# 3dReHo¶

```
REHO/Kendall W code, written by PA Taylor (July, 2012), part of FATCAT
(Taylor & Saad, 2013) in AFNI.
ReHo (regional homogeneity) is just a renaming of the Kendall's W
(or Kendall's coefficient of concordance, KCC, (Kendall & Babington
Smith, 1939)) for set of time series. Application to fMRI data was
described in paper: <<Regional homogeneity approach to fMRI data
analysis>> by Zang, Jiang, Lu, He, and Tiana (2004, NeuroImage),
where it was applied to the study of both task and resting state
functional connectivity (RSFC).
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+ USAGE: This program is made to read in data from 4D time series data set
and to calculate Kendall's W per voxel using neighborhood voxels.
Instead of the time series values themselves, Kendall's W uses the
relative rank ordering of a 'hood over all time points to evaluate
a parameter W in range 0-1, with 0 reflecting no trend of agreement
between time series and 1 reflecting perfect agreement. From W, one
can simply get Friedman's chi-square value (with degrees of freedom
equal to `the length of the time series minus one'), so this can
also be calculated here and returned in the second sub-brick:
chi-sq = (N_n)*(N_t - 1)*W, with N_dof = N_t - 1,
where N_n is the size of neighborhood; N_t is the number of
time points; W is the ReHo or concordance value; and N_dof is the
number of degrees of freedom. A switch is included to have the
chi-sq value output as a subbrick of the ReHo/W. (In estimating W,
tied values are taken into account by averaging appropriate
rankings and adjusting other factors in W appropriately, which
only makes a small difference in value, but the computational time
still isn't that bad).
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+ COMMAND: 3dReHo -prefix PREFIX -inset FILE {-nneigh 7|19|27} \
{-chi_sq} {-mask MASK} {-in_rois INROIS}
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+ RUNNING, need to provide:
-prefix PREFIX :output file name part.
-inset FILE :time series file.
-chi_sq :switch to output Friedman chi-sq value per voxel
as a subbrick.
-mask MASK :can include a whole brain mask within which to
calculate ReHo. Otherwise, data should be masked
already.
-nneigh NUMBER :number of voxels in neighborhood, inclusive; can be:
7 (for facewise neighbors, only),
19 (for face- and edge-wise neighbors),
27 (for face-, edge-, and node-wise neighbors).
The default is: 27.
-neigh_RAD R :for additional voxelwise neighborhood control, the
radius R of a desired neighborhood can be put in; R is
a floating point number, and must be >1. Examples of
the numbers of voxels in a given radius are as follows
(you can roughly approximate with the ol' 4*PI*(R^3)/3
thing):
R=2.0 -> V=33,
R=2.3 -> V=57,
R=2.9 -> V=93,
R=3.1 -> V=123,
R=3.9 -> V=251,
R=4.5 -> V=389,
R=6.1 -> V=949,
but you can choose most any value.
-neigh_X A
-neigh_Y B :as if *that* weren't enough freedom, you can even have
-neigh_Z C ellipsoidal volumes of voxelwise neighbors. This is
done by inputing the set of semi-radius lengths you
want, again as floats/decimals. The 'hood is then made
according to the following relation:
(i/A)^2 + (j/B)^2 + (k/C)^2 <=1.
which will have approx. V=4*PI*A*B*C/3. The impetus for
this freedom was for use with data having anisotropic
voxel edge lengths.
-box_RAD BR :for additional voxelwise neighborhood control, the
one can make a cubic box centered on a given voxel;
BR specifies the number of voxels outward in a given
cardinal direction, so the number of voxels in the
volume would be as follows:
BR=1 -> V=27,
BR=2 -> V=125,
BR=3 -> V=343,
etc. In this case, BR should only be integer valued.
-box_X BA
-box_Y BB :as if that *still* weren't enough freedom, you can have
-box_Z BC box volume neighborhoods of arbitrary dimension; these
values put in get added in the +/- directions of each
axis, so the volume in terms of number of voxels would
be calculated:
if BA = 1, BB = 2 and BC = 4,
then V = (1+2*1)*(1+2*2)*(1+2*4) = 135.
--> NB: you can't mix-n-match '-box_*' and '-neigh_*' settings.
Mi dispiace (ma sol'un po).
-in_rois INROIS :can input a set of ROIs, each labelled with distinct
integers. ReHo will be calculated per ROI. The output
for this info is in a file called PREFIX_ROI_reho.vals
(or PREFIX_ROI_reho_000.vals, PREFIX_ROI_reho_001.vals,
etc. if the INROIS has >1 subbrick); if `-chi_sq'
values are being output, then those values for the
ROIs will be output in an analogously formatted
file called PREFIX_ROI_reho.chi (with similar
zeropadded numbering for multibrick input).
As of March, text format in the *.vals and *.chi files
has changed: it will be 2 columns of numbers per file,
with the first column being the ROI (integer) value
and the second column being the ReHo or Chi-sq value.
Voxelwise ReHo will still be calculated and output.
+ OUTPUT:
[A] single file with name, e.g., PREFIX+orig.BRIK, which may have
two subbricks (2nd subbrick if `-chi_sq' switch is used):
[0] contains the ReHo (Kendall W) value per voxel;
[1] contains Friedman chi-square of ReHo per voxel (optional);
note that the number of degrees of freedom of this value
is the length of time series minus 1.
[B] can get list of ROI ReHo values, as well (optional).
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+ EXAMPLE:
3dReHo \
-mask MASK+orig. \
-inset REST+orig \
-prefix REST_REHO \
-neigh_RAD 2.9 \
-chi_sq
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If you use this program, please reference the introductory/description
paper for the FATCAT toolbox:
Taylor PA, Saad ZS (2013). FATCAT: (An Efficient) Functional
And Tractographic Connectivity Analysis Toolbox. Brain
Connectivity 3(5):523-535.
```