# The difference of FOD

Dear all

I have a question about the difference of FOD. According to the picture,A is the original FOD, B is the wider FOD compared to the A（the height is same）,C is a scaled FOD（the shape is same,the size is bigger than A）
Q1. The differences of A and B、A and C are meaningful?
Q2. If it is meaningful,what’t the relationship of the different FODs with the physiological basis ? Could you give me some examples?

Thanks

So the way we think about these things these days, the difference between A & C is that C simply corresponds to a larger amount of fibres, with an otherwise identical spread in the orientations. B on the other hand also corresponds to a larger amount of fibres than A, but with a greater spread in the orientations (the apparent fibre density in B & C might actually be similar, but it’s hard to tell). This is because the amount of fibre (the apparent fibre density) is essentially the integral of the FOD over the solid angle corresponding to the fibre bundle of interest. So the FOD B & C might have a similar amount of fibres overall (i.e. similar FOD integrals), but because there is greater dispersion in B, its peak amplitude is by necessity lower.

Importantly, the fact that A & B have similar peak amplitudes is essentially meaningless given the difference in dispersion - at least if what you’re interested in is the apparent fibre density.

Importantly, the fact that A & B have similar peak amplitudes is essentially meaningless given the difference in dispersion - at least if what you’re interested in is the apparent fibre density.

… If what you’re interested in is the modern definition of Apparent Fibre Density. In the original AFD paper, the FOD amplitude in any particular direction was defined as “the AFD”. Nowadays, we use the term “AFD” to refer to the spherical integral Donald described, precisely for this reason: it quantifies the fibre density within a bundle relatively independently of the degree of fibre dispersion (whereas the amplitude in any particular direction is dependent on both the overall density and the orientation dispersion of the bundle).

The integral of the FOD lobe is related to the amounts of fibres,So the integral of the FOD lobes in different voxels (one people),or in different people(using the group average response function) are comparable?

According to the definition of FOD(fibre orientation density) ,it includes the information of orientation and volume fraction.So What’s the meaning of the amplitude of FOD?
Is the the amplitude of FOD comparable in different voxels or in different people?

And What’s the use of the amplitude of FOD? Just tractography ?

My understanding of FOD is incomplete，expecting you can provide me some advises !

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So the integral of the FOD lobes in different voxels (one people),or in different people(using the group average response function) are comparable?

As long as you have performed the requisite pre-processing steps: yes. The former requires B1 bias field correction. The latter requires inter-subject intensity normalisation, and use of a group average response function. More details in documentation page here.

According to the definition of FOD(fibre orientation density) ,it includes the information of orientation and volume fraction.So What’s the meaning of the amplitude of FOD?

Firstly, we try to avoid use of the term “volume fraction”, since (unlike other spherical deconvolution solutions) we do not normalise the tissue(s) in each voxel to a unit volume / probability density function over the sphere. So what you get in this case is proportional to the MR signal amplitude, which is dependent on both the volume of the relevant tissue as well as e.g. T2 effects.

Secondly, in an ideal scenario, the FOD amplitude would correspond to the fibre volume per steradian (solid angle = angle on the S2 sphere rather than the circle). However in reality the limited bandwidth of the response function and the limited lmax at which the FOD is estimated mean that this is never actually the case. So the precise FOD amplitude along a precise direction doesn’t really mean all that much (though, as you say, it is used directly by some tractography algorithms). The integral of the FOD over a solid angle corresponding to a particular fibre bundle is however relatively robust & useful.

Is the the amplitude of FOD comparable in different voxels or in different people?

Theoretically if you do the pre-processing steps described above, then yes it is. Indeed this is precisely how statistical testing of AFD was done in the original 2012 publication. However even minor residual mis-alignments in FODs between subjects after registration cause substantial variance in these amplitudes. Hence why the modern statistical approach uses segmented FODs, parameterising the FOD lobe integral as the fibre density for each particular fibre bundle within each template image voxel (i.e. each fixel).