Skip to main content
SpringerLink
Log in

A 1D–3D Hybrid Model of Patient-Specific Coronary Hemodynamics

  • Original Article
  • Published:
Cardiovascular Engineering and Technology Aims and scope Submit manuscript

Abstract

Purpose

Coronary flow is affected by evolving events such as atherosclerotic plaque formation, rupture, and thrombosis, resulting in myocardial ischemia and infarction. Highly resolved 3D hemodynamic data at the stenosis is essential to model shear-sensitive thrombotic events in coronary artery disease.

Methods

We developed a hybrid 1D–3D simulation framework to compute patient-specific coronary hemodynamics efficiently. A 1D model of the coronary flow is coupled to an image-based 3D model of the region of interest. This framework affords the advantages of reduced-order modeling, decreasing the global computational cost, without sacrificing the accuracy of the quantities of interest.

Results

We validated our 1D–3D model against full 3D coronary simulations in healthy and diseased conditions. Our results showed good agreement between the 3D and the 1D–3D models while reducing the computational cost by 40-fold compared to the 3D simulation. The 1D–3D model predicted left/right coronary flow distribution within 3% and provided an accurate estimation of fractional flow reserve and wall shear stress distribution at the stenosis comparable to the 3D simulation.

Conclusion

Savings in computational cost may be significant in situations with changing geometry, such as growing thrombosis. Also, this approach would allow quantifying the time-dependent effect of thrombotic growth and occlusion on the global coronary circulation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7

Similar content being viewed by others

References

  1. Blanco, P. J., C. A. Bulant, L. O. Müller, G. D. M. Talou, C. G. Bezerra, P. A. Lemos, and R. A. Feijóo. Comparison of 1D and 3D models for the estimation of fractional flow reserve. Sci. Rep. 8:1–12, 2018.

    Google Scholar 

  2. Blanco, P. J., and R. A. Feijóo. A dimensionally-heterogeneous closed-loop model for the cardiovascular system and its applications. Med. Eng. Phys. 35:652–667, 2013.

    Article  CAS  Google Scholar 

  3. Blanco, P. J., M. R. Pivello, S. A. Urquiza, and R. A. Feijóo. On the potentialities of 3D–1D coupled models in hemodynamics simulations. J. Biomech. 42:919–930, 2009.

    Article  CAS  Google Scholar 

  4. Blanco, P. J., S. A. Urquiza, and R. A. Feijóo. Assessing the influence of heart rate in local hemodynamics through coupled 3D–1D–0D models. Int. J. Numer. Method. Biomed. Eng. 26:890–903, 2010.

    Google Scholar 

  5. Bluestein, D., L. Niu, R. T. Schoephoerster, and M. K. Dewanjee. Fluid mechanics of arterial stenosis: relationship to the development of mural thrombus. Ann. Biomed. Eng. 25:344–356, 1997.

    Article  CAS  Google Scholar 

  6. Boileau, E., P. Nithiarasu, P. J. Blanco, L. O. Müller, F. E. Fossan, L. R. Hellevik, W. P. Donders, W. Huberts, M. Willemet, and J. Alastruey. A benchmark study of numerical schemes for one-dimensional arterial blood flow modelling. Int. J. Numer. Method Biomed. Eng. 31:1–33, 2015.

    Article  Google Scholar 

  7. Boileau, E., S. Pant, C. Roobottom, I. Sazonov, J. Deng, X. Xie, and P. Nithiarasu. Estimating the accuracy of a reduced-order model for the calculation of fractional flow reserve (FFR). Int. J. Numer. Method Biomed. Eng. 2018. https://doi.org/10.1002/cnm.2908.

    Article  PubMed  Google Scholar 

  8. Esmaily Moghadam, M., I. E. Vignon-Clementel, R. Figliola, and A. L. Marsden. A modular numerical method for implicit 0D/3D coupling in cardiovascular finite element simulations. J. Comput. Phys. 244:63–79, 2013.

