gqi.odfvmf: Fibre Orientation Estimation Based on von Mises Distributions with GQI Reconstruction

Description

Fibre orientations in multiple fibre voxels are estimated using a mixture of von Mises-Fisher (vMF) distributions. This statistical estimation procedure is used to resolve crossing fibre mappings.

Usage

gqi.odfvmf(gdi="gqi", run=TRUE, fbase=NULL, rg=NULL, swap=FALSE, lambda=NULL,
 depth=3, btoption=2, threshold=0.4, showglyph=FALSE, bview="coronal",
 savedir=tempdir())

Arguments

gdi

method of ODF reconstruction to use c("gqi", "gqi2") (default: "gqi").

run

logical variable enabling loading previously processed data (default: TRUE).

fbase

Directory where the required input data files are located.

range of slices to process; default option rg=NULL processes all slices.

swap

toggle radiological/neurological orientation (default: FALSE).

lambda

diffusion sampling length in gdi="gqi" and gdi="gqi2". By default the following default values are used when lambda=NULL is specified: 1.24 in gqi, 3 in gqi2.

depth

sampling density on the hemisphere used in simulation (default N=321; depth=3).

btoption

b-table selection between btable.txt (btoption=1), and the 3D-DSI grid b-table extracted from the diffusion data set (data.bvec and data.bval). By default, the 3D-DSI grid b-table is used (btoption

threshold

thresholding generalized fractional anisotropy (GFA) value at each voxel (default: 0.4).

bview

MRI slice view selection in {axial, coronal, sagittal} (default: "coronal").

showglyph

logical variable controlling visualization of voxel glyphs (default: FALSE).

savedir

directory for saving/loading processed results (default: tempdir().

Value

gqi.odfvmf outputs three data files in NIfTI format named data_V1_gqi.nii.gz, data_V2_gqi.nii.gz, and data_gfa_gqi.nii.gz. The first and second main fibre directions per voxel are contained in data_V1_gqi.nii.gz, data_V2_gqi.nii.gz, respectively. The file data_gfa_gqi.nii.gz contains the GFA metric per voxel.

concept

Diffusion Magnetic Resonance
GQI Reconstruction
von Mises distributions
Orientation Distribution Function
RGB maps

Details

GQI methods specify an operational sampling scheme in q-space from which the ODF can be estimated. GQI (Yeh et.al. 2010) or GQI2 (Garyfallidis 2012) may be used for ODF reconstruction. For directional clustering estimation gqi.odfvmf uses a mixture of 2 and 4 von Mises-Fisher (vMF) distributions that serves as a model for directional ODF profile data, corresponding to multiple fibre orientations. Statistical orientation estimation in gqi.odfvmf is based on von Mises clustering procedures provided by the R-package movMF, by Kurt Hornik and Bettina Gruen.

Starting with the raw diffusion signal acquired on a grid of q-space, the ODF profile is estimated at each voxel, considering a sampling density of unit vectors on a unit S2 grid. When a threshold is applied to the estimated ODF at each voxel, the non-thresholded unit vectors provide directional statistics information about the estimated ODF profile. The main ODF orientations at each voxel relevant for fibre tracking may be estimated by clustering the non-thresholded unit vectors.

The main diffusion data set used in the examples is a DICOM data set provided by the "Advanced Biomedical MRI Lab, National Taiwan University Hospital", which is included in the "DSI Studio" package, publicly available from the NITRC repository (http://www.nitrc.org). Two b-tables defining the acquisition setup are specified. One is a b-table for a S2-like grid denoted by btable.txt. The other is the b-table for the 3D-DSI sampling scheme used in the DICOM data acquisition. This b-table has 203 points uniformly distributed on a 3D grid limited to the volume of the unit sphere. In both tables, the b-values range from 0 to 4000. Sampling densities of N=81 (depth=2) and N=321 (depth=3) on the hemisphere are often used in ODF profile reconstruction from diffusion acquisitions.

The output files data_V1_gqi.nii.gz, data_V2_gqi.nii.gz and data_gfa_gqi.nii.gz may be used for probabilistic white matter tractography. The principal diffusion direction (PDD) files data_V1_gqi.nii.gz, data_V2_gqi.nii.gz retain information about the 'theta' and 'alpha' parameters of the von Mises-Fisher mixture at each voxel. For visualization purposes via a external tool such as "FSL/fslview" the voxel PDDs must be normalized to the unit sphere beforehand by using niinorm.

References

Ferreira da Silva, A. R. Computational Representation of White Matter Fiber Orientations, International Journal of Biomedical Imaging, Vol. 2013, Article ID 232143, Hindawi Publishing Corporation http://dx.doi.org/10.1155/2013/232143.

Ferreira da Silva, A. R. Facing the Challenge of Estimating Human Brain White Matter Pathways. In Proc. of the 4th International Joint Conference on Computational Intelligence (Oct. 2012), K. Madani, J. Kacprzyk, and J. Filipe, Eds., SciTePress, pp. 709-714.

Hornik, K., and Gruen, B. movMF: Mixtures of von Mises-Fisher Distributions, 2012. R package version 0.1-0.

Yeh, F.-C., Wedeen, V. J., and Tseng, W.-Y. I. Generalized q-Sampling Imaging. IEEE Transactions on Medical Imaging 29, 9 (2010), 1626-1635.

Garyfallidis E., Towards an Accurate Brain Tractography, 2012, PhD Thesis, University of Cambridge.

Jenkinson, M., Beckmann, C. F., Behrens, T. E., Woolrich, M. W., and Smith, S. M. FSL. NeuroImage 62, 2 (2012), 782-790.

Examples

Run this code

## Generate ODF volumes (GQI volume processing)
    ## for a range of slices using von Mises-Fisher clustering
    gqi.odfvmf(depth=2, showglyph=FALSE, threshold=0.5, savedir=tempdir())
    ## RGB maps for range of slices processed by gqi.odfvmf()
    rgbvolmap(fbase=tempdir(), rg=c(1,4), bview="coronal")
    ##-------------
    ## Show reconstructed glyphs in ODF processing 
    ## for first and second main fibre direction determination
    gqi.odfvmf(gdi="gqi", rg=c(1,1), bview="coronal", depth=3,
      showglyph=TRUE, threshold=0.5)
    gqi.odfvmf(gdi="gqi2", rg=c(1,1), bview="coronal", depth=3,
      showglyph=TRUE, threshold=0.5)

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