[Mrtrix-discussion] SIFT: normalise to the b0 image
J-Donald Tournier
jdtournier at gmail.com
Fri Dec 19 09:59:30 PST 2014
Hi Jan,
Well, there is one 'theoretical' reason for using signal attenuation that I
can think of: estimating the spin propagator or derivatives. This would
encompass q-space based approaches such as DSI and QBI, as well as ADC and
tensor-based approaches. The idea is that the spin propagator is a
probability density function, and so should inherently be normalised.
However, this doesn't mean that these approaches don't suffer from the
exact same issues, far from it. There is no getting away from the fact that
some tissue types have different T2 values, and hence provide very
different contributions to the b=0 signal. If the signal was purely
proton-density weighed, this wouldn't be such an issue - all tissue types
would give roughly the same b=0 signal per unit volume. Unfortunately they
don't, so the relative contributions to the signal attenuation will be
biased by their volume fractions, just the same as we've described here.
So I think the 'theoretical' justification for using signal attenuation is
just that: theoretical. It is built on assumptions that can trivially be
shown to be invalid. As to how much of an impact this has in practice, well
I guess the jury is still out...
As to T2 shine-through, that's something that I'd like to look into
further. It depends on what's causing the shine-through. If for instance
the shine-though is well modeled as an increase in extracellular fluid with
CSF-like properties, I would argue that normalising to the b=0 signal is
very precisely the wrong thing to do, for exactly the reasons I've given in
previous emails: all it would do is suppress the apparent contributions of
shorter T2 components (i.e. WM & GM) and drastically reduce the apparent
fibre density. This would for instance make it much harder to track through
such regions, since termination thresholds (e.g. FA, FOD amplitude) would
be artificially reduced. In contrast, using the raw signal would have given
you the right (relative) volume fraction - especially when using more
complete models like Ben Jeurissen's multi-tissue CSD. That said, there are
probably many ways that large changes in T2 can occur, so this would
clearly depend on the pathology.
So clearly there's a lot to think about here, but I reckon we all need to
have a long hard look at this idea that we can only work with the signal
attenuation... I've certainly managed to get by without it for the last 10
years or so - and I should point out, so has anyone using MRtrix... ;)
Cheers, and merry Christmas to everyone!
Donald
--
Dr J-Donald Tournier (PhD)
Senior Lecturer, Biomedical Engineering
Division of Imaging Sciences & Biomedical Engineering
King's College London
A: Department of Perinatal Imaging & Health, 1st Floor South Wing, St
Thomas' Hospital, London. SE1 7EH
T: +44 (0)20 7188 7118 ext 53613
W:
http://www.kcl.ac.uk/medicine/research/divisions/imaging/departments/biomedengineering
On 19 Dec 2014 15:55, "Jan Schreiber" <schreiber at cbs.mpg.de> wrote:
> Hi Rob and Donald,
>
> thank you so much for your comprehensive answers!
>
> I do see the point with the partial volumes, that is very convincing.
>
> Still, I thought theoretically the fibre structure should be described by
> the signal attenuation. Using the raw signal one not only has a bias field
> but also the T2 shine through.
> But if the negative influence of the partial volume effects are much
> stronger than T2 shine through and bias field then it is of course a good
> reason to go with the raw DW signal...
>
> Do you think that other local models suffer from the partial volume issue
> equally?
>
> Looking very much forward to reading your future publication!
>
> Cheers,
> Jan
>
>
> On 12/15/2014 02:18 PM, J-Donald Tournier wrote:
>
>> Hi Jan,
>>
>> Just to expand a little further on what Rob said, the main reason for
>> not normalising to the b=0 signal is essentially to preserve the
>> apparent fibre density. Really, the problem is that normalising to the
>> b=0 signal breaks the linearity of the DWI signal to the FOD
>> (irrespective of the log transform), and that is something we think
>> should be avoided if at all possible. This is an issue that I wish I'd
>> described explicitly in my original 2004 spherical deconvolution paper
>> (even back then, all the processing was done on the raw signal)... As
>> Rob mentioned, we'll try to rectify this is a future paper, but for now,
>> here's a brief description of my reasons for this.
>>
>> This is based on a fundamental aspect of spherical deconvolution and
>> mixture models in general: that the DWI signal scales /linearly/ with
>> the amount of tissue present. While the simulations done by Dave
>> Rafflelt in the paper Rob mentioned do make the point very nicely, their
>> purpose is a lot more specific than is required for this argument.
>> Basically, If a voxel contains two fibre bundles, the signal you measure
>> is the sum of the signals for each bundle individually (at least, it's
>> modelled as such). This however does not necessarily hold for the signal
>> /attenuation/, since the b=0 signal is not uniform throughout the brain.
