As a general rule, from a velocity field you compute the vorticity field and define the vortex line as the curve that is tangent at any point to the vector vorticity.

This is the theory (see for example the Chorin’s book), in your specific case is your experimental set of data quite detailed in the velocity components ? You need to compute the numerical derivatives.

Have you already started from the visualization of the streamlines?

Filippo Maria Denaro I have many 192x192 matrices containing x and y velocity data. Means the flow field is divided into a 192x192 matrix and the value of x and y velocity is computed at each of the matrix cells at different time instants throughout the cardiac cycle. So there are many such matrices computed at different time instants. Now I have plotted the velocity vectors and streamlines in Mathematica but the streamlines are not getting curved which will signify a vortical flow. This is my problem.

And also I have computed the vorticity by taking finite difference approximation of the derivatives (∂ v/ ∂ x - ∂ u/ ∂ y).

Post the plots you have

Filippo Maria Denaro The plots 1.png and 2.png are at the start of cardiac cycle(i.e.start of filling of left atrium) and the plots 74.png and 75.png are at the end of the cardiac cycle(i.e. end of emptying of left atrium). The plots basically shows the flow inside the left atrium. The geometry of the plots is roughly the geometry of left atrium.

Is the left atrium filling the goal of your visualization? the blood comes from the pulmunary veins with the mitral valve in closed position, there is an increasing of left atrium volume but there is no strong vortical structures as you will see when the mitral valve opens and flow in left ventricular enters. If you have a look to my RG articles, I have some papers about the study of the flow in the diastolic phases, you can see the pattern. Your velocity field seems quite reasonable but where is the location of the pulmunary veins in the figures? I suggest to organize the visualization with such indication and the position of the mitral valve.

Filippo Maria Denaro My goal is actually visualizing and analyzing the flow inside the left atrium throughout the cardiac cycle from the start of its filling to the end of its emptying. The location of the pulmonary veins and mitral valve is not accurately known to me since I have only 1 directional view of the heart. Only I can make an intellectual guess.

I have posted only four plots. Are you interested to see all the 75 plots throughout the cardiac cycle? Then I can upload all 75 plots.

Where is located the plane of your vector plot in the atrium? You need to figure it out if the velocity field is congruent to the physics you have to analyse. The inflow come from the pulmunary veins and you should see that from the images. Then the atrium should increase slightly the volume until the opening of the mitral valve, therefore you should also locate the position of the valve from you images. Without that it is difficult to assess what happens. You have the images only until to the end of the filling, no images during diastole??

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Filippo Maria Denaro The plane of vector plot is a vertical long axis slice which cuts the left atrium. I don't have the accurate location of the slice.

I have images from the start of filling of left atrium to the end of emptying of left atrium which is also the end of left ventricular diastole. So I have diastolic images. The images 74.png and 75.png which i uploaded previously corresponds to the end of ventricular diastole.

I am getting an impression that the flow field is not physically congruent. I am getting an increase in left atrial volume. But the position of flow lines are not at the location where the pulmonary vein and mitral valve are expected to be. So I am trying to figure out if the data needs more refinement?

I think you should come back at the source of your image. You need to know all possible details about the way the measurements are done. Do not forget that this is a 2D representation of a 3D velocity field. From your image is hard to immagine where the plane is located and how it intersect the mitral valve.

It seems the atrium is located at the top of the figures and the ventricle is below in the images so the opening of the mitral should appears towards the bottom of the figures. If you see my papers you will find some experimental patterns obtained by the eco-cardiodoppler.