A study on three-dimensional reconstruction of coronary arteries and numerical simulation of fractional flow reserve based on deep learning_Journal of Biomedical Engineering

Authors：

WEI Jiangchao ¹ , WANG Lihua ² ,  ZHANG Wenpu ¹

1. Institute of Fluid Engineering, College of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027, P. R. China;
2. Department of Radiology, The Second Affiliated Hospital, Zhejiang University School of Medicine, Hangzhou 310009, P. R. China;

Corresponding?author：

ZHANG Wenpu, Email: wpzhang@zju.edu.cn

Keywords：

Coronary artery; Deep learning; Three-dimensional reconstruction; Hemodynamics; Fractional flow reserve

DOI：

10.7507/1001-5515.202603042

Video：

Export PDF Favorites Scan Get Citation

Abstract Full text Figures/Tables Video References Cited by

To address the needs of geometric modeling and hemodynamic analysis in the noninvasive functional assessment of coronary heart disease, this study establishes a deep learning-based integrated framework for coronary artery segmentation, three-dimensional reconstruction, and hemodynamic analysis. The nnU-Net model was used to achieve automatic coronary artery segmentation, and point cloud modeling techniques based on the Point Cloud Library (PCL) were further applied to construct patient-specific coronary artery models. Based on the reconstructed models, coronary hemodynamic numerical simulations were performed to analyze the variation characteristics of key indicators, including the blood flow velocity field, fractional flow reserve derived from computed tomography (CT-FFR), and wall shear stress (WSS), under different degrees of coronary artery stenosis. The results showed that, with increasing stenosis severity, local flow acceleration and high-velocity jet flow in the stenotic segment were enhanced, while the pressure distal to the stenosis decreased, leading to a gradual reduction in CT-FFR. Meanwhile, WSS increased in the stenotic region and adjacent vessel walls, and the high-WSS region expanded. These results indicate that the combination of machine learning-based three-dimensional reconstruction and hemodynamic analysis can help compensate for the limitations of conventional CT imaging in functional assessment, providing a numerical simulation basis for the noninvasive functional evaluation of coronary artery stenosis.

Citation： WEI Jiangchao, WANG Lihua, ZHANG Wenpu. A study on three-dimensional reconstruction of coronary arteries and numerical simulation of fractional flow reserve based on deep learning. Journal of Biomedical Engineering, 2026, 43(4): 751-759. doi: 10.7507/1001-5515.202603042 Copy

