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Annals of Biomedical Engineering

, Volume 33, Issue 3, pp 284–300 | Cite as

Physics-Driven CFD Modeling of Complex Anatomical Cardiovascular Flows—A TCPC Case Study

  • Kerem Pekkan
  • Diane de Zélicourt
  • Liang Ge
  • Fotis Sotiropoulos
  • David Frakes
  • Mark A. Fogel
  • Ajit P. Yoganathan
Article

Abstract

Recent developments in medical image acquisition combined with the latest advancements in numerical methods for solving the Navier-Stokes equations have created unprecedented opportunities for developing simple and reliable computational fluid dynamics (CFD) tools for meeting patient-specific surgical planning objectives. However, for CFD to reach its full potential and gain the trust and confidence of medical practitioners, physics-driven numerical modeling is required. This study reports on the experience gained from an ongoing integrated CFD modeling effort aimed at developing an advanced numerical simulation tool capable of accurately predicting flow characteristics in an anatomically correct total cavopulmonary connection (TCPC). An anatomical intra-atrial TCPC model is reconstructed from a stack of magnetic resonance (MR) images acquired in vivo. An exact replica of the computational geometry was built using transparent rapid prototyping. Following the same approach as in earlier studies on idealized models, flow structures, pressure drops, and energy losses were assessed both numerically and experimentally, then compared. Numerical studies were performed with both a first-order accurate commercial software and a recently developed, second-order accurate, in-house flow solver. The commercial CFD model could, with reasonable accuracy, capture global flow quantities of interest such as control volume power losses and pressure drops and time-averaged flow patterns. However, for steady inflow conditions, both flow visualization experiments and particle image velocimetry (PIV) measurements revealed unsteady, complex, and highly 3D flow structures, which could not be captured by this numerical model with the available computational resources and additional modeling efforts that are described. Preliminary time-accurate computations with the in-house flow solver were shown to capture for the first time these complex flow features and yielded solutions in good agreement with the experimental observations. Flow fields obtained were similar for the studied total cardiac output range (1–3 l/min); however hydrodynamic power loss increased dramatically with increasing cardiac output, suggesting significant energy demand at exercise conditions. The simulation of cardiovascular flows poses a formidable challenge to even the most advanced CFD tools currently available. A successful prediction requires a two-pronged, physics-based approach, which integrates high-resolution CFD tools and high-resolution laboratory measurements.

Keyword

Fontan operation Digital Particle Image Velocimetry (DPIV) Flow instability Computational Fluid Dynamics (CFD) Exact replicate models Patient specific Surgical planning Total Cavopulmonary Connection (TCPC) 

