On 04/23/2010 02:33 AM, Jesper Andersson wrote:
> Dear Burkhard,
>
>> but your answer did not satisfy. If the mean <l>=0 that can only
>> happen if all
>> eigenvalues are zero (unless you allow negative eigenvalues which is
>> exactly
>> my point: Negative eigenvalues should not be permitted no matter what
>> algorithm
>> you are going to use to calculate them - they have no physical meaning
>> in the diffusion tensor).
>
> Yes, FA outside the range of 0-1 means that an estimated eigenvalue is
> negative.
>
>>
>> If all li=0 than also <l>=0 but now the ratio of numerator and
>> denominator
>> in the equation of FA becomes ill-defined sqrt(0/0). Unless you have
>> another
>> explanation. Jesper mentioned something about the "true FA" implicating
>> that FSL calculates FA-values by statistical means (which by the way
>> is nowhere
>> explained or mentioned in the documents).
>
> I am not sure what you mean by "statistical means". The eigenvalues
> calculated by FSL are estimates (from the data) of some true (unknown)
> eigenvalue. Every estimate is associated with an uncertainty (error),
> the magnitude of which depends on the quality of the data. Let us assume
> in a given voxel the "true" eigenvalue is very small. The estimate will
> then be this true eigenvalue +/- some random number that depends on the
> uncertainty. And sometimes this estimate will be negative.
>
> It would be easy enough to simply (in the FSL code) set any negative
> eigenvalue to zero. This is not done because we think that
> 1. They do no harm as they stand
> 2. It might do harm to set them to zero since that would skew
> distributions.
>
> Is that clearer?
>
> Jesper
>
I think people are quite divided on this negative eigenvalue issue.
Personally, I would agree with Jesper if you are only analyzing MD, FA,
or Lambda1. However, I would try to use a non-linear non-negative DTI
fitting routine to avoid negative eigenvalues if Radial diffusivity,
Lambda2, or Lambda3 is what I am after.
Practically, most people are only interested in MD and FA. Besides, in a
decent quality DTI data set, the number of negative eigenvalue voxels is
quite small with a decently sized ROI. So in most cases it's ok to leave
it as is.
From my personal experience, I don't care this issue much for brain DTI
data set, but I care this a lot when analyzing radial diffusivity in
optic nerve and spinal cord where I only have a handful of voxels in my ROI.
Regards
Gordon
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