Cardiovascular Engineering and Technology

, Volume 6, Issue 3, pp 281–293 | Cite as

Quantitative Assessment of Turbulence and Flow Eccentricity in an Aortic Coarctation: Impact of Virtual Interventions

  • Magnus AnderssonEmail author
  • Jonas Lantz
  • Tino Ebbers
  • Matts Karlsson


Turbulence and flow eccentricity can be measured by magnetic resonance imaging (MRI) and may play an important role in the pathogenesis of numerous cardiovascular diseases. In the present study, we propose quantitative techniques to assess turbulent kinetic energy (TKE) and flow eccentricity that could assist in the evaluation and treatment of stenotic severities. These hemodynamic parameters were studied in a pre-treated aortic coarctation (CoA) and after several virtual interventions using computational fluid dynamics (CFD), to demonstrate the effect of different dilatation options on the flow field. Patient-specific geometry and flow conditions were derived from MRI data. The unsteady pulsatile flow was resolved by large eddy simulation including non-Newtonian blood rheology. Results showed an inverse asymptotic relationship between the total amount of TKE and degree of dilatation of the stenosis, where turbulent flow proximal the constriction limits the possible improvement by treating the CoA alone. Spatiotemporal maps of TKE and flow eccentricity could be linked to the characteristics of the jet, where improved flow conditions were favored by an eccentric dilatation of the CoA. By including these flow markers into a combined MRI–CFD intervention framework, CoA therapy has not only the possibility to produce predictions via simulation, but can also be validated pre- and immediate post treatment, as well as during follow-up studies.


Computational fluid dynamics Large eddy simulation Turbulent kinetic energy Flow displacement Non-Newtonian Carreau Virtual treatment Magnetic resonance imaging 



This research was supported by grants from the Swedish Research Council and the Center for Industrial Information Technology (CENIIT). We also like to acknowledge the Center of Medical Image Science and Visualization (CMIV, for providing necessary MRI data and the National Supercomputer Centre (NSC) for the computational resources via grants from the Swedish National Infrastructure for Computing (SNIC).

Conflict of interest

M. Karlsson received non-financial support from the Swedish National Infrastructure for Computing, T. Ebbers grants from the Center for Industrial Information Technology at Linköping University, the Swedish Research Council and the Swedish e-Science Research Center.

Statement of human studies

All procedures followed were in accordance with the ethical standards of the responsible committee on human experimentation (institutional and national) and with the Helsinki Declaration of 1975, as revised in 2000 (5). Informed consent was obtained from all patients for being included in the study.

Statement of animal studies

No animal studies were carried out by the authors for this article.

Supplementary material

13239_2015_218_MOESM1_ESM.pdf (32.5 mb)
Supplementary material 1 (PDF 33324 kb)

Supplementary material 2 (MPG 9509 kb)

Supplementary material 3 (MPG 1009 kb)


