Mathematics for multitensor diffusion reconstruction


I have been performing neuroimaging analyses for about 7 years in many domains (fMRI, dMRI, M/EEG, etc). I feel like I have a deep understanding of the concepts that underlie the analyses that I perform, especially with diffusion imaging, but I want to understand it at the mathematical level. I have a decent background in statistics, but that is about all the math that I’ve had as my doctorate is in neuropsychology.

In particular, I found the DBSI technique (Quantification of increased cellularity during inflammatory demyelination) that I have attempted to implement in house, but I’m realizing my limits due to my lack of math training. This experience has led me to doubt my “true” understanding of what is happening under the hood for many of the algorithms used in imaging analyses.

Does anyone have a recommendation of a resource (online course, textbook, subject of study, etc) that would provide the mathematical background needed to perform this type of analysis? (I.e., diffusion reconstruction). I am specifically interested in the application of these methods, like how to implement them in code.

Thanks for any and all suggestions,

Hi Brady,

This answer is more geared towards other higher-order tensor models like constrained spherical deconvolution, which I think is more commonly used than multi-tensor models. A video series I found helpful was The MRIllustrated series. In terms of code, I would suggest using QSIprep (Website, Paper) to process your data and make use of these methods, but if you want to take a more hands-on approach you can always fool around with DIPY or MRtrix3 code bases. These are both open-source tools, so you can take a look at the code used for each step.


Thanks for the reply! Those are very useful resources and I will be sure to explore them. I have used DIPY and MRtrix3 previously but never really explored their code deeply.

I guess as opposed to just focusing on diffusion imaging, I should have also mentioned that I am interested in learning the math concepts themselves and how to code them, like how to recreate the equations in the linked paper. I understand all of the terms and where they come from, but I don’t know how to apply the method. For example, in the paper linked, in the first equation that needs to be solved to use DBSI, I have calculated the set of diffusion bases and their angles, but I am lost as to how to calculate values for C and Cn+1 (equation 2-4), then use those values in the subsequent equations to eventually get the final DBSI parameters.

Any suggestions as to how to learn the appropriate skills to be able to solve these types of equations?

Thanks again!