Prediction of hemodynamic parameters in pathological arterial vessels based on physics-informed neural networks_Journal of Biomedical Engineering

Authors：

JI Mengqiang ¹ ,  SANG Jianbing ¹ ,  SUN Lifang ² , ZHANG Chen ¹ , ZHONG Xingyu ¹ , LI Yongjia ¹

1. School of Mechanical Engineering, Hebei University of Technology, Tianjin 300401, P. R. China;
2. Hospital of Hebei University of Technology, Tianjin 300401, P. R. China;

Corresponding?author：

SANG Jianbing, Email: sangjianbing@hebut.edu.cn; SUN Lifang, Email: sunlfang@hebut.edu.cn

Keywords：

Physics-informed neural networks; Hemodynamic; Hard boundary constraint method; Computational fluid dynamics

DOI：

10.7507/1001-5515.202510026

Video：

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Atherosclerosis, aneurysms, and other vascular pathologies are closely associated with hemodynamic parameters. Non-invasive measurement of these hemodynamic parameters is of great significance for the prevention and treatment of cardiovascular diseases. In this study, eight idealized models of diseased vessels with varying stenosis rates and dilation extents were constructed. Transient simulations were performed under realistic physiological boundary conditions, and spatiotemporal coordinates as well as hemodynamic parameters were extracted from the models over one cardiac cycle to construct the dataset. Subsequently, by integrating hard boundary constraint methods with a physics-informed neural network (PINN), a prediction model for hemodynamic parameters in diseased vessels was established. The superiority of this model was demonstrated through validation on steady-state problems. With only limited supervised data, the proposed model achieves high-accuracy predictions of key hemodynamic parameters in lesioned vessels, including velocity, pressure, wall shear stress (WSS), time-averaged wall shear stress (TAWSS), oscillatory shear index (OSI), and relative residence time (RRT). The results indicate that the developed hemodynamic prediction model can accurately capture flow field characteristics such as velocity and pressure distributions, and exhibits excellent performance in predicting WSS and TAWSS. This study provides a novel approach and scientific basis for mechanistic investigations, clinical diagnosis, therapeutic strategies, and risk assessment of atherosclerosis, aneurysms, and related cardiovascular diseases.

Citation： JI Mengqiang, SANG Jianbing, SUN Lifang, ZHANG Chen, ZHONG Xingyu, LI Yongjia. Prediction of hemodynamic parameters in pathological arterial vessels based on physics-informed neural networks. Journal of Biomedical Engineering, 2026, 43(2): 344-352. doi: 10.7507/1001-5515.202510026 Copy