1.	Carr J J, Jacobs D R Jr, Terry J G, et al. Association of coronary artery calcium in adults aged 32 to 46 years with incident coronary heart disease and death[J]. JAMA Cardiol, 2017, 2(4): 391-399.
2.	Zeng A, Wu C, Lin G, et al. ImageCAS: a large-scale dataset and benchmark for coronary artery segmentation based on computed tomography angiography images[J]. Med Image Anal, 2023, 89: 102892.
3.	Boas F E, Fleischmann D. CT artifacts: causes and reduction techniques[J]. Imaging Med, 2012, 4: 229-240.
4.	Ning Y, Zhang S, Xi X, et al. CAC-EMVT: efficient coronary artery calcium segmentation with multi-scale vision transformers[C]//2021 IEEE International Conference on Bioinformatics and Biomedicine (BIBM). Houston: IEEE, 2021: 1462-1467.
5.	Shams M, Salem M A, Hamad S, et al. Coronary artery tree segmentation in computed tomography angiography using Otsu method[C]//2017 Eighth International Conference on Intelligent Computing and Information Systems (ICICIS). Cairo: IEEE, 2017: 416-420.
6.	Kerkeni A, Benabdallah A, Manzanera A, et al. A coronary artery segmentation method based on multiscale analysis and region growing[J]. Comput Med Imaging Graph, 2016, 48: 49-61.
7.	Zhao J, Gong W, Jiang S, et al. Automatic segmentation and reconstruction of coronary arteries based on sphere model and Hessian matrix using CCTA images[J]. J Phys Conf Ser, 2019, 1213(4): 042049.
8.	Cui H, Wang D, Wan M, et al. Coronary artery segmentation via Hessian filter and curve-skeleton extraction[C]//2014 IEEE Conference on Biomedical Engineering and Sciences (IECBES). Kuala Lumpur: IEEE, 2014: 93-98.
9.	Ge S, Shi Z, Peng G, et al. Two-steps coronary artery segmentation algorithm based on improved level set model in combination with weighted shape-prior constraints[J]. J Med Syst, 2019, 43(7): 1-10.
10.	Du H, Shao K, Bao F, et al. Automated coronary artery tree segmentation in coronary CTA using a multiobjective clustering and toroidal model-guided tracking method[J]. Comput Methods Programs Biomed, 2021, 199: 105908.
11.	Itu L, Rapaka S, Passerini T, et al. A machine-learning approach for computation of fractional flow reserve from coronary computed tomography[J]. J Appl Physiol, 2016, 121(1): 42-52.
12.	Ronneberger O, Fischer P, Brox T. U-Net: convolutional networks for biomedical image segmentation[C]//Medical Image Computing and Computer-Assisted Intervention (MICCAI) 2015. Cham: Springer, 2015: 234-241.
13.	Lopes D, Puga H, Teixeira J, et al. Blood flow simulations in patient-specific geometries of the carotid artery: a systematic review[J]. J Biomech, 2020, 111: 110019.
14.	Zaromytidou M, Siasos G, Coskun A U, et al. Intravascular hemodynamics and coronary artery disease: new insights and clinical implications[J]. Hellenic J Cardiol, 2016, 57(6): 389-400.
15.	Guccione J M, Kassab G S, Ratcliffe M B. Computational cardiovascular mechanics[M]. Boston: Springer, 2010.
16.	Isensee F, Jaeger P F, Kohl S A A, et al. nnU-Net: a self-configuring method for deep learning-based biomedical image segmentation[J]. Nat Methods, 2021, 18(2): 203-211.
17.	Gharleghi R, Adikari D, Ellenberger K, et al. Annotated computed tomography coronary angiogram images and associated data of normal and diseased arteries[J]. Sci Data, 2023, 10: 128.
18.	Xu R, Dai L, Wang J, et al. SADiff: coronary artery segmentation in CT angiography using spatial attention and diffusion model[J]. J Imaging, 2025, 11(6): 192.
19.	Milletari F, Navab N, Ahmadi S A. V-Net: fully convolutional neural networks for volumetric medical image segmentation[C]//2016 Fourth International Conference on 3D Vision (3DV). Stanford: IEEE, 2016: 565-571.
20.	Chen L C, Papandreou G, Kokkinos I, et al. DeepLab: semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected CRFs[J]. IEEE Trans Pattern Anal Mach Intell, 2018, 40(4): 834-848.
21.	Rusu R B, Cousins S. 3D is here: Point Cloud Library (PCL)[C]//IEEE International Conference on Robotics and Automation (ICRA). Shanghai: IEEE, 2011: 1-4.
22.	Li R, Lu X, Wang Q, et al. Research progress on 3D point cloud processing algorithms and applications in medical imaging[J]. Comput Biol Med, 2024, 153: 107012.
23.	Sulzer R, Marlet R, Vallet B, et al. A survey and benchmark of automatic surface reconstruction from point clouds[J]. IEEE Trans Pattern Anal Mach Intell, 2025, 47(3): 2000-2019.
