I have only x and y directional blood flow velocity data obtained from MRI. I have no z-directional velocity data . I have learnt that the vortex detection methods like q-criterion, lambda2 method needs velocity data for all three directions (x,y and z) to identify vortex core locations. Is there any method that i can apply for identifying vortex core locations for my two directional data?
In a 2D field you can directly compute the vorticity field du/dy-dv/dx and plot the iso-vorticity lines. A vortex tube section in the (x,y) plane can be identified this way (envelope of the vorticity vector over a closed line).
This has been described nicely in the following papers:
MRI studies:
Kim WY et al. Left ventricular blood flow patterns in normal subjects: a quantitative analysis by three-dimensional magnetic resonance velocity mapping. J Am Coll Cardiol. 1995 Jul;26(1):224-38.
Töger J et al. Vortex ring formation in the left ventricle of the heart: analysis by 4D flow MRI and Lagrangian coherent structures. Ann Biomed Eng. 2012 Dec;40(12):2652-62.
Ultrasound PIV studies:
Kheradvar A et al. Echocardiographic particle image velocimetry: a novel technique for quantification of left ventricular blood vorticity pattern. J Am Soc Echocardiogr. 2010 Jan;23(1):86-94.
Garcia D et al. Two-dimensional intraventricular flow mapping by digital processing conventional color-Doppler echocardiography images. IEEE Trans Med Imaging. 2010 Oct;29(10):1701-13.
Prinz C et al. Echocardiographic particle image velocimetry for the evaluation of diastolic function in hypertrophic nonobstructive cardiomyopathy. Echocardiography. 2014 Aug;31(7):886-94.
I advise you to look into Lagrangian coherent structures (see paper of Töger).
Hope this will be helpful.
Jos Westenberg sir, the MRI papers which you have suggested have all three directional velocities (x,y and z). I know if we have all three directional velocities then we can apply methods like q-criterion and lambda2.
But I have only two directional velocities (only x and y). So I asked for some suggestions.
Shataneek Banerjee the MRI papers I referred to are indeed using 4D flow MRI data but then use that data reconstructed into 2D planes. From there on they use only in-plane velocity components.
Shataneek Banerjee
be careful about an issue: in a 2D model the vorticity has only one component normal to the plane and by using the iso-vorticity lines you can identify the curve of the vortex tube. But in your case you have 2 components in the plane of a real 3D flow, therefore you have only one of the three components of the vorticity vector field which is not normal to the plane.
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