>>
>> Consider for example voxels containing mixtures of WM & CSF. The b=0
>> signal for CSF is typically very high relative to WM (due to its long
>> T2). If half the voxel contains CSF, the other half WM, the b=0 signal
>> for that voxel would be essentially double what it would be for pure WM
>> (assuming CSF b=0 signal is ~3x that of WM). On the other hand, the DW
>> signal for CSF is small, and to all intents and purposes negligible at
>> high b-values. This means the /raw/ DW signal would be what you would
>> expect to measure for a voxel containing half the volume of WM, but the
>> signal attenuation would be halved again (since the b=0 signal is
>> double). So the apparent relative volume fraction (fibre density)
>> derived using signal /attenuation/ would be ~a quarter that of pure WM,
>> while using the/raw/ DW signal would give you the correct answer: half
>> that of pure WM. If you care about being able to compare apparent fibre
>> densities across voxels in the presence of large variations in the b=0
>> signal between different tissue types (i.e. as you would expect in the
>> brain), you shouldn't normalise to the b=0 image.
>>
>> Note this isn't just about voxel-based analysis of apparent fibre
>> density or SIFT: this is also important for example during the
>> tractography itself, since the termination criteria are applied on the
>> FOD amplitude directly. It is also important for anything that involves
>> consistent scaling of the noise (e.g. bootstrap analysis), since
>> normalising to the b=0 will also introduce large and rapid spatial
>> variations in the noise characteristics of the data. There are many
>> facets to this issue, and I won't bother going into them in any more
>> detail here - I'll leave that for the future paper Rob mentioned. But in
>> a nutshell, this is the reason MRtrix has always operated on the raw DW
>> signal, not its attenuated version.
>>
>> Hope this all makes sense.
>> Cheers,
>>
>> Donald.
>>
>>
>> On 15 December 2014 at 00:32, Robert Smith <robert.smith at florey.edu.au
>> <mailto:robert.smith at florey.edu.au>> wrote:
>>
>> Hi Jan,
>>
>> This is an important point, and one that we sometimes forget that we
>> (as in, the MRtrix dev team) think about quite differently to others
>> in Diffusion MR.
>> We will draw attention to this issue in an upcoming publication, but
>> I'll try to give a succinct explanation here.
>>
>> Conventionally, the log-transform with respect to the b=0 image
>> converts a signal amplitude to an apparent diffusion coefficient;
>> nothing controversial here. However if you were to then apply a
>> spherical deconvolution transform, the FOD amplitude along a
>> particular direction would be proportional to the ADC of the fibre
>> population oriented along that direction. This isn't particularly
>> useful information; it doesn't tell us much about differences
>> between fibre populations throughout the image, or indeed within a
>> voxel.
>>
>> Ideally what we actually want for a number of applications is the
>> volume of each fibre population element, in all voxels throughout
>> the image. Based on David Raffelt's early simulations
>> <http://www.sciencedirect.com/science/article/pii/S1053811911012092>,
>> it
>> turns out that (under certain conditions) the radial component of
>> the DWI signal amplitude is actually a pretty decent marker for
>> intra-cellular volume. Therefore, by ignoring the b=0 images
>> completely and just running SD on the raw DWI intensities, we get
>> pretty useful biological information and interpretation from the
>> FOD; we also conveniently bypass the issue of Gibbs ringing in the
>> b=0 images. Caveat is that you need a uniform B1 field (i.e.
>> intensity bias field correction); for applications like AFD you also
>> need inter-subject intensity normalisation, but that's not
>> necessarily a problem for SIFT depending on how you're using it.
>>
>> That's all for now. Hope that clarifies why we choose to apply SD in
>> this way; in fact, this approach dates all the way back to the
>> original SD paper.
>> Rob
>>
>>
>> --
>>
>> *Robert Smith, Ph.D*
>> Research Officer, Imaging Division
>>
>> The Florey Institute of Neuroscience and Mental Health
>> Melbourne Brain Centre - Austin Campus
>> 245 Burgundy Street
>> Heidelberg Vic 3084
>> Ph: +61 3 9035 7128
>> Fax: +61 3 9035 7301
>> www.florey.edu.au <http://www.florey.edu.au/>
>>
>> On Sat, Dec 13, 2014 at 1:37 AM, Jan Schreiber <schreiber at cbs.mpg.de
>> <mailto:schreiber at cbs.mpg.de>> wrote:
>>
>> Dear MRtrix Team,
>>
>> thank you very much for this great software and for making it
>> freely
>> available!
>>
>> In your publication "SIFT: Spherical-deconvolution informed
>> filtering of
>> tractograms" you state
>>
>> "The diffusion signal must not be normalised to the b = 0 image
>> intensity. This preserves the linearity of the spherical
>> deconvolution
>> transform between the measured DW signal and the resulting FOD."
>>
>> Shouldn't we preserve the linearity of the spherical deconvolution
>> transform between the FOD and the DW _signal attenuation_ rather
>> than
>> the DW _signal_?
>>
>> Thanks,
>> Jan
>>
>>
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>>
>>
>> --
>> *Dr J-Donald Tournier (PhD)*
>>
>> /Senior Lecturer, //Biomedical Engineering/
>> /Division of Imaging Sciences & Biomedical Engineering
>> King's College London/
>> /
>> /
>> /*A:* Department of Perinatal Imaging & Health, 1^st Floor South Wing,
>> St Thomas' Hospital, London. SE1 7EH
>> /
>> /*T:* +44 (0)20 7188 7118 ext 53613/
>> /*W:*
>> http://www.kcl.ac.uk/medicine/research/divisions/imaging/
>> departments/biomedengineering/
>>
>
>
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