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Patient-Specific Modeling of Blood Flow and Pressure in Human Coronary Arteries

Abstract

Coronary flow is different from the flow in other parts of the arterial system because it is influenced by the contraction and relaxation of the heart. To model coronary flow realistically, the compressive force of the heart acting on the coronary vessels needs to be included. In this study, we developed a method that predicts coronary flow and pressure of three-dimensional epicardial coronary arteries by considering models of the heart and arterial system and the interactions between the two models. For each coronary outlet, a lumped parameter coronary vascular bed model was assigned to represent the impedance of the downstream coronary vascular networks absent in the computational domain. The intramyocardial pressure was represented with either the left or right ventricular pressure depending on the location of the coronary arteries. The left and right ventricular pressure were solved from the lumped parameter heart models coupled to a closed loop system comprising a three-dimensional model of the aorta, three-element Windkessel models of the rest of the systemic circulation and the pulmonary circulation, and lumped parameter models for the left and right sides of the heart. The computed coronary flow and pressure and the aortic flow and pressure waveforms were realistic as compared to literature data.

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References

  1. Berry, J. L., A. Santamarina, J. E. Moore, S. Roychowdhury, and W. D. Routh. Experimental and computational flow evaluation of coronary stents. Ann. Biomed. Eng. 28(4):386–398, 2000.

    CAS  Article  PubMed  Google Scholar 

  2. Brooks, G. A., T. D. Fahey, T. P. White, and K. M. Baldwin. Exercise Physiology Human Bioenergetics and Its Applications. Berkshire, UK: McGraw-Hill Companies, 2004.

    Google Scholar 

  3. Burattini, R., P. Sipkema, G. van Huis, and N. Westerhof. Identification of canine coronary resistance and intramyocardial compliance on the basis of the waterfall model. Ann. Biomed. Eng. 13(5):385–404, 1985.

    CAS  Article  PubMed  Google Scholar 

  4. Cebral, J. R., M. A. Castro, J. E. Burgess, R. S. Pergolizzi, M. J. Sheridan, and C. M. Putman. Characterization of cerebral aneurysms for assessing risk of rupture by using patient-specific computational hemodynamics models. Am. J. Neuroradiol. 26(10):2550–2559, 2005.

    PubMed  Google Scholar 

  5. Figueroa, C. A., I. E. Vignon-Clementel, K. E. Jansen, T. J. R. Hughes, and C. A. Taylor. A coupled momentum method for modeling blood flow in three-dimensional deformable arteries. Comput. Methods Appl. Mech. Eng. 195(41–43):5685–5706, 2006.

    Article  Google Scholar 

  6. Gijsen, F. J. H., J. J. Wentzel, A. Thury, F. Mastik, J. A. Schaar, J. C. H. Schuurbiers, C. J. Slager, W. J. van der Giessen, P. J. de Feyter, A. F. W. van der Steen, and P. W. Serruys. Strain distribution over plaques in human coronary arteries relates to shear stress. Am. J. Physiol. Heart Circ. Physiol. 295(4):H1608–1614, 2008.

    CAS  Article  PubMed  Google Scholar 

  7. Gould, K. L., K. Lipscomb, and G. W. Hamilton. Physiologic basis for assessing critical coronary stenosis. Instantaneous flow response and regional distribution during coronary hyperemia as measures of coronary flow reserve. Am. J. Cardiol. 33(1):87–94, 1974.

    CAS  Article  PubMed  Google Scholar 

  8. Hunter, P. J., A. J. Pullan, and B. H. Smaill. Modeling total heart function. Annu. Rev. Biomed. Eng. 5(1):147–177, 2003.

    CAS  Article  PubMed  Google Scholar 

  9. Kerckhoffs, R. C. P., M. L. Neal, Q. Gu, J. B. Bassingthwaighte, J. H. Omens, and A. D. McCulloch. Coupling of a 3D finite element model of cardiac ventricular mechanics to lumped systems models of the systemic and pulmonic circulation. Ann. Biomed. Eng. 35(1):1–18, 2007.