24.	Cveti? J, ?olji? F. Triplanar point cloud reconstruction of head skin surface from computed tomography images in markerless image-guided surgery[J]. Bioengineering, 2025, 12(5): 498.
25.	Kigka V I, Rigas G, Sakellarios A, et al. 3D reconstruction of coronary arteries and atherosclerotic plaques based on computed tomography angiography images[J]. Biomed Eng Online, 2019, 18: 32.
26.	Guo H, Qiu T, Xu H, et al. Automatic coronary artery segmentation from cardiac data volume using statistical region growing and heuristic decision method[J]. Biomed Res Int, 2016, 2016: 4548605.
27.	Cox R W, Ashburner J, Bremen H, et al. A sort of new image data format standard: NIfTI-1[J]. Neuroimage, 2004, 22: e1440.
28.	Point Cloud Library. pcl: : ConcaveHull< PointInT > Class Template Reference[EB/OL]. [2026-07-30]. https://pointclouds.org/documentation/classpcl_1_1_concave_hull.html.
29.	Alexa M, Behr J, Cohen-Or D, et al. Point set surfaces[C]//IEEE Visualization 2001. San Diego: IEEE, 2001: 21-28.
30.	Berger M, Tagliasacchi A, Seversky L M, et al. A survey of surface reconstruction from point clouds[J]. ACM Comput Surv, 2017, 49(1): 1-40.
31.	Johnston B M, Johnston P R, Corney S, et al. Non-Newtonian blood flow in human right coronary arteries: steady state simulations[J]. J Biomech, 2004, 37(5): 709-720.
32.	Carvalho V, Rodrigues N, Ribeiro R, et al. Hemodynamic study in 3D printed stenotic coronary artery models: experimental validation and transient simulation[J]. Comput Methods Biomech Biomed Engin, 2021, 24(6): 623-636.
33.	Morbiducci U, Gatti G, Rizzo G. Inlet boundary conditions for image-based computational hemodynamics: impact of idealized versus measured velocity profiles in the human aorta[J]. J Biomech, 2013, 46(1): 102-109.
34.	Kamangar S, Salman Ahmed N J, Badruddin I A, et al. Effect of stenosis on hemodynamics in left coronary artery based on patient-specific CT scan[J]. Biomed Mater Eng, 2019, 30(4): 463-473.
35.	Mahalingam A, Gawandalkar U U, Kini G, et al. Numerical analysis of the effect of turbulence transition on the hemodynamic parameters in human coronary arteries[J]. Cardiovasc Diagn Ther, 2016, 6(3): 208-220.
36.	Ryval J, Straatman A G, Steinman D A. Two-equation turbulence modeling of pulsatile flow in a stenosed tube[J]. J Biomech Eng, 2004, 126(5): 625-635.
37.	Menter F R. Two-equation eddy-viscosity turbulence models for engineering applications[J]. AIAA J, 1994, 32(8): 1598-1605.
38.	Tang C X, Liu C Y, Lu M J, et al. CT FFR for ischemia-specific CAD with a new computational fluid dynamics algorithm: a Chinese multicenter study[J]. JACC Cardiovasc Imaging, 2020, 13(4): 980-990.
39.	Rehman S, Al-Shaikh B. Physiology, coronary circulation[M/OL]. Treasure Island: StatPearls Publishing, 2023 [2026-07-30]. https://www.ncbi.nlm.nih.gov/books/NBK482413/.
40.	Fernandes M, Sousa L C, António C C, et al. A review of computational methodologies to predict the fractional flow reserve in coronary arteries with stenosis[J]. J Biomech, 2025, 178: 112299.
41.	Zhang J, Wang L, Liu Y, et al. Branch flow distribution approach and its application in the calculation of fractional flow reserve in coronary artery[J]. Math Biosci Eng, 2021, 18(5): 6094-6110.
42.	Chemla D, Antony I, Zamani K, et al. Mean aortic pressure is the geometric mean of systolic and diastolic aortic pressure in resting humans[J]. J Appl Physiol, 2005, 99(6): 2278-2284.
43.	Tonino P A L, De Bruyne B, Pijls N H J, et al. Fractional flow reserve versus angiography for guiding percutaneous coronary intervention[J]. N Engl J Med, 2009, 360(3): 213-224.
44.	曾思源, 陳宏偉. 影像學壁剪切應力在冠狀動脈粥樣硬化中的研究進展[J]. 國際醫學放射學雜志, 2022, 45(3): 313-317.
45.	Driessen R S, Stuijfzand W J, van Rosendael A R, et al. Mechanical wall stress and wall shear stress are associated with atherosclerosis development in non-calcified coronary segments[J]. Atherosclerosis, 2023, 387: 117387.
46.	Candreva A, Buongiorno A L, Matter M A, et al. Impact of endothelial shear stress on coronary atherosclerotic plaque progression and composition: a meta-analysis and systematic review[J]. Int J Cardiol, 2024, 407: 132061.
47.	喬愛科, 侯映映, 侯陽. 冠狀動脈狹窄幾何構型對血流儲備分數影響的有限元分析[J]. 中國生物醫學工程學報, 2015, 34(2): 198-203.

