Dear Burkhard,
there has been a lot of posts on this. I suggest you have a quick
search through the archives.
In short: Our estimate of the FA is the "true FA" +/- some
uncertainty. The magnitude of the uncertainty will depend on the noise
of your data (recent post on that by Matt Glaser). If the "true FA" is
close to 1, then with a positive "uncertainty deviation" it may become
greater than 1. If it is close to 0 it may become negative with a
negative "uncertainty deviation". Neither of these values are of
course physically meaningful.
BUT, they do no harm. They will enter into the statistics as any other
values. If we on the other hand were to truncate the values to the 0-1
range we would mess with the distribution of the errors. And that
might possibly do some harm.
Hope that was clear.
Good luck Jesper
On 22 Apr 2010, at 15:01, Burkhard Maedler wrote:
> Dear FSL-community,
> I recognize that the histogram output from calculated DTI-FA data
> with FSL
> always produces a value range that exceeds 1.0 (typical max values
> for FA
> are on the order of 1.2).
> According to the calculation for FA (Conturo MRM1916)
>
> FA=sqrt(3/2)*sqrt((l1-<l>)^2+(l2-<l>)^2+(l3-<l>)^2)/
> (sqrt(l1^2+l2^2+l3^2))
>
> with: <l>=(l1+l2+l3)/3
>
> this seems to be impossible no matter what actual numerical value
> the eigenvalues
> li have, unless one allows negative eigenvalues.
> Since negative li don't have physical meaning they should be omitted
> and constraint
> to : {li}>=0 !
> Has somebody an explanation that causes this strange "normalization"
> behaviour for FA in FSL?
>
> Thanks Burkhard.
>
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