Annals of Biomedical Engineering

, Volume 40, Issue 4, pp 860–870 | Cite as

In Vivo Validation of Numerical Prediction for Turbulence Intensity in an Aortic Coarctation

  • Amirhossein Arzani
  • Petter Dyverfeldt
  • Tino Ebbers
  • Shawn C. Shadden
Article

Abstract

This paper compares numerical predictions of turbulence intensity with in vivo measurement. Magnetic resonance imaging (MRI) was carried out on a 60-year-old female with a restenosed aortic coarctation. Time-resolved three-directional phase-contrast (PC) MRI data was acquired to enable turbulence intensity estimation. A contrast-enhanced MR angiography (MRA) and a time-resolved 2D PCMRI measurement were also performed to acquire data needed to perform subsequent image-based computational fluid dynamics (CFD) modeling. A 3D model of the aortic coarctation and surrounding vasculature was constructed from the MRA data, and physiologic boundary conditions were modeled to match 2D PCMRI and pressure pulse measurements. Blood flow velocity data was subsequently obtained by numerical simulation. Turbulent kinetic energy (TKE) was computed from the resulting CFD data. Results indicate relative agreement (error ≈10%) between the in vivo measurements and the CFD predictions of TKE. The discrepancies in modeled vs. measured TKE values were within expectations due to modeling and measurement errors.

Keywords

Computational fluid dynamics Phase-contrast magnetic resonance imaging Turbulent kinetic energy Blood flow 

