Optimal gradient distribution for DTI and tractography

Hi all,

I’m in the process of evaluating a diffusion protocol. The purpose is to do tractography of some main fiber tracts (CST, SLF, Cingulum, IFOF) and to quantify the DTI parameters in them. There is time for 60 DWIs (and some b-zeroes) and voxel size is 2 x 2 x 2.6 mm (this was the most isotropic that could be reached). I’m now wondering what the optimal configuration would be for the DWIs:

  1. 20 unique gradient directions repeated 3 times.
  2. 30 unique gradient directions repeated 2 times
  3. 60 unique gradient directions (not repeated)

What would you recommend, taking into account that more repetitions will result in higher SNR, but more unique directions will facilitate tractography? We tested the first version (3 x 20 unique directions) and the tracts already looked good using iFOD2 as tractography method. But perhaps there are reasons to push for one of the other options?


I would always recommend acquiring unique directions – i.e. your option 3.

All these directions contribute to the overall SNR regardless of whether they’re unique or not – if you have the same overall number of volumes, you’ll have the same overall SNR, all other things being equal. Yes, your individual images might have higher SNR if they’ve been averaged, but that’s not what you’re interested in – you’re interested in the overall fit (whether DTI or CSD, or whatever else you might be using these data for), and the number of measurements is the same in both.

But averaging directions like this is not something we recommend: if there is any scope for motion during your acquisition, you might end up taking two perfectly usable image volumes that happen to be misaligned (which can be corrected) and averaging them produce a single volume degraded by motion – and potentially mixing diffusion orientations in the process if there is rotation in the motion. So you’re generally better off treating volumes independently, regardless of whether they’re supposed to be sampling the same direction or not.

On top of that, more repeats of the same direction means fewer unique directions, and that definitely reduces the uniformity of your angular coverage, and ultimately impacts on your angular resolution. In fact, the ability to process 20 directions data so easily is a relatively new feature, it wasn’t so easy to get a decent response function from such data until recently. If given the choice, I would always recommend increasing the number of unique directions, and avoiding averaging.

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Thank you Donald for the elaborate response. That’s what I was looking for.
For some reason in clinical practice (or semi-clinical, as the dMRI portion is often added for research), this repeated acquisition of ‘few’ gradients is still frequently done. Now I have some more arguments to push for maximal unique directions :slight_smile:

Is there a reference for the relatively new ability to get the response function from fewer (e.g.20) directions? Perhaps this one https://www.researchgate.net/publication/331165168_Improved_white_matter_response_function_estimation_for_3-tissue_constrained_spherical_deconvolution ?

Kind regards,

No, that’s a different approach to response estimation, but doesn’t by itself allow estimation of high angular resolution responses from low angular resolution data. I don’t know of a reference for this, other than the pull request on GitHub – though there is mention of an abstract / poster from @rsmith on the topic, but I can’t remember where that was presented…

The reference for ability to estimate anisotropic response functions of a higher maximal spherical harmonic degree than is supported by the number of unique DWI directions is listed in the help page of the amp2response command (which all dwi2response algorithms rely upon for this specific step). The abstract describing the method is accessible here.

On the topic of repeating diffusion directions, I’ll drop the phrase “condition number” into the mix for anyone interested. This is one of the many things reported by the dirstat command for assessing direction schemes.

Let’s say you have 60 volumes, and so expect an lmax=8 fit to be achievable in each voxel. One of the first steps in spherical deconvolution is a conversion of the DWI data from discrete signal intensities as a function of direction of diffusion sensitisation into the continuous spherical harmonic basis. This is just a transformation via matrix multiplication. If your 60 directions are well-distributed, this transformation is well-posed, and the condition number of the transformation will be close to 1.0, indicating that fluctuations in the input image intensities would propagate “nicely” to corresponding changes in the spherical harmonic coefficients. If you actually only have 20 unique directions, you don’t actually have enough information to fit lmax=8 spherical harmonic coefficients, regardless of how many repeats of each direction you may have acquired. In this case, the condition number will approach infinity, reflecting how the resulting spherical harmonic coefficients are completely unpredictable, and not robust to even tiny fluctuations in the input image data1.

The reason this limitation doesn’t arise specifically in response function estimation is because the method linked utilises data from across multiple image voxels, and the fibre orientations in those voxels are all different.


1 Interestingly, doing motion correction actually mitigates this slightly, as it means that the diffusion sensitisation directions relative to the image sample are no longer precisely equivalent, even if the applied diffusion sensitisation gradients were identical. But it’s nevertheless still preferable to get as much unique image information as possible rather than repeats.