1. Carr J J, Jacobs D R Jr, Terry J G, et al. Association of coronary artery calcium in adults aged 32 to 46 years with incident coronary heart disease and death[J]. JAMA Cardiol, 2017, 2(4): 391-399.
2. Zeng A, Wu C, Lin G, et al. ImageCAS: a large-scale dataset and benchmark for coronary artery segmentation based on computed tomography angiography images[J]. Med Image Anal, 2023, 89: 102892.
3. Boas F E, Fleischmann D. CT artifacts: causes and reduction techniques[J]. Imaging Med, 2012, 4: 229-240.
4. Ning Y, Zhang S, Xi X, et al. CAC-EMVT: efficient coronary artery calcium segmentation with multi-scale vision transformers[C]//2021 IEEE International Conference on Bioinformatics and Biomedicine (BIBM). Houston: IEEE, 2021: 1462-1467.
5. Shams M, Salem M A, Hamad S, et al. Coronary artery tree segmentation in computed tomography angiography using Otsu method[C]//2017 Eighth International Conference on Intelligent Computing and Information Systems (ICICIS). Cairo: IEEE, 2017: 416-420.
6. Kerkeni A, Benabdallah A, Manzanera A, et al. A coronary artery segmentation method based on multiscale analysis and region growing[J]. Comput Med Imaging Graph, 2016, 48: 49-61.
7. Zhao J, Gong W, Jiang S, et al. Automatic segmentation and reconstruction of coronary arteries based on sphere model and Hessian matrix using CCTA images[J]. J Phys Conf Ser, 2019, 1213(4): 042049.
8. Cui H, Wang D, Wan M, et al. Coronary artery segmentation via Hessian filter and curve-skeleton extraction[C]//2014 IEEE Conference on Biomedical Engineering and Sciences (IECBES). Kuala Lumpur: IEEE, 2014: 93-98.
9. Ge S, Shi Z, Peng G, et al. Two-steps coronary artery segmentation algorithm based on improved level set model in combination with weighted shape-prior constraints[J]. J Med Syst, 2019, 43(7): 1-10.
10. Du H, Shao K, Bao F, et al. Automated coronary artery tree segmentation in coronary CTA using a multiobjective clustering and toroidal model-guided tracking method[J]. Comput Methods Programs Biomed, 2021, 199: 105908.
11. Itu L, Rapaka S, Passerini T, et al. A machine-learning approach for computation of fractional flow reserve from coronary computed tomography[J]. J Appl Physiol, 2016, 121(1): 42-52.
12. Ronneberger O, Fischer P, Brox T. U-Net: convolutional networks for biomedical image segmentation[C]//Medical Image Computing and Computer-Assisted Intervention (MICCAI) 2015. Cham: Springer, 2015: 234-241.
13. Lopes D, Puga H, Teixeira J, et al. Blood flow simulations in patient-specific geometries of the carotid artery: a systematic review[J]. J Biomech, 2020, 111: 110019.
14. Zaromytidou M, Siasos G, Coskun A U, et al. Intravascular hemodynamics and coronary artery disease: new insights and clinical implications[J]. Hellenic J Cardiol, 2016, 57(6): 389-400.
15. Guccione J M, Kassab G S, Ratcliffe M B. Computational cardiovascular mechanics[M]. Boston: Springer, 2010.
16. Isensee F, Jaeger P F, Kohl S A A, et al. nnU-Net: a self-configuring method for deep learning-based biomedical image segmentation[J]. Nat Methods, 2021, 18(2): 203-211.
17. Gharleghi R, Adikari D, Ellenberger K, et al. Annotated computed tomography coronary angiogram images and associated data of normal and diseased arteries[J]. Sci Data, 2023, 10: 128.
18. Xu R, Dai L, Wang J, et al. SADiff: coronary artery segmentation in CT angiography using spatial attention and diffusion model[J]. J Imaging, 2025, 11(6): 192.
19. Milletari F, Navab N, Ahmadi S A. V-Net: fully convolutional neural networks for volumetric medical image segmentation[C]//2016 Fourth International Conference on 3D Vision (3DV). Stanford: IEEE, 2016: 565-571.
20. Chen L C, Papandreou G, Kokkinos I, et al. DeepLab: semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected CRFs[J]. IEEE Trans Pattern Anal Mach Intell, 2018, 40(4): 834-848.
21. Rusu R B, Cousins S. 3D is here: Point Cloud Library (PCL)[C]//IEEE International Conference on Robotics and Automation (ICRA). Shanghai: IEEE, 2011: 1-4.
22. Li R, Lu X, Wang Q, et al. Research progress on 3D point cloud processing algorithms and applications in medical imaging[J]. Comput Biol Med, 2024, 153: 107012.
23. Sulzer R, Marlet R, Vallet B, et al. A survey and benchmark of automatic surface reconstruction from point clouds[J]. IEEE Trans Pattern Anal Mach Intell, 2025, 47(3): 2000-2019.
