Establishing hemodynamic convergence framework for coronary digital twins under realistic dynamic heart rates

The advent of digital twins has increased the demand for longer-duration simulations that span multiple physiological states. Digital twins have emerged as powerful tools in cardiovascular modeling, enabling patient-specific simulations of coronary blood flow for noninvasive diagnosis and treatment planning. Although these simulations achieve high fidelity under steady or periodic heart rates, modeling real-world transitions, such as those arising from physical activity, requires careful evaluation of temporal convergence, the stabilization of hemodynamic parameters through the simulation of preceding cardiac cycles, or pre-flows. In this study, we present a physiologically grounded approach for determining the minimum number of preceding cardiac pre-flows necessary to achieve temporal convergence following abrupt heart rate (HR) changes. Using high-resolution patient-specific three-dimensional (3D) simulations and inflow waveforms scaled from both synthetic and wearable-derived HR data, we quantify convergence behavior across velocity, pressure gradient, and wall shear stress at both cross-sectional and full-domain levels. Results show that simulating just two pre-flows is sufficient to achieve physiologically stable outputs across high-to-low and low-to-high HR transitions (<2% difference). These findings are further verified using continuous HR data obtained from wearable devices, with low- and high-HR segments extracted to represent natural extremes, confirming the robustness of the proposed convergence criterion under real-world dynamic inputs (<1% difference). This work establishes a computationally efficient and physiologically consistent criterion for dynamic-state simulations, facilitating the integration of cardiovascular digital twins with real-time sensing technologies.