Skip to main content
Log in

Vortex Ring Formation in the Left Ventricle of the Heart: Analysis by 4D Flow MRI and Lagrangian Coherent Structures

  • Published:
Annals of Biomedical Engineering Aims and scope Submit manuscript

Abstract

Recent studies suggest that vortex ring formation during left ventricular (LV) rapid filling is an optimized mechanism for blood transport, and that the volume of the vortex ring is an important measure. However, due to lack of quantitative methods, the volume of the vortex ring has not previously been studied. Lagrangian Coherent Structures (LCS) is a new flow analysis method, which enables in vivo quantification of vortex ring volume. Therefore, we aimed to investigate if vortex ring volume in the human LV can be reliably quantified using LCS and magnetic resonance velocity mapping (4D PC-MR). Flow velocities were measured using 4D PC-MR in 9 healthy volunteers and 4 patients with dilated ischemic cardiomyopathy. LV LCS were computed from flow velocities and manually delineated in all subjects. Vortex volume in the healthy volunteers was 51 ± 6% of the LV volume, and 21 ± 5% in the patients. Interobserver variability was −1 ± 13% and interstudy variability was −2 ± 12%. Compared to idealized flow experiments, the vortex rings showed additional complexity and asymmetry, related to endocardial trabeculation and papillary muscles. In conclusion, LCS and 4D PC-MR enables measurement of vortex ring volume during rapid filling of the LV.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6

Similar content being viewed by others

Abbreviations

LCS:

Lagrangian coherent structures

FTLE:

Finite-time Lyapunov exponent

EDV:

End-diastolic volume (see Fig. 3)

ESV:

End-systolic volume (see Fig. 3)

DV:

Diastatic volume (see Fig. 3)

SV:

Stroke volume (see Fig. 3)

EWV:

E-wave volume (see Fig. 3)

VV:

Vortex volume

VV%:

Vortex volume relative to LV volume at diastasis (VV/DV)

CMR:

Cardiovascular magnetic resonance

4D PC-MR:

Four-dimensional (3D + time), three-directional, time-resolved phase contrast magnetic resonance velocity mapping

References

  1. Alfakih, K., S. Plein, H. Thiele, T. Jones, J. P. Ridgway, and M. U. Sivananthan. Normal human left and right ventricular dimensions for MRI as assessed by turbo gradient echo and steady-state free precession imaging sequences. J. Magn. Reson. Imaging 17:323–329, 2003.

    Article  PubMed  Google Scholar 

  2. Dabiri, J. O. Optimal vortex formation as a unifying principle in biological propulsion. Annu. Rev. Fluid Mech. 41:17–33, 2009.

    Article  Google Scholar 

  3. Dabiri, J. O., and M. Gharib. Fluid entrainment by isolated vortex rings. J. Fluid Mech. 511:311–331, 2004.

    Article  Google Scholar 

  4. Didden, N. On the formation of vortex rings: rolling-up and production of circulation. Zeitschrift für angewandte Mathematik und Physik ZAMP 30:101–116, 1979.

    Article  Google Scholar 

  5. Dyverfeldt, P., J. P. 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 28:655–663, 2008.

    Article  PubMed  Google Scholar 

  6. Eriksson, J., C. J. Carlhäll, P. Dyverfeldt, J. Engvall, A. F. Bolger, and T. Ebbers. Semi-automatic quantification of 4D left ventricular blood flow. J. Cardiovasc. Magn. Reson. 12:9, 2010.

    Article  PubMed  Google Scholar 

  7. Gharib, M., E. Rambod, A. Kheradvar, D. J. Sahn, and J. O. Dabiri. Optimal vortex formation as an index of cardiac health. Proc. Natl. Acad. Sci. USA 103:6305–6308, 2006.

    Article  PubMed  CAS  Google Scholar 

  8. Gharib, M., E. Rambod, and K. Shariff. A universal time scale for vortex ring formation. J. Fluid Mech. 360:121–140, 1998.

    Article  CAS  Google Scholar 

  9. Ghosh, E., L. Shmuylovich, and S. J. Kovács. Vortex formation time-to-left ventricular early rapid filling relation: model-based prediction with echocardiographic validation. J. Appl. Physiol. 109:1812–1819, 2010.

    Article  PubMed  Google Scholar 

  10. Haller, G. Lagrangian coherent structures from approximate velocity data. Phys. Fluids 14:1851–1861, 2002.

    Article  CAS  Google Scholar 

  11. Heiberg, E., T. Ebbers, L. Wigström, and M. Karlsson. Three-dimensional flow characterization using vector pattern matching. IEEE Trans. Visual Comput. Graphics 9:313–319, 2003.