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References

  1. 1.
    August, A. D., D. C. Barratt, A. D. Hughes, F. P. Glor, T. SAMcG, and X. Y. Xu. Accuracy and reproducibility of CFD predicted wall shear stress using 3D ultrasound images. J. Biomech. Eng. 125:218–22, 2003.Google Scholar
  2. 2.
    Bale-Glickman, J., K. Selby, D. Saloner, and Ö. Savas. Experimental flow studies in exact-replica phantoms of atherosclerotic carotid bifurcations under steady input conditions. J. Biomech. Eng. 125:38-48, 2003.Google Scholar
  3. 3.
    Bolzon, G., G. Pedrizzetti, M. Grigioni, L. Zovatto, C. Daniele, and G. D’Avenio. Flow on the symmetry plane of a total cavo-pulmonary connection, J. Biomech. 35:595–608, 2002.Google Scholar
  4. 4.
    Cebral, J. R., P. J. Yim, R. Lo, O. Soto, and P. L. Choyke. Blood flow modeling in carotid arteries with computational fluid dynamics and MR imaging. Acad. Radiol. 9:1286–1299, 2002.Google Scholar
  5. 5.
    Celik, I., C. J. Chen, P. J. Roache, and G. Scheuerer (editors). Symposium on quantification of uncertainty in computational fluid dynamics. In: Proceedings of ASME Fluids Engineering Division, Washington, DC, 1993.Google Scholar
  6. 6.
    Cochrane, A. D., C. P. Brizard, D. J. Penny, S. Johansson, J. V. Comas, T. Malm, and T. R. Karl. Management of the univentricular connection: are we improving? Eur. J. Cardiothorac. Surg. 12:107–115, 1997.Google Scholar
  7. 7.
    Coleman, H. W. Some observations on uncertainties and the verification and validation of a simulation. J. Fluids Eng. 125:733–735, 2003.Google Scholar
  8. 8.
    de Laval, M. R., P. Kilner, M. Gewillig, and C. Bull. Total cavopulmonary connection: A logical alternative to atriopulmonary connection for complex Fontan operations. Experimental studies and early clinical experience. J. Thorac. Cardiovasc. Surg. 96:682–695, 1988.Google Scholar
  9. 9.
    DeGroff, C. G., B. L. Thornburg, J. O. Pentecost, K. L. Thornburg, M. Gharib, D. J. Sahn, and A. Babtista. Flow in the early embryonic human heart: A numerical study. Pediatr. Cardiol. 24:375–380, 2003.Google Scholar
  10. 10.
    Ensley, A. E., A. Ramuzat, T. M. Healy, G. P. Chatzimavroudis, C. Lucas, S. Sharma, R. Pettigrew, and A. P. Yoganathan. Fluid mechanic assessment of the total cavopulmonary connection using magnetic resonance phase velocity mapping and digital particle image velocimetry. Ann. Biomed. Eng. 28:1172–1183, 2000.Google Scholar
  11. 11.
    Ensley, A. E., P. Lynch, G. P. Chatzimavroudis, C. Lucas, S. Sharma, and A. P. Yoganathan. Toward designing the optimal total cavopulmonary connection: An in vitro study. Ann. Thorac. Surg. 68:1384–1390, 1999.Google Scholar
  12. 12.
    Farhat, C., S. Lanteri, and H. D. Simon. TOP/DOMEC A software tool for mesh partitioning and parallel processing. J. Comput. Sys. Eng. 6:13–26, 1995.Google Scholar
  13. 13.
    Fogel, M. A., A. Hubbard, and P. M. Weinberg. A simplified approach for assessment of intercardiac baffles and extracardiac conduits in congenital heart surgery with two- and three-dimensional magnetic resonance imaging. Am. Heart J. 142(6):1028–1036, 2001.Google Scholar
  14. 14.
    Fogel, M. A., P. M. Weinberg, J. Rychik, A. Hubbard, M. Jacobs, T. L. Spray, and J. Haselgrove. Caval contribution to flow in the branch pulmonary arteries of Fontan patients with a novel application of magnetic resonance presaturation pulse. Circulation 99:1215–1221, 1999.Google Scholar
  15. 15.
    Formaggia, L., F. Nobile, A. Quarteroni, and A. Veneziani. Multiscale modelling of the circulatory system: A preliminary analysis. Comput. Visual Sci. 2:75–83, 1999.MATHGoogle Scholar
  16. 16.
    Frakes, D., C. Conrad, T. Healy, J. Monaco, M. Smith, M. Fogel, S. Sharma, and A. P. Yoganathan. Application of an adaptive control grid interpolation technique to morphological vascular reconstruction. IEEE Trans. Bio. Eng. 50(2):197–206, 2003.Google Scholar
  17. 17.
    Frakes, D., M. Smith, D. de Zélicourt, K. Pekkan, A. Yoganathan. Three-dimensional velocity field reconstruction. J. Biomech. Eng. 126(6):727–735, 2004.Google Scholar
