[Neuroimaging] [Dipy] RE: Interpretation of beta in the Sparse Fascicle Model

[Ariel Rokem]

Hi Rob,

Apologies for the delay in responding. This is not straightforward to do,
and I believe that it would be an oversimplification to think of the SFM
weights directly as indicating the volume fraction of nerve fibers in a
particular direction. One reason for that is that the SFM does not
separately model the constrained and hindered components of the signal (see
this paper for some more details of this issue:
https://www.ncbi.nlm.nih.gov/pubmed/15979342). Instead an interpretation
that I think is more appropriate (if less satisfying) is that the weights
are roughly proportional to a reduction in the variance of the signal,
relative to an isotropic, that is explained by fibers in any given
directions. As you noted, there is nothing that enforces that these sum to
1, or that they do not exceed 1.

As for ways to do what you want to do, one approach to estimation of fiber
density in any given direction is provided through the AFD framework,
proposed by Raffelt and colleagues here:

https://www.ncbi.nlm.nih.gov/pubmed/22036682

Another approach, more closely related to the SFM, is provided by
Dell'Acqua and colleagues in their HMOA measure:

https://www.ncbi.nlm.nih.gov/pubmed/22488973

Note the normalization procedure that they take when interpreting fODF
weights (left column of page 2469). You would need to do something like
that with SFM weights to increase their interpretability in this direction.

Cheers,

Ariel



On Tue, Nov 22, 2016 at 2:32 PM, Reid, Robert I. (Rob) <Reid.Robert at mayo.edu
> wrote:

> Hi again,
>
>
>
> Does anybody have any suggestions on quantitatively estimating the
> fraction of each fiber bundle in a voxel?
>
>
>
> Thanks,
>
>
>
>      Rob
>
>
>
> --
>
> Robert I. Reid, Ph.D. | Sr. Analyst/Programmer, Information Technology
>
> Aging and Dementia Imaging Research | Opus Center for Advanced Imaging
> Research
>
> Mayo Clinic | 200 First Street SW | Rochester, MN 55905 | mayoclinic.org
> <http://www.mayoclinic.org/>
>
>
>
> *From:* Neuroimaging [mailto:neuroimaging-bounces+reid.robert=
> mayo.edu at python.org] *On Behalf Of *Reid, Robert I. (Rob)
> *Sent:* Monday, November 14, 2016 11:42 AM
> *To:* 'neuroimaging at python.org'
> *Subject:* [Neuroimaging] Interpretation of beta in the Sparse Fascicle
> Model
>
>
>
> Hi,
>
>
>
> I am trying to use a set of simulations to optimize the b values in a
> multishell acquisition for general use.  My current choice for the
> objective (cost) function is the difference between the true input and
> apparent recovered “total fiber vector”s, which I define as
>
> (f0 * d0, f1 * d1, f2 * d2),
>
> where fi and di are the voxel fraction and direction of fiber I, so it is
> a 9 dimensional vector, and the error in each fiber’s direction is weighted
> by its voxel fraction.  My problem is getting the fiber fractions.  I have
> mostly followed the sparse fascicle model tutorial in
> http://nipy.org/dipy/examples_built/sfm_reconst.html#example-sfm-reconst
> , and the beta values seem to be what I should use.  I set the apparent
> fiber fraction to sum(beta_j), for j in the part of the sphere closest to
> the true direction of fiber i.  (That can misassign outliers, I know, but
> that’s a different problem.)
>
>
>
> It **almost** works, but sum(beta) is often a bit larger than 1,
> especially as  b of the outer shell is raised from 2000 to 3000.
>
>
>
> For example, with (f0, f1, f2) = (0.500, 0.250, 0.125),
>
> with b_hi = 2000 I get [ 0.50418062,  0.21846355,  0.15918703]
>
> with b_hi = 3000 I get [ 0.63809217,  0.36634215,  0.30759466]
>
>
>
> When averaged over a large number of simulations and scenarios the trend
> is that there is less angular error at b_hi = 3000, but the overall error
> function favors b_hi = 2000, because the fiber fraction estimates are so
> bad at b_hi = 3000.  I am using the ExponentialIsotropicModel for the
> isotropic part.
>
>
>
> Am I abusing beta in some way, or is it just overestimating the fiber
> fractions “naturally” and I should accept the indication that the fiber
> fraction estimation degrades when going from 2000 to 3000?
>
>
>
> Note that beta should not (in my understanding) be normalized so that
> sum(beta) = 1.  In the above example the sum of the fiber fractions is
> 0.875, and in general this is a quantity that I would like to estimate.
>
>
>
> Thanks,
>
>
>
>      Rob
>
>
>
> --
>
> Robert I. Reid, Ph.D. | Sr. Analyst/Programmer, Information Technology
>
> Aging and Dementia Imaging Research | Opus Center for Advanced Imaging
> Research
>
> Mayo Clinic | 200 First Street SW | Rochester, MN 55905 | mayoclinic.org
> <http://www.mayoclinic.org/>
>
>
>
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>
>
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