  9. Flamm, M. H., and S. L. Diamond. Multiscale systems biology and physics of thrombosis under flow. Ann. Biomed. Eng. 40:2355–2364, 2012.

    Article  Google Scholar 

  10. Fleeter, C. M., G. Geraci, D. E. Schiavazzi, A. M. Kahn, and A. L. Marsden. Multilevel and multifidelity uncertainty quantification for cardiovascular hemodynamics. Comput. Methods Appl. Mech. Eng. 2020. https://doi.org/10.1016/j.cma.2020.113030.

    Article  PubMed  PubMed Central  Google Scholar 

  11. Fogelson, A. L., and K. B. Neeves. Fluid mechanics of blood clot formation. Annu. Rev. Fluid. Mech. 47:377–403, 2015.

    Article  Google Scholar 

  12. Formaggia, L., J.-F. Gerbeau, F. Nobile, and A. Quarteroni. On the coupling of 3D and 1D Navier-Stokes equations for flow problems in compliant vessels. Comput. Methods Appl. Mech. Eng. 191:561–582, 2001.

    Article  Google Scholar 

  13. Formaggia, L., D. Lamponi, and A. Quarteroni. One-dimensional models for blood flow in arteries. J. Eng. Math. 47:251–276, 2003.

    Article  Google Scholar 

  14. Fossan, F. E., J. Sturdy, L. O. Müller, A. Strand, A. T. Bråten, A. Jørgensen, R. Wiseth, and L. R. Hellevik. Uncertainty quantification and sensitivity analysis for computational FFR estimation in stable coronary artery disease. Cardiovasc. Eng. Technol. 9:597–622, 2018.

    Article  Google Scholar 

  15. Hughes, T. J. R., and J. Lubliner. On the one-dimensional theory of blood flow in the larger vessels. Math. Biosci. 18:161–170, 1973.

    Article  Google Scholar 

  16. Kim, H. J., I. E. Vignon-Clementel, J. S. Coogan, C. A. Figueroa, K. E. Jansen, and C. A. Taylor. Patient-specific modeling of blood flow and pressure in human coronary arteries. Ann. Biomed. Eng. 38:3195–3209, 2010.

    Article  CAS  Google Scholar 

  17. Krams, R., J. J. Wentzel, J. A. F. Oomen, R. Vinke, J. C. H. Schuurbiers, P. J. de Feyter, P. W. Serruys, and C. J. Slager. Evaluation of endothelial shear stress and 3d geometry as factors determining the development of atherosclerosis and remodeling in human coronary arteries in vivo. Arterioscler. Thromb. Vasc. Biol. 17:2061–2065, 1997.

    Article  CAS  Google Scholar 

  18. Leiderman, K., and A. L. Fogelson. Grow with the flow: a spatial-temporal model of platelet deposition and blood coagulation under flow. Math. Med. Biol. 28:47–84, 2011.

    Article  Google Scholar 

  19. Lu, Y., M. Y. Lee, S. Zhu, T. Sinno, and S. L. Diamond. Multiscale simulation of thrombus growth and vessel occlusion triggered by collagen/tissue factor using a data-driven model of combinatorial platelet signalling. Math. Med. Biol. 34:523–546, 2017.

    PubMed  Google Scholar 

  20. Mahmoudi, M., A. Farghadan, D. R. McConnell, A. J. Barker, J. J. Wentzel, M. J. Budoff, and A. Arzani. The story of wall shear stress in coronary artery atherosclerosis: biochemical transport and mechanotransduction. J. Biomech. Eng. 2021. https://doi.org/10.1115/1.4049026.

    Article  PubMed  Google Scholar 

  21. Mirramezani, M., S. Diamond, H. Litt, and S. C. Shadden. Reduced order models for transstenotic pressure drop in the coronary arteries. J Biomech Eng. 2018. https://doi.org/10.1115/1.4042184.

