Hard-Constrained Physics-Informed Neural Network for Steady Axisymmetric Blood Flow in Healthy and Stenotic Veins

Abstract

The dynamics of blood flow in veins can be significantly affected by changes in the vessel geometry, especially if the latter includes stenosis, which may lead to changes in the velocity field as well as increased flow resistance. In this study, we seek to develop a PINN-based representation of the steady, axisymmetric flow in normal and stenotic veins and test its stability and accuracy against the established analytical solutions. This can help in achieving fast and accurate simulations, while maintaining existing physical boundary conditions. To implement the healthy vein problem, we used the exact solution to the Poiseuille flow, where we applied the hard constraint of zero tangential velocity at the walls. As for the stenotic problem, we constructed a manufactured target profile, dependent on the radius, and used the same physical boundary constraints. The neural network was trained on both interior points and axis-sampled points, using Adam optimizer and learning rate scheduling strategy. According to the results, the network can accurately predict the healthy solution with very little deviation and capture the necessary flow acceleration in the stenotic vein. The simulated velocity field corresponds very closely to the reference solution. Thus, the developed method allows obtaining an accurate representation of the steady state venous flow in a healthy and stenotic vein. Further development will focus on incorporating unsteady flows and more realistic vessel shapes, as well as enforcing the Navier-Stokes residuals.

Keywords

Natural Science - Physics, Natural Science - Biology, Applied Science - Applied Biological Science

Citation

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