  Investigating blood flow in the cardiovascular system is crucial for
assessing cardiovascular health. Computational approaches offer some
non-invasive alternatives to measure blood flow dynamics. Numerical simulations
based on traditional methods such as finite-element and other numerical
discretizations have been extensively studied and have yielded excellent
results. However, adapting these methods to real-life simulations remains a
complex task. In this paper, we propose a method that offers flexibility and
can efficiently handle real-life simulations. We suggest utilizing the
physics-informed neural network (PINN) to solve the Navier-Stokes equation in a
deformable domain, specifically addressing the simulation of blood flow in
elastic vessels. Our approach models blood flow using an incompressible,
viscous Navier-Stokes equation in an Arbitrary Lagrangian-Eulerian form. The
mechanical model for the vessel wall structure is formulated by an equation of
Newton's second law of momentum and linear elasticity to the force exerted by
the fluid flow. Our method is a mesh-free approach that eliminates the need for
discretization and meshing of the computational domain. This makes it highly
efficient in solving simulations involving complex geometries. Additionally,
with the availability of well-developed open-source machine learning framework
packages and parallel modules, our method can easily be accelerated through GPU
computing and parallel computing. To evaluate our approach, we conducted
experiments on regular cylinder vessels as well as vessels with plaque on their
walls. We compared our results to a solution calculated by Finite Element
Methods using a dense grid and small time steps, which we considered as the
ground truth solution. We report the relative error and the time consumed to
solve the problem, highlighting the advantages of our method.
