Strain measurement

Hi,

I have a sequence of cardiac MRI and I would like to plot the circumferential strain (deformation) during the time.

For that, I made the hypothesis that I can measure the strain between every two successive points. For that, I wrote this code :

for i=1:loopimages % my images sequence
   for j=1:looppoints % all points
     % Initial distance between the 1st and 2nd points
      distance_initiale = (MAT_Xinitial(1,j+1) - MAT_Xinitial(1,1)).^2 + (MAT_Yinitial(1,j+1) - MAT_Yinitial(1,1)).^2; 

        Mat_dist_init(1,j) = distance_initiale;

        for k=1:((j+1) - 1) % every pair of points
           distance = (MAT_Xfinal_track(j+1,i) - MAT_Xfinal_track(j,i)).^2 + (MAT_Yfinal_track(j+1,i) - MAT_Yfinal_track(j,i)).^2;
           Mat_dist(1,j) = distance;

           strain = (Mat_dist - Mat_dist_init) / Mat_dist_init;
           Mat_strain(j,:) = strain;
        end

   end

      plot(mm,Mat_strain,'+r')
end

I'm sure that my code is far to be perfect but I would appreciate any remarks that can help me ameliorate it.

Thank you in advance !

[Cynthia]

Hi if you could share your full code. It would be much helpful.

[DGM]

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Answer 1

[Sean de Wolski]

If you explain your use case and your data (maybe with an image to help!) I think I can help you. Strain is notoriously hard to calculate as it requires differentiation, which in turn amplifies noise.

For my MS thesis I calculated strain in CT image deformation using a method that smooths. It was still difficult since I lost a fair amount of points to noise, but overall it did a good job. I don't have my thesis or the code on me right now so I can't get you the paper until later.

For what you have above, a comment:

• Shouldn't there be a sqrt() in there? If so look at hypot(), to calculate dist_initial and dist_final

Answer 2

[K BV]

Thanks for your answer !

I have a sequence of MRI images, the number of these images is stored in loopimages.

I used two filters "median" and "gaussian" to have a better contour smoothing.

Also, I have about 23 points (markers) to track stored in looppoints.

MAT_Xinitial is a matrix containing the X-position of j-th markers in the first image, same for MAT_Yinitial which contains the Y-position of j-th markers in the first image. Its size is 1x(looppoints)

MAT_Xfinal_track is a matrix again containing the X-position of j markers in i images (after the tracking), same for MAT_Yfinal_track is a matrix again containing the Y-position of the j-th markers in i-th images (after the tracking).

distance_initiale is the distance between the first and the second marker in the first image. It will be my reference distance.

distance is the distance between two successive markers through the rest of images : 2 -> loopimages.

I omitted sqrt to have big values to plot, I'll add it right now.

[Sean de Wolski]

So you have displacements for markers that are not on a regular grid? How irregular is your grid (i.e. marker distriubution)? The strain calculation method that I was thinking of (I believe, though I could very well be wrong) requires markers to be on a regular grid. This would require interpolating to a regular grid first or finding a different method.

[K BV]

I think that we can call my grid regular since the markers I'm tracking are sampled with a sampling rate of 9 pixels.