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Hello Dr Pierpaoli, I am wondering if you have, in fact, posted the DTI software that computes LI? Thankyou, Dianne Patterson On Wed, Feb 6, 2008 at 10:56 AM, Carlo Pierpaoli <[log in to unmask]> wrote: > 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." >>> >>> >>> ============================================================================================ >>> 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 >> >> --------------------------------------------------------------------------- >> >> > -- Dianne Patterson, Ph.D. [log in to unmask] University of Arizona SLHS 328 621-5105