# 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
will be similar to the format of 3dROIstats: one row
of numbers per INROIS subbrick, and the number of
columns determined by the number of ROIs per subbrick
(but only numbers are output). The output of this is
in a file called PREFIX_ROI_reho.vals, and if
`-chi_sq' values are being output, then those for the
ROI values will be output in an analogously formatted
file called PREFIX_ROI_reho.chi.
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.
```