Flow, Turbulence and Combustion

, Volume 102, Issue 1, pp 3–26 | Cite as

High Resolution Simulation of Diastolic Left Ventricular Hemodynamics Guided by Four-Dimensional Flow Magnetic Resonance Imaging Data

  • Trung Bao Le
  • Mohammed S. M. Elbaz
  • Rob J. Van Der Geest
  • Fotis SotiropoulosEmail author


We investigate the diastolic hemodynamics in a patient-specific left ventricle (LV) of a healthy subject using four dimensional flow magnetic resonance imaging (4D-Flow MRI) measurement and numerical simulation. From four dimensional Cardiac Magnetic Resonance (CMR) Imaging data, the kinematics of the endocardium is reconstructed. The endocardial kinematics and the time varying velocity distribution from 4D-Flow MRI at the mitral orifice are prescribed as boundary conditions for the numerical simulation. Both 4D-Flow MRI data and numerical results show the classical formation of the mitral vortex ring (MVR) during E-wave filling. The in-vivo data reveals that a large three-dimensional vortex structure forms near in the mid-level region of LV during diastasis (mid-level vortex). This mid-level vortex is formed simultaneously with the MVR and has not been reported in the literature. Quantitative comparison shows that the computed kinetic energy (KE) evolves in a similar manner to one derived from 4D-Flow MRI data during early E-wave filling. Both computational and measurement data show that the peak KE at E-wave is approximately 8 mJ. Our results suggest that numerical simulation can be used to provide useful hemodynamic data given the inputs from 4D-Flow MRI, which is now available in clinical practice. However, further investigation is needed to understand the formation mechanism of the mid-level vortex and its implication on the end-diastolic flow pattern.


Left ventricle 4D-Flow MRI Vortex ring Immersed boundary method 



We acknowledge the support of computational time from the Minnesota Supercomputing Institute (University of Minnesota) and the Institute for Advanced Computational Science (Stony Brook University). The lead author (Trung Bao Le) acknowledges the support for the computational time from the Director’s Discretionary Allocation of of Argonne Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC02-06CH11357.

Ethical Statements

This work was supported by Leilei Institute of Heart at the University of Minnesota. The authors declare that they have no conflict of interest.


