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.
Citation: Meiyuan Du, Chi Zhang, Sheng Xie, Fang Pu, Da Zhang, Deyu Li. Investigation on aortic hemodynamics based on physics-informed neural network[J]. Mathematical Biosciences and Engineering, 2023, 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.
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Meiyuan Du, Chi Zhang, Sheng Xie, Fang Pu, Da Zhang, Deyu Li. Investigation on aortic hemodynamics based on physics-informed neural network[J]. Mathematical Biosciences and Engineering, 2023, 20(7): 11545-11567. doi: 10.3934/mbe.2023512
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