Annals of Biomedical Engineering

, Volume 38, Issue 10, pp 3195–3209 | Cite as

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

  • H. J. Kim
  • I. E. Vignon-Clementel
  • J. S. Coogan
  • C. A. Figueroa
  • K. E. Jansen
  • C. A. Taylor
Article

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.

Keyterms

Blood flow Coronary flow Coronary pressure Coupled multidomain method 

References

  1. 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.CrossRefPubMedGoogle Scholar
  2. 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. 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.CrossRefPubMedGoogle Scholar
  4. 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.PubMedGoogle Scholar
  5. 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.CrossRefGoogle Scholar
  6. 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.CrossRefPubMedGoogle Scholar
  7. 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.CrossRefPubMedGoogle Scholar
  8. 8.
    Hunter, P. J., A. J. Pullan, and B. H. Smaill. Modeling total heart function. Annu. Rev. Biomed. Eng. 5(1):147–177, 2003.CrossRefPubMedGoogle Scholar
  9. 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.CrossRefPubMedGoogle Scholar
  10. 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.CrossRefGoogle Scholar
  11. 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.CrossRefPubMedGoogle Scholar
  12. 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.CrossRefPubMedGoogle Scholar
  13. 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.PubMedGoogle Scholar
  14. 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.CrossRefPubMedGoogle Scholar
  15. 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.CrossRefPubMedGoogle Scholar
  16. 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.CrossRefPubMedGoogle Scholar
  17. 17.
    Opie, L. H. Heart Physiology: From Cell to Circulation. Philadelphia, PA, USA: Lippincott Williams and Wilkins, 2003.Google Scholar
  18. 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.CrossRefPubMedGoogle Scholar
  19. 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.CrossRefPubMedGoogle Scholar
  20. 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.CrossRefGoogle Scholar
  21. 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.CrossRefPubMedGoogle Scholar
  22. 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.Google Scholar
  23. 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.CrossRefPubMedGoogle Scholar
  24. 24.
    Taylor, C. A., and C. A. Figueroa. Patient-specific model of cardiovascular mechanics. Annu. Rev. Biomed. Eng. 11:109–134, 2009.CrossRefPubMedGoogle Scholar
  25. 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.CrossRefGoogle Scholar
  26. 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.Google Scholar
  27. 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.CrossRefGoogle Scholar
  28. 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. 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.CrossRefPubMedGoogle Scholar
  30. 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.CrossRefPubMedGoogle Scholar
  31. 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.CrossRefPubMedGoogle Scholar

Copyright information

© Biomedical Engineering Society 2010

Authors and Affiliations

  • H. J. Kim
    • 1
  • I. E. Vignon-Clementel
    • 2
  • J. S. Coogan
    • 3
  • C. A. Figueroa
    • 3
  • K. E. Jansen
    • 1
  • C. A. Taylor
    • 3
    • 4
  1. 1.Aerospace Engineering SciencesUniversity of Colorado at BoulderBoulderUSA
  2. 2.INRIALe Chesnay CedexFrance
  3. 3.Department of BioengineeringStanford UniversityStanfordUSA
  4. 4.Department of SurgeryStanford UniversityStanfordUSA

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