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.

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.

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.

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. Competing Interest Statement The authors have declared no competing interest. Funding Statement This work was (partly) funded by the National Institute for Health Research Great Ormond Street Hospital Biomedical Research Centre. The views expressed are those of the author(s) and not necessarily those of the National Health Service, the National Institute for Health Research, or the Department of Health. Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes The details of the IRB/oversight body that provided approval or exemption for the research described are given below: Ethics committee of Great Ormond Street Hospital for Children, London gave ethical approval for this work I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable. Yes Footnotes The authors have no conflicts of interest to disclose. Revisions to the manuscript to clarify Methods and Results. Data Availability All data produced in the present study are available upon reasonable request to the authors