Mathematical modelling of the acid–base chemistry and oxygenation of blood: a mass balance, mass action approach including plasma and red blood cells

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Abstract
Mathematical models of the acid–base chemistry of blood based upon mass action and mass balance equations have become popular as diagnostic tools in intensive care. The reference models using this approach are those based on the strong ion approach, but these models do not currently take into account the effects of oxygen on the buffering characteristics of haemoglobin. As such these models are limited in their ability to simulate physiological situations involving simultaneous changes of O2 and CO2 levels in the blood. This paper describes a model of acid–base chemistry of blood based on mass action and mass balance equations and including the effects of oxygen. The model is used to simulate the mixing of venous blood with the same blood at elevated O2 and reduced CO2 levels, and the results compared with the mixing of blood sampled from 21 healthy subjects. Simulated values of pH, PCO2, PO2 and SO2 in the mixed blood compare well with measured values with small bias (i.e. 0.000 pH, −0.06 kPa PCO2, −0.1% SO2, −0.02 kPa PO2), and values of standard deviations (i.e. 0.006 pH, 0.11 kPa PCO2, 0.8% SO2, 0.13 kPa PO2) comparable to the precision seen in direct measurement of these variables in clinical practice. These results indicate that the model can reliably simulate the mixing of blood and has potential for application in describing physiological situations involving the mixing of blood at different O2 and CO2 levels such as occurs in the mixing of lung capillary and shunted pulmonary blood.

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