24. Cveti? J, ?olji? F. Triplanar point cloud reconstruction of head skin surface from computed tomography images in markerless image-guided surgery[J]. Bioengineering, 2025, 12(5): 498.
25. Kigka V I, Rigas G, Sakellarios A, et al. 3D reconstruction of coronary arteries and atherosclerotic plaques based on computed tomography angiography images[J]. Biomed Eng Online, 2019, 18: 32.
26. Guo H, Qiu T, Xu H, et al. Automatic coronary artery segmentation from cardiac data volume using statistical region growing and heuristic decision method[J]. Biomed Res Int, 2016, 2016: 4548605.
27. Cox R W, Ashburner J, Bremen H, et al. A sort of new image data format standard: NIfTI-1[J]. Neuroimage, 2004, 22: e1440.
28. Point Cloud Library. pcl: : ConcaveHull< PointInT > Class Template Reference[EB/OL]. [2026-07-30]. https://pointclouds.org/documentation/classpcl_1_1_concave_hull.html.
29. Alexa M, Behr J, Cohen-Or D, et al. Point set surfaces[C]//IEEE Visualization 2001. San Diego: IEEE, 2001: 21-28.
30. Berger M, Tagliasacchi A, Seversky L M, et al. A survey of surface reconstruction from point clouds[J]. ACM Comput Surv, 2017, 49(1): 1-40.
31. Johnston B M, Johnston P R, Corney S, et al. Non-Newtonian blood flow in human right coronary arteries: steady state simulations[J]. J Biomech, 2004, 37(5): 709-720.
32. Carvalho V, Rodrigues N, Ribeiro R, et al. Hemodynamic study in 3D printed stenotic coronary artery models: experimental validation and transient simulation[J]. Comput Methods Biomech Biomed Engin, 2021, 24(6): 623-636.
33. Morbiducci U, Gatti G, Rizzo G. Inlet boundary conditions for image-based computational hemodynamics: impact of idealized versus measured velocity profiles in the human aorta[J]. J Biomech, 2013, 46(1): 102-109.
34. Kamangar S, Salman Ahmed N J, Badruddin I A, et al. Effect of stenosis on hemodynamics in left coronary artery based on patient-specific CT scan[J]. Biomed Mater Eng, 2019, 30(4): 463-473.
35. Mahalingam A, Gawandalkar U U, Kini G, et al. Numerical analysis of the effect of turbulence transition on the hemodynamic parameters in human coronary arteries[J]. Cardiovasc Diagn Ther, 2016, 6(3): 208-220.
36. Ryval J, Straatman A G, Steinman D A. Two-equation turbulence modeling of pulsatile flow in a stenosed tube[J]. J Biomech Eng, 2004, 126(5): 625-635.
37. Menter F R. Two-equation eddy-viscosity turbulence models for engineering applications[J]. AIAA J, 1994, 32(8): 1598-1605.
38. Tang C X, Liu C Y, Lu M J, et al. CT FFR for ischemia-specific CAD with a new computational fluid dynamics algorithm: a Chinese multicenter study[J]. JACC Cardiovasc Imaging, 2020, 13(4): 980-990.
39. Rehman S, Al-Shaikh B. Physiology, coronary circulation[M/OL]. Treasure Island: StatPearls Publishing, 2023 [2026-07-30]. https://www.ncbi.nlm.nih.gov/books/NBK482413/.
40. Fernandes M, Sousa L C, António C C, et al. A review of computational methodologies to predict the fractional flow reserve in coronary arteries with stenosis[J]. J Biomech, 2025, 178: 112299.
41. Zhang J, Wang L, Liu Y, et al. Branch flow distribution approach and its application in the calculation of fractional flow reserve in coronary artery[J]. Math Biosci Eng, 2021, 18(5): 6094-6110.
42. Chemla D, Antony I, Zamani K, et al. Mean aortic pressure is the geometric mean of systolic and diastolic aortic pressure in resting humans[J]. J Appl Physiol, 2005, 99(6): 2278-2284.
43. Tonino P A L, De Bruyne B, Pijls N H J, et al. Fractional flow reserve versus angiography for guiding percutaneous coronary intervention[J]. N Engl J Med, 2009, 360(3): 213-224.
44. 曾思源, 陳宏偉. 影像學壁剪切應力在冠狀動脈粥樣硬化中的研究進展[J]. 國際醫學放射學雜志, 2022, 45(3): 313-317.
45. Driessen R S, Stuijfzand W J, van Rosendael A R, et al. Mechanical wall stress and wall shear stress are associated with atherosclerosis development in non-calcified coronary segments[J]. Atherosclerosis, 2023, 387: 117387.
46. Candreva A, Buongiorno A L, Matter M A, et al. Impact of endothelial shear stress on coronary atherosclerotic plaque progression and composition: a meta-analysis and systematic review[J]. Int J Cardiol, 2024, 407: 132061.
47. 喬愛科, 侯映映, 侯陽. 冠狀動脈狹窄幾何構型對血流儲備分數影響的有限元分析[J]. 中國生物醫學工程學報, 2015, 34(2): 198-203.

Journal of Biomedical Engineering

A study on three-dimensional reconstruction of coronary arteries and numerical simulation of fractional flow reserve based on deep learning

Abstract Full text Figures/Tables Video References Cited by

Previous Article

Next Article

Format

Content