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。计算方法提供了测量血流动力学的非侵入性替代方案。基于有限元及其他数值离散等传统方法的数值模拟已被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是一项复杂的任务。本文提出一种灵活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求解可变形域中的纳维-斯托克斯方程，特别针对弹性血管中的血流模拟。该方法采用任意拉格朗日-欧拉形式下的不可压缩粘性纳维-斯托克斯方程对血流建模，同时基于牛顿第二定律和线性弹性理论建立血管壁结构的力学模型，描述流体施加的力。作为无网格方法，本方法无需对计算域进行离散和网格划分，从而在解决复杂几何形状的模拟时具有高效性。此外，借助成熟的机器学习开源框架包和并行模块，该方法可通过GPU计算和并行计算轻松加速。为评估效果，我们在规则圆柱血管及含斑块血管上进行了实验，并将结果与基于密集网格和小时间步长的有限元法计算结果进行对比（视为基准解）。通过报告相对误差和求解时间，凸显了本方法的优势。