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Annals of Biomedical Engineering

, Volume 38, Issue 7, pp 2314–2330 | Cite as

Incorporating Autoregulatory Mechanisms of the Cardiovascular System in Three-Dimensional Finite Element Models of Arterial Blood Flow

  • H. J. Kim
  • K. E. Jansen
  • C. A. TaylorEmail author
Article

Abstract

The cardiovascular system is a closed-loop system in which billions of vessels interact with each other, and it enables the control of the systemic arterial pressure and varying organ flow through autoregulatory mechanisms. In this study, we describe the development of mathematical models of autoregulatory mechanisms for systemic arterial pressure and coronary flow and discuss the connection of these models to a hybrid numerical/analytic closed-loop model of the cardiovascular system. The closed-loop model consists of two lumped parameter heart models representing the left and right sides of the heart, a three-dimensional finite element model of the aorta with coronary arteries, three-element Windkessel models and lumped parameter coronary vascular models that represent the systemic circulation, and a three-element Windkessel model to approximate the pulmonary circulation. Using the connection between the systemic arterial pressure and coronary flow regulation systems, and the hybrid closed-loop model, we studied how the heart, coronary vascular beds, and arterial system respond to physiologic changes during light exercise and showed that these models can realistically simulate temporal behaviors of the heart, coronary vascular beds, and arterial system during exercise of healthy subjects. These models can be used to study temporal changes occurring in the heart, coronary vascular beds, and arterial system during cardiovascular intervention or changes in physiological states.

Keywords

Blood flow Autoregulation Coronary Aorta Exercise Finite elements 

Notes

Acknowledgments

Hyun Jin Kim was supported by a Stanford Graduate Fellowship. The authors gratefully acknowledge the assistance of Jessica Shih for the construction of the thoracic aorta model with coronary arteries, Dr. C. Alberto Figueroa for providing with a computer tomography image, and Dr. Nathan Wilson for assistance with software development. We also wish to thank 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.

