# FOD amplitudes

In tckgen, there’s a cutoff setting for terminating tracts if the FOD amplitude falls below it.

Do you determinate if an FOD is below the cutoff by finding the maximum amplitude of the FOD or is it the amplitude of the FOD for whatever direction was chosen to grow the streamline?
How is the amplitude computed?

Thanks

Hi @Goku,

This is getting quite deep into the guts of exactly how the streamlines algorithms operate…

For the iFOD2 algorithm specifically, the threshold is applied at this point. The algorithm draws a series of “candidate paths”, which are arcs through space constrained by the step size and the maximum turning angle. For the number of samples specified for the algorithm (4 by default), the FOD field is interpolated at a spatial position along the arc, and the amplitude of the FOD in the direction specified by the tangent of the arc at that location in space is measured. If that amplitude is less than the specified threshold for any of the samples along that arc, then that candidate path is given a “probability” of zero, i.e. it’s not a valid candidate path.

So essentially, In the case of iFOD1 & iFOD2, the FOD amplitude in the direction of the tangent of the streamline must be above this threshold. That threshold is not applied to the maximum amplitude of the FOD, since that would require determination of the direction of the FOD peak, and such is never actually performed within iFOD1 / iFOD2. Conversely, the SD_STREAM algorithm, which explicitly determines the orientation of the local FOD peak and traverses in that direction, there the equivalent cutoff would in fact apply to the amplitude of the peak being traversed.

I hope that makes sense. If not, @jdtournier will need to write a paper explaining how iFOD2 works…

Rob

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Thanks for the info rsmith that makes sense. I guess I’m wondering if there’s a simple way to tell if an FOD is in white matter tissue or not. For instance, with FA you can just set a simple threshold of 0.2. Is there something similar for FODs maybe the L2 norm?

I guess I’m wondering if there’s a simple way to tell if an FOD is in white matter tissue or not

I would personally re-phrase this question as: Is it possible to both label a voxel as white matter or some other tissue, and estimate the underlying fibre orientations? The answer would then be yes: this is precisely what multi-tissue CSD does, but relies on incorporating additional image data during FOD estimation rather than subsequent to such.

If I instead take your question literally, i.e. “tissue segmentation based on FODs”, then one method I would suggest looking at is anisotropic power. I actually have code lying around somewhere to do this… As far as an approximate equivalent for “labelling voxels as White Matter or otherwise based on Fractional Anisotropy”, there is the Generalised FA, but it tends to be looked at with a degree of disdain within the spherical deconvolution community, and I don’t think it gives a very good tissue separation.

For instance, with FA you can just set a simple threshold of 0.2.

Just to be clear for anyone who comes across this: Setting an FA threshold only gives a crude approximation of a white matter segmentation. This is far from an optimal tissue segmentation technique, and not something we advocate using without a clear knowledge of the limitations of such.

The L2 norm can be exactly computed, but you’re probably after the “size” / integral of the FOD instead. That’s simply a voxel-wise “total apparent fibre density” map. Long story short: you can obtain that one directly by extracting the first volume from the FOD file (mrconvert ..... -coord 3 0). However, that’ll still be T2 weighted, and feature some T2 shine-through that might be entirely unrelated to whether the voxel is in WM or not (so a magnitude you’d optimally want to not take into account for your goals). If you’re performing a 3-tissue CSD variant on the data, you can try and normalise the aforementioned WM FOD integral by the sum of this integral with that of the other tissue types (GM and CSF). You’d then be looking at the WM-likeness ( https://www.researchgate.net/publication/315836029_Towards_interpretation_of_3-tissue_constrained_spherical_deconvolution_results_in_pathology ) as a map, given the 3-tissue CSD model. Again, long story very short, that one will “embody” some information similar to the anisotropic power, but also factor in the diffusivity information and the fact that different tissues have different T2’s, etc… all in one metric. Using effectively that, I was for instance able to directly generate a map with a very similar contrast to a T1-weighted image: https://www.researchgate.net/publication/307862882_Generating_a_T1-like_contrast_using_3-tissue_constrained_spherical_deconvolution_results_from_single-shell_or_multi-shell_diffusion_MR_data … so effectively a piece of information that identifies the WM pretty well, and with a metric that is relatively constant in most areas therein.
We’re using WM-likeness (and GM- and CSF-likeness) now also directly to study e.g. pathology (among others): https://www.researchgate.net/publication/324771728_Investigating_microstructural_heterogeneity_of_white_matter_hyperintensities_in_Alzheimer’s_disease_using_single-shell_3-tissue_constrained_spherical_deconvolution . Note how well the (normal appearing) white matter can be separated from lesions (and thus also from healthy GM and CSF).

Expect to see more in this space soon.

Cheers,
Thijs