Description:
STEimg computes the symbolic transfer entropy for source activity between pairs of voxels. Symbolic transfer entropy is a directional entropy giving the information transfered in each direction from pairs of voxel locations. The inputs are the MEG dataset, the SAM beamformer coefficients (weights) from SAMwts, and a parameter file. The command line usage is:
STEimg -r <dataset_name> -m < parameter_file_name> -v
The -r flag is followed by the dataset name (with or without the .ds suffix). The -m flag is followed by the parameter file name without the .param suffix. The -v argument specifies verbose output - else STEimg works silently.
In addition, there are optional flags. The -b flag directs STEimg to read the transfer entropy matrix from a previous result, instead of recomputing it. The -s flag directs STEimg to compute a surrogate test of each seed versus a random symbolic time series.
STEimg processes the entire dataset and does not use any markers. For those users needing transfer entropy specific to events or tasks, the user should design and acquire MEG data under those conditions.
STEimg first computes the source time series for each voxel. The source time series is then parsed into vectors of 5 or 6 measurements, with the last measurement advanced by a specified time relative to the last lagged sample (the prior samples are lagged relative to one another by an amount determined by the data lowpass corner frequency. The entire group of 6 (5) measurements are ranked and the last rank value used as a symbol for the advanced measure. The remaining 5 (6) measures are re-ranked to obtain another set of symbols. Given a measurement vector of length 6, the symbols are 5!=120 (1-120) and 1-6 for the advanced symbol value. For a measurement vector length of 5, the symbols are 4!=24 (1-24) plus 1-5 for the advance. The lagged sample vector is advanced one sample at a time through the source time series, generating a pair of symbolic time series. This is saved in two matrices: N!xV and NxV, where V is the number of voxels in the ROI. The symbolic transfer entropy for all pairs of voxels X and Y is computed from the joint and marginal conditional probabilities of occurrence of the symbols. The transfer entropy is computed as a triple integral over the probabilities and conditional probabilities:
In the above equation, S is the number of states for an embedding dimension of 4 or 5 (24 or 120, respectively), while N is the number of states for the advanced symbol (5 or 6). The capital X and Y refer to the advanced symbol.
Since the information transfer in each direction is a pair-wise measure, the output is two V x V matrices. These matrices are written to the SAM subdirectory, and to NIFTI 3D+V image files, written to the directory designated by ImageDirectory (default is the SAM subdirectory). Depending upon the voxel grid spacing, this can by a huge file to view using AFNI.
The NIFTI image files will be either "ortho" (the designated ROI and grid spacing from the parameter file) or "tlrc" (Talairach space and resolution) depending upon the ImageFormat keyword used to compute the SAM weights.
The required parameter file keywords for STEimg are:
Optional keywords include:
Examples parameters for imaging the symbolic transfer entropy, in Taliarach space on an 8mm grid for STEimg:
NumMarkers | 0 | ||
XBounds | -10.0 | 10.0 | YBounds | -9.0 | 9.0 |
ZBounds | -2.0 | 15.0 | |
ImageStep | 0.5 | ||
ImageFormat | TLRC | 8.0 | |
CovBand | 50.0 | 300.0 | |
ImageBand | 50.0 | 300.0 | |
OrientBand | 14.0 | 30.0 | |
ImageMetric | TransferEntropy | 8.5 | 5 |
CovType | GLOBAL | ||
MRIDirectory | /data1/mri | ||
ImageDirectory | /data2/SMI/Rest/Images |
In the above example, the keyword ImageMetric directs STEimg to compute symbolic transfer entropy using N=5 (120 symbolic states), with an advance of 8.5 ms characterized by 6 symbolic states.