A model to describe the rate of oxyhaemoglobin desaturation during apnoea

We have developed a model to describe the rate of oxyhaemoglobin desaturation during apnoea. This model takes into account the non-steady-state kinetics which pertain to this situation. We first derived a mathematical expression for instantaneous oxygen flux rate from the alveolar compartment. We then derived an expression to describe the effect of shunt on this flux. The effect of circulation time on real-time arterial mixed venous oxygen content difference and oxygen flux in the lung was determined graphically. We finally described a manoeuvre to accommodate the effect of the Bohr shift which is related to the increase in FA(CO2) during apnoea. We present plots of arterial oxyhaemoglobin saturation (Sa(O2)) vs duration of apnoea to illustrate the individual effects of the initial fractional concentration of oxygen in the alveolus (FA(O2)initial), alveolar volume (VA), shunt fraction (QS/QT), oxygen consumption rate (VO2), total blood volume (QT) and haemoglobin concentration (Hb). The model is illustrated by examples of paediatric, morbidly obese and post-operative scenarios. The postoperative scenario is particularly notable for the effect of a combination of small changes in individual variables leading to a large overall effect on the rate of oxyhaemoglobin desaturation.