Hi Dianne,
the main motivation for proposing the lattice anisotropy index (LI)  
was to reduce noise effects in the computed anisotropy. At that time,   
we had just realized that noise in the DWIs would not only increase  
the variance of diffusion anisotropy measures but also bias their mean  
value. in other words, the noisier the images the higher the  
anisotropy computed from them.  This was a very troubling finding  
because statistical tests do not generally handle bias in the data.   
The problem is still unresolved today, although it is partially  
mitigated by the fact that data quality is much improved.

The main idea behind the definition of the lattice index is that if  
anisotropy is spurious (i.e. originating from white noise) the  
orientation of the anisotropic tensors in adjacent voxels should be  
uncorrelated, while if anisotropy is reflecting a true tissue feature,  
tensor in adjacent voxels should show some degree of orientational  
coherence.
In the lattice index, lack of orientational similarity results in  
lower anisotropy, intrinsically compensating for the noise-induced  
bias.  indeed, LI proved to be a very powerful way to counteract noise- 
induced  bias in the anisotropy images.

As Stefano and Steve mentioned one may have some concerns that the  
lattice index is not a purely intravoxel measure and that  it may  
iintroduce some spatial averaging in the data.  This is a reasonable  
concerns, although in my experience it is not a practically relevant  
problem.  In the lattice index, anisotropy is still an "intravoxel"  
feature, that however, is modulated (de-noised) by the degree of  
orientational coherence of tensors in surrounding voxels. If you think  
carefully, even in regions of transition between anisotropic to  
isotropic structures, the orientational field is varying smoothly,  
affecting slightly the lattice index.  The only regions where the  
assumption of slowly varying orientation is violated is at the  
interfaces between highly anisotropic white matter tracts with  
significantly different orientation, for example at the interface  
between corpus callosum and cingulum.

So, to answer your question: why the lattice index and is not more  
widely used ?  Probably for a combination of factors:  the concern for  
spatial averaging, the perception that its meaning is more difficult  
to interpret biologically,  the complexity of its definition,  the  
fact that its formula had a typo in the original publication (an  
erratum with the correct formula was subsequently published), and that  
it takes longer to compute.  Moreover, at this stage the community  
needs to find a common language and FA is so widely used that it makes  
a lot of sense to report FA data just to allow for comparisons with  
work in the literature.

This said,  I still find very convenient to inspect LI images in  
parallel with FA images and I still use LI as a filter for all  
directionally encoded color maps that we produce. The usefulness of LI  
is very evident when dealing with high resolution noisy data. i would  
not use LI for low resolution, good SNR data.
If you have a few datasets for which you would like to compare FA and  
LI we would be happy to process them. In a few months we should have  
our DTI processing software released which  compute LI and LI-filtered  
DEC maps .
Hope this helps.
Best wishes,

Carlo Pierpaoli, NIH


On Feb 6, 2008, at 2:03 AM, Steve Smith wrote:

> Thanks. Also, I would say that FA has been the most popular measure  
> of anisotropy _within_ a voxel. If you are interested in quantifying  
> anisotropy (etc.) using longer-range measures then IC may indeed be  
> interesting but is no longer a purely within-voxel measure, and so  
> the gates are open to also potentially consider methods such as  
> tractography in your analysis.
>
> Cheers, Steve.
>
>
> On 5 Feb 2008, at 21:17, Marenco, Stefano (NIH/NIMH) [E] wrote:
>
>> I think that this measure was originally named Lattice Index in the  
>> Pierpaoli paper cited. It is more stable than FA (less sensitive to  
>> noise), but more prone to partial volume effects. I used this in a  
>> recent PNAS paper (Marenco et al. 2007). Some discussion of the  
>> reasons to choose LI or IC instead of FA are mentioned in the  
>> supplementary material of the paper. Stefano Marenco
>>
>> From: Dianne Patterson [mailto:[log in to unmask]]
>> Sent: Tuesday, February 05, 2008 3:38 PM
>> To: [log in to unmask]
>> Subject: [FSL] Intervoxel Coherence, anyone?
>>
>> Dear Group,
>>
>> I recently came across the following:
>>
>> Begre, S., Frommer, A., von Kanel, R., Kiefer, C., & Federspiel, A.  
>> (2007). Relation of white matter anisotropy to visual memory in 17  
>> healthy subjects. Brain Research, 1168, 60-66.
>>
>> "DTI measures diffusion-driven displacements of molecules during  
>> their random path along axonal fibers, expressed as fractional  
>> anisotropy (FA) or intervoxel coherence (IC) ranging from 0  
>> (isotropic medium) to 1 (fully anisotropic medium). FA is a measure  
>> that quantifies the degree to which diffusion differs in the three  
>> dimensions. IC considers the degree of collinearity between the  
>> diffusion tensor of the reference voxel and the adjacent voxels,  
>> and, in addition, guarantees a better signal-to-noise ratio than  
>> the commonly used FA (Pierpaoli and Basser, 1996). Hence, based on  
>> the determination of the similarity of orientation of adjacent  
>> voxels, IC reflects a measure of connectivity, expressing fiber  
>> coherence at the voxel level with a spatial sampling limited by  
>> voxel size."
>>
>> "To compute the difference of intervoxel coherence values between  
>> the low performer and the high performer group, a t-test was  
>> computed for each voxel within the 3-D white matter template. To  
>> identify volume-corrected regions, clusters were defined as 6 or  
>> more neighboring voxels (6 mm3) exceeding the t-test value of 2.9  
>> (P < .01). For each cluster, IC values were averaged and tabulated  
>> and Talairach coordinates (Talairach and Tournoux, 1988) of the  
>> centers of gravity were noted. Clusters were assigned to the  
>> underlying white matter using 3-D anatomical data."
>>
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>> =====================================================================
>> I can find little else on the subject, and I wondered, if IC is so  
>> superior to FA, why isn't it a commonplace dti measure?
>> Has anyone out there used this technique, and would you care to  
>> comment on it?
>>
>> Thankyou,
>>
>> Dianne
>>
>> -- 
>> Dianne Patterson, Ph.D.
>> [log in to unmask]
>> ERP Lab
>> University of Arizona
>> 621-3256 (Office)
>
>
> ---------------------------------------------------------------------------
> Stephen M. Smith, Professor of Biomedical Engineering
> Associate Director,  Oxford University FMRIB Centre
>
> FMRIB, JR Hospital, Headington, Oxford  OX3 9DU, UK
> +44 (0) 1865 222726  (fax 222717)
> [log in to unmask]    http://www.fmrib.ox.ac.uk/~steve
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>