References

  1. 1.
    Barnea, O. Mathematical analysis of coronary autoregulation and vascular reserve in closed-loop circulation. Comput. Biomed. Res. 27(4):263–275, 1994CrossRefPubMedGoogle Scholar
  2. 2.
    Brooks, A. N., and T. J. R. Hughes. Streamline upwind Petrov–Galerkin formulation for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations. Comput. Methods Appl. Mech. Eng. 32:199–259, 1982CrossRefGoogle Scholar
  3. 3.
    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. AJNR Am. J. Neuroradiol. 26(10):2550–2559, 2005PubMedGoogle Scholar
  4. 4.
    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, 2006CrossRefGoogle Scholar
  5. 5.
    Formaggia, L., J. F. Gerbeau, F. Nobile, and A. Quarteroni. Numerical treatment of defective boundary conditions for the Navier–Stokes equations. SIAM J. Numer. Anal. 40(1):376–401, 2002CrossRefGoogle Scholar
  6. 6.
    Frauenfelder, T., M. Lotfey, T. Boehm, and S. Wildermuth. Computational fluid dynamics: hemodynamic changes in abdominal aortic aneurysm after stent-graft implantation. Cardiovasc. Intervent. Radiol. 29(4):613–623, 2006CrossRefPubMedGoogle Scholar
  7. 7.
    Guyton, A. Textbook of Medical Physiology, 8th edn. Philadelphia, PA: W.B. Sanders, 1991Google Scholar
  8. 8.
    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, 2009CrossRefGoogle Scholar
  9. 9.
    Kim, H. J., I. E. Vignon-Clementel, C. A. Figueroa, K. E. Jansen, and C. A. Taylor. Developing computational methods for three-dimensional finite element simulations of coronary blood flow. Finite Elem. Anal. Des., 2010. doi: 10.1016/j.finel.2010.01.007.
  10. 10.
    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, 2009CrossRefPubMedGoogle Scholar
  11. 11.
    Kim, H. J., I. E. Vignon-Clementel, J. Shih, 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., in review, 2009.Google Scholar
  12. 12.
    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, 1990PubMedGoogle Scholar
  13. 13.
    Li, Z., and C. Kleinstreuer. Blood flow and structure interactions in a stented abdominal aortic aneurysm model. Med. Eng. Phys. 27(5):369–382, 2005CrossRefPubMedGoogle Scholar
  14. 14.
    Lu, K., J. W. Clark Jr., F. H. Ghorbel, D. L. Ware, and A. Bidani. A human cardiopulmonary system model applied to the analysis of the Valsalva maneuver. Am. J. Physiol. Heart Circ. Physiol. 281:H2661–2679, 2001PubMedGoogle Scholar
  15. 15.
    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, 2006CrossRefPubMedGoogle Scholar
  16. 16.
    Miyashiro, J. K., and E. O. Feigl. A model of combined feedforward and feedback control of coronary blood flow. Am. J. Physiol. Heart Circ. Physiol. 268(2):H895–908, 1995Google Scholar
  17. 17.
    Olufsen, M. S., H. T. Tran, J. T. Ottesen, L. A. Lipsitz, and V. Novak. Modeling baroreflex regulation of heart rate during orthostatic stress. Am. J. Physiol. Regul. Integr. Comp. Physiol. 291(5):R1355–R1368, 2006PubMedGoogle Scholar
  18. 18.
    Ottesen, J. T., M. S. Olufsen, and J. K. Larsen. Applied Mathematical Models in Human Physiology. SIAM Monographs on Mathematical Modeling and Computation. Philadelphia, USA: SIAM, 2004.Google Scholar
  19. 19.
    Quarteroni, A., S. Ragni, and A. Veneziani. Coupling between lumped and distributed models for blood flow problems. Comput. Visual. Sci. 4(2):111–124, 2001CrossRefGoogle Scholar
  20. 20.
    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, 2004CrossRefPubMedGoogle Scholar
  21. 21.
    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, 2006CrossRefGoogle Scholar
  22. 22.
    Scheel, P., C. Ruge, U. R. Petruch, and M. Schoning. Color duplex measurement of cerebral blood flow volume in healthy adults. Stroke 31(1):147–150, 2000PubMedGoogle Scholar
  23. 23.
    Soerensen, D. D., K. Pekkan, D. de Zelicourt, S. Sharma, K. Kanter, M. Fogel, and A. P. Yoganathan. Introduction of a new optimized total cavopulmonary connection. Ann. Thorac. Surg. 83(6):2182–2190, 2007CrossRefPubMedGoogle Scholar
  24. 24.
    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, 1999Google Scholar
  25. 25.
    Taylor, C. A., and M.T. Draney. Experimental and computational methods in cardiovascular fluid mechanics. Annu. Rev. Fluid Mech. 36:197–231, 2004CrossRefGoogle Scholar
  26. 26.
    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, 1998CrossRefGoogle Scholar
  27. 27.
    Tune, J. D., M. W. Gorman, and E. O. Feigl. Matching coronary blood flow to myocardial oxygen consumption. J. Appl. Physiol. 97(1):404–415, 2004CrossRefPubMedGoogle Scholar
  28. 28.
    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, 2006CrossRefGoogle Scholar
  29. 29.
    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. Meth. Biomech. Biomed. Eng., 2008. doi: 10.1080/10255840903413565.
  30. 30.
    Whiting, C. H., and K. E. Jansen. A stabilized finite element method for the incompressible Navier–Stokes equations using a hierarchical basis. Int. J. Numer. Meth. Fluids 35:93–116, 2001CrossRefGoogle Scholar
  31. 31.
    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, 1992CrossRefPubMedGoogle Scholar
  32. 32.
    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, 2008CrossRefPubMedGoogle Scholar

Copyright information

© Biomedical Engineering Society 2010

Authors and Affiliations

  1. 1.Department of Aerospace Engineering SciencesUniversity of Colorado at BoulderBoulderUSA
  2. 2.Department of BioengineeringStanford UniversityStanfordUSA
  3. 3.Department of SurgeryStanford UniversityStanfordUSA
  4. 4.StanfordUSA

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