# [Neuroimaging] Interpretation of beta in the Sparse Fascicle Model

Reid, Robert I. (Rob) Reid.Robert at mayo.edu
Mon Nov 14 12:42:11 EST 2016

```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/>

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://mail.python.org/pipermail/neuroimaging/attachments/20161114/a82cf5a0/attachment.html>
```