  18. 18.
    Frakes, D., M. Fogel, J. Parks, S. Sharma, M. J. T. Smith, and A. P. Yoganathan. MRI-based 3D modeling of cardiac vascular anatomies for surgical applications. In: Proceedings of the American College of Cardiology Annual Scientific Session 2004, New Orleans, LA, March 2004.Google Scholar
  19. 19.
    Freitas, C. J. Journal of fluids engineering editorial policy statement on the control of numerical accuracy. J. Fluids Eng. 115:339–340, 1993.CrossRefGoogle Scholar
  20. 20.
    Freitas, C. J. Perspective: Selected benchmarks from commercial CFD codes. J. Fluids Eng. 117(2):208–218, 1995.Google Scholar
  21. 21.
    Freitas, C. J. The issue of numerical uncertainty. Appl. Math. Model. 26:237–248, 2002.MATHGoogle Scholar
  22. 22.
    Friesen, C. L. H., and J. M. Forbess. Surgical management of the single ventricle. Prog Pediatr. Cardiol. 16:47–68, 2002.Google Scholar
  23. 23.
    Ge, L., S. C. Jones, F. Sotiropoulos, T. M. Healy, and A. P. Yoganathan. Numerical simulation of flow in mechanical heart valves: Grid resolution and the assumption of flow symmetry. J. Biomech. Eng. 125(5):709–718, 2003.Google Scholar
  24. 24.
    Geva, T., D. J. Sahn, and A. J. Powell. Magnetic resonance imaging of congenital heart disease in adults. Prog. Pediatr. Cardiol. 17:21–39, 2003.Google Scholar
  25. 25.
    Guadagni, G., E. L. Bove, F. Migliavacca, and G. Dubini. Effects of pulmonary afterload on the hemodynamics after the hemi-Fontan procedure. Med. Eng. Phys. 23:293–298, 2001.Google Scholar
  26. 26.
    Guide for the Verification and Validation of Computational Fluid Dynamics Simulations. American Institute of Aeronautics and Astronautics (AIAA), 1998, G-077-1998.Google Scholar
  27. 27.
    Haas, G. S., H. Hess, M. Black, J. Onnasch, F. W. Mohr, and J. A. M. van Son. Extracardiac conduit Fontan procedure: Early and intermediate results. Eur. J. Cardiothorac. Surg. 17:648–654, 2000.Google Scholar
  28. 28.
    Haroutunian, V., M. S. Engelman, and I. Hasbani. Segregated finite element algorithms for the numerical solution of large-scale incompressible flow problems. Int. J. Numer. Methods Fluids 17:323–348, 1993.MATHGoogle Scholar
  29. 29.
    Healy, T. M., C. Lucas, and A. P. Yoganathan. Noninvasive fluid dynamic power loss assessments for total cavopulmonary connections using the viscous dissipation function: A feasibility study. J. Biomech. Eng. 123:317–324, 2001.Google Scholar
  30. 30.
    Hjortdal, V. E., K. Emmertsen, E. Stenbog, T. Frund, M. R. Schmidt, O. Kromann, K. Sorensen, and E. M. Pedersen. Effects of exercise and respiration on blood flow in total cavopulmonary connection. A real-time magnetic resonance flow study. Circulation 108:1227–1231, 2003.Google Scholar
  31. 31.
    Hughes, T. R. J., and A. N. Brooks. A multidimensional upwind scheme with no crosswind diffusion. In: Finite Element Methods for Convection Dominated Flows, edited by T. J. R. Hughes. ASME Press, New York, 1979, pp. 19–35.Google Scholar
  32. 32.
    Hughes, T. R. J., L. P. Franca, and M. Becestra. A new finite element formulation for computational fluid dynamics, V. Circumventing the Babuska-Brezzi conduction, A stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations. Comp. Meth. Appl. Mech. Eng. 59:85–99, 1986.MATHGoogle Scholar
  33. 33.
    California Institute of Technology. In: Proceedings of the International Biofluid Mechanics Conference, organized by S. Einav, R. Ethier, M. Gharib, R. Kamm, D. Liepsch, and A. P. Yoganathan. California Institute of Technology, December 12–14, 2003.Google Scholar
  34. 34.
    Iordanis, C., V. D. Butty, V. B. Makhijani, D. Poulikakos, and Y. Ventikos. Pulsatile blood flow in anatomically accurate vessels with multiple aneurysms: A medical intervention planning application of computational haemodynamics. Flow Turbul. Combust. 71:333–346, 2003.MATHGoogle Scholar
  35. 35.
    Jacobs, P. Stereolithography and Other RP&M Technologies. ASME Press, New York, 1996.Google Scholar