    Article  PubMed  Google Scholar 

  22. Moake, J. L., N. A. Turner, N. A. Stathopoulos, L. H. Nolasco, and J. D. Hellums. Involvement of large plasma von Willebrand factor (vWF) multimers and unusually large vWF forms derived from endothelial cells in shear stress-induced platelet aggregation. J. Clin. Invest. 78:1456–1461, 1986.

    Article  CAS  Google Scholar 

  23. Nesbitt, W. S., E. Westein, F. J. Tovar-Lopez, E. Tolouei, A. Mitchell, J. Fu, J. Carberry, A. Fouras, and S. P. Jackson. A shear gradient-dependent platelet aggregation mechanism drives thrombus formation. Nat. Med. 15:665–673, 2009.

    Article  CAS  Google Scholar 

  24. Nobile, F. Coupling strategies for the numerical simulation of blood flow in deformable arteries by 3D and 1D models. Math. Comput. Model. 49:2152–2160, 2009.

    Article  Google Scholar 

  25. Nobili, M., J. Sheriff, U. Morbiducci, A. Redaelli, and D. Bluestein. Platelet activation due to hemodynamic shear stresses: damage accumulation model and comparison to in vitro measurements. ASAIO J. 54:64–72, 2008.

    Article  Google Scholar 

  26. Seeley, B. D., and D. F. Young. Effect of geometry on pressure losses across models of arterial stenoses. J. Biomech. 9:439–448, 1976.

    Article  CAS  Google Scholar 

  27. Seo, J., D. E. Schiavazzi, A. M. Kahn, and A. L. Marsden. The effects of clinically-derived parametric data uncertainty in patient-specific coronary simulations with deformable walls. Int. J. Numer. Method. Biomed. Eng. 2020. https://doi.org/10.1002/cnm.3351.

    Article  PubMed  PubMed Central  Google Scholar 

  28. Sheriff, J., D. Bluestein, G. Girdhar, and J. Jesty. High-shear stress sensitizes platelets to subsequent low-shear conditions. Ann. Biomed. Eng. 38:1442–1450, 2010.

    Article  Google Scholar 

  29. Sheriff, J., J. S. Soares, M. Xenos, J. Jesty, M. J. Slepian, and D. Bluestein. Evaluation of shear-induced platelet activation models under constant and dynamic shear stress loading conditions relevant to devices. Ann. Biomed. Eng. 41:1279–1296, 2013.

    Article  Google Scholar 

  30. Sherwin, S. J., V. Franke, J. Peiró, and K. Parker. One-dimensional modelling of a vascular network in space-time variables. J. Eng. Math. 47:217–250, 2003.

    Article  Google Scholar 

  31. Si, H. TetGen, a Delaunay-based quality tetrahedral mesh generator. ACM Trans. Math. Softw. 41:11, 2015.

    Article  Google Scholar 

  32. Team, T. T. P. The Trilinos Project Website, 2020. At https://trilinos.github.io.

  33. Tonino, P. A. L., B. De Bruyne, N. H. J. Pijls, U. Siebert, F. Ikeno, M. vant Veer, V. Klauss, G. Manoharan, T. Engstrøm, and K. G. Oldroyd. Fractional flow reserve versus angiography for guiding percutaneous coronary intervention. N. Engl. J. Med. 360:213–224, 2009.

  34. Updegrove, A., N. M. Wilson, J. Merkow, H. Lan, A. L. Marsden, and S. C. Shadden. SimVascular: an open source pipeline for cardiovascular simulation. Ann. Biomed. Eng. 45:525–541, 2017.

    Article  Google Scholar 

  35. Urquiza, S. A., P. J. Blanco, M. J. Vénere, and R. A. Feijóo. Multidimensional modelling for the carotid artery blood flow. Comput. Methods Appl. Mech. Eng. 195:4002–4017, 2006.