References

  1. 1.
    Boussel, L., V. Rayz, A. Martin, G. Acevedo-Bolton, M. T. Lawton, R. Higashida, W. S. Smith, W. L. Young, and D. Saloner. Phase-contrast magnetic resonance imaging measurements in intracranial aneurysms in vivo of flow patterns, velocity fields, and wall shear stress: comparison with computational fluid dynamics. Magn. Reson. Med. 61(2):409–417, 2009.PubMedCrossRefGoogle Scholar
  2. 2.
    Deissler, R. G. Turbulent Fluid Motion. Philadelphia: Taylor and Francis, 1998.Google Scholar
  3. 3.
    Dyverfeldt, P., R. Gardhagen, A. Sigfridsson, M. Karlsson, and T. Ebbers. On MRI turbulence quantification. Magn. Reson. Med. 27(7):913–922, 2009.Google Scholar
  4. 4.
    Dyverfeldt, P., J. P. E. Kvitting, A. Sigfridsson, J. Engvall, A. F. Bolger, and T. Ebbers. Assessment of fluctuating velocities in disturbed cardiovascular blood flow: in vivo feasibility of generalized phase-contrast MRI. J. Magn. Reson Imaging 28(3):655–663, 2008.PubMedCrossRefGoogle Scholar
  5. 5.
    Dyverfeldt, P., A. Sigfridsson, J. P. E. Kvitting, and T. Ebbers. Quantification of intravoxel velocity standard deviation and turbulence intensity by generalizing phase-contrast MRI. Magn. Reson. Med. 56(4):850–858, 2006.PubMedCrossRefGoogle Scholar
  6. 6.
    Elkins, C., M. Alley, L. Saetran, and J. Eaton. Three-dimensional magnetic resonance velocimetry measurements of turbulence quantities in complex flow. Exp. Fluids 46(2):285–296, 2009.CrossRefGoogle Scholar
  7. 7.
    Firmin, D. N., P. D. Gatehouse, J. P. Konrad, G. Z. Yang, P. J. Kilner, and D. B. Longmore. Rapid 7-dimensional imaging of pulsatile flow. In: Proceedings in Computers in Cardiology, 1993.Google Scholar
  8. 8.
    Ford, M. D., H. N. Nikolov, J. S. Milner, S. P. Lownie, E. M. DeMont, W. Kalata, F. Loth, D. W. Holdsworth, and D. A. Steinman. Virtual angiography for visualization and validation of computational models of aneurysm hemodynamics. IEEE Trans. Med. Imaging 24(12):1586–1592, 2005PubMedCrossRefGoogle Scholar
  9. 9.
    Ford, M. D., G. R. Stuhne, H. N. Nikolov, D. F. Habets, S. P. Lownie, D. W. Holdsworth, and D. A. Steinman. PIV-measured versus CFD-predicted flow dynamics in anatomically realistic cerebral aneurysm models. J. Biomech. Eng. 130(2):021015, 2008.PubMedCrossRefGoogle Scholar
  10. 10.
    Gao, J., and J. C. Gore. Turbulent flow effects on NMR imaging: measurement of turbulent intensity. Med. Phys. 18(5):1045–1051, 1991.PubMedCrossRefGoogle Scholar
  11. 11.
    Gatenby, J. C., T. R. McCauley, and J. C. Gore. Mechanisms of signal loss in magnetic resonance imaging of stenoses. Med. Phys. 20(4):1049–1057, 1993.PubMedCrossRefGoogle Scholar
  12. 12.
    Hoi, Y., S. H. Woodward, M. Kim, D. B. Taulbee, and H. Meng. Validation of CFD simulations of cerebral aneurysms with implication of geometric variations. J. Biomech. Eng. 128(6):844–851, 2006.PubMedCrossRefGoogle Scholar
  13. 13.
    Jansen, K. E., C. H. Whiting, and G. M. Hulbert. Generalized-alpha method for integrating the filtered Navier-Stokes equations with a stabilized finite element method. Comput. Methods Appl. Mech. Eng. 190(3):305–319, 2000.CrossRefGoogle Scholar
  14. 14.
    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
  15. 15.
    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. Validation of numerical prediction of blood flow in arterial bypass grafts. Ann. Biomed. Eng. 30(6):743–752, 2002.PubMedCrossRefGoogle Scholar
  16. 16.
    Ku, J. P., C. J. Elkins, and C. A. Taylor. Comparison of CFD and MRI flow and velocities in an in vitro large artery bypass graft mode. Ann. Biomed. Eng. 33(3):257–269, 2005.PubMedCrossRefGoogle Scholar
  17. 17.
    Kung, E. O., A. S. Les, C. A. Figueroa, F. Medina, K. Arcaute, R. B. Wicker, M. V. McConnell, and C. A. Taylor. In vitro validation of finite element analysis of blood flow in deformable models. Ann. Biomed. Eng. 39:1947–1960, 2011.Google Scholar
  18. 18.
    Kung, E. O., A. S. Les, F. Medina, R. B. Wicker, M. V. McConnell, and C. A. Taylor. In vitro validation of finite-element model of AAA hemodynamics incorporating realistic outlet boundary conditions. J. Biomech. Eng. 133(4):041003, 2011.PubMedCrossRefGoogle Scholar
  19. 19.
    LaDisa, J. F., Jr., R. J. Dholakia, C. A. Figueroa, I. E. Vignon-Clementel, F. P. Chan, M. M. Samyn, J. R. Cava, C. A. Taylor, and J. A. Feinstein. Computational simulations demonstrate altered wall shear stress in aortic coarctation patients previously treated by resection with end-to-end anastomosis. Congenit. Heart Dis. 6(5):432–443, 2011.PubMedCrossRefGoogle Scholar
  20. 20.
    LaDisa, J. F., C. A. Taylor, and F. A. Jeffrey FA. Aortic coarctation: recent developments in experimental and computational methods to assess treatments for this simple condition. Prog. Pediatr. Cardiol. 30(1–2):45–49, 2010.PubMedCrossRefGoogle Scholar
  21. 21.
