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.

References

References
1.
Markl
,
M.
,
Kilner
,
P. J.
, and
Ebbers
,
T.
,
2011
, “
Comprehensive 4D Velocity Mapping of the Heart and Great Vessels by Cardiovascular Magnetic Resonance
,”
J. Cardiovasc. Magn. Reson.
,
13
,
p
. 7.10.1186/1532-429X-13-7
2.
Bluestein
,
D.
,
Chandran
,
K. B.
, and
Manning
,
K. B.
,
2010
, “
Towards Non-Thrombogenic Performance of Blood Recirculating Devices
,”
Ann. Biomed. Eng.
,
38
(
3
), pp.
1236
1256
.10.1007/s10439-010-9905-9
3.
Sengupta
,
P. P.
,
Pedrizzetti
,
G.
,
Kilner
,
P. J.
,
Kheradvar
,
A.
,
Ebbers
,
T.
,
Tonti
,
G.
,
Fraser
,
A. G.
, and
Narula
,
J.
,
2012
, “
Emerging Trends in CV Flow Visualization
,”
JACC Cardiovasc. Imag.
,
5
(
3
), pp.
305
316
.10.1016/j.jcmg.2012.01.003
4.
Dabiri
,
J. O.
, and
Gharib
,
M.
,
2005
, “
The Role of Optimal Vortex Formation in Biological Fluid Transport
,”
Proc. Biol. Sci.
,
272
(
1572
), pp.
1557
1560
.10.1098/rspb.2005.3109
5.
Gharib
,
M.
,
Rambod
,
E.
,
Kheradvar
,
A.
, and
Sahn
,
D.
,
2006
, “
Optimal Vortex Formation as an Index of Cardiac Health
,”
Proc. Natl. Acad. Sc. USA
,
103
(
16
), pp.
6305
6308
.10.1073/pnas.0600520103
6.
Luff
,
J. D.
,
Drouillard
,
T.
,
Rompage
,
A. M.
,
Linne
,
M. A.
, and
Hertzberg
,
J. R.
,
1999
, “
Experimental Uncertainties Associated With Particle Image Velocimetry (PIV) Based Vorticity Algorithms
,”
Experiments Fluids
,
26
, pp.
36
54
.10.1007/s003480050263
7.
Chapra
,
S.
,
1998
,
Numerical Methods for Engineers
,
2nd ed.
McGraw-Hill Inc
,
New York
, p.
529
.
8.
Etebari
,
A.
, and
Vlachos
,
P. P.
,
2005
, “
Improvements on the Accuracy of Derivative Estimation From DPIV Velocity Measurements
,”
Experiments Fluids
,
39
, pp.
1040
1050
.10.1007/s00348-005-0037-1
9.
Shinneeb
,
A.-M.
,
Bugg
,
J. D.
, and
Balachandar
,
R.
,
2004
, “
Variable Threshold Outlier Identification in PIV Data
,”
Meas. Sci. Technol.
,
15
(
9
), pp.
1722
1732
.10.1088/0957-0233/15/9/008
10.
Gao
,
J. H.
, and
Gore
,
J. O.
,
1991
, “
Turbulent Flow Effects on NMR Imaging: Measurement of Turbulent Intensity
,”
Med. Phys.
,
18
(
5
), pp.
1045
1051
.10.1118/1.596645
11.
Bonow
,
R. O.
,
Carabello
,
B.
,
Chatterjee
,
K.
,
de Leon
,
A.
,
Faxon
,
D.
,
Freed
,
M.
,
Gaasch
,
W.
,
Lytle
,
B.
,
Nishimura
,
R.
,
O'Gara
,
P.
,
O'Rourke
,
R.
,
Otto
,
C.
,
Shah
,
P.
, and
Shanewise
,
J.
,
2008
, “
2008 Focused Update Incorporated Into the ACC/AHA 2006 Guidelines for the Management of Patients With Valvular Heart Disease: A Report of the American College of Cardiology/American Heart Association Task Force on Practice Guidelines
,”
Circulation
,
118
(
15
), pp.
e523
e661
.10.1161/CIRCULATIONAHA.108.190748
12.
Garcia
,
J.
,
Kadem
,
L.
,
Larose
,
E.
,
Clavel
,
M.-A.
, and
Pibarot
,
P.
,
2011
, “
Comparison Between Cardiovascular Magnetic Resonance and Transthoracic Doppler Echocardiography for the Estimation of Effective Orifice Area in Aortic Stenosis
,”
J. Cardiovasc. Magn. Reson.
,
13
,
p
. 25.10.1186/1532-429X-13-25
13.
Vincentelli
,
A.
,
Susen
,
S.
,
Le Tourneau
,
T.
,
Six
,
I.
,
Fabre
,
O.
,
Juthier
,
F.
,
Bauters
,
A.
,
Decoene
,
C.
,
Goudemand
,
J.
,
Prat
,
A.
, and
Jude
,
B.
,
2003
, “
Acquired von Willebrand Syndrome in Aortic Stenosis
,”
N. Engl. J. Med.
,
349
(
4
), pp.
343
349
.10.1056/NEJMoa022831
You do not currently have access to this content.