Equivalence between one step kinetics and Hill's equation.

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.