Hi
You can show using a little algebra that the mode is given by:
e1=l1-MD, e2=l2-MD, e3=l3-MD;
n = (e1 + e2 - 2*e3)*(2*e1 - e2 - e3)*(e1 - 2*e2 + e3);
d = (e1*e1 + e2*e2 + e3*e3 - e1*e2 - e2*e3 - e1*e3);
d = 2*d*d*d;
mode = n/d;
which is what the script does (and dtifit as well).
Saad.
On 16 Mar 2011, at 11:03, Riccardo Navarra wrote:
> From your script I can find (see #s) FA formula [13] in Ennis 2006:
>
> ${FSLDIR}/bin/fslmaths ${bn}_L1 -add ${bn}_L2 -add ${bn}_L3 -div 3 tmpMD
> # -> mu = (l1 + l2 +l3) /3
> ${FSLDIR}/bin/fslmaths ${bn}_L1 -sqr tmpL1sq
> ${FSLDIR}/bin/fslmaths ${bn}_L2 -sqr tmpL2sq
> ${FSLDIR}/bin/fslmaths ${bn}_L3 -sqr tmpL3sq
> ${FSLDIR}/bin/fslmaths ${bn}_L1 -sub tmpMD -sqr tmpl1subsq
> ${FSLDIR}/bin/fslmaths ${bn}_L2 -sub tmpMD -sqr tmpl2subsq
> ${FSLDIR}/bin/fslmaths ${bn}_L3 -sub tmpMD -sqr tmpl3subsq
> ${FSLDIR}/bin/fslmaths tmpL1sq -add tmpL2sq -add tmpL3sq denom
> # -> denom = l1^2 + l2^2 + l3^2
> ${FSLDIR}/bin/fslmaths tmpl1subsq -add tmpl2subsq -add tmpl3subsq -mul 1.5 numer
> # -> numer = 3/2 * ( (l1-mu)^2 + (l2-mu)^2 + (l3-mu)^2 )
> ${FSLDIR}/bin/fslmaths numer -div denom -sqrt ${ob}_FA
> # -> FA = sqrt ( numer / denom ) --> [13] in Ennis 2006
>
> How to translate MO script to get [8], [9], [14] or l1*l2*l3 / sqrt( (l1-mu)^2 + (l2-mu)^2 + (l3-mu)^2)^3 ?
>
> ${FSLDIR}/bin/fslmaths ${bn}_L1 -sub tmpMD tmpE1
> ${FSLDIR}/bin/fslmaths ${bn}_L2 -sub tmpMD tmpE2
> ${FSLDIR}/bin/fslmaths ${bn}_L3 -sub tmpMD tmpE3
> ${FSLDIR}/bin/fslmaths tmpE3 -mul -2 -add tmpE1 -add tmpE2 tmpN1
> ${FSLDIR}/bin/fslmaths tmpE1 -mul -2 -add tmpE2 -add tmpE3 tmpN2
> ${FSLDIR}/bin/fslmaths tmpE2 -mul -2 -add tmpE1 -add tmpE3 tmpN3
> ${FSLDIR}/bin/fslmaths tmpN1 -mul tmpN2 -mul tmpN3 -mul -1 tmpN
> # -> tmpN = -[(l1-mu)+(l2-mu)-2(l3-mu)]*[(l2-mu)+(l3-mu)-2(l1-mu)]*[(l1-mu)+(l3-mu)-2(l2-mu)] (???)
> ${FSLDIR}/bin/fslmaths tmpE1 -sub tmpE2 -sub tmpE3 -mul tmpE1 tmpD
> ${FSLDIR}/bin/fslmaths tmpE2 -sub tmpE3 -mul tmpE2 -add tmpD tmpD
> ${FSLDIR}/bin/fslmaths tmpE3 -mul tmpE3 -add tmpD
> ${FSLDIR}/bin/fslmaths tmpD -thr 0 -sqrt tmpD
> ${FSLDIR}/bin/fslmaths tmpD -mul tmpD -mul tmpD -mul 2 tmpD
> # -> tmpD ???
> ${FSLDIR}/bin/fslmaths tmpN -div tmpD -max -1 -min 1 ${ob}_MO
>
--
Saad Jbabdi
University of Oxford, FMRIB Centre
JR Hospital, Headington, OX3 9DU, UK
(+44)1865-222466 (fax 717)
www.fmrib.ox.ac.uk/~saad
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