Actual step size used in iFOD2 and Calibrate List.

[yourtheron]

Hi there,

I am new to study MRtrix. I ran tckgen using a single-voxel seed image

tckgen -algorithm iFOD2 -mask  MaskImage.nii.gz -seed_image OneVoxelSeedImage.nii.gz -nthread 16 -step 0.5 -minlength 30 -maxlength 2000 -cutoff 0.1 -select 100 -stop FODImage0T.nii.gz -force  FODmOutT.tck -downsample 1 -output_seeds seesInd.txt
tckconvert FODmOutT.tck -force FODmOutiFOD2T_forDebug.vtk
tckstats FODmOutT.tck -dump lengths.txt -force

Then I used VTK to read all streamlines from FODmOutiFOD2T_forDebug.vtk, found out the longest one, and dumped all points inside. I then found that the step size between each successive point ( I keep -sample 4 as default) became around 0.66, not 0.5 (spacings of my image is 1mm along all axes). Looking at MRtrix's code, void SharedBase::set_step_and_angle() and float vox () const, the step size should be 0.5mm. I cannot find out where MRtrix changed the value internally as I have examined all init(), next(), and other functions in exec.h and iFOD2.h etc. Could you please explain what MRtrix does internally, and show me the location of the code? Many thanks.

The second issue is that from MRtrix's code, it seems that is pre-computed a set of calibrate list of directions that are independent of FOD images. Given all parameters being default and lmax=2, I found that it always produces 7 directions. Is it correct?

Best Wishes,
Yours faithfully,
Theron

[yourtheron]

Furthermore, I checked -debug information from tckgen, it does say that min_radius is 0.65 in my case, which is confirmed by the distance of the first and last points of each group of 4 successive points in my dumped data. But since my downsampling ratio is 1, in downsampler.cpp, the in streamline is directly assigned to the out streamline, hence I have no idea where either step size is changed or where and how min_radius affects the final positions of points in a streamline

[Lestropie]

Hi Theron,

It's possible that the confusion is primarily arising due to a nuance in the definition of "number of samples" in iFOD2. But that alone does not seem to fully resolve all contradictions here, so I'll just talk through it, and we'll see where we land.

With the default iFOD2 # samples being 4, this in fact constitutes three "internal" steps. This is because the set of samples for which FOD amplitudes contribute to the calculation of path probability includes the current vertex and the next vertex that is a "nominal" step size distance away. So eg. for a straight streamline with a 0.5mm nominal step size, that "step" contains 3 chords of length 0.1667mm, resulting in 4 vertices from which FOD amplitudes are sampled. Both the initial streamline seed point (assuming bidirectional tracking), and each subsequent nominal-step-size vertex, actually contribute to the calculation of path probabilities of two "nominal steps", as the first and last vertices along each arc are re-used.

https://github.com/MRtrix3/mrtrix3/blob/3.0.8/src/dwi/tractography/algorithms/iFOD2.h#L87-L88

I am however unsure how it is that you are landing on a 0.66mm step size. For -samples 4 and -downsample 1, which results in preserving all of the intermediate vertices within each arc, I would expect the inter-vertex distances to be of the order of (1mm x 0.5) x (1.0 / (4-1)) = 0.1667mm. My best guess here is that what you're doing is running tckgen with -downsample 1, then yourself manually removing 3 out of every 4 vertices. This would indeed lead to around a 0.1667 x 4 = 0.667mm inter-vertex distance; but in that case your downsampling step not shown would not be faithful to how iFOD2 is re-using vertices between adjacent arcs.

https://github.com/MRtrix3/mrtrix3/blob/3.0.8/src/dwi/tractography/algorithms/iFOD2.h#L91-L95

It's also worth bearing in mind the confounds of length calculations in this context, in two respects:

1. The streamline length will change considerably as a function of the density of vertex sampling, given it is computed based on a sum of chord lengths rather than a sum of arc lengths. See eg. Precise quantification of streamlines lengths #1507. I'd like to be able to compute streamline length as the line integral of a Hermite spline but never gotten around to trying it.

2. When iFOD2 generates candidate paths, it does so based not on a fixed arc length, but based on the resulting chord length between the first and last vertex being the nominal step size. So with the default downsampling (which is one less than # samples), the inter-vertex distance will be precisely the nominal step size, despite the second-order nature of the method. This means that with -downsample 1, the inter-vertex distances will change quite a lot depending on the curvature of the arc.
   This additionally has consequences for the conversion between "maximum angle per step" and "minimum radius of curvature", which is based on chord rather than arc lengths regardless of order of integration of algorithm: https://github.com/MRtrix3/mrtrix3/blob/3.0.8/src/dwi/tractography/tracking/shared.cpp#L205

RE calibration: Yes, the calibration is agnostic to image content. It only needs to know the sharpest possible FOD features, which are band-limited by lmax, and the tracking parameters. 7 directions for lmax=2 sounds right given how restrictive lmax=2 is (has the same number of model coefficients as the tensor).

Cheers
Rob