So2)、二氧化碳分压(Pco2)、pH值和碳酸氢根含量,其中缓冲值是根据二氧化碳解离曲线新推导得出的。在计算哈代效应时,缓冲值取为44mmol×l(RBC)-1×pHc-1,这样由So2变化引起的细胞内溶解二氧化碳的变化就会被随后的二氧化碳扩散完全补偿。血红蛋白的氧合和脱氧速率因子分别假定为2.09×(1-S)2.02和0.3s-1×Torr-1。由玻尔效应引起的Po2变化根据希尔方程计算,其中K值由细胞内pH的函数给出。当使用迄今测量的参数值时,计算得到的玻尔效应和哈代效应与实验数据吻合良好,支持了这些方程的有效性。在肺毛细血管模型中计算得到的整体气体交换曲线表明,二氧化碳平衡时间明显长于氧合时间。

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Numerical solution of partial differential equations describing the simultaneous O2 and CO2 diffusions in the red blood cell.描述红细胞中氧气和二氧化碳同时扩散的偏微分方程的数值解。
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引用本文的文献

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Theory of oxygen transport to tissue.组织氧输送理论
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