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Subject:

Re: DTI eigenvectors

From:

Tim Behrens <[log in to unmask]>

Reply-To:

FSL - FMRIB's Software Library <[log in to unmask]>

Date:

Fri, 1 Oct 2004 08:25:01 +0100

Content-Type:

TEXT/PLAIN

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TEXT/PLAIN (124 lines)

Hi Stamatis -

I'm not sure I can be more specific, but I can try to explain a bit
better. I'm sure you know a lot of what I'm about to say. I am writing it
down partly just to have it on the list so I can refer back to it next
time someone asks!!

A) Diffusion Tensor Imaging:

 When you acquired "DTI scans", you didn't actually acquire a diffusion
tensor at each voxel; you acquired various spin echo images. Some of these
images will just be spin echo images. In these images the signal is
weighted by the T2 decay. In terms of contrast, these images will probably
be different from your high resolution image, but the same structures will
be present in the two images. Other images that you acquire during your
DTI scan will have had diffusion encoding gradients applied along
different orientations during the Spin echo sequence. In these images,
different structures will be visible, as white matter pathways will appear
different depending on their orientation with respect to the orientation
of the diffusion encoding gradient.

You then took all these Spin Echo images and, by looking at what the
signal was when different diffusion encoding gradients were applied, and
when no diffusion encoding gradient was applied, you were able to fit a
diffusion tensor at each voxel.

B) Registration:

Flirt will compute the transformation matrix (xfm) between two _spaces_ .
It will also apply this xfm to take an image from one space to another
space.  If you have lots of images in the same space (as in DTI) then you
only need to compute the xfm between _one_ of these images and your
reference image, and you can then apply the same xfm to all of the other
images.


So going back to the questions:

1) When you initially run flirt, you need to choose which image (in
"diffusion space") you are going to use to compute the xfm. You should
choose an image in which the visible structures are as similar as possible
to those in the reference image. In my experience, the best image to use
to compute this xfm is the original (brain extracted) T2-weighted
spin-echo image. However, the Mean diffusivity image from the diffusion
tensor fit should also do a reasonable job. Anybody use anything else??

You can then use Flirt (yes, it is a good idea to go via a high res image)
to copmpute the single xfm which takes _every one_ of your diffusion space
images to reference space. You can then apply this xfm to each diffusion
space image that you want in reference space. Note that you can apply an
xfm by using the ApplyXFM GUI.

2) Now, if you just want the FA, MD images in standard space, then you can
do exactly as described above and linear interpolation should work fine.
Just apply the transform to the images in question. However, if you want
the eigenvectors there then you've got a slight problem.

(A) Interpolating the eigenvectors will often give you a bunch of rubbish
(e.g. two vectors pointing in opposite directions could be interpolated to
make zero!)

(B) the orientation of the vector which was correct in scanner space is
now wrong in reference space - the vector will point to the wrong place!!

You will end up with a bit of a headache. The easiest solution to this
problem is only ever to transform scalar rotationally invariant
properties (e.g. MD,FA).

There are two other solutions:

1) use nearest neighbour interpolation, and rotate the eigenspace of the
tensor after the registration. This is described in a paper by
Danny Alexander about 4 years ago.

2) Apply the transform to the original Spin echo images (both diffusion-
and non-diffusion- weighted), rotate your diffusion encoding directions
according to the same transform, and refit the diffusion tensors to create
new DTI images in standard space.

Both of these other solutions require a bit of programming (e.g. matlab to
rotate the gradient directions) - Unless you have good reason, I'd leave
the vectors in their original space, and transform the rotationally
invariant quantities.


Hope this is clearer

Any questions, just ask

T





-------------------------------------------------------------------------------
Tim Behrens
Centre for Functional MRI of the Brain
The John Radcliffe Hospital
Headley Way Oxford OX3 9DU
Oxford University
Work 01865 222782
Mobile 07980 884537
-------------------------------------------------------------------------------

On Fri, 1 Oct 2004, Stamatis Sotiropoulos wrote:

> Hi all,
>   I have calculated some DTI images of the eigen vectors and eigen values
> of the diffusion tensor, using some DTI scans. In other words I have 3 DTI
> images for the eigenvalues (one image for each eigenvalue) and 9 images
> for the eigen vectors (3 images per vector, 1 image for each coordinate of
> the vector). I am trying to register these calculated images with MNI (or
> Talairach) space. It is obvious that for eigenvalues images I can use
> FLIRT, since these images are comprised of scalar quantities. What about
> the eigenvectors images? Do you think that I can use FLIRT? Will the
> interpolation (that makes sense for scalar quantities) work for the
> vectors?
>
>
> Thank you in advance,
> Stamatis
>

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