Sorry about the delay, things have been a hectic of late with exams, marking, etcâŚ
OK, this is a very grey area, and there will be lots of different opinions on the topic. I get asked this question a lot, and my answer is invariably a lot more nuanced than just setting minimum criteria. The reason for this is that there is no clear breakdown point as far as I can tell â more directions is always better (if only because it means more data), more SNR is always better, and higher b-values (up to ~3,000 s/mm²) is also better. But you can obtain remarkably good reconstructions with relatively few directions if you have good SNR, or with relatively poor SNR if you have enough directions/measurements. The one criterion I would impose is a minimum SNR in the b=0 images of at least 15 â lower than that and the Rician bias becomes really problematic, and a lot of the preprocessing can also start to deteriorate.
Regarding the reviewerâs specific objection, the paper they refer to does make recommendations for the sampling density required to fully capture all observable spectral features in the DW signal, which at b=2,000 s/mm², will indeed include the l=8 terms (figure 3). However, youâll also note (figure 4 & table 1) that at this b-value, the amplitude of the l=8 terms is ~1% of the mean (l=0) signal. Youâll also see from figure 5 that the SNR required to even detect these l=8 terms (never mind actually characterising them reliably) is around SNR=60 for ~50% statistical power (more like SNR=80 for 80% statistical power) â and that assumes you have 100 DW directions. For your acquisition with 40 DW directions, the SNR required would climb to ~â(100/40) = ~1.6Ă higher, i.e. SNRâ95 (for 50% power) and SNRâ125 (for 80% power). In other words, when fitting at the single-voxel level (which is what youâre doing for tractography), the l=8 terms are completely lost in the noise for any realistic SNR level. Moreover, for CSD in particular, the non-negativity constraint would completely dominate any information contained in the l=8 terms â such constraints are not taken into account in that 2013 publication.
Finally, you can point to Figure 7 in that paper, which clearly shows that the fibre orientation estimates obtained using CSD at b=3,000 s/mm² do not improve beyond ~40 DW directions (when the effect of the increased number of measurements is accounted for â obviously in practice more DW directions always helps, but crucially, after that point, it helps by increasing the overall SNR, not the angular resolution). Note that this doesnât suggest that 40 directions is always sufficient, but that itâs likely to be sufficient in terms of angular coverage for a realistic SNR level (with much higher SNRs, there would most likely be further improvements with more directions).
I will typically measure SNR by extracting the b=0 images, and measuring the temporal SNR in those images â i.e. the standard deviation of the signal across volumes, divided by the mean signal. I typically compute this voxel-wise and smooth the resulting image (using a wide median filter for example). This provides a spatial map of the SNR in the b=0 images, accounting for the fact that on modern multiâchannel systems, the SNR is spatially variable. I would normally report the SNR as measured in the periventricular areas since these regions are reasonably representative â the SNR in the periphery will be much higher (closer to the coils), but much lower in the brainstem (much further from the coils).
As to the cut-off value, as mentioned above I would always recommend an SNR of at least 15 in the b=0 images â but more is always better!
