Numerical accuracy of closed-loop steady state in a zero-dimensional cardiovascular model

Closed-loop cardiovascular models are becoming vital tools in clinical settings, making their accuracy and reliability paramount. While these models rely heavily on steady-state simulations, accuracy because of steady-state convergence is often assumed negligible. Using a reduced-order cardiovascular model created with the CircAdapt framework as a case study, we investigated steady-state convergence behaviour across various integration methods and simulation protocols. To minimize the effect of numerical errors, we first quantified the numerical errors originating from integration methods and model assumptions. We subsequently investigate this steady-state convergence error under two distinct conditions: first without, and then with homeostatic pressure-flow control (PFC), providing a comprehensive assessment of the CircAdapt framework's numerical stability and accuracy. Our results demonstrated that achieving a clinically accurate steady state required 7-15 heartbeats in simulations without regulatory mechanisms. When homeostatic control mechanisms were included to regulate mean arterial pressure and blood volume, more than twice the number of heartbeats was needed. By simulating a variable number of heartbeats tailored to each simulation's characteristics, an efficient balance between computational cost and steady-state accuracy can be achieved. Understanding this balance is crucial as cardiovascular models progress towards clinical use. This article is part of the theme issue 'Uncertainty quantification for healthcare and biological systems (Part 2)'.