  1. 1.
    ANSYS® Academic Research, Release 14.0, Help System, CFX-Solver Modeling Guide, Ch. LES Timestep Considerations, ANSYS, Inc.Google Scholar
  2. 2.
    Arzani, A., P. Dyverfeldt, T. Ebbers, and S. C. Shadden. In vivo validation of numerical prediction for turbulence intensity in an aortic coarctation. Ann. Biomed. Eng. 4:860–870, 2012.CrossRefGoogle Scholar
  3. 3.
    Barker, A. J., M. Markl, J. Bürk, R. Lorenz, J. Bock, S. Bauer, J. Schulz-Menger, and F. von Knobelsdorff-Brenkenhoff. Bicuspid aortic valve is associated with altered wall shear stress in the ascending aorta. Circ. Cardiovasc. Imaging. 4:457–466, 2012.CrossRefGoogle Scholar
  4. 4.
    Baumgartner, H., P. Bonhoeffer, N. M. De Groot, F. de Haan, J. E. Deanfield, N. Galie, M. A. Gatzoulis, C. Gohlke-Baerwolf, H. Kaemmerer, P. Kilner, F. Meijboom, B. J. Mulder, E. Oechslin, J. M. Oliver, A. Serraf, A. Szatmari, E. Thaulow, P. R. Vouhe, E. Walma, Task Force on the Management of Grown-up Congenital Heart Disease of the European Society of Cardiology (ESC), Association for European Paediatric Cardiology (AEPC), and ESC Committee for Practice Guidelines (CPG). ESC guidelines for the management of grown-up congenital heart disease (new version 2010). Eur. Heart J. 23:2915–2957, 2010.Google Scholar
  5. 5.
    Binter, C., R. Manka, S. H. Sündermann, V. Knobloch, M. Stuber, and S. Kozerke. Assessment of energy loss in aortic stenosis using Bayesian multipoint phase-contrast MRI. J. Cardiovasc. Magn. Reson. 15(Suppl 1):P47, 2013.CrossRefGoogle Scholar
  6. 6.
    Caballero, A., and S. Laín. A review on computational fluid dynamics modelling in human thoracic aorta. Cardiovasc. Eng. Technol. 2:103–130, 2013.CrossRefGoogle Scholar
  7. 7.
    Carreau, P. J. Rheological equations from molecular network theories. Trans. Soc. Rheol. (1957–1977) 1:99–127, 1972.CrossRefGoogle Scholar
  8. 8.
    Cho, Y., and K. Kensey. Effects of the non-Newtonian viscosity of blood on flows in a diseased arterial vessel. Part 1: steady flows. Biorheology 3–4:241–262, 1990.Google Scholar
  9. 9.
    Cohen, M., V. Fuster, P. Steele, D. Driscoll, and D. McGoon. Coarctation of the aorta. Long-term follow-up and prediction of outcome after surgical correction. Circulation 4:840–845, 1989.CrossRefGoogle Scholar
  10. 10.
    Coogan, J. S., F. P. Chan, J. F. LaDisa, Jr, C. A. Taylor, F. L. Hanley, and J. A. Feinstein. Computational fluid dynamic simulations for determination of ventricular workload in aortic arch obstructions. J. Thorac. Cardiovasc. Surg. 2:489–495, 2013.CrossRefGoogle Scholar
  11. 11.
    Coogan, J. S., F. P. Chan, C. A. Taylor, and J. A. Feinstein. Computational fluid dynamic simulations of aortic coarctation comparing the effects of surgical-and stent-based treatments on aortic compliance and ventricular workload. Catheter Cardiovasc. Interv. 5:680–691, 2011.CrossRefGoogle Scholar
  12. 12.
    Coogan, J. S., J. D. Humphrey, and C. A. Figueroa. Computational simulations of hemodynamic changes within thoracic, coronary, and cerebral arteries following early wall remodeling in response to distal aortic coarctation. Biomech. Model. Mechanobiol. 1:79–93, 2013.CrossRefGoogle Scholar
  13. 13.
    Davidson, L. Large eddy simulations: how to evaluate resolution. Int. J. Heat Fluid Flow 5:1016–1025, 2009.CrossRefGoogle Scholar
  14. 14.
    den Reijer, P. M., D. Sallee III, P. van der Velden, E. R. Zaaijer, W. J. Parks, S. Ramamurthy, T. Q. Robbie, G. Donati, C. Lamphier, and R. P. Beekman. Hemodynamic predictors of aortic dilatation in bicuspid aortic valve by velocity-encoded cardiovascular magnetic resonance. J. Cardiovasc. Magn. Reson. 12:4, 2010. doi: 10.1186/1532-429X-12-4.
