A Physiologically Constrained Calibration Framework for Cardiovascular Models applied in Paediatric Sepsis

Calibration of mechanistic cardiovascular models is a central barrier to their use in population analysis and patient-specific simulation, particularly in settings where key physiological variables are unobservable and multiple parameter combinations can reproduce the same haemodynamic targets. In this work, we present Embedded Gradient Descent (EGD), a calibration framework for ODE-based lumped-parameter cardiovascular models in which selected physiological parameters are promoted to dynamic states and driven toward prescribed targets through embedded controller equations. By exploiting the qualitative structure of the governing equations, EGD enforces physiologically consistent parameter-variable relationships, yielding unique calibrated solutions that are robust to initial conditions and scale efficiently with model complexity. The framework is demonstrated using a mechanistic cardiovascular model to generate virtual paediatric populations spanning normal physiology and two septic shock phenotypes (warm and cold shock), achieving low residual error across pressures, flows, and compartmental volumes. The resulting parameter distributions are consistent with known haemodynamic adaptations in paediatric sepsis, including alterations in vascular resistance, compliance, cardiac elastance, and effective blood volume. Importantly, persistent calibration residuals arise only when target combinations are structurally incompatible with the model, providing an explicit and interpretable diagnostic of feasibility limits rather than an optimisation failure. These results establish EGD as a general, scalable calibration strategy for mechanistic cardiovascular models and a practical foundation for virtual population generation and future patient-specific digital twin applications in critical care. NEW & NOTEWORTHYThis study introduces a novel, embedded gradient descent calibration framework that enables scalable generation of mechanistically interpretable virtual populations of patients from ODE-based cardiovascular models. By treating parameter inference as a dynamical extension of the governing equations and calibrating directly against cycle-derived physiological targets, the method preserves physiologically meaningful parameter-variable relationships. Applied to paediatric sepsis, the framework reproduces warm and cold shock phenotypes while exposing infeasible target combinations, while providing efficient calibration and physiological insight.