Sharon M, Singh M P
J Biomed Eng. 1984 Oct;6(4):297-301. doi: 10.1016/0141-5425(84)90078-5.
One step kinetics between oxygen and haemoglobin are shown to be equivalent to the well-known Hill's equation. We have modified the one step kinetics while dealing with the mathematical modelling of simultaneous transport of oxygen and carbon-dioxide in the blood flowing through the pulmonary and the systemic capillaries. In the process, the Hill's equation has been modified showing an explicit dependence on PCO2. We have proposed comparatively simpler equations to represent Hb saturation with O2 and CO2 allowing for the interaction between the gases. It is shown that the oxygen dissociation curve, obtained from modified equations, fits in fairly well with the experimental data and shows realistic shift with PCO2. The results computed from our comparatively simpler equations based on physical laws, are in good agreement with those obtained from Kelman's empirical relations that are accepted in anaesthesia and respiratory physiology as providing very good matches to reality.
氧气与血红蛋白之间的一步动力学被证明等同于著名的希尔方程。在处理流经肺毛细血管和体毛细血管的血液中氧气和二氧化碳同时运输的数学模型时，我们对一步动力学进行了修正。在此过程中，希尔方程得到了修正，显示出对二氧化碳分压（PCO₂）的明确依赖。我们提出了相对更简单的方程来表示血红蛋白与氧气和二氧化碳的饱和度，同时考虑了气体之间的相互作用。结果表明，从修正后的方程得到的氧解离曲线与实验数据拟合得相当好，并且随着二氧化碳分压的变化呈现出符合实际的偏移。基于物理定律由我们相对更简单的方程计算得出的结果，与从凯尔曼经验关系获得的结果高度一致，在麻醉和呼吸生理学领域，凯尔曼经验关系被认为与实际情况匹配度非常高。
