Gradient scaling of dirgen output

[ThijsDhollander]

@rnibbs

So if the output of dirgen is 0.4326302799 -0.8109177734 0.394009398 and I wanted a b=1000 with a bmax of 3000 I would multipy the 3 numbers by sqrt(1000/3000).

I agree with @bjeurissen : this is correct. I double checked the example vector you provided, and it also has (correctly) an L2 norm of 1.

See for more information also this quote (and the full post that it links to):

@jdtournier

I’d assume that the right scaling here should actually be sqrt(1000/3000) = 0.57735, not 0.33 - this is what the code in the MRtrix3 backend assumes, and I’m pretty sure we verified this was correct at the time…

and this one just to confirm (comes from the same original thread):

@ThijsDhollander

Yep, I can confirm this. It’s the squares of the (L2) norms of your vectors that must scale like the b-values, with the highest b-value just having a unit norm (and then setting that as the b-value of your scan). So for example for a multi-shell acquisition with b-values = 0,1000,2000,3000 your diffusion vector norms as specified in that file should be 0, 0.5773, 0.8165 and 1. The squares of these norms are 0, 0.333…, 0.666… and 1.

I’ve never had problems creating multi-shell protocols for Siemens scanners in this fashion, always using (combinations of) direction sets from dirgen… Maybe copy paste the text of your problematic scheme here, so we could have a look what could’ve gone wrong.