    Article  PubMed  Google Scholar 

  10. Kim, H. J., C. A. Figueroa, T. J. R. Hughes, K. E. Jansen, and C. A. Taylor. Augmented Lagrangian method for constraining the shape of velocity profiles at outlet boundaries for three-dimensional finite element simulations of blood flow. Comput. Methods Appl. Mech. Eng. 198(45–46):3551–3566, 2009.

    Article  Google Scholar 

  11. Kim, H. J., I. E. Vignon-Clementel, C. A. Figueroa, J. F. LaDisa, K. E. Jansen, J. A. Feinstein, and C. A. Taylor. On coupling a lumped parameter heart model and a three-dimensional finite element aorta model. Ann. Biomed. Eng. 37(11):2153–2169, 2009.

    CAS  Article  PubMed  Google Scholar 

  12. Lagana, K., R. Balossino, F. Migliavacca, G. Pennati, E. L. Bove, M. R. de Leval, and G. Dubini. Multiscale modeling of the cardiovascular system: application to the study of pulmonary and coronary perfusions in the univentricular circulation. J. Biomech. 38(5):1129–41, 2005.

    Article  PubMed  Google Scholar 

  13. Laskey, W. K., H. G. Parker, V. A. Ferrari, W. G. Kussmaul, and A. Noordergraaf. Estimation of total systemic arterial compliance in humans. J. Appl. Physiol. 69(1):112–119, 1990.

    CAS  PubMed  Google Scholar 

  14. Li, Z., and C. Kleinstreuer. Blood flow and structure interactions in a stented abdominal aortic aneurysm model. Med. Eng. Phys. 27(5):369–382, 2005.

    Article  PubMed  Google Scholar 

  15. Mantero, S., R. Pietrabissa, and R. Fumero. The coronary bed and its role in the cardiovascular system: a review and an introductory single-branch model. J. Biomed. Eng. 14:109–115, 1992.

    CAS  Article  PubMed  Google Scholar 

  16. Migliavacca, F., R. Balossino, G. Pennati, G. Dubini, T. Y. Hsia, M. R. de Leval, and E. L. Bove. Multiscale modelling in biofluidynamics: application to reconstructive paediatric cardiac surgery. J. Biomech. 39(6):1010–1020, 2006.

    Article  PubMed  Google Scholar 

  17. Opie, L. H. Heart Physiology: From Cell to Circulation. Philadelphia, PA, USA: Lippincott Williams and Wilkins, 2003.

    Google Scholar 

  18. Qiu, Y., and J. M. Tarbell. Numerical simulation of pulsatile flow in a compliant curved tube model of a coronary artery. J. Biomech. Eng. 122(1):77–85, 2000.

    CAS  Article  PubMed  Google Scholar 

  19. Ramaswamy, S. D., S. C. Vigmostad, A. Wahle, Y. G. Lai, M. E. Olszewski, K. C. Braddy, T. M. H. Brennan, J. D. Rossen, M. Sonka, and K. B. Chandran. Fluid dynamic analysis in a human left anterior descending coronary artery with arterial motion. Ann. Biomed. Eng. 32(12):1628–1641, 2004.

    CAS  Article  PubMed  Google Scholar 

  20. Sahni, O., J. Muller, K. E. Jansen, M. S. Shephard, and C. A. Taylor. Efficient anisotropic adaptive discretization of the cardiovascular system. Comput. Methods Appl. Mech. Eng. 195(41–43):5634–5655, 2006.

    Article  Google Scholar 

  21. Santamarina, A., E. Weydahl, Jr. J. M. Siegel, and J. E. Moore, Jr. Computational analysis of flow in a curved tube model of the coronary arteries: effects of time-varying curvature. Ann. Biomed. Eng. 26:944–954, 1998.