  15. 15.
    Dyverfeldt, P., M. D. Hope, E. E. Tseng, and D. Saloner. Magnetic resonance measurement of turbulent kinetic energy for the estimation of irreversible pressure loss in aortic stenosis. JACC Cardiovasc. Imaging 1:64–71, 2013.CrossRefGoogle Scholar
  16. 16.
    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 3:655–663, 2008.CrossRefGoogle Scholar
  17. 17.
    Faggiano, E., L. Antiga, G. Puppini, A. Quarteroni, G. B. Luciani, and C. Vergara. Helical flows and asymmetry of blood jet in dilated ascending aorta with normally functioning bicuspid valve. Biomech. Model. Mechanobiol. 4:801–813, 2013.CrossRefGoogle Scholar
  18. 18.
    Gårdhagen, R., F. Carlsson, and M. Karlsson. Large eddy simulation of pulsating flow before and after CoA repair: CFD for intervention planning. Adv. Mech. Eng., Article ID 971418, 2014.Google Scholar
  19. 19.
    Gårdhagen, R., J. Lantz, F. Carlsson, and M. Karlsson. Large eddy simulation of stenotic flow for wall shear stress estimation-validation and application. WSEAS Trans. Biol. Biomed. 3:86–101, 2011.Google Scholar
  20. 20.
    Goubergrits, L., R. Mevert, P. Yevtushenko, J. Schaller, U. Kertzscher, S. Meier, S. Schubert, E. Riesenkampff, and T. Kuehne. The impact of MRI-based Inflow for the hemodynamic evaluation of aortic coarctation. Ann. Biomed. Eng. 12:2575–2587, 2013.CrossRefGoogle Scholar
  21. 21.
    Hager, A., S. Kanz, H. Kaemmerer, C. Schreiber, and J. Hess. Coarctation Long-term Assessment (COALA): significance of arterial hypertension in a cohort of 404 patients up to 27 years after surgical repair of isolated coarctation of the aorta, even in the absence of restenosis and prosthetic material. J. Thorac. Cardiovasc. Surg. 3:738–745, 2007.CrossRefGoogle Scholar
  22. 22.
    Hathcock, J. J. Flow effects on coagulation and thrombosis. Arterioscler. Thromb. Vasc. Biol. 8:1729–1737, 2006.CrossRefGoogle Scholar
  23. 23.
    Heiberg, E., J. Sjogren, M. Ugander, M. Carlsson, H. Engblom, and H. Arheden. Design and validation of segment-freely available software for cardiovascular image analysis. BMC Med. Imaging 10:1, 2010.CrossRefGoogle Scholar
  24. 24.
    Hope, M. D., T. Sedlic, and P. Dyverfeldt. Cardiothoracic magnetic resonance flow imaging. J. Thorac. Imaging 4:217–230, 2013.CrossRefGoogle Scholar
  25. 25.
    Hope, M. D., J. Wrenn, M. Sigovan, E. Foster, E. E. Tseng, and D. Saloner. Imaging biomarkers of aortic disease: increased growth rates with eccentric systolic flow. J. Am. Coll. Cardiol. 4:356–357, 2012.CrossRefGoogle Scholar
  26. 26.
    Jackson, S. P., W. S. Nesbitt, and E. Westein. Dynamics of platelet thrombus formation. J. Thromb. Haemost. 7:17–20, 2009.CrossRefGoogle Scholar
  27. 27.
    Karino, T., and H. Goldsmith. Role of blood cell-wall interactions in thrombogenesis and atherogenesis: a microrheological study. Biorheology 4:587–601, 1983.Google Scholar
  28. 28.
    Kefayati, S., D. W. Holdsworth, and T. L. Poepping. Turbulence intensity measurements using particle image velocimetry in diseased carotid artery models: effect of stenosis severity, plaque eccentricity, and ulceration. J. Biomech. 1:253–263, 2014.CrossRefGoogle Scholar
  29. 29.
    Kim, H. J., I. E. Vignon-Clementel, C. A. Figueroa, J. 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. 11:2153–2169, 2009.CrossRefGoogle Scholar
  30. 30.
    Kwon, S., J. A. Feinstein, R. J. Dholakia, and J. F. LaDisa Jr. Quantification of local hemodynamic alterations caused by virtual implantation of three commercially available stents for the treatment of aortic coarctation. Pediatr. Cardiol. 35:732–740, 2014.Google Scholar
  31. 31.
