Parametrized sampling for 3D blood simulation in deformable vessels using Physics-Informed Neural Networks

Simulating blood flow in deformable vessels is crucial for advancing the understanding of cardiovascular dynamics. To address this, we employ Physics-Informed Neural Networks (PINNs) to solve the Navier–Stokes equations in full 3D formulations within elastic, deformable vessel geometries. To achieve this, we developed a parameterized sampling strategy that ensures a continuous fluid domain and smooth vessel wall surfaces, facilitating accurate differentiation calculations for various physical interactions across interface surfaces. To enforce periodicity, which poses an even greater challenge to the modeled multi-physics problem, we incorporated periodic feature layers into the neural networks. Additionally, Windkessel boundary conditions were applied at the outlet to replicate physiological behavior through Monte-Carlo integration. Dynamic weighting strategy is introduced to balance multiple loss terms associated with PDE constraints and boundary conditions. Experiments on various geometries are conducted to validate the accuracy of the full 3D model. Comparative studies between the full and reduced-order models highlight the respective advantages and limitations of each approach. Additional analyses of Windkessel parameters further elucidate their impact on flow dynamics.