A physiologically constrained calibration framework for cardiovascular models applied to a paediatric synthetic sepsis population

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 Feedback Controller (EFC), 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, EFC enforces physiologically consistent parameter-variable relationships and converges to the single solution admitted by an over-determined set of targets, reproducibly and independently of the initial conditions, at a cost that scales efficiently with model complexity. The framework is demonstrated in silico, using a mechanistic cardiovascular model to generate virtual paediatric populations spanning normal physiology and two septic shock phenotypes (warm and cold shock) from literature-derived target ranges, achieving <1% residual error across pressures, flows, and compartmental volumes. The resulting parameter distributions are consistent, by construction with theoretical haemodynamic adaptations in paediatric sepsis, including alterations in vascular resistance, compliance, cardiac elastance, and effective blood volume. Importantly, persistent calibration residuals arise when target combinations are structurally incompatible with the model and the parameter carrying the residual is held at a bound, providing an explicit and interpretable diagnostic of feasibility limits. These results establish EFC 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.