  1. 1.
    Faludi, R., Szulik, M., D’hooge, J., Herijgers, P., Rademakers, F., Pedrizzetti, G., Voigt, J.U.: Left ventricular flow patterns in healthy subjects and patients with prosthetic mitral valves: an in vivo study using echocardiographic particle image velocimetry. J. Thorac. Cardiovasc Surg. 139(6), 1501–1510 (2010)CrossRefGoogle Scholar
  2. 2.
    Gharib, M., Rambod, E., Kheradvar, A., Sahn, D.J., Dabiri, J.O.: Optimal vortex formation as an index of cardiac health. Proc. Natl. Acad. Sci. 103(16), 6305–6308 (2006)CrossRefGoogle Scholar
  3. 3.
    Calkoen, E.E., Elbaz, M.S., Westenberg, J.J., Kroft, L.J., Hazekamp, M.G., Roest, A.A., van der Geest, R.J.: Altered left ventricular vortex ring formation by 4-dimensional flow magnetic resonance imaging after repair of atrioventricular septal defects. J. Thorac. Cardiovasc. Surg. 150(5), 1233–1240 (2015)CrossRefGoogle Scholar
  4. 4.
    Elbaz, M.S., van der Geest, R.J., Calkoen, E.E., de Roos, A., Lelieveldt, B.P., Roest, A.A., Westenberg, J.J.: Assessment of viscous energy loss and the association with three-dimensional vortex ring formation in left ventricular inflow: in vivo evaluation using four-dimensional flow MRI. Magn. Reson. Med. 77(2), 794–805 (2017)CrossRefGoogle Scholar
  5. 5.
    Stewart, K.C., Charonko, J.C., Niebel, C.L., Little, W.C., Vlachos, P.P.: Left ventricle filling vortex formation is unaffected by diastolic impairment. Am. J. Physiol. Heart Circ. Physiol. 303, H1255–H1262 (2012)CrossRefGoogle Scholar
  6. 6.
    Sotiropoulos, F., Le, T.B., Gilmanov, A.: Fluid mechanics of heart valves and their replacements. Annu. Rev. Fluid Mech. 48, 259–283 (2016)Google Scholar
  7. 7.
    Elbaz, M.S., Calkoen, E.E., Westenberg, J.J., Lelieveldt, B.P., Roest, A.A., van der Geest, R.J.: Vortex flow during early and late left ventricular filling in normal subjects: quantitative characterization using retrospectively-gated 4D flow cardiovascular magnetic resonance and three-dimensional vortex core analysis. J. Cardiovasc. Magn. Reson. 16(1), 78 (2014)CrossRefGoogle Scholar
  8. 8.
    Zajac, J., Eriksson, J., Dyverfeldt, P., Bolger, A.F., Ebbers, T., Carlhäll, C.J.: Turbulent kinetic energy in normal and myopathic left ventricles. J. Magn. Reson. Imaging 41(4), 1021–1029 (2015)CrossRefGoogle Scholar
  9. 9.
    Carlsson, M., Heiberg, E., Toger, J., Arheden, H.: Quantification of left and right ventricular kinetic energy using four-dimensional intracardiac magnetic resonance imaging flow measurements. Am. J. Physiol. Heart Circ. Physiol. 302(4), H893–H900 (2011)CrossRefGoogle Scholar
  10. 10.
    Dyverfeldt, P., Bissell, M., Barker, A.J., Bolger, A.F., Carlhäll, C.J., Ebbers, T., Francios, C.J., Frydrychowicz, A., Geiger, J., Giese, D., Hope, M.D.: 4D flow cardiovascular magnetic resonance consensus statement. J. Cardiovasc. Magn. Reson. 17(1), 72 (2015)CrossRefGoogle Scholar
  11. 11.
    Okafor, I.U., Santhanakrishnan, A., Chaffins, B.D., Mirabella, L., Oshinski, J.N., Yoganathan, A.P.: Cardiovascular magnetic resonance compatible physical model of the left ventricle for multi-modality characterization of wall motion and hemodynamics. J. Cardiovasc. Magn. Reson. 17(1), 51 (2015)CrossRefGoogle Scholar
  12. 12.
    Schenkel, T., Malve, M., Reik, M., Markl, M., Jung, B., Oertel, H.: MRI-based CFD analysis of flow in a human left ventricle: methodology and application to a healthy heart. Ann. Biomed. Eng. 37(3), 503–515 (2009)CrossRefGoogle Scholar
  13. 13.
    Nguyen, V.T., Wibowo, S.N., Leow, Y.A., Nguyen, H.H., Liang, Z., Leo, H.L.: A patient-specific computational fluid dynamic model for hemodynamic analysis of left ventricle diastolic dysfunctions. Cardiovasc. Eng. Technol. 6(4), 412–429 (2015)CrossRefGoogle Scholar
  14. 14.
