Tools for bi- multiple exponential decay of a MRI pixel

Hello Folk!

I would be really happy if someone could help me to solve this problem. A MRI dataset should be analysed according to the T2 FID and displayed within a bi or multiple exponential decay diagram (time vs. intensity).

My professor says, he does not know where but there should be programs within MATLAB. Therefore I would like to know if there are programs for that or how to construct a new script for that?

Probably you can help me?

Thanks in advance for all useful answers, Chris

Answer 1

[Henric Rydén]

use fittype to create your fittype object, and pass that to the fit command. Something like this

g = fittype('a0*exp(-x/t2)','coefficients',{'a0','t2'});
f = fit(x,y,g);

You will likely need to set limits on your model. Here is an example where I limit a0 between 0 and +Inf, and t2 between 10 and 50:

opts = fitoptions(g)
opts.Upper = [Inf 50]
opts.Lower = [0 10]

[Christoph]

Okay thanks for your answer. :) Your example shows me a mono exponential decay. However I would need at least a bi - exponential decay.

I have this piece of code where I have to implement the values (times and intensities of a selected pixel). Afterwards it should work.

However I stuck at the point to figure out how to implement the pixel information of the individual images.

Do you have an idea how?

Piece of code: function d=myfun(a,x)

I1 = x(1); I2 = x(2);

t1 = x(3); t2 = x(4);

te=a(:,1); I=a=(:,2);

d=[];

for k=1:length(te)

d=[d (I-I1*exp(-te/t1)-I2*exp(-te/t2)) ];

end

end

startingvals=[0.5 0.5 3 4];

f = @(x)myfun(a,x);

options = optimset('lsqnonlin'); options = optimset(options,'Algorithm','levenberg-marquardt','TolFun',1e-9,'TolX',1e-7,'MaxFunEvals',12000,'MaxIter',1000);

[x,resnorm,residual,exitflag] = lsqnonlin(f,startingvals,[],[],options);

%disp(x);

fprintf('I1= %.2f, I2= %.2f \n',x(1),x(2)); fprintf('t1= %.2f, t2= %.2f \n',x(3),x(4));

Answer 2

[Henric Rydén]

If you want another model, simply change this line

g = fittype('a0*exp(-x/t2)','coefficients',{'a0','t2'});

to something like this

g = fittype('a0*exp(-x/z1) + a1*exp(-x/z2)','coefficients',{'a0','a1','z1','z2'});

I don't know your exact model so adjust it to what you want to do. I tried running your code but there is an error here:

I=a=(:,2);

[Christoph]

Wow it looks simpler. But I think the approach (optimset) to get the correct values for the four unkowns is missing?

I have made a zip file of one image which I should use. How could I get the info out of this image (intensity and time) for the binary equation?

Would be great if you know that?

Thanks in advance

[Henric Rydén]

I don't know what you mean with the binary equation, but you get the fitted parameters from f after you applied your fit:

f = fit(x,y,g);
disp(f.a0)

Load the image with dicomread . To read the header, use dicominfo . The image you sent me is a 256-by-256 that contains only one echo, you need more echoes to do this analysis.

[Christoph]

Thank you very much for your help.

Okay I know I can get the values one by one of the images with dicomread. It would be a lot of work to do that for all images. How can I get the info a certain pixel with crosshairs to use these values for the binary decay equation (fittype('a0*exp(-x/z1) + a1*exp(-x/z2))?

I think this is quite tricky?

[Henric Rydén]

No problem. This is a different question from your original one and you should post it separately next time. Once you've loaded your images in a 3D matrix A:

figure;
imshow(A(:,:,1),[])
h = impoint; 
wait(h); % Double-click the ROI to finish
mask = h.createMask;
mask = repmat(mask,1,1,size(A,3)); % Make the mask 3D
y = A(mask);

[Christoph]

Okay thanks again. It´s pretty hard to understand. How can I summarize this in a script? Do I have at first to load the file with CD('path')then I have to pass the info to A and how do I transfer the information of the binary decay afterwards to the diagram?

I really try to understand it but it quite complex for me.

[Henric Rydén]

Are you asking how you load the images into A?

[Christoph]

Sry for the delay in response. It is great to have some help from you. I try to learn and understand.

However I thing I am far away from the solution to couple the output with the binary decay equation? This is the code which I user and I get the following error (watch screenshot in the appendix) clear all close all

clc

loadpath = (pwd);

cd(loadpath)

figure; imshow(loadpath(:,:,1),[]) h = impoint; wait(h); % Double-click the ROI to finish mask = h.createMask; mask = repmat(mask,1,1,size(A,3)); % Make the mask 3D y = A(mask);

[Henric Rydén]

The error occurs because you are passing a string to the imshow command. You need to load the image first, using dicomread (for DICOM files) or imread (for jpg, png, ...).

A=imread('fileName.IMA');
figure;
imshow(A,[]);