Hi,
I’m posting because some have encouraged me to clarify. I will do a brief effort to clarify some things; don’t hesitate to ask if not clear.
Minor error in there: using the “single-tissue” approach, you’d use dwi2response tournier and dwi2fod csd. What this does is (using your b=1000 dataset as an example): dwi2response tournier uses only your b=1000 data (i.e. not b=0) and extracts a single-fibre white matter response function for the b=1000 signal. Then dwi2fod csd uses only your b=1000 data, and deconvolves your b=1000 single-fibre white matter response function form that data, resulting in an FOD. This assumes that all signal in the brain is “100% WM”, i.e., the resulting FOD fits all that signal using the (single-tissue) WM response function. For example in the cortex, this means all the non-axonal signal will also be part of that FOD, which you often see as a “too large” FOD that has many random false positive peaks. There’s then also less WM-GM contrast, somewhat limiting the precision of other steps in the FBA pipeline, including registration, but also what you can do for bias field correction and intensity normalisation, etc… In any case, all of this is called “single-tissue”, because only a single WM fibre response was used. The response just also happens to only represent your b=1000 data (not including b=0), making it a single-shell or single-b-value technique.
Correct. For completeness sake, what this does is: dwi2response dhollander extracts 3 tissue response functions, i.e. for single-fibre WM, isotropic GM and isotropic CSF, from your complete multi-shell dataset. The latter means all your b-values, including b=0! Then dwi2fod msmt_csd deconvolves these 3 (WM/GM/CSF) response functions from your full multi-shell dataset (including b=0), resulting in 3 tissue maps or compartments. The WM map/compartment is a full WM FOD, whereas the GM and CSF map/compartments are a single scalar number (not an orientational function). For FBA, you only use the WM FOD, but now the benefit is that the GM/CSF compartment have “filtered out” the signal of those tissues from the WM FOD. Put simple: the WM FOD is “cleaned up”, most markedly in cortical and subcortical GM. Technically, also in CSF, but even single-tissue CSD (as above) already has little to no false positive WM FOD in CSF due to CSF having very little DWI signal anyway. So the main benefit for e.g. FBA, lies arguably in the removal of the GM signal. This improves things like image registration, but the WM/GM/CSF compartments also allow for better bias field correction and intensity normalisation, etc.
This can also just be called a “multi-tissue” pipeline. I sometimes call it more specifically a “3-tissue” pipeline, to distinguish is more overtly from MSMT-CSD, but also to make clear that this is strictly 3 tissues only; not more, not less. But indeed, this does correspond to what you do most of the time with MSMT-CSD arguably. Only difference: it can do so on single-shell data. However, don’t forget that single-shell data is actually “2 b-value data”, if you include b=0. That’s what this pipeline also does. So in practice: dwi2response dhollander still estimates 3 tissue response functions (single-fibre WM, isotropic GM and CSF), but from your single-shell +b=0 data. So each of these 3 response functions is based on, and includes, your b=1000 as well as your b=0 signal. The SS3T-CSD method then (ss3t_csd_beta1 in the external fork that shall not be named) deconvolves this again from the full (b=1000 and b=0) data, with a bit of a trick to make this work, resulting in a WM FOD and GM/CSF compartment maps, just like the MSMT-CSD pipeline. Same benefits also, of filtering out GM, leading to better WM FODs, better registration, and all compartment images allowing better intensity normalisation and bias field correction, etc…
For completeness sake, another variant that you will or might have seen on the forum, or even seen me describe long ago, would be “2-tissue CSD”. This is what was done before with single-shell (+b=0) data and the MSMT-CSD algorithm. Since this algorithm typically needs x b-values to estimate x tissues, having only 2 b-values would limit you to 2 tissues. To be able to fit all signal then, these typically have to be WM and CSF (simplified reason being that these 2 have the lowest and highest diffusivities, whereas GM sits in between them). You can then still use the more advanced method (mtnormalise) for bias field correction and intensity normalisation, however, it works slightly less accurately, mostly for the bias field correction (and a little bit for the intensity normalisation). Also, most other benefits such as improved registration, etc… do not follow here, because those are mostly the benefit of modelling GM, which this approach does not. Sometimes people link to these old posts of me describing the 2-tissue approach, however, this was long ago and the context has changed.
Basically, with the availability of the SS3T-CSD technique, you can always follow the multi-tissue (or “3-tissue”) CSD pipeline. If you have good multi-shell data, then you can use MSMT-CSD as long as you take responsibility for inclusion of low b-values (if these are relatively many and/or very low b-values on average, they bring in extra-axonal signal into the FD metric). If you have good single-shell (+b=0) data, you can use SS3T-CSD; but similarly always take into account your b-value for the purpose of interpreting the FD metric. Apart from the CSD technique then, the actual pipeline is always the same (the “multi-tissue” pipeline), and includes all benefits from GM removal and using all tissues for e.g. bias field correction, etc…
We have also documented this pipeline, along with in-depth discussion on e.g. the aforementioned impact of that/those b-value(s) mentioned above, etc… in a recent review paper:
“Fixel-based Analysis of Diffusion MRI: Methods, Applications, Challenges and Opportunities” NeuroImage Volume 241, 118417
Google the title or copy-paste this link: https://doi.org/10.1016/j.neuroimage.2021.118417 (as last time I checked, my account here was not allowed to post links of any kind).
So for clarity sake: that is outdated advice from me, back from 2017. I highly recommend reading the aforementioned review paper for more details and references.
As mentioned, don’t hesitate to ask if anything is unclear. I agree the terminology has been running a bit wild, and it doesn’t help that we have used very similar sounding phrases such as “single-shell”, “single-tissue”, “single-fibre”, etc… 
. That said, if you read it carefully, and know that “shell” refers to the data and b-values, whereas “tissue” refers to the number of tissue compartments, and “single-fibre” is just a thing we always say together with “WM response”, it should hopefully still make sense! 
All the best,
Thijs (Thursday, 19-May-22 11:40:28 UTC)
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