    Ladisa, J. F., C. A. Figueroa, I. E. Vignon-Clementel, H. J. Kim, N. Xiao, L. M. Ellwein, F. P. Chan, J. A. Feinstein, and C. A. Taylor. Computational simulations for aortic coarctation: representative results from a sampling of patients. J. Biomech. Eng. 9:091008, 2011.CrossRefGoogle Scholar
  32. 32.
    Lantz, J., T. Ebbers, J. Engvall, and M. Karlsson. Numerical and experimental assessment of turbulent kinetic energy in an aortic coarctation. J. Biomech. 11:1851–1858, 2013.CrossRefGoogle Scholar
  33. 33.
    Lantz, J., R. Gårdhagen, and M. Karlsson. Quantifying turbulent wall shear stress in a subject specific human aorta using large eddy simulation. Med. Eng. Phys. 8:1139–1148, 2012.CrossRefGoogle Scholar
  34. 34.
    Lantz, J., and M. Karlsson. Large eddy simulation of LDL surface concentration in a subject specific human aorta. J. Biomech. 3:537–542, 2011.Google Scholar
  35. 35.
    Liu, J., S. Chu, and P. Lu. Turbulence characteristics downstream of bileaflet aortic valve prostheses. J. Biomech. Eng. 2:118–124, 2000.CrossRefGoogle Scholar
  36. 36.
    Markl, M., P. J. Kilner, and T. Ebbers. Comprehensive 4D velocity mapping of the heart and great vessels by cardiovascular magnetic resonance. J. Cardiovasc. Magn. Reson. 7:1–22, 2011.Google Scholar
  37. 37.
    Marrero, V. L., J. A. Tichy, O. Sahni, and K. E. Jansen. Numerical study of purely viscous non-Newtonian flow in an abdominal aortic aneurysm. J. Biomech. Eng. 10:101001, 2014.CrossRefGoogle Scholar
  38. 38.
    Menon, A., D. C. Wendell, H. Wang, T. J. Eddinger, J. M. Toth, R. J. Dholakia, P. M. Larsen, E. S. Jensen, and J. F. LaDisa, Jr. A coupled experimental and computational approach to quantify deleterious hemodynamics, vascular alterations, and mechanisms of long-term morbidity in response to aortic coarctation. J. Pharmacol. Toxicol. Methods 1:18–28, 2012.CrossRefGoogle Scholar
  39. 39.
    Mittal, R., S. Simmons, and F. Najjar. Numerical study of pulsatile flow in a constricted channel. J. Fluid Mech. 485:337–378, 2003.zbMATHCrossRefGoogle Scholar
  40. 40.
    Molla, M. M., and M. C. Paul. LES of non-Newtonian physiological blood flow in a model of arterial stenosis. Med. Eng. Phys. 8:1079–1087, 2012.CrossRefGoogle Scholar
  41. 41.
    Nichols, W., M. O’Rourke, and C. Vlachopoulos. McDonald’s Blood Flow in Arteries: Theoretical, Experimental and Clinical Principles. New York: CRC Press, pp. 52–54, 2011.Google Scholar
  42. 42.
    Nicoud, F., and F. Ducros. Subgrid-scale stress modelling based on the square of the velocity gradient tensor. Flow Turbul. Combust. 3:183–200, 1999.CrossRefGoogle Scholar
  43. 43.
    O’Rourke, M. F., and T. B. Cartmill. Influence of aortic coarctation on pulsatile hemodynamics in the proximal aorta. Circulation 2:281–292, 1971.CrossRefGoogle Scholar
  44. 44.
    Ou, P., E. Mousseaux, D. S. Celermajer, E. Pedroni, P. Vouhe, D. Sidi, and D. Bonnet. Aortic arch shape deformation after coarctation surgery: effect on blood pressure response. J. Thorac. Cardiovasc. Surg. 5:1105–1111, 2006.CrossRefGoogle Scholar
  45. 45.
    Paul, M. C., M. Mamun Molla, and G. Roditi. Large–Eddy simulation of pulsatile blood flow. Med. Eng. Phys. 1:153–159, 2009.CrossRefGoogle Scholar
  46. 46.
    Peacock, J., T. Jones, C. Tock, and R. Lutz. The onset of turbulence in physiological pulsatile flow in a straight tube. Exp. Fluids 1:1–9, 1998.CrossRefGoogle Scholar
  47. 47.
    Rosenthal, E. Coarctation of the aorta from fetus to adult: curable condition or life long disease process? Heart 11:1495–1502, 2005.CrossRefGoogle Scholar
  48. 48.
    Ryval, J., D. Steinman, and A. Straatman. Two-equation turbulence modeling of pulsatile flow in a stenosed tube. J. Biomech. Eng. 5:625–635, 2004.CrossRefGoogle Scholar
