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

Sun Nov 27 22:13:31 EST 2016

Hi Rob,

On Sun, Nov 27, 2016 at 1:36 PM, Reid, Robert I. (Rob) <Reid.Robert at mayo.edu
> wrote:

> > 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
>
>
>
> Ah, that’s what I was missing.  I was hoping to use a sparse formulation
> since those appear more tolerant of lower b than deconvolution approaches
> (which are also solving for the bundle dispersion), but maybe I can apply a
> post-hoc compromise.  I think for now though I will continue with a
> constrained deconvolution and HMOA approach, since it explicitly includes
> normalization to the bundle fraction ~ 1 case.
>
>
If you end up writing code that calculates the HMOA from SFM weights,
please consider sharing this code. I'd be happy to have something like that
integrated into Dipy, and I know of others who would find this useful.

Best,

Ariel

>
>
> 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 *Ariel Rokem
> *Sent:* Thursday, November 24, 2016 3:03 PM
> *To:* Neuroimaging analysis in Python
> *Subject:* Re: [Neuroimaging] [Dipy] RE: Interpretation of beta in the
> Sparse Fascicle Model
>
>
>
> 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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