Membrane artificial lungs (oxygenators) are used in cardiopulmonary surgery as well as, in some cases, in severe lung disease to support the natural lung by means of ECMO (extracorporeal membrane oxygenation). The oxygen and carbon dioxide transfer rates of any oxygenator are usually assessed by considering several blood gas parameters, such as oxygen saturation, hemoglobin concentration, partial pressure of oxygen and carbon dioxide, bicarbonate concentration, and $pH$. Here, we report a set of semi-empirical equations that calculate such parameters directly from their partial pressures and assess the acid–base balance during ECMO. The implementation of this equation set permits the evaluation of any oxygenator, existing or prototypes in development, as well as the development of clinical decision-making tools for predicting the blood gas state and acid–base balance during surgical interventions and ECMO. The predicted results are then compared with experimental data obtained from in vitro gas exchange investigations with a commercial oxygenator using fresh porcine blood. The high correlation, $R^2>0.95$, between the predicted and the experimental data suggests a possibility of using such empirical equations in the simulation of gas transfer in a cardiopulmonary system with an oxygenator for any venous inlet blood gas data and also for estimating the acid–base balance during such therapy.

Artificial lungs are commonly used in cardiopulmonary-bypass surgery (CPB), extracorporeal life support (ECLS), and extracorporeal carbon dioxide removal therapy (ECCO2R). In this study, a semi-empirical model for O₂ and CO₂ transfer in an oxygenator was formulated to evaluate the gas exchange performance at different blood/gas flow rates and various inlet conditions. The model uses experimentally obtained mass transfer coefficients together with blood-gas and acid-base inlet parameters to determine the corresponding outlet values by considering the mass transfer equations for both O₂ and CO₂. Increasing the blood flow rate (17L/min) decreases pO₂ at the outlet (from 376 to 120mmHg), but linearly increases the total oxygen transfer rate (OTR) from 76 to 450mL/min. CTR, the CO₂ transfer rate (64648mL/min), depends primarily on the ratio of gas to blood flow rate (1:15:1). In addition, venous concentrations of O₂CO₂ play a pivotal role in the overall gas exchange efficiency of the oxygenator. Conclusively, a good agreement (R²=0.99) could be observed between the experimental data and the models predictions for OTR and CTR alike at standard inlet conditions. The model's capabilities can be extended by modeling gas exchange during CPB, ECLS and ECCO2R therapies for different connection configurations.