  36. 36.
    Johnston, B. M., P. R. Johnston, S. Corney, and D. Kilpatrick. Non-Newtonian blood flow in human right coronary arteries: Steady state simulations. J. Biomech. 37(5):709–720, 2004.Google Scholar
  37. 37.
    Karypis, G., and V. Kumar. MeTIS—A Software Package for Partitioning Unstructured Graphs, Partitioning Meshes and Computing Fill-Reducing Orderings of Sparse Matrices (Version 3.0). Minnesota: University of Minnesota, Department of Computer Science/Army HPC research center, October 1997.Google Scholar
  38. 38.
    Khunatron, Y., R. Shandas, C. DeGroff, and S. Mahalingam. Comparison of in vitro velocity measurements in a scaled total cavopulmonary connection with computational predictions. Ann. Biomed. Eng. 31:810–822, 2003.Google Scholar
  39. 39.
    Kim, Y. H., P. G. Walker, A. A. Fontaine, S. Panchal, A. E. Ensley, J. Oshinski, S. Sharma, B. Ha, C. L. Lucas, and A. P. Yoganathan. Hemodynamics of the Fontan connection: An in vitro study. J. Biomech. Eng. 117:423–428, 1995.Google Scholar
  40. 40.
    Ku, J. P., M. T. Draney, F. R. Arko, W. A. Lee, F. P. Chan, N. J. Pelc, C. K. Zarins, and C. A. Taylor. In vivo validation of numerical prediction of blood flow in arterial bypass grafts. Ann. Biomed. Eng. 30:743–752, 2002.Google Scholar
  41. 41.
    Laccarino, G. Predictions of a turbulent separated flow using commercial CFD codes. J. Fluids Eng. 123:819–828, 2001.Google Scholar
  42. 42.
    Liu, Y., K. Pekkan, S. C. Jones, and A. P. Yoganathan. The effects of different mesh generation methods on fluid dynamic analysis and power loss in total cavopulmonary connection (TCPC). J. Biomech. Eng. 126(5):594–603, 2004.Google Scholar
  43. 43.
    Masters, J. C., M. Ketner, M. S. Bleiweis, M. Mill, A. P. Yoganathan, and C. L. Lucas. The effect of incorporating vessel compliance in a computational model of blood flow in a total cavopulmonary connection (TCPC) with caval offset. J. Biomech. Eng. 2002.Google Scholar
  44. 44.
    Metcalfe, R. W. The promise of computational fluid dynamics as a tool for delineating therapeutic options in the treatment of aneurysms. AJNR Am. J. Neuroradiol. 24:553–554, 2003.Google Scholar
  45. 45.
    Migliavacca, F., G. Dubini, E. L. Bove, and M. R. de Leval. Computational fluid dynamics simulations in realistic 3-D geometries of the total cavopulmonary anastomosis: The influence of the inferior caval anastomosis. J. Biomech. Eng. 125:805–813, 2003.Google Scholar
  46. 46.
    Migliavacca, F., P. J. Kilner, G. Pennati, G. Dubini, R. Pietrabissa, R. Fumero, and M. R. de Leval. Computational fluid dynamic and magnetic resonance analyses of flow distribution between the lungs after total cavopulmonary connection. IEEE Trans. Bio. Eng. 46(4):393–399, 1999.Google Scholar
  47. 47.
    Moore, J. A., D. A. Steinman, S. Prakash, K. W. Johnston, and C. R. Either. A numerical study of blood flow patterns in anatomically realistic and simplified end-to-side anastomoses. J. Biomech. Eng. 121:265–272, 1999.Google Scholar
  48. 48.
    Nowak, N., P. P. Kakade, and A. V. Annapragada. Computational fluid dynamics simulation of airflow and aerosol deposition in human lungs. Ann. Biomed. Eng. 31:374–390, 2003.Google Scholar
  49. 49.
    Oshima, M., R. Torii, T. Kobayashi, N. Taniguchi, and K. Takagi. Finite element simulation of blood flow in the cerebral artery. Comput. Methods Appl. Mech. Eng. 191:661–671, 2001.MATHGoogle Scholar
  50. 50.
    Pekkan, K., D. A. de Zélicourt, and A. P. Yoganathan. In vitro flow visualization of a post-surgery total cavopulmonary connection anatomy, 21st Annual Gallery of Fluid Motion (movie). In: Proceedings of the Applied Physical Society Division of Fluid Dynamics 56th Annual Meeting, 2003.Google Scholar
  51. 51.
    Perot, B. Conservation properties of unstructured staggered mesh schemes. J. Comput. Phys. 159(1):58–59, 2000.MATHMathSciNetGoogle Scholar
  52. 52.
