[Mrtrix-discussion] SIFT: normalise to the b0 image

Mon Dec 15 15:11:40 PST 2014

This is a very interesting discussion, thanks Rob and Donald for the
detailed answers.

Rob, you mention that for inter-subject studies you would need
a) B1 field correction (presumably accomplished by N3 or N4 or similar
tools), and
b) inter-subject intensity normalisation.

If not using a b=0 singnal normalisation, how can we get signal units
comparable between individuals?

Dr. Luis Concha
Instituto de Neurobiología
Laboratorio C-13
UNAM, Campus Juriquilla
Boulervard Juriquilla 3001
Juriquilla, Querétaro.
C.P. 76230
México
Tel (442) 2 38 10 54
Fax (442) 2 38 10 46
http://personal.inb.unam.mx/lconcha/

On Mon, Dec 15, 2014 at 7:18 AM, J-Donald Tournier <jdtournier at gmail.com>
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>
> 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
>>
>> On Sat, Dec 13, 2014 at 1:37 AM, Jan Schreiber <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 EngineeringKing'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
> <%2B44%20%280%2920%207188%207118%20ext%2053613>*
> *W: http://www.kcl.ac.uk/medicine/research/divisions/imaging/departments/biomedengineering
> <http://www.kcl.ac.uk/medicine/research/divisions/imaging/departments/biomedengineering>*
>
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