    Article  Google Scholar 

  12. Heiberg, E., J. Sjögren, 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.

    Article  PubMed  Google Scholar 

  13. Hong, G. R., G. Pedrizzetti, G. Tonti, P. Li, Z. Wei, J. K. Kim, A. Baweja, S. Liu, N. Chung, H. Houle, et al. Characterization and quantification of vortex flow in the human left ventricle by contrast echocardiography using vector particle image velocimetry. JACC: Cardiovasc. Imaging 1:705–717, 2008.

    Article  Google Scholar 

  14. Kheradvar, A., R. Assadi, A. Falahatpisheh, and P. P. Sengupta. Assessment of transmitral vortex formation in patients with diastolic dysfunction. J. Am. Soc. Echocardiogr. 25:220–227, 2012.

    Article  PubMed  Google Scholar 

  15. Kheradvar, A., and M. Gharib. Influence of ventricular pressure drop on mitral annulus dynamics through the process of vortex ring formation. Ann. Biomed. Eng. 35:2050–2064, 2007.

    Article  PubMed  Google Scholar 

  16. Kheradvar, A., and M. Gharib. On mitral valve dynamics and its connection to early diastolic flow. Ann. Biomed. Eng. 37:1–13, 2009.

    Article  PubMed  Google Scholar 

  17. Kheradvar, A., M. Milano, and M. Gharib. Correlation between vortex ring formation and mitral annulus dynamics during ventricular rapid filling. ASAIO J. 53:8–16, 2007.

    Article  PubMed  Google Scholar 

  18. Kilner, P. J., G. Z. Yang, A. J. Wilkes, R. H. Mohiaddin, D. N. Firmin, and M. H. Yacoub. Asymmetric redirection of flow through the heart. Nature 404:759–761, 2000.

    Article  PubMed  CAS  Google Scholar 

  19. Kim, W. Y., P. G. Walker, E. M. Pedersen, J. K. Poulsen, S. Oyre, K. Houlind, and A. P. Yoganathan. Left ventricular blood flow patterns in normal subjects: a quantitative analysis by three-dimensional magnetic resonance velocity mapping. J. Am. Coll. Cardiol. 26:224–238, 1995.

    Article  PubMed  CAS  Google Scholar 

  20. Kovács, S. J., D. M. Mcqueen, and C. S. Peskin. Modelling cardiac fluid dynamics and diastolic function. Phil. Trans. R. Soc. Lond. A 359:1299–1314, 2001.

    Article  Google Scholar 

  21. Krishnan, H., C. Garth, J. Guhring, M. A. Gulsun, A. Greiser, and K. I. Joy. Analysis of time-dependent flow-sensitive PC-MRI data. IEEE Trans. Vis. Comput. Graph. 18:966–977, 2012.

    Article  PubMed  Google Scholar 

  22. Maceira, A. M., S. K. Prasad, M. Khan, and D. J. Pennell. Normalized left ventricular systolic and diastolic function by steady state free precession cardiovascular magnetic resonance. J. Cardiovasc. Magn. Reson. 8:417–426, 2006.

    Article  PubMed  CAS  Google Scholar 

  23. Olcay, A. B., T. S. Pottebaum, and P. S. Krueger. Sensitivity of Lagrangian coherent structure identification to flow field resolution and random errors. Chaos 20:017506, 2010.

    Article  PubMed  Google Scholar 

  24. Olcay, A., and P. Krueger. Measurement of ambient fluid entrainment during laminar vortex ring formation. Exp. Fluids 44:235–247, 2008.

    Article  Google Scholar 

  25. Pasipoularides, A. The Heart’s Vortex: Intracardiac Blood Flow Phenomena. Shelton: People’s Medical Publishing House, 927 pp., 2010.

  26. Poh, K. K., L. C. Lee, L. Shen, E. Chong, Y. L. Tan, P. Chai, T. C. Yeo, and M. J. Wood. Left ventricular fluid dynamics in heart failure: echocardiographic measurement and utilities of vortex formation time. Eur. Heart J. Cardiovasc. Imaging 13:385–393, 2012.

    Article  PubMed  Google Scholar 

  27. Ringgaard, S., S. A. Oyre, and E. M. Pedersen. Arterial MR imaging phase-contrast flow measurement: improvements with varying velocity sensitivity during cardiac cycle. Radiology 232:289–294, 2004.

    Article  PubMed  Google Scholar 

  28. Schenkel, T., M. Malve, M. Reik, M. Markl, B. Jung, and H. Oertel. MRI-based CFD analysis of flow in a human left ventricle: methodology and application to a healthy heart. Ann. Biomed. Eng. 37:503–515, 2009.

