Efficient Reduced Order Modeling Based on HODMD to Predict Intraventricular Flow Dynamics

Abstract: Accurate and efficient modeling of cardiac blood flow is crucial for advancing data-driven tools in cardiovascular research and clinical applications. Recently, the accuracy and availability of computational fluid dynamics (CFD) methodologies for simulating intraventricular flow have increased. However, these methods remain complex and computationally costly. This study presents a reduced order model (ROM) based on higher order dynamic mode decomposition (HODMD). The proposed approach enables accurate reconstruction and long term prediction of left ventricle flow fields. The method is tested on two idealized ventricular geometries exhibiting distinct flow regimes to assess its robustness under different hemodynamic conditions. By leveraging a small number of training snapshots and focusing on the dominant periodic components representing the physics of the system, the HODMD-based model accurately reconstructs the flow field over entire cardiac cycles and provides reliable long-term predictions beyond the training window. The reconstruction and prediction errors remain below 5\% for the first geometry and below 10\% for the second, even when using as few as the first 3 cycles of simulated data, representing the transitory regime. Additionally, the approach reduces computational costs with a speed-up factor of at least $10^{5}$ compared to full-order simulations, enabling fast surrogate modeling of complex cardiac flows. These results highlight the potential of spectrally-constrained HODMD as a robust and interpretable ROM for simulating intraventricular hemodynamics. This approach shows promise for integration in real-time analysis and patient specific models.