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

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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.

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Lagrangian coherent structures


Finite-time Lyapunov exponent


End-diastolic volume (see Fig. 3)


End-systolic volume (see Fig. 3)


Diastatic volume (see Fig. 3)


Stroke volume (see Fig. 3)


E-wave volume (see Fig. 3)


Vortex volume


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


Cardiovascular magnetic resonance


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


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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.

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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)

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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).

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