1.	劉明波, 何新葉, 楊曉紅, 等. 《中國心血管健康與疾病報告2023》要點解讀. 中國心血管雜志, 2024, 29(4): 305-324.
2.	宣風琦, 王祖祿. 《中國心血管病一級預防指南》解讀. 臨床軍醫雜志, 2022, 50(6): 551-553.
3.	Kucher A N, Koroleva I A, Nazarenko M S. Exploring disparities in atherosclerosis comorbidity with aortic aneurysm. Biomedicines, 2025, 13(3): 593.
4.	劉夢辰, 潘霽超, 蔡彥, 等. 動脈粥樣硬化斑塊的生物力學模型和數值模擬研究. 生物醫學工程學雜志, 2020, 37(6): 948-955.
5.	何家勝, 鐘偉健. 動脈粥樣硬化斑塊的斷裂力學數值模擬研究. 生物醫學工程學雜志, 2021, 38(6): 1097-1102.
6.	石政加, 桑建兵, 孫麗芳, 等. 合并血管狹窄左冠狀動脈血管瘤的血流動力學仿真與分析. 生物醫學工程學雜志, 2024, 41(5): 1026-1034.
7.	Malek S, Eskandari A, Sharbatdar M. Machine learning-based prediction of hemodynamic parameters in left coronary artery bifurcation: A CFD approach. Heliyon, 2025, 11(2): e41973.
8.	Liang L, Mao W, Sun W. A feasibility study of deep learning for predicting hemodynamics of human thoracic aorta. J Biomech, 2020, 99: 109544.
9.	吳佳澤, 梁昊, 陳明. 基于卷積神經網絡-長短期記憶神經網絡模型利用光學體積描記術重建動脈血壓波信號. 生物化學與生物物理進展, 2024, 51(2): 447-458.
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11.	Liu Y, Cai L, Chen Y, et al. ICPINN: Integral conservation physics-informed neural networks based on adaptive activation functions for 3D blood flow simulations. Comput Phys Commun, 2025, 311: 109569.
12.	Liang M, Liu J, Wang H, et al. Ultrasound super-resolved hemodynamic estimation in microvessel using physics-informed neural networks and data assimilation. Comput Methods Programs Biomed, 2025: 109136.
13.	Zhang X, Wu F, Feng S, et al. Rapid prediction of pulsatile hemodynamics in the aortic arch based on physics-informed neural networks. Eur Heart J, 2025, 46: 1.
14.	Lagaris I E, Likas A, Fotiadis D I. Artificial neural networks for solving ordinary and partial differential equations. IEEE Trans Neural Netw, 1998, 9(5): 987-1000.
15.	Xiao Z, Ju Y, Li Z, et al. On the hard boundary constraint method for fluid flow prediction based on the physics-informed neural network. Appl Sci, 2024, 14(2): 859.
16.	Leon C, Scheinker A, Bormanis A. Solving the Orszag-Tang vortex magnetohydrodynamics problem with physics-constrained convolutional neural networks. Phys Plasmas, 2024: 894-897.
17.	Jing G, Wang H, Li X, et al. Physics-informed neural network-based Reynolds-averaged Navier-Stokes approach with limited observations for indoor airflow field reconstruction. Build Environ, 2025: 114107.
18.	Feng J, Xiao Y, Imin R, et al. Kernel derivative free-based physics-informed neural network for steady incompressible flows. Eng Anal Bound Elem, 2025, 181: 106523.
19.	Paz C, Suárez E, Cabarcos A, et al. FSI modeling on the effect of artery-aneurysm thickness and coil embolization in patient cases. Comput Methods Programs Biomed, 2021, 206: 106148.
20.	Raissi M, Perdikaris P, Karniadakis G E. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J Comput Phys, 2019, 378: 686-707.
21.	Rao C, Sun H, Liu Y. Physics-informed deep learning for computational elastodynamics without labeled data. J Eng Mech, 2021, 147(8): 04021043.
22.	Chou Y E, Liu T H, Lin C A. Impact of loss weight and model complexity on physics-informed neural networks for computational fluid dynamics. arXiv, 2025: 2509.21393.
23.	Mahmoudi M, Farghadan A, McConnell D R, et al. The story of wall shear stress in coronary artery atherosclerosis: biochemical transport and mechanotransduction. J Biomech Eng, 2021, 143(4): 041002.
24.	Souilhol C, Serbanovic-Canic J, Fragiadaki M, et al. Endothelial responses to shear stress in atherosclerosis: a novel role for developmental genes. Nat Rev Cardiol, 2020, 17(1): 52-63.
25.	Kli? K M, Wójtowicz D, Kwinta B M, et al. Association of arterial tortuosity with hemodynamic parameters-A computational fluid dynamics study. World Neurosurg, 2023, 180: e69-e76.
26.	Wen J, Yan T, Su Z, et al. Risk evaluation of type B aortic dissection based on WSS-based indicators distribution in different types of aortic arch. Comput Methods Programs Biomed, 2022, 221: 106872.
27.	Xu L, Chen X, Cui M, et al. The improvement of the shear stress and oscillatory shear index of coronary arteries during enhanced external counterpulsation in patients with coronary heart disease. PLoS One, 2020, 15(3): e0230144.
28.	Yamada S, Ito H, Ishikawa M, et al. Quantification of oscillatory shear stress from reciprocating CSF motion on 4D flow imaging. Am J Neuroradiol, 2021, 42(3): 479-486.
29.	Hyodo R, Takehara Y, Ishizu Y, et al. Evaluation of 4D flow MRI-derived relative residence time as a marker for cirrhosis associated portal vein thrombosis. J Magn Reson Imaging, 2024, 60(6): 2592-2601.
30.	Mutlu O, Salman H E, Al-Thani H, et al. How does hemodynamics affect rupture tissue mechanics in abdominal aortic aneurysm: Focus on wall shear stress derived parameters, time-averaged wall shear stress, oscillatory shear index, endothelial cell activation potential, and relative residence time. Comput Biol Med, 2023, 154: 106609.
31.	Rigatelli G, Zuin M, Roncon L. Increased blood residence time as markers of high-risk patent foramen ovale. Transl Stroke Res, 2023, 14(3): 304-310.