    Chnafa, C., Mendez, S., Nicoud, F.: Image-based large-eddy simulation in a realistic left heart. Comput. Fluids 94, 173–187 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Vedula, V., Seo, J.H., Lardo, A.C., Mittal, R.: Effect of trabeculae and papillary muscles on the hemodynamics of the left ventricle. Theor. Comput. Fluid Dyn. 30(1-2), 3–21 (2014)CrossRefGoogle Scholar
  16. 16.
    Acharya, U.R., Joseph, K.P., Kannathal, N., Min, L.C., Suri, J.S.: Heart rate variability. In: Advances in cardiac signal processing, pp 121–165. Springer, Berlin (2007)Google Scholar
  17. 17.
    Su, B., San Tan, R., Le Tan, J., Guo, K.W. Q., Zhang, J.M., Leng, S., Zhao, X., Allen, J.C., Zhong, L.: Cardiac MRI based numerical modeling of left ventricular fluid dynamics with mitral valve incorporated. J. Biomech. 49(7), 1199–1205 (2016)CrossRefGoogle Scholar
  18. 18.
    Klein, S., Staring, M., Murphy, K., Viergever, M.A., Pluim, J.P.: Elastix: a toolbox for intensity-based medical image registration. IEEE Trans. Med. Imaging 29(1), 196–205 (2010)CrossRefGoogle Scholar
  19. 19.
    Westenberg, J.J., Roes, S.D., Ajmone Marsan, N., Binnendijk, N.M., Doornbos, J., Bax, J.J., Reiber, J.H., De Roos, A., van der Geest, R.J.: Mitral valve and tricuspid valve blood flow: accurate quantification with 3D velocity-encoded MR imaging with retrospective valve tracking. Radiology 249(3), 792–800 (2008)CrossRefGoogle Scholar
  20. 20.
    Long, Q., Merrifield, R., Yang, G.Z., Xu, X.Y., Kilner, P.J., Firmin, D.N.: The influence of inflow boundary conditions on intra left ventricle flow predictions. J. Biomech. Eng. 125(6), 922–927 (2003)CrossRefGoogle Scholar
  21. 21.
    Jung, B., Markl, M., Föll, D., Hennig, J.: Investigating myocardial motion by MRI using tissue phase mapping. Eur. J. Cardiothorac. Surg. 29(Supplement_1), S150–S157 (2006)CrossRefGoogle Scholar
  22. 22.
    Chnafa, C., Mendez, S., Nicoud, F.: Image-based simulations show important flow fluctuations in a normal left ventricle: what could be the implications? Ann. Biomed. Eng. 44(11), 3346–3358 (2016)CrossRefGoogle Scholar
  23. 23.
    Ge, L., Sotiropoulos, F.: A numerical method for solving the 3D unsteady incompressible Navier–Stokes equations in curvilinear domains with complex immersed boundaries. J. Comput. Phys. 225(2), 1782–1809 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Le, T. B., Borazjani, I., Kang, S., Sotiropoulos, F.: On the structure of vortex rings from inclined nozzles. J. Fluid Mech. 686, 451–483 (2011)Google Scholar
  25. 25.
    Gilmanov, A., Le, T.B., Sotiropoulos, F.: A numerical approach for simulating fluid structure interaction of flexible thin shells undergoing arbitrarily large deformations in complex domains. J. Comput. Phys. 300, 814–843 (2015)Google Scholar
  26. 26.
    Le, T.B., Troolin, D.R., Amatya, D., Longmire, E.K., Sotiropoulos, F.: Vortex phenomena in sidewall aneurysm hemodynamics: experiment and numerical simulation. Ann. Biomed. Eng. 41(10), 2157–2170 (2013)Google Scholar
  27. 27.
    Le, T.B., Sotiropoulos, F.: Fluid-structure interaction of an aortic heart valve prosthesis driven by an animated anatomic left ventricle. J. Comput. Phys. 244, 41–62 (2013)Google Scholar
  28. 28.
    Le, T.B., Sotiropoulos, F.: On the three-dimensional vortical structure of early diastolic flow in a patient-specific left ventricle. Eur. J. Mech. B. Fluids 35, 20–24 (2012)Google Scholar
  29. 29.
    Le, T.B., Sotiropoulos, F., Coffey, D., Keefe, D.: Vortex formation and instability in the left ventricle. Phys. Fluids 24(9), 091110 (2012)Google Scholar
  30. 30.
    Seo, J.H., Vedula, V., Abraham, T., Lardo, A.C., Dawoud, F., Luo, H., Mittal, R.: Effect of the mitral valve on diastolic flow patterns. Phys. Fluids 26 (12), 121901 (2014)CrossRefGoogle Scholar
  31. 31.
    Arvidsson, P.M., Toger, J., Heiberg, E., Carlsson, M., Arheden, H.: Quantification of left and right atrial kinetic energy using four-dimensional intracardiac magnetic resonance imaging flow measurements. J. Cardiovasc. Magn. Reson. 15(1), P218 (2013)CrossRefGoogle Scholar
  32. 32.