    CAS  Article  PubMed  Google Scholar 

  22. Stergiopulos, N., P. Segers, and N. Westerhof. Use of pulse pressure method for estimating total arterial compliance in vivo. Am. J. Physiol. Heart Circ. Physiol. 276(2):H424–H428, 1999.

    CAS  Google Scholar 

  23. Taylor, C. A., M. T. Draney, J. P. Ku, D. Parker, B. N. Steele, K. Wang, and C. K. Zarins. Predictive medicine: computational techniques in therapeutic decision-making. Comput. Aided Surg. 4(5):231–247, 1999.

    CAS  Article  PubMed  Google Scholar 

  24. Taylor, C. A., and C. A. Figueroa. Patient-specific model of cardiovascular mechanics. Annu. Rev. Biomed. Eng. 11:109–134, 2009.

    CAS  Article  PubMed  Google Scholar 

  25. Taylor, C. A., T. J. R. Hughes, and C. K. Zarins. Finite element modeling of blood flow in arteries. Comput. Methods Appl. Mech. Eng. 158(1–2):155–196, 1998.

    Article  Google Scholar 

  26. Van Huis, G. A., P. Sipkema, and N. Westerhof. Coronary input impedance during cardiac cycle as determined by impulse response method. Am. J. Physiol. Heart Circ. Physiol. 253(2):H317–H324, 1987.

    CAS  Google Scholar 

  27. Vignon-Clementel, I.E., C.A. Figueroa, K.E. Jansen, and C.A. Taylor. Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries. Comput. Methods Appl. Mech. Eng. 195(29–32):3776–3796, 2006.

    Article  Google Scholar 

  28. Vignon-Clementel, I. E., C. A. Figueroa, K. E. Jansen, and C. A. Taylor. Outflow boundary conditions for three-dimensional simulations of non-periodic blood flow and pressure fields in deformable arteries. Comput. Methods Biomech. Biomed. Eng., 2008. doi:10.1080/10255840903413565.

  29. Zamir, M., P. Sinclair, and T.H. Wonnacott. Relation between diameter and flow in major branches of the arch of the aorta. J. Biomech. 25(11):1303–1310, 1992.

    CAS  Article  PubMed  Google Scholar 

  30. Zeng, D., E. Boutsianis, M. Ammann, K. Boomsma, S. Wildermuth, and D. Poulikakos. A study on the compliance of a right coronary artery and its impact on wall shear stress. J. Biomech. Eng. 130(4):041014, 2008.

    Article  PubMed  Google Scholar 

  31. Zhou, Y., G. S. Kassab, and S. Molloi. On the design of the coronary arterial tree: a generalization of Murray’s law. Phys. Med. Biol. 44:2929–2945, 1999.

    CAS  Article  PubMed  Google Scholar 

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Acknowledgments

Hyun Jin Kim was supported by a Stanford Graduate Fellowship. This material is based upon work supported by the National Science Foundation under Grant No. 0205741. The authors gratefully acknowledge the assistance of Dr. Nathan M. Wilson for assistance with software development. The authors gratefully acknowledge Dr. Farzin Shakib for the use of his linear algebra package AcuSolve™ (http://www.acusim.com) and the support of Simmetrix, Inc. for the use of the MeshSim™ (http://www.simmetrix.com) mesh generator.

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Correspondence to C. A. Taylor.

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Associate Editor Peter E. McHugh oversaw the review of this article.

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Kim, H.J., Vignon-Clementel, I.E., Coogan, J.S. et al. Patient-Specific Modeling of Blood Flow and Pressure in Human Coronary Arteries. Ann Biomed Eng 38, 3195–3209 (2010). https://doi.org/10.1007/s10439-010-0083-6

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  • DOI: https://doi.org/10.1007/s10439-010-0083-6

Keyterms

  • Blood flow
  • Coronary flow
  • Coronary pressure
  • Coupled multidomain method