[Mristudio-users] second and tertiary eigenvalue equal to 0

[Hangyi Jiang]

hi, 

theoretically, the tensor is positive definite matrix.  practically, it is not.  the eigen values could be zero or negative.  in DtiStudio, the zeros are kept there, the negatives are forced as zeros. 

regards,

hangyi





________________________________________
From: smoriw at gmail.com [smoriw at gmail.com] On Behalf Of susumu mori [susumu at mri.jhu.edu]
Sent: Wednesday, April 07, 2010 5:39 PM
To: Yi Jiang; DTI Studio, ROI Editor, DiffeoMap Questions/Support; Hangyi Jiang
Subject: Re: [Mristudio-users] second and tertiary eigenvalue equal to 0

Hi Yi,

I want to hear from Hangyi for detailed response, but there are known issues in tensor fitting. In the linear tensor fitting, we assume that the tensor has positive diagonal elements. This means, for example, when gradients are applied (diffusion-weighted), signal becomes lower than non-weighted images (b0). However, there are situation when this assumption is violated. At the edge of the brain, subject motion (non-reproducible) and eddy current (reproducible) causes pixel mis-registration, meaning, the pixel is sometimes inside and sometime outside the brain. Then the fitting blows up. Also, for the very highly anisotropic area such as CC, DWIs with the gradients applied perpendicular to the fiber (say, we expect only 5% signal loss) could have higher intensity than b0 due to SNR (say more than 5% signal fluctuation). In this case, the fitting blows up again.

In these situations, it is not uncommon to get negative diagonal elements or FA higher than 1.0. To prevent this, there are several proposed methods. I believe DtiStudio simply replace the negative diagonal elements with 0.

The issues of the CC should be reduced if you have higher SNR (or more DWIs). What is the resolution and the number of DWIs you are using?
For the brain edge, please check the fitting error map based on the DtiStudio Updage file I recently distributed.

Susumu

On Wed, Apr 7, 2010 at 5:21 PM, Yi Jiang <yj3 at duke.edu<mailto:yj3 at duke.edu>> wrote:
Dear All,

I computed diffusion tensors and FA, va0 (primary eigenvalue), va1 (secondary eigenvalue), and va2 (tertiary eigenvalue) by linear fitting in DTIStudio. Then I save them into raw matrix and read them in matlab.

I found the number of non-zero (the background is all zero) voxels for va1 and va2 is less than that of va0 or FA. Such as:

number of non-zeros voxels for va0 =     6311454
number of non-zeros voxels for va1 =     6310767
number of non-zeros voxels for va2 =     6248757
number of non-zeros voxels for va0 =     6311454

This happens in all my datasets, consistently.

The voxels where va0~=0 & va1==0 are not a lot (a few hundred), and they mostly are at the edge of the brain, not inside white mattter.

But the voxels where va0~=0 & va2==0 are quite a lot (tens of thousand), and they resides mostly inside white matter, such as corpus callosum.

I would like to know why this happens.

Moreover, when I try to, for example, calculate the mean va2 within corpus callosum, how can I deal with those voxels where va2==0 ? I think to treat them as equal to 0 sounds not correct physiologically. But because there are a lot, I want to count those points in, especially for small white matter structures (sometimes those va2==0 voxels can take up to 10% of a white matter structure).

Also, when I calculate radial diffusivity (va1+va2)/2, the va2==0 points generate incorrect radial diffusivity.

Thank you very much!

Best,
Yi


_______________________________________________
Mristudio-users mailing list
Mristudio-users at mristudio.org<mailto:Mristudio-users at mristudio.org>
http://lists.mristudio.org/mailman/listinfo/
Unsubscribe, send a blank email to: Mristudio-users-unsubscribe at mristudio.org<mailto:Mristudio-users-unsubscribe at mristudio.org>