    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
  22. 22.
    Les, A. S., S. C. Shadden, C. A. Figueroa, J. M. Park, M. M. Tedesco, R. J. Herfkens, R. L. Dalman, and C. A. Taylor. Quantification of hemodynamics in abdominal aortic aneurysms during rest and exercise using magnetic resonance imaging and computational fluid dynamics. Ann. Biomed. Eng. 38:1288–1313, 2010.PubMedCrossRefGoogle Scholar
  23. 23.
    Marshall, I., S. Zhao, P. Papathanasopoulou, P. Hoskins, X. Y. Xu. MRI and CFD studies of pulsatile flow in healthy and stenosed carotid bifurcation models. J. Biomech. 37(5):679–687, 2004.PubMedCrossRefGoogle Scholar
  24. 24.
    Morris, L., P. Delassus, A. Callanan, M. Walsh, F. Wallis, P. Grace, and T. McGloughlin T. 3-D numerical simulation of blood flow through models of the human aorta. J. Biomech. Eng. 127(5):767–775, 2005.PubMedCrossRefGoogle Scholar
  25. 25.
    Nichols, W. W., and M. F. O’Rourke. McDonald’s Blood Flow in Arteries: Theoretical, Experimental and Clinical Principles. London: Hodder Arnold Publication, 2005.Google Scholar
  26. 26.
    Papathanasopoulou, P., S. Zhao, U. Kohler, M. B. Robertson, Q. Long, P. Hoskins, X. Y. Xu, and I. Marshall. MRI measurement of time-resolved wall shear stress vectors in a carotid bifurcation model, and comparison with CFD predictions. J. Magn. Reson. Imaging 17(2):153–162, 2003.PubMedCrossRefGoogle Scholar
  27. 27.
    Petersson, S., P. Dyverfeldt, R. Gardhagen, M. Karlsson, and T. Ebbers. Simulation of phase contrast MRI of turbulent flow. Magn. Reson. Med. 64(4):1039–1046, 2010.PubMedCrossRefGoogle Scholar
  28. 28.
    Rayz, V. L., L. Boussel, G. Acevedo-Bolton, A. J. Martin, W. L. Young, M. T. Lawton, R. Higashida, and D. Saloner. Numerical simulations of flow in cerebral aneurysms: comparison of CFD results and in vivo MRI measurements. J. Biomech. Eng. 130(5):051011, 2008.PubMedCrossRefGoogle Scholar
  29. 29.
    Richter, Y., and E. R. Elazer. Cardiology is flow. Circulation 113(23):2679–2682, 2006.PubMedCrossRefGoogle Scholar
  30. 30.
    Seed, W. A., and N. B. Wood. Velocity patterns in the aorta. Cardiovasc. Res. 5(3):319–330, 1971.PubMedCrossRefGoogle Scholar
  31. 31.
    Steinman, D. A., C. R. Ethier, and B. K. Rutt. Combined analysis of spatial and velocity displacement artifacts in phase contrast measurements of complex flows. J. Magn. Reson. Imaging 7(2):339–346, 1997.PubMedCrossRefGoogle Scholar
  32. 32.
    Stergiopulos, N., J. Meister, and N. Westerhof. Simple and accurate way for estimating total and segmental arterial compliance: the pulse pressure method. Ann. Biomed. Eng. 22:392–397, 1994.PubMedCrossRefGoogle Scholar
  33. 33.
    Stergiopulos, N., D. F. Young, and T. R. Rogge. Computer simulation of arterial flow with applications to arterial and aortic stenoses. J. Biomech. 25(12):1477–1488, 1992.PubMedCrossRefGoogle Scholar
  34. 34.
    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.PubMedCrossRefGoogle Scholar
  35. 35.
    Taylor, C. A., and C. A. Figueroa CA. Patient-specific modeling of cardiovascular mechanics. Annu. Rev. Biomed. Eng. 11(1):109–134, 2009.PubMedCrossRefGoogle Scholar
  36. 36.
    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
  37. 37.
    Taylor, C. A., and D. A. Steinman. Image-based modeling of blood flow and vessel wall dynamics: applications, methods and future directions. Ann. Biomed. Eng. 38(3):1188–1203, 2010.PubMedCrossRefGoogle Scholar
  38. 38.
    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
  39. 39.
    Wigstrom, L., L. Sjoqvist, and B. Wranne B. Temporally resolved 3D phase-contrast imaging. Magn. Reson. Med. 36(5):800–803, 1996.PubMedCrossRefGoogle Scholar
  40. 40.
    Wilson, N., K. Wang, R. Dutton, and C. A. Taylor. A software framework for creating patient specific geometric models from medical imaging data for simulation based medical planning of vascular surgery. Lect. Notes Comput. Sci. 2208:449–456, 2001.CrossRefGoogle Scholar
  41. 41.
    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.PubMedCrossRefGoogle Scholar

Copyright information

© Biomedical Engineering Society 2011

Authors and Affiliations

  • Amirhossein Arzani
    • 1
  • Petter Dyverfeldt
    • 2
    • 3
    • 5
  • Tino Ebbers
    • 2
    • 3
    • 4
  • Shawn C. Shadden
    • 1
  1. 1.Department of Mechanical, Materials and Aerospace EngineeringIllinois Institute of TechnologyChicagoUSA
  2. 2.Division of Applied Thermodynamics and Fluid Mechanics, Department of Management and EngineeringLinköping UniversityLinköpingSweden
  3. 3.Center for Medical Image Science and Visualization (CMIV)Linköping UniversityLinköpingSweden
  4. 4.Division of Cardiovascular Medicine, Department of Medical and Health SciencesLinköping UniversityLinköpingSweden
  5. 5.Department of Radiology and Biomedical ImagingUniversity of California San FranciscoSan FranciscoUSA

Personalised recommendations