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Technical Briefs

On the Evaluation of Vorticity Using Cardiovascular Magnetic Resonance Velocity Measurements

[+] Author and Article Information
J. Garcia

Québec Heart and Lung Institute,
Laval University,
Quebec City, QC G1V 0A6, Canada
Laboratory of Cardiovascular Fluid Dynamics,
Concordia University,
Montréal QC H3G 1M8, Canada

P. Pibarot

Québec Heart and Lung Institute,
Laval University
Quebec City, QC G1V 0A6, Canada

L. Kadem

Laboratory of Cardiovascular Fluid Dynamics,
Concordia University,
Montréal QC H3G 1M8, Canada
e-mail: kadem@encs.concordia.ca

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received April 2, 2012; final manuscript received June 15, 2012; accepted manuscript posted September 12, 2013; published online October 24, 2013. Assoc. Editor: Hai-Chao Han.

J Biomech Eng 135(12), 124501 (Oct 24, 2013) (6 pages) Paper No: BIO-12-1127; doi: 10.1115/1.4025385 History: Received April 02, 2012; Revised June 15, 2012; Accepted September 12, 2013

Vorticity and vortical structures play a fundamental role affecting the evaluation of energetic aspects (mainly left ventricle work) of cardiovascular function. Vorticity can be derived from cardiovascular magnetic resonance (CMR) imaging velocity measurements. However, several numerical schemes can be used to evaluate the vorticity field. The main objective of this work is to assess different numerical schemes used to evaluate the vorticity field derived from CMR velocity measurements. We compared the vorticity field obtained using direct differentiation schemes (eight-point circulation and Chapra) and derivate differentiation schemes (Richardson 4* and compact Richardson 4*) from a theoretical velocity field and in vivo CMR velocity measurements. In all cases, the effect of artificial spatial resolution up-sampling and signal-to-noise ratio (SNR) on vorticity computation was evaluated. Theoretical and in vivo results showed that the eight-point circulation method underestimated vorticity. Up-sampling evaluation showed that the artificial improvement of spatial resolution had no effect on mean absolute vorticity estimation but it affected SNR for all methods. The Richardson 4* method and its compact version were the most accurate and stable methods for vorticity magnitude evaluation. Vorticity field determination using the eight-point circulation method, the most common method used in CMR, has reduced accuracy compared to other vorticity schemes. Richardson 4* and its compact version showed stable SNR using both theoretical and in vivo data.

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Figures

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Fig. 1

Vorticity computation. (a) shows an example of vortical flow. (b) shows the vorticity computation using the finite differences. (c) shows the theoretical vortical cellular flow used to test vorticity schemes.

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Fig. 2

Vorticity computed for Vmax of 5 m/s. Vorticity profile, as determined by each method, corresponding to the central line of the top cells in Fig. 1(c).

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Fig. 3

Theoretical comparison of vorticity schemes and up-sampling effect. (a) shows the mean absolute vorticity computed using vorticity schemes from the theoretical velocity field. (b) shows the evaluation of signal-to-noise ratio (SNR). (c) shows the effect of image up-sampling on vorticity computation and (d) on the evaluation of SNR.

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Fig. 4

Up-sampling evaluation of vorticity schemes using velocity map from a patient with severe aortic stenosis at peak systole. (a) shows the mean absolute vorticity computed using vorticity schemes. (b) shows the effect of image up-sampling on SNR. (c) shows the maximum absolute vorticity using vorticity schemes.

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Fig. 5

Effect of image up-sampling on vorticity computation in vivo. First raw: low resolution vorticity magnitude. Second raw: high resolution (four times original) vorticity magnitude. Vorticity magnitude was computed from velocity measurements in a patient with severe aortic stenosis at peak systole phase. Ao is the ascending aorta; LV is the left ventricle.

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Fig. 6

Vorticity magnitude computation in the ascending aorta and left ventricle at different instants of cardiac cycle using R4*. Top panels show the ascending aorta region in a patient with severe aortic stenosis, whereas the bottom panels show the mitral valve region for the same patient. Ao is the ascending aorta; LV is the left ventricle; LA is the left atrium. Black line is the flow plot over cardiac cycle.

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Fig. 7

Vorticity magnitude computation in the left atrium at three different instants of cardiac cycle using R4*. Ao is the ascending aorta; LV is the left ventricle; LA is the left atrium. White line is the flow plot over time.

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