    Article  PubMed  Google Scholar 

  29. Shadden, S. C., M. Astorino, and J.-F. Gerbeau. Computational analysis of an aortic valve jet with Lagrangian coherent structures. Chaos 20:0175120, 2010.

    Article  Google Scholar 

  30. Shadden, S. C., J. O. Dabiri, and J. E. Marsden. Lagrangian analysis of fluid transport in empirical vortex ring flows. Phys. Fluids 18:047105, 2006.

    Article  Google Scholar 

  31. Shadden, S. C., K. Katija, M. Rosenfeld, J. E. Marsden, and J. O. Dabiri. Transport and stirring induced by vortex formation. J. Fluid Mech. 593:315–331, 2007.

    Article  Google Scholar 

  32. Shadden, S. C., and C. A. Taylor. Characterization of coherent structures in the cardiovascular system. Ann. Biomed. Eng. 36:1152–1162, 2008.

    Article  PubMed  Google Scholar 

  33. Sharma, N. D., P. A. McCullough, E. F. Philbin, and W. D. Weaver. Left ventricular thrombus and subsequent thromboembolism in patients with severe systolic dysfunction. Chest 117:314–320, 2000.

    Article  PubMed  CAS  Google Scholar 

  34. Shmuylovich, L., C. S. Chung, and S. J. Kovács. Point: left ventricular volume during diastasis is the physiological in vivo equilibrium volume and is related to diastolic suction. J. Appl. Physiol. 109:606–608, 2010.

    Article  PubMed  Google Scholar 

Download references

Acknowledgments

Anders Nilsson and Freddy Ståhlberg at the Department of Medical Radiation Physics, Lund University, Lund, Sweden and Karin Markenroth-Bloch, Philips Healthcare, Best, the Netherlands substantially improved the study through many fruitful discussions. Johannes Ulén at the Mathematical Imaging Group, Centre for Mathematical Sciences, Lund University, Lund, Sweden is acknowledged for work on LCS visualizations. Ann-Helen Arvidsson and Christel Carlander at the Department of Clinical Physiology, Skåne University Hospital Lund, Lund, Sweden are gratefully acknowledged for assistance in data collection.

This study was supported by Swedish Research Council grants VR 621-2005-3129, VR 621-2008-2949, and VR K2009-65X-14599-07-3, National Visualization Program and Knowledge Foundation grant 2009-0080, the Medical Faculty at Lund University, Sweden, the Region of Scania, Sweden and the Swedish Heart–Lung Foundation. SJK is supported in part by the Alan A. and Edith L. Wolff Charitable Trust, St. Louis, MO, USA, and the Barnes-Jewish Hospital Foundation, St Louis, MO, USA.

Conflicts of Interest

None.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Einar Heiberg.

Additional information

Associate Editor Jane Grande-Allen oversaw the review of this article.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Descriptions of supplementary files (PDF 39 kb)

Individual data for each subject (XLSX 25 kb)

Timing information for video files (XLS 30 kb)

Vortex ring LCS animation in healthy volunteer 1 (MPG 1090 kb)

Vortex ring LCS animation in healthy volunteer 2 (MPG 1689 kb)

Vortex ring LCS animation in healthy volunteer 2 (2-ch view) (MPG 2038 kb)

Vortex ring LCS animation in healthy volunteer 3 (MPG 1231 kb)

Vortex ring LCS animation in healthy volunteer 4 (MPG 1508 kb)

Vortex ring LCS animation in healthy volunteer 5 (MPG 821 kb)

Vortex ring LCS animation in healthy volunteer 6 (MPG 2250 kb)

Vortex ring LCS animation in healthy volunteer 7 (MPG 1834 kb)

Vortex ring LCS animation in healthy volunteer 8 (MPG 1706 kb)

Vortex ring LCS animation in healthy volunteer 9 (MPG 1311 kb)

Vortex ring LCS animation in patient 1 (MPG 1261 kb)

Vortex ring LCS animation in patient 2 (MPG 1437 kb)

Vortex ring LCS animation in patient 3 (MPG 2221 kb)

Vortex ring LCS animation in patient 4 (MPG 2148 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Töger, J., Kanski, M., Carlsson, M. et al. Vortex Ring Formation in the Left Ventricle of the Heart: Analysis by 4D Flow MRI and Lagrangian Coherent Structures. Ann Biomed Eng 40, 2652–2662 (2012). https://doi.org/10.1007/s10439-012-0615-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10439-012-0615-3

Keywords

Navigation