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Golding_fixel_segmenter

Identifies fixel orientation from .mif FODF files (MRTrix3)

Improved Angular Resolution of Neuronal Fiber Segmentation in Diffusion Magnetic Resonance Imaging

Project Description

This repository takes as input a Fiber Orientation Distribution Function (FODF) .mif file, as well as some supporting MRTrix3 filetype files, and outputs a Fixel.mif file. Our method allows for the identification of more than one fixel per FODF lobe and is based on the following observation: FODFs of parallel fiber populations demonstrate cylindrical symmetry about the fiber axis, so cylindrical asymmetry in FODF lobes suggests the presence of non-parallel fiber populations. The algorithm iteratively scales, rotates, and fits a brain-specific model FODF (a FODF modeling a population of parallel fiber bundles) to every FODF in the white matter. It does this (potentially) multiple times per target FODF, until a threshold is reached.

The algorithm is thresholded to find fixels with max heights no smaller than 0.1 units. This is to prevent noise effects. Found fixels are also passed through a geometric continuity filter wherein a voxel’s fixel model is considered acceptable only when each candidate fixel deviates less than N degrees from matching fixels in the nearest-neighbor voxels (we use 35 degrees).

The results of this algorithm can be found in the poster file (Improved Angular Resolution of Neuronal Fiber Segmentation in Diffusion Magnetic Resonance Imaging.pdf). A short summation - this algorithm found ~9% more (validated) fixels than current best segmentation algorithms (peak-finding and SIFT), and found multiple fixels in ~48.5% of white matter voxels (compared to multiple fixels being found in ~ 41.5- 41.9% of WM voxels via peak-finding and SIFT protocols). Information on datasets used for evaluation can be found in the POSTER file as well. My Macbook Air M2 took ~ 2 hours to run this algorithm on a 96x96x60 whole brain dataset with FODF degree 8 (45 coefficients per voxel). I am presenting this algorithm and its results at the BMES annual meeting in October of this year (2023). I am currently working on rewriting all functions in python.

Dependencies

I wrote this algorithm when I had a student license, and as such had access to about as many MATLAB toolboxes as I wanted. A lot of these functions can be replicated without the toolbox. The toolboxes used are as follows.

  • The DSP System Toolbox
    • Dependency for Phased Array System Toolbox
  • The Image Processing Toolbox
    • boundary_adjacent_wrapper uses imgradient3 to write simulated fixels normal to edge of brain (used in validation of edge voxels)
  • Optimization Toolbox
    • Fixel_wrapper used eqnproblem to fit the model FODF to the cylindrically symmetric cap of the target FODF
  • Phased Array System Toolbox
    • Roty and rotz are used for rotating FODFs (used in multiple functions)
  • Signal Processing Toolbox
    • Dependency for Phase Array System Toolbox

*Note, three of the toolboxes are needed just for Roty and Rotz. The transform matrices used are 3x3 matrices and really very simple and easily replicated. The formulas can be found on the help page for rotz - https://www.mathworks.com/help/phased/ref/rotz.html

The algorithm also uses a few suites of functions written by others

How to use it

The files I used are all in the fixel_segmeneter_test_files.zip file. Each file's command history can be viewed with mrinfo (from MRTrix3). You can create analogous files from your own dataset using those command histories. The function pipeline_github.m shows a clear example of how this algorithm is used. First, a white matter FODF file, and a fixel.mif file (SIFT-segmentation fixel file) is loaded, as well as a file containing index information about the voxels used in white matter response function estimation. MRtrix3 has more information on all these file types. From here, the steps are as follows

  • Create mask using fixel.mif file
  • only segment WM voxels with fixels found using other fixel finding means (easy way to delineate WM vs CSF and GM voxels, also done as to be able to compare this algorithm to other algorithms)
  • Equidistant sample points on a sphere
  • Evaluate spherical harmonics of even degrees from degree 0, order 0 all the way through degree 8 order 8 (45 coefficients) with all coefficients equal to 1. This matrix when multiplied with coefficient vectors allows for a quick and easy way to evaluate future spherical harmonics in the same directions
  • Use indices of wm rf voxels to calculate single fiber FODF (average of all (normalized) FODFs used in wm rf estimation, with only m=0 values kept to preserve cylindrical symmetry)
  • Simulate fixels around the edge of WM as fixels normal to the edge of the WM (as to help validate edge cases.)
  • Segment every FODF in wm of the brain into constituent fixels
  • Use geometric validation to filter out erroneous fixels
  • Create histograms to compare fixel segmentation results to those of peak-finding and SIFT protocols (optional)
  • Write fixel .mif files
    • Use transform matrices from WM FODF file for writing index files, and use transform matrices from fixel direction file for writing directions and AFD files.

Credits

This research was conducted under the guidance of Dr. Adam Anderson of Vanderbilt University. It was supported by the VUSRP, and conducted with the Vanderbilt University Institute of Imaging Science.

License

Mozilla Public License 2.0 (found in LICENSE file)

Citations

Please cite this research with the following:

Golding, S. & Anderson, A. (2023, October 11-14) 'Improved Angular Resolution of Neuronal Fiber Segmentation in Diffusion Magnetic Resonance Imaging' [Conference presentation abstract] 2023 Biomedical Engineering Society Annual Meeting, Seattle, WA, United States.