    Article  Google Scholar 

  36. Wan, J., B. Steele, S. A. Spicer, S. Strohband, G. R. Feijóo, T. J. Hughes, and C. A. Taylor. A one-dimensional finite element method for simulation-based medical planning for cardiovascular disease. Comput. Methods Biomech. Biomed. Eng. 5:195–206, 2002.

    Article  Google Scholar 

  37. Watanabe, I., T. A. Johnson, J. Buchanan, C. L. Engle, and L. S. Gettes. Effect of graded coronary flow reduction on ionic, electrical, and mechanical indexes of ischemia in the pig. Circulation. 76:1127–1134, 1987.

    Article  CAS  Google Scholar 

  38. Wilson, R. F., K. Wyche, B. V. Christensen, S. Zimmer, and D. D. Laxson. Effects of adenosine on human coronary arterial circulation. Circulation. 82:1595–1606, 1990.

    Article  CAS  Google Scholar 

  39. Xiao, N., J. Alastruey, and C. Alberto Figueroa. A systematic comparison between 1-D and 3-D hemodynamics in compliant arterial models. Int. J. Numer. Method. Biomed. Eng. 30:204–231, 2014.

    Article  Google Scholar 

  40. Xu, Z., N. Chen, M. M. Kamocka, E. D. Rosen, and M. Alber. A multiscale model of thrombus development. J. R. Soc. Interface. 5:705–722, 2008.

    Article  Google Scholar 

  41. Xu, Z., N. Chen, S. C. Shadden, J. E. Marsden, M. M. Kamocka, E. D. Rosen, and M. Alber. Study of blood flow impact on growth of thrombi using a multiscale model. Soft Matter. 5:769–779, 2009.

    Article  CAS  Google Scholar 

  42. Yazdani, A., H. Li, J. D. Humphrey, and G. E. Karniadakis. A general shear-dependent model for thrombus formation. PLoS Comput. Biol. 2017. https://doi.org/10.1371/journal.pcbi.1005291.

    Article  PubMed  PubMed Central  Google Scholar 

  43. Yin, M., A. Yazdani, and G. E. Karniadakis. One-dimensional modeling of fractional flow reserve in coronary artery disease: uncertainty quantification and Bayesian optimization. Comput. Methods Appl. Mech. Eng. 353:66–85, 2019.

    Article  Google Scholar 

  44. Young, D. F. Fluid mechanics of arterial stenoses. J. Biomech. Eng. 101:157–175, 1979.

    Article  Google Scholar 

  45. Zheng, X., A. Yazdani, H. Li, J. D. Humphrey, and G. E. Karniadakis. A three-dimensional phase-field model for multiscale modeling of thrombus biomechanics in blood vessels. PLoS Comput. Biol. 2020. https://doi.org/10.1371/journal.pcbi.1007709.

    Article  PubMed  PubMed Central  Google Scholar 

Download references

Funding

This work was supported by R01-HL-103419 (N.G.G and S.L.D).

Data Availability

Not applicable.

Code Availability

Code developed for this study will be available via online code repository.

Conflict of interest

The authors declare that they have no conflict of interest.

Author information

Authors and Affiliations

  1. Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, USA

    Noelia Grande Gutiérrez, Talid Sinno & Scott L. Diamond

  2. Department of Bioengineering, University of Pennsylvania, Philadelphia, USA

    Scott L. Diamond

Authors
  1. Noelia Grande Gutiérrez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Talid Sinno
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Scott L. Diamond
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Scott L. Diamond.

Additional information

Associate Editor Igor Efimov oversaw the review of this article.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file 1 (DOCX 2324 kb)

Supplementary file 2 (MP4 6598 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Grande Gutiérrez, N., Sinno, T. & Diamond, S.L. A 1D–3D Hybrid Model of Patient-Specific Coronary Hemodynamics. Cardiovasc Eng Tech 13, 331–342 (2022). https://doi.org/10.1007/s13239-021-00580-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13239-021-00580-5

Keywords

Search

Navigation