During cardiopulmonary bypass (CPB), goal-directed perfusion (GDP) seeks to match oxygen delivery to metabolic demand, but the dynamics of oxygen extraction and intraoperative oxygen demand remain poorly understood, especially in paediatric populations. Existing models rely on limited data and assume, for example, a linear relationship between log oxygen demand and temperature.

We developed GARIX (Global AutoRegressive Integrated model with eXogenous variables and an equilibrium force) to predict minute-by-minute changes in oxygen extraction ratio (OER) using high-resolution intraoperative data. GARIX combines: (1) an autoregressive term group (ATG) encoding memory of past OER; (2) an exogenous term group (XTG) incorporating recent and planned changes in cardiac index (CI), haemoglobin (Hb), SaO₂, and temperature; and (3) an equilibrium term group (ETG) that aligns oxygen consumption with demand via nonlinear temperature and patient-specific terms (log age, log weight, and interaction). A baseline model (bGARIX) used a linear temperature term and no patient-specific covariates. We trained on 20,443 min from 293 paediatric CPB procedures and evaluated performance through repeated K-fold cross-validation, simulations, and bootstrap confidence intervals.

GARIX reproduced physiologically plausible OER dynamics. Lagged coefficients captured adaptive responses to CI, Hb, SaO₂, and temperature. Equilibrium analysis estimated a Q₁₀ of 2.5 with bGARIX, matching textbook values (2.4–2.7). Likelihood ratio tests confirmed GARIX’s improved fit, revealing age- and weight-related heterogeneity and nonlinearity in temperature dependence. Variable importance showed ATG and XTG dominated predictive accuracy, underscoring the role of system dynamics. Simulations indicated slow OER response to CI and Hb and faster adaptation to temperature.

GARIX offers an interpretable, physiology-aligned model of oxygenation dynamics in paediatric CPB, enabling estimation of dynamic responses and latent demand. It provides a foundation for clinical insights and future real-time monitoring and intelligent perfusion control.