TODI as a geometric quantification

Dear all,

I’m trying to compare the geometry of different tractograms for a sensitivity analysis. I’d like to quantify the geometry of the tractograms and then determine their (euclidean) difference. I was looking into TODI and wondered if that gives me the geometric information I’m looking for, by encoding the orientation and density of fibers in a voxel. As it is not usually used for that purpose, I was wondering, if it makes sense the way I thought it. I’d be very happy about your point of view on this!



Hi Ella,

There’s a whole can of worms being opened here; I will attempt to restrain myself from writing a thesis…

Use of TODI

The TOD data are ultimately stored as a set of spherical harmonic coefficients per voxel, just as are Fibre Orientation Distribution images. While they may:

  • Be secondary derivatives from tractogram data rather than directly from the diffusion MRI image data;
  • Be of a different harmonic order by default;
  • Encode a slightly different quantitative metric (streamline density vs. fibre density);
  • Possess grossly different absolute magnitude scaling;

, their fundamental data representation is the same. Indeed the SIFT(2) methods are based on the premise that the TODs and FODs should be identical in the absence of biases. Nevertheless, I think this clarification provides a couple of insights:

  • Whether the information contained within such encodes “geometry” of the tractogram is potentially subjective. Trouble is that in the context of tractograms, most would consider “geometry” to correspond to higher-order bundle-wise features, e.g. curvature or cross-sectional area, rather than voxel-wise measures (even if there is orientation information within each voxel).

  • The mechanism by which one might utilise those data in a subsequent analysis is likely no different to that of FOD data. Or, alternatively, anything novel in this respect designed to operate on TOD data would be equivalently applicable to FOD data.

“Quantification of geometry of tractograms”

If I overlook your own proposal of use of TOD and instead consider the general question as quoted, there’s a wide array of prospective interpretations. Again, I’ll try to restrain myself…

  • For geometry of bundles (as opposed to a whole-brain tractogram), the first thing that comes to mind is F-C Yeh’s work.

  • If considering something like “Euclidean distance” between such data, one could consider this to be simply the magnitude of the displacements determined through FOD-based registration as per the FBA pipeline. While this is slightly limited in that the 3D displacement at any point in space is fixed (i.e. is not dependent on the streamline / fibre orientation at that point in space), it’s nevertheless faithful to at least a low-resolution description of what you’re looking for.

  • If concurrently interested in both spatial distances and density differences between data, this makes me think of work I did way back in my undergraduate degree, looking at quantifying differences between 3D density maps in radiotherapy. Depends on how creative you want to get with a potential analysis technique for addressing your hypothesis as to whether it’s relevant. That’s only to say, there’s all sorts of possibilities here, but it’s predicated on having a sufficiently accurate description of exactly what you want to do, and the ability to address any gaps in image processing capabilities requisite to actually do it.


Hi Rob,

Thank you for your detailed response!
I’m currently working on my bachelor’s thesis, so (for now) my resources to get creative are rather limited, but your input helps a lot. My main idea is to look at the significance of different parameters on tractography results (on a single subject at a time). I’m using a reference tractogram, created with default parameters and try to compare that tractogram to other tractograms, obtained with varied parameters. I use connectivity as one output-quantification and was looking into other suitable options and thought a geometric comparison could also be valuable.

What I take from your answer is that using the TOD data could hold some value for comparison, as it could be compared to the FOD and therefore can hint towards quality of the resulting tractogram, but I misclassified this as a geometric measure.

Thank you so much for the paper-recommendation for a real geometric measure, I will investigate that! I’m not sure, if I could use the FBA pipeline though. I had a (quick) look into that and as far as I understand, this would rather make sense, if I was looking at multiple subjects at a time. But I’d be interested in what you did in your undergraduate degree, although I’m not sure if I can use it within the scope of my thesis.