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.

翻译：研究心血管系统中的血流对于评估心血管健康至关重要。计算方法为测量血流动力学提供了一些非侵入性替代方案。基于传统方法（如有限元和其他数值离散化）的数值模拟已得到广泛研究并取得了优异成果。然而，将这些方法应用于实际模拟仍然是一项复杂的任务。本文提出一种具有灵活性且能高效处理实际模拟的方法。我们建议利用物理信息神经网络（PINN）求解可变形域中的Navier-Stokes方程，特别针对弹性血管中的血流模拟问题。我们的方法采用任意拉格朗日-欧拉形式的不可压缩粘性Navier-Stokes方程对血流进行建模。血管壁结构的力学模型通过牛顿第二动量定律方程和线性弹性方程对流体施加的作用力进行描述。本方法是一种无网格方法，无需对计算域进行离散化和网格划分，使其在求解复杂几何形状的模拟问题时具有高效性。此外，借助成熟的开源机器学习框架包和并行模块，本方法可通过GPU计算和并行计算轻松实现加速。为评估本方法，我们在规则圆柱血管及血管壁存在斑块的模型上进行了实验。我们将计算结果与采用密集网格和小时间步长的有限元法求解结果（视为基准真值）进行了比较。我们报告了相对误差和求解耗时，从而凸显本方法的优势。