Key Laboratory of Biomechanics and Mechanobiology, Beijing Advanced Innovation Center for Biomedical Engineering, School of Biological Science and Medical Engineering, Beihang University, No. 37 Xueyuan Road, Haidian District, Beijing 100083, China.
State Key Laboratory of Virtual Reality Technology and Systems, Beihang University, No. 37 Xueyuan Road, Haidian District, Beijing 100083, China.
Math Biosci Eng. 2023 May 5;20(7):11545-11567. doi: 10.3934/mbe.2023512.
Pressure in arteries is difficult to measure non-invasively. Although computational fluid dynamics (CFD) provides high-precision numerical solutions according to the basic physical equations of fluid mechanics, it relies on precise boundary conditions and complex preprocessing, which limits its real-time application. Machine learning algorithms have wide applications in hemodynamic research due to their powerful learning ability and fast calculation speed. Therefore, we proposed a novel method for pressure estimation based on physics-informed neural network (PINN). An ideal aortic arch model was established according to the geometric parameters from human aorta, and we performed CFD simulation with two-way fluid-solid coupling. The simulation results, including the space-time coordinates, the velocity and pressure field, were obtained as the dataset for the training and validation of PINN. Nondimensional Navier-Stokes equations and continuity equation were employed for the loss function of PINN, to calculate the velocity and relative pressure field. Post-processing was proposed to fit the absolute pressure of the aorta according to the linear relationship between relative pressure, elastic modulus and displacement of the vessel wall. Additionally, we explored the sensitivity of the PINN to the vascular elasticity, blood viscosity and blood velocity. The velocity and pressure field predicted by PINN yielded good consistency with the simulated values. In the interested region of the aorta, the relative errors of maximum and average absolute pressure were 7.33% and 5.71%, respectively. The relative pressure field was found most sensitive to blood velocity, followed by blood viscosity and vascular elasticity. This study has proposed a method for intra-vascular pressure estimation, which has potential significance in the diagnosis of cardiovascular diseases.
动脉内的压力很难进行非侵入式测量。虽然计算流体动力学（CFD）根据流体力学的基本物理方程提供高精度的数值解，但它依赖于精确的边界条件和复杂的预处理，这限制了其实时应用。机器学习算法由于其强大的学习能力和快速的计算速度，在血液动力学研究中得到了广泛的应用。因此，我们提出了一种基于物理信息神经网络（PINN）的新型压力估计方法。根据人体主动脉的几何参数建立了理想的主动脉弓模型，并进行了双向流固耦合的 CFD 模拟。将包括时空坐标、速度和压力场在内的模拟结果作为训练和验证 PINN 的数据集。无因次纳维-斯托克斯方程和连续性方程被用作 PINN 的损失函数，以计算速度和相对压力场。根据血管壁的相对压力、弹性模量和位移之间的线性关系，提出了一种后处理方法来拟合主动脉的绝对压力。此外，我们还探讨了 PINN 对血管弹性、血液粘度和血流速度的敏感性。PINN 预测的速度和压力场与模拟值具有良好的一致性。在主动脉感兴趣的区域，最大和平均绝对压力的相对误差分别为 7.33%和 5.71%。相对压力场对血流速度最敏感，其次是血液粘度和血管弹性。本研究提出了一种血管内压力估计方法，对心血管疾病的诊断具有潜在意义。
