A mathematical model of CO₂, O₂ and N₂ exchange during venovenous extracorporeal membrane oxygenation

Venovenous extracorporeal membrane oxygenation (vv-ECMO) is an effective treatment for severe respiratory failure. The interaction between the cardiorespiratory system and the oxygenator can be explored with mathematical models. Understanding the physiology will help the clinician optimise therapy. As others have examined O₂ exchange, the main focus of this study was on CO₂ exchange.

A model of the cardiorespiratory system during vv-ECMO was developed, incorporating O₂, CO₂ and N₂ exchange in both the lung and the oxygenator. We modelled lungs with shunt fractions varying from 0 to 1, covering the plausible range from normal lung to severe acute respiratory distress syndrome. The effects on P_aCO₂ of varying the input parameters for the cardiorespiratory system and for the oxygenator were examined.

P_aCO₂ increased as the shunt fraction in the lung and metabolic CO₂ production rose. Changes in haemoglobin and F_IO₂ had minimal effect on P_aCO₂. The effect of cardiac output on P_aCO₂ was variable, depending on the shunt fraction in the lung. P_aCO₂ decreased as extracorporeal circuit blood flow was increased, but the changes were relatively small in the range used clinically for vv-ECMO of > 2 l/min. P_aCO₂ decreased as gas flow to the oxygenator rose and increased with recirculation. The oxygen fraction of gas flow to the oxygenator had minimal effect on P_aCO₂.

This mathematical model of gas exchange during vv-ECMO found that the main determinants of P_aCO₂ during vv-ECMO were pulmonary shunt fraction, metabolic CO₂ production, gas flow to the oxygenator and extracorporeal circuit recirculation.