    Roache, P. J. Verification and Validation in Computational Science and Engineering. Albuquerque, New Mexico: Hermosa publishers, 1998.Google Scholar
  53. 53.
    Ryu, K., T. M. Healy, A. E. Ensley, S. Sharma, C. L. Lucas, and A. P. Yoganathan. Importance of accurate geometry in the study of the total cavopulmonary connection: Computational simulations and in vitro experiments. Ann. Biomed. Eng. 29:844–853, 2001.Google Scholar
  54. 54.
    Saber, N. R., A. D. Gosman, N. B. Wood, P. J. Kilner, C. L. Charrier, and D. N. Firmin. Computational flow modeling of the left ventricle based on in vivo MRI data: Initial experience. Ann. Biomed. Eng. 29:275–283, 2001.Google Scholar
  55. 55.
    Shahcheraghi, N., H. A. Dwyer, A. Y. Cheer, A. I. Barakat, and T. Rutaganira. Unsteady and three-dimensional simulation of blood flow in the human aortic arch. J. Biomech. Eng. 124:378–397, 2002.Google Scholar
  56. 56.
    Sharma, S., A. E. Ensley, K. Hopkins, G. P. Chatzimavroudis, T. M. Healy, V. H. K. Tam, K. R. Kanter, and A. P. Yoganathan. In vivo flow dynamics of the total cavopulmonary connection from three-dimensional multi slice magnetic resonance imaging. Ann. Thorac. Surg. 71:889–898, 2001.Google Scholar
  57. 57.
    Sheu, T. W. H., S. F. Tsai, W. S. Hwang, and T. M. Chang. A finite element study of the blood flow in total cavopulmonary connection. Comput. Fluids 28:19–39, 1999.MATHGoogle Scholar
  58. 58.
    Special issue on verification and validation in CFD. AIAA J. 36(5), 1998.Google Scholar
  59. 59.
    Swann, S. Integration of MRI and stereolithography to build medical models: A case study. Rapid Prototyp. J. 2(4):41–46, 1996.Google Scholar
  60. 60.
    Tang, H. S., S. C. Jones, and F. Sotiropoulos. An overset-grid method for 3D unsteady incompressible flows. J. Comput. Phys. 191(2):567–600, 2003.MATHGoogle Scholar
  61. 61.
    Thomas, J. B., J. S. Milner, B. K. Rutt, and D. A. Steinman. Reproducibility of image-based computational fluid dynamics models of the human carotid bifurcation. Ann. Biomed. Eng. 31:132–41, 2003.Google Scholar
  62. 62.
    NATO Advisory Group for Aeronautical Research and Development. Validation of Computational Fluid Dynamics. Portugal: NATO Advisory Group for Aeronautical Research and Development, AGARD CP 437, December 1988.Google Scholar
  63. 63.
    Van Haesdonck, J. M., L. Mertens, R. Sizaire, G. Montas, B. Purnode, W. Daenen, M. Crochet, and M. Gewling. Comparisons by computerized numeric modeling of energy losses in different Fontan connections. Circulation 92:322–326, 1995.Google Scholar
  64. 64.
    Verdonck, P. Guest Editorial, The role of computational fluid dynamics for artificial organ design. Artif. Organs 26(7):569–570, 2002.Google Scholar
  65. 65.
    Workshop, British Heart Foundation, Imperial College, London: Breaking Symmetry in Haemodynamics. Biorheology (Special Issue), 39(3–4):289–575, 2001.Google Scholar
  66. 66.
    Yedavalli, R. V., F. Loth, A. Yardimci, W. F. Pritchard, J. N. Oshinski, L. Sadler, F. Charbel, and N. Alperin. Construction of a physical model of the human carotid artery based upon in vivo magnetic resonance images. J. Biomech. Eng. 123:372–376, 2001.Google Scholar
  67. 67.
    Zhang, X., D., Schimdt, and B. Perot. Accuracy and conservation properties of a three-dimensional unstructured staggered mesh scheme for fluid dynamics. J. Comput. Phys. 175(2):764–791, 2002.MATHGoogle Scholar

Copyright information

© Biomedical Engineering Society 2005

Authors and Affiliations

  • Kerem Pekkan
    • 1
  • Diane de Zélicourt
    • 1
  • Liang Ge
    • 2
  • Fotis Sotiropoulos
    • 2
  • David Frakes
    • 1
  • Mark A. Fogel
    • 3
  • Ajit P. Yoganathan
    • 1
    • 4
  1. 1.Wallace H. Coulter Department of Biomedical EngineeringAtlanta
  2. 2.School of Civil and Environmental EngineeringGeorgia Institute of Technology
  3. 3.Division of CardiologyThe Children’s Hospital of Philadelphia
  4. 4.Wallace H. Coulter School of Biomedical EngineeringGeorgia Institute of Technology & Emory University

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