Background During cardiopulmonary bypass (CPB), maintaining adequate oxygen consumption (VO₂i) can only be achieved indirectly either by modifying oxygen delivery (DO₂i) through its component parts or by modulating metabolic demand through altering body temperature. The body reacts to these actions by changing OER and consequently VO₂i. Understanding the body’s adaptive OER dynamics can elucidate its oxygen consumption goals during CPB and help improve our ability to safely manage the patient’s journey.

Methods An autoregressive, integrated time-series model was trained on granular perfusion data from 879 paediatric patients (age: newborn to 18 years old) undergoing 963 CPB operations, with the outcome variable being the minute-by-minute changes in the logit transformation of OER. Variables were cardiac index, haemoglobin concentration, oxygen saturation of arterial haemoglobin and temperature. An explicit ‘disequilibrium term group’ was also included, proportional to the difference between the logarithm of VO₂i and logarithm of a ‘latent’ (i.e. unobserved) oxygen demand – or ‘target’ VO₂ (tVO₂i) – term, with the logarithm of tVO₂i assumed to be a linear function of body temperature (the Van’t Hoff model). The trained time-series models were studied using permutation-based variable importance, deterministic and stochastic simulations, and subgroup analysis by acute kidney injury (AKI) grade and by temperature.

Results Model coefficients are consistent with an adaptive OER response to keep VO₂i in line with tVO₂i, according to body temperature. This adaptation consists of a primary rapid response for 5-10 minutes, and a secondary slow response that is estimated to last up to several hours. The model reproduces the hyperbolic shape of DO₂i-VO₂i curves – first published in 1982 – as an artefact of insufficient wait times between equilibrium-state transitions. Asymptotically, however, the model converges to a piecewise linear relationship between DO₂i and VO₂i, with supply-independence of oxygen consumption occurring above a threshold DO₂i. Subgroup analysis by temperature suggests that the dependence of tVO₂i on temperature (expressed as Q10) may be significantly stronger at low temperatures (< 28C) than at high temperatures (> 28C).

Conclusions This study proposes a physiologically plausible model of OER changes during CPB that is consistent with past experimental data. While during CPB, under-oxygenation is the dominant risk in the long term, slow adaptation of OER during CPB creates short-term opportunities for over-oxygenation following significant changes in variables such as cardiac index. The model provides well-defined values for tVO₂i at a given temperature, paving the way for further research into the effects of over- and under-oxygenation during CPB on postoperative outcomes such as AKI, and hence improvements in goal-directed perfusion protocols.