Response function- spherical harmonic coefficients

Dear experts,

This is a question of what constitute a “good” single-fibre response function in the WM.

Specifically, I want to find out any “rules” regarding the pattern (+ or -), and size of the spherical harmonic coefficients from the low to high-order terms.

I already know:

  1. shview response.txt…expect a flat disc-shaped profile with a centre pit.
  2. Check the FOD/fODF profile in the expected single-fibre regions.

Many thanks,


Yes, we used to have clearer guidelines as to what to expect for the response function coefficients in the documentation for MRtrix version 0.2, but these haven’t made it across to the new version. I’ll add that to the to-do list…

Just copy/pasting what the docs for the old version used up say:

Normally, the values in the response file should alternate between positive and negative while decreasing in magnitude. The first value should be positive, and have an amplitude similar to (but not necessarily the same as) the b=0 brain white matter signal (you can verify this by loading the dwi.mif image and placing the focus within a white matter region - the intensity is displaced in the bottom right of the statusbar). Note that this is only an approximate guideline: it is not unusual for the first coefficient to differ from the b=0 signal quite significantly (on the other hand, if they differ by orders of magnitude, something has definitely gone wrong).

Bear in mind that these still remain pretty rough guidelines: you can find a response that ticks all these boxes, yet nonetheless looks completely wrong when inspected in shview. There’s no real substitute for having a quick look…

Thanks, Donald.

“Normally, the values in the response file should alternate between positive and negative while decreasing in magnitude”.

Are there rules about order of magnitude reductions from the lowest to the highest coefficients?

For example, I often found the consecutive coefficients differ in amplitude by ~3-4x folds, except between the highest two coefficients. ( I would guess the estimated RF coefficient gets less reliable at higher, compared to lower order terms?)

Thanks again,

Happy holiday, Joseph

Nothing beyond what my 2013 NMR Biomed article reported (Figure 3 & Table 1). It’s b-value dependent, and will depend on the SNR for the higher terms - eventually those terms will be dominated by noise, which is why they level off for the higher coefficients.

So what you report sounds about right :slight_smile:

Great, thanks Donald

Happy New Year