    Khalighi, A.H., Drach, A., Bloodworth, C.H., Pierce, E.L., Yoganathan, A.P., Gorman, R.C., Gorman, J.H., Sacks, M.S.: Mitral valve chordae tendineae: topological and geometrical characterization. Ann. Biomed. Eng. 45(2), 378–393 (2017)CrossRefGoogle Scholar
  33. 33.
    Pedrizzetti, G., Domenichini, F., Tonti, G.: On the left ventricular vortex reversal after mitral valve replacement. Ann. Biomed. Eng. 38(3), 769–773 (2010)CrossRefGoogle Scholar
  34. 34.
    Pope. S.B.: Turbulent flows. Cambridge University Press (2000)Google Scholar
  35. 35.
    Toma, M., Bloodworth, C.H., Einstein, D.R., Pierce, E.L., Cochran, R.P., Yoganathan, A.P., Kunzelman, K.S.: High-resolution subject-specific mitral valve imaging and modeling: experimental and computational methods. Biomech. Model. Mechanobiol. 15(6), 1619–1630 (2016)CrossRefGoogle Scholar
  36. 36.
    Markl, M., Schnell, S., Wu, C., Bollache, E., Jarvis, K., Barker, A., Robinson, J.D., Rigsby, C.K.: Advanced flow MRI: emerging techniques and applications. Clin. Radiol. 71(8), 779–795 (2016)CrossRefGoogle Scholar
  37. 37.
    Al-Wakeel, N., Fernandes, J. F., Amiri, A., Siniawski, H., Goubergrits, L., Berger, F., Kuehne, T.: Hemodynamic and energetic aspects of the left ventricle in patients with mitral regurgitation before and after mitral valve surgery. J. Magn. Reson. Imaging 42(6), 1705–1712 (2015)CrossRefGoogle Scholar
  38. 38.
    Kanski, M., Arvidsson, P.M., Töger, J., Borgquist, R., Heiberg, E., Carlsson, M., Arheden, H.: Left ventricular fluid kinetic energy time curves in heart failure from cardiovascular magnetic resonance 4D flow data. J. Cardiovasc. Magn. Reson. 17(1), 111 (2015)CrossRefGoogle Scholar
  39. 39.
    Seo, J.H., Mittal, R.: Effect of diastolic flow patterns on the function of the left ventricle. Phys. Fluids 25(11), 110801 (2013)CrossRefGoogle Scholar
  40. 40.
    McCarthy, K.P., Ring, L., Rana, B.S.: Anatomy of the mitral valve: understanding the mitral valve complex in mitral regurgitation. Eur. J. Echocardiogr. 11(10), i3–i9 (2010)CrossRefGoogle Scholar
  41. 41.
    Jeong, J., Hussain, F.: On the identification of a vortex. J. Fluid Mech. 285, 69–94 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  42. 42.
    Govindarajan, V., Mousel, J., Udaykumar, H.S., Vigmostad, S.C., McPherson, D.D., Kim, H., Chandran, K.B.: Synergy between diastolic mitral valve function and left ventricular flow aids in valve closure and blood transport during systole. Sci. Rep. 8(1), 6187 (2018)CrossRefGoogle Scholar
  43. 43.
    Toma, M., Jensen, M.Ø., Einstein, D. R., Yoganathan, A.P., Cochran, R. P., Kunzelman, K.S.: Fluid-structure interaction analysis of papillary muscle forces using a comprehensive mitral valve model with 3D chordal structure. Ann. Biomed. Eng. 44 (4), 942–953 (2016)CrossRefGoogle Scholar
  44. 44.
    Khalafvand, S.S., Voorneveld, J.D., Muralidharan, A., Gijsen, F.J.H., Bosch, J.G., van Walsum, T., Haak, A., de Jong, N., Kenjeres, S.: Assessment of human left ventricle flow using statistical shape modelling and computational fluid dynamics. J. Biomech. 74, 116–125 (2018)CrossRefGoogle Scholar
  45. 45.
    Kamphuis, V.P., Roest, A.A.W., Westenberg, J.J., Elbaz, M.S.: Biventricular vortex ring formation corresponds to regions of highest intraventricular viscous energy loss in a Fontan patient: analysis by 4D Flow MRI. Int. J. Cardiovasc. Imaging 34(3), 441–442 (2018)CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Trung Bao Le
    • 1
    • 2
  • Mohammed S. M. Elbaz
    • 3
  • Rob J. Van Der Geest
    • 3
  • Fotis Sotiropoulos
    • 4
    Email author
  1. 1.Hydraulics DivisionThuy Loi UniversityHanoiVietnam
  2. 2.Department of Civil and Environmental EngineeringNorth Dakota State UniversityFargoUSA
  3. 3.Division of Image Processing, Department of RadiologyLeiden University Medical CenterLeidenThe Netherlands
  4. 4.Department of Civil EngineeringStony Brook UniversityStony BrookUSA

Personalised recommendations