  49. 49.
    Scotti, A., and U. Piomelli. Turbulence models in pulsating flows. AIAA J. 3:537–544, 2002.CrossRefGoogle Scholar
  50. 50.
    Sigovan, M., M. D. Hope, P. Dyverfeldt, and D. Saloner. Comparison of four-dimensional flow parameters for quantification of flow eccentricity in the ascending aorta. J. Magn. Reson. Imaging 5:1226–1230, 2011.CrossRefGoogle Scholar
  51. 51.
    Tennekes, H., and J. L. Lumley. A First Course in Turbulence. Cambridge: MIT Press, 1972.Google Scholar
  52. 52.
    Toro-Salazar, O. H., J. Steinberger, W. Thomas, A. P. Rocchini, B. Carpenter, and J. H. Moller. Long-term follow-up of patients after coarctation of the aorta repair. Am. J. Cardiol. 5:541–547, 2002.CrossRefGoogle Scholar
  53. 53.
    Varghese, S. S., S. H. Frankel, and P. F. Fischer. Direct numerical simulation of stenotic flows. Part 2. Pulsatile flow. J. Fluid Mech. 582:281–318, 2007.zbMATHMathSciNetCrossRefGoogle Scholar
  54. 54.
    Versteeg, H. K., and W. Malalasekera. An Introduction to Computational Fluid Dynamics: The Finite Volume Method. Harlow: Pearson Education, pp. 49–50, 2007.Google Scholar
  55. 55.
    Viscardi, F., C. Vergara, L. Antiga, S. Merelli, A. Veneziani, G. Puppini, G. Faggian, A. Mazzucco, and G. B. Luciani. Comparative finite element model analysis of ascending aortic flow in bicuspid and tricuspid aortic valve. Artif. Organs 12:1114–1120, 2010.CrossRefGoogle Scholar
  56. 56.
    Vriend, J. W., and B. J. Mulder. Late complications in patients after repair of aortic coarctation: implications for management. Int. J. Cardiol. 3:399–406, 2005.CrossRefGoogle Scholar
  57. 57.
    Wendell, D. C., M. M. Samyn, J. R. Cava, L. M. Ellwein, M. M. Krolikowski, K. L. Gandy, A. N. Pelech, S. C. Shadden, and J. F. LaDisa, Jr. Including aortic valve morphology in computational fluid dynamics simulations: initial findings and application to aortic coarctation. Med. Eng. Phys. 6:723–735, 2013.CrossRefGoogle Scholar
  58. 58.
    Wentzel, J. J., R. Corti, Z. A. Fayad, P. Wisdom, F. Macaluso, M. O. Winkelman, V. Fuster, and J. J. Badimon. Does shear stress modulate both plaque progression and regression in the thoracic aorta? Human study using serial magnetic resonance imaging. J. Am. Coll. Cardiol. 6:846–854, 2005.CrossRefGoogle Scholar
  59. 59.
    Yoganathan, A. P., K. Chandran, and F. Sotiropoulos. Flow in prosthetic heart valves: state-of-the-art and future directions. Ann. Biomed. Eng. 12:1689–1694, 2005.CrossRefGoogle Scholar
  60. 60.
    Zajac, J., J. Eriksson, P. Dyverfeldt, A. F. Bolger, T. Ebbers, and C. Carlhäll. Turbulent kinetic energy in normal and myopathic left ventricles. J. Magn. Reson. Imaging. in press. doi: 10.1002/jmri.24633.
  61. 61.
    Zamir, M., P. Sinclair, and T. H. Wonnacott. Relation between diameter and flow in major branches of the arch of the aorta. J. Biomech. 11:1303–1310, 1992.CrossRefGoogle Scholar

Copyright information

© Biomedical Engineering Society 2015

Authors and Affiliations

  • Magnus Andersson
    • 1
    • 5
    Email author
  • Jonas Lantz
    • 2
    • 5
  • Tino Ebbers
    • 2
    • 3
    • 4
    • 5
  • Matts Karlsson
    • 1
    • 4
    • 5
  1. 1.Department of Management and Engineering (IEI)Linköping UniversityLinköpingSweden
  2. 2.Department of Science and TechnologyLinköping UniversityLinköpingSweden
  3. 3.Department of Medical and Health SciencesLinköping UniversityLinköpingSweden
  4. 4.Center for Medical Image Science and Visualization (CMIV)Linköping UniversityLinköpingSweden
  5. 5.Swedish e-Science Research Center (SeRC)StockholmSweden

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