Choosing your response function

Dear Mrtrix team,

Hope this message finds you well.

I am relatively new to the DWI/DTI field and really excited to pick up a new set of skills to look at the brain differently.

My question is regarding generating and using the basis functions to estimate the FOD. Based on the documentation and some of the messages, it seems that the common basis function is preferable when comparing different groups. Then, here are my two questions.

  1. Should you use only control (presumed to be healthy subjects) to create the basis function and apply this to all the cohort that will be part of the analysis?

  2. More specifically, I work with Alzheimer’s disease and we know that the white matter is damaged during the disease process. However, I am not sure whether or how the disease processes will affect the estimation of basis functions in different tissue classes. Then, would the use of a common response function introduce any bias in estimating the FOD, and subsequent connectomic, track density, etc analyses? My understanding is that the basis functions of the different tissues are used together with the DWI data to estimate the FOD, which is used subsequently to quantify all the metrics (connectome, density, tractography, etc), through deconvolution. Then, I can only imagine that the quality of basis functions (in other words, depending on how you estimate the basis functions) will affect your results.

Your expertise and guidance would be very much appreciated.
Best regards,

Hi Peter,

Have you seen this thread?

If there is an effect of disease on the response functions, I’d guess its effect will be small. You can always run dwi2response on all data and compare response functions across groups to verify this (shview, or via plotting of the numerical values). If response functions genuinely are different, you’d still need to decide on a common set of response functions so that your ODFs are directly comparable. For interpretation reasons, I’d use the response functions from the control group. If abnormal single fibre WM in AD brains looks genuinely different, you’d see the effect in the ODFs (unless the non-negativity constraint or multi-shell signal signature prevent this).

Dear Max,

Thank you for your response and directing me to the interesting thread!

I will definitely take a look. I do have a follow-up question though.

  1. How do you assess whether the response functions are different? I see that the response function txt file has some numbers, which I presume is a vector? Would you just compare these vectors?

  2. How would you evaluate “unless the non-negativity constraint or multi-shell signal signature prevents this”?

Thank you very much for your support!
Best regards,

Yes, the response functions store zonal harmonic coefficients. Columns correspond to the angular components (l=0, 2, 4, …), rows correspond to b-values. You can plot these yourself but in case it is useful, here is a command that allows visualising angular profiles and l=0 terms of multiple response functions.

The MSMT CSD mapping from signal to ODFs is not a bijection, so there can be variations to the signal that result in the same set of ODFs. However, in practice, this is unlikely to be an issue. You can output the part of the signal that is captured by MSMT CSD and the response functions with dwi2fod msmt_csd -predicted_signal and compare that to the actual signal, the difference is not explained by the fit. If you genuinely see systematic differences in the residuals then the set of response functions does not capture all aspects of abnormal tissue. Experimentation with the response functions might change this, if you find a set of responses that given the constraints and model explain the signal better. Note that inspecting residual maps and tinkering with response functions won’t be necessary except for extreme tissue abnormalities. Realistically, for WM abnormalities, the WM ODFs will capture the abnormality as altered density and/or there will be a shift between components.

Dear Max,

Thank you for your response. This is very useful to know and I will visit these steps closely to examine the fits, residuals, and signals.

This is an interesting discussion though. I am not experienced with the DTI field much as I am coming from other imaging modalities. But I trust you and take your words. :slight_smile: But realistically, to imagine that the WM abnormalities would be captured as ODF’s abnormality rather than the basis function, it’s interesting as this may even suggest that the basis function is rather determined by your tissue physical/chemical properties/characteristics more so than the “health” of the tissue. I imagine that even if you have WM disease your WM will still be WM; it won’t share the physical/chemical properties of GM or CSF.

Thank you again.
Best regards,