1. 劉明波, 何新葉, 楊曉紅, 等. 《中國心血管健康與疾病報告2023》要點解讀. 中國心血管雜志, 2024, 29(4): 305-324.
2. 宣風琦, 王祖祿. 《中國心血管病一級預防指南》解讀. 臨床軍醫雜志, 2022, 50(6): 551-553.
3. Kucher A N, Koroleva I A, Nazarenko M S. Exploring disparities in atherosclerosis comorbidity with aortic aneurysm. Biomedicines, 2025, 13(3): 593.
4. 劉夢辰, 潘霽超, 蔡彥, 等. 動脈粥樣硬化斑塊的生物力學模型和數值模擬研究. 生物醫學工程學雜志, 2020, 37(6): 948-955.
5. 何家勝, 鐘偉健. 動脈粥樣硬化斑塊的斷裂力學數值模擬研究. 生物醫學工程學雜志, 2021, 38(6): 1097-1102.
6. 石政加, 桑建兵, 孫麗芳, 等. 合并血管狹窄左冠狀動脈血管瘤的血流動力學仿真與分析. 生物醫學工程學雜志, 2024, 41(5): 1026-1034.
7. Malek S, Eskandari A, Sharbatdar M. Machine learning-based prediction of hemodynamic parameters in left coronary artery bifurcation: A CFD approach. Heliyon, 2025, 11(2): e41973.
8. Liang L, Mao W, Sun W. A feasibility study of deep learning for predicting hemodynamics of human thoracic aorta. J Biomech, 2020, 99: 109544.
9. 吳佳澤, 梁昊, 陳明. 基于卷積神經網絡-長短期記憶神經網絡模型利用光學體積描記術重建動脈血壓波信號. 生物化學與生物物理進展, 2024, 51(2): 447-458.
10. Kalajahi A P, Csala H, Mamun Z B, et al. Input parameterized physics informed neural networks for de noising, super-resolution, and imaging artifact mitigation in time resolved three dimensional phase-contrast magnetic resonance imaging. Eng Appl Artif Intell, 2025, 150: 110600.
11. Liu Y, Cai L, Chen Y, et al. ICPINN: Integral conservation physics-informed neural networks based on adaptive activation functions for 3D blood flow simulations. Comput Phys Commun, 2025, 311: 109569.
12. Liang M, Liu J, Wang H, et al. Ultrasound super-resolved hemodynamic estimation in microvessel using physics-informed neural networks and data assimilation. Comput Methods Programs Biomed, 2025: 109136.
13. Zhang X, Wu F, Feng S, et al. Rapid prediction of pulsatile hemodynamics in the aortic arch based on physics-informed neural networks. Eur Heart J, 2025, 46: 1.
14. Lagaris I E, Likas A, Fotiadis D I. Artificial neural networks for solving ordinary and partial differential equations. IEEE Trans Neural Netw, 1998, 9(5): 987-1000.
15. Xiao Z, Ju Y, Li Z, et al. On the hard boundary constraint method for fluid flow prediction based on the physics-informed neural network. Appl Sci, 2024, 14(2): 859.
16. Leon C, Scheinker A, Bormanis A. Solving the Orszag-Tang vortex magnetohydrodynamics problem with physics-constrained convolutional neural networks. Phys Plasmas, 2024: 894-897.
17. Jing G, Wang H, Li X, et al. Physics-informed neural network-based Reynolds-averaged Navier-Stokes approach with limited observations for indoor airflow field reconstruction. Build Environ, 2025: 114107.
18. Feng J, Xiao Y, Imin R, et al. Kernel derivative free-based physics-informed neural network for steady incompressible flows. Eng Anal Bound Elem, 2025, 181: 106523.
19. Paz C, Suárez E, Cabarcos A, et al. FSI modeling on the effect of artery-aneurysm thickness and coil embolization in patient cases. Comput Methods Programs Biomed, 2021, 206: 106148.
20. Raissi M, Perdikaris P, Karniadakis G E. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J Comput Phys, 2019, 378: 686-707.
21. Rao C, Sun H, Liu Y. Physics-informed deep learning for computational elastodynamics without labeled data. J Eng Mech, 2021, 147(8): 04021043.
22. Chou Y E, Liu T H, Lin C A. Impact of loss weight and model complexity on physics-informed neural networks for computational fluid dynamics. arXiv, 2025: 2509.21393.
23. Mahmoudi M, Farghadan A, McConnell D R, et al. The story of wall shear stress in coronary artery atherosclerosis: biochemical transport and mechanotransduction. J Biomech Eng, 2021, 143(4): 041002.
24. Souilhol C, Serbanovic-Canic J, Fragiadaki M, et al. Endothelial responses to shear stress in atherosclerosis: a novel role for developmental genes. Nat Rev Cardiol, 2020, 17(1): 52-63.
25. Kli? K M, Wójtowicz D, Kwinta B M, et al. Association of arterial tortuosity with hemodynamic parameters-A computational fluid dynamics study. World Neurosurg, 2023, 180: e69-e76.
26. Wen J, Yan T, Su Z, et al. Risk evaluation of type B aortic dissection based on WSS-based indicators distribution in different types of aortic arch. Comput Methods Programs Biomed, 2022, 221: 106872.
27. Xu L, Chen X, Cui M, et al. The improvement of the shear stress and oscillatory shear index of coronary arteries during enhanced external counterpulsation in patients with coronary heart disease. PLoS One, 2020, 15(3): e0230144.
28. Yamada S, Ito H, Ishikawa M, et al. Quantification of oscillatory shear stress from reciprocating CSF motion on 4D flow imaging. Am J Neuroradiol, 2021, 42(3): 479-486.
29. Hyodo R, Takehara Y, Ishizu Y, et al. Evaluation of 4D flow MRI-derived relative residence time as a marker for cirrhosis associated portal vein thrombosis. J Magn Reson Imaging, 2024, 60(6): 2592-2601.
30. Mutlu O, Salman H E, Al-Thani H, et al. How does hemodynamics affect rupture tissue mechanics in abdominal aortic aneurysm: Focus on wall shear stress derived parameters, time-averaged wall shear stress, oscillatory shear index, endothelial cell activation potential, and relative residence time. Comput Biol Med, 2023, 154: 106609.
31. Rigatelli G, Zuin M, Roncon L. Increased blood residence time as markers of high-risk patent foramen ovale. Transl Stroke Res, 2023, 14(3): 304-310.

Journal of Biomedical Engineering

Prediction of hemodynamic parameters in pathological arterial vessels based on physics-informed neural networks

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