Mathematical Modelling of Oxygenation Dynamics using High-Resolution Perfusion Data – Part 1: Statistical Framework

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 (SaO2) – 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, SaO2, 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 Q10). 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 Q10 = 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 Q10, given limitations on clinical experimentation.