A Dynamic Time-Series Model of Oxygen Consumption during Paediatric Cardiopulmonary Bypass

Background Balancing oxygen supply and demand during cardiopulmonary bypass (CPB) is crucial to minimise adverse outcomes. This is managed by adjusting oxygen delivery components – cardiac index (CI), haemoglobin concentration (Hb), arterial oxygen saturation (SaO 2 ) – and metabolic demand through temperature (Temp) changes. The oxygen extraction ratio (OER) responds to these adjustments, affecting oxygen consumption, but this response is not well understood. We aimed to develop a mathematical model to capture OER dynamics during CPB and quantify oxygen demand’s dependence on temperature. Methods We developed GARIX, a time-series model predicting minute-by-minute OER changes during CPB, incorporating exogenous variables (CI, Hb, SaO 2 , Temp) and an equilibrium term representing the difference between oxygen consumption and temperature-dependent oxygen demand, modelled linearly per the van’t Hoff specification (constant Q 10 ). The model was trained on data from 343 CPB operations (20,000 minutes) in 334 paediatric patients at a UK centre (2019–2021). We used variable importance analysis and simulations to study the model’s properties. Results The model shows OER adapts to align oxygen consumption with demand. The adaptive response has a rapid phase (<10 minutes) and a slower phase extending up to several hours. Equilibrium analysis yields Q 10 = 2.25, indicating oxygen demand doubles with every 8.5°C increase in temperature during CPB. Conclusions Our model provides a physiologically plausible framework for explaining OER changes during CPB, capturing dynamic adjustments and steady-state oxygen consumption. These findings highlight the value of mathematical modelling in estimating key oxygenation parameters like Q 10 , given limitations on clinical experimentation.