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 non-invasive 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 3-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.