# 3dInvFMRI¶

```
Usage: 3dInvFMRI [options]
Program to compute stimulus time series, given a 3D+time dataset
and an activation map (the inverse of the usual FMRI analysis problem).
-------------------------------------------------------------------
OPTIONS:
-data yyy =
*OR* = Defines input 3D+time dataset [a non-optional option].
-input yyy =
-map aaa = Defines activation map; 'aaa' should be a bucket dataset,
each sub-brick of which defines the beta weight map for
an unknown stimulus time series [also non-optional].
-mapwt www = Defines a weighting factor to use for each element of
the map. The dataset 'www' can have either 1 sub-brick,
or the same number as in the -map dataset. In the
first case, in each voxel, each sub-brick of the map
gets the same weight in the least squares equations.
[default: all weights are 1]
-mask mmm = Defines a mask dataset, to restrict input voxels from
-data and -map. [default: all voxels are used]
-base fff = Each column of the 1D file 'fff' defines a baseline time
series; these columns should be the same length as
number of time points in 'yyy'. Multiple -base options
can be given.
-polort pp = Adds polynomials of order 'pp' to the baseline collection.
The default baseline model is '-polort 0' (constant).
To specify no baseline model at all, use '-polort -1'.
-out vvv = Name of 1D output file will be 'vvv'.
[default = '-', which is stdout; probably not good]
-method M = Determines the method to use. 'M' is a single letter:
-method C = least squares fit to data matrix Y [default]
-method K = least squares fit to activation matrix A
-alpha aa = Set the 'alpha' factor to 'aa'; alpha is used to penalize
large values of the output vectors. Default is 0.
A large-ish value for alpha would be 0.1.
-fir5 = Smooth the results with a 5 point lowpass FIR filter.
-median5 = Smooth the results with a 5 point median filter.
[default: no smoothing; only 1 of these can be used]
-------------------------------------------------------------------
METHODS:
Formulate the problem as
Y = V A' + F C' + errors
where Y = data matrix (N x M) [from -data]
V = stimulus (N x p) [to -out]
A = map matrix (M x p) [from -map]
F = baseline matrix (N x q) [from -base and -polort]
C = baseline weights (M x q) [not computed]
N = time series length = length of -data file
M = number of voxels in mask
p = number of stimulus time series to estimate
= number of parameters in -map file
q = number of baseline parameters
and ' = matrix transpose operator
Next, define matrix Z (Y detrended relative to columns of F) by
-1
Z = [I - F(F'F) F'] Y
-------------------------------------------------------------------
The method C solution is given by
-1
V0 = Z A [A'A]
This solution minimizes the sum of squares over the N*M elements
of the matrix Y - V A' + F C' (N.B.: A' means A-transpose).
-------------------------------------------------------------------
The method K solution is given by
-1 -1
W = [Z Z'] Z A and then V = W [W'W]
This solution minimizes the sum of squares of the difference between
the A(V) predicted from V and the input A, where A(V) is given by
-1
A(V) = Z' V [V'V] = Z'W
-------------------------------------------------------------------
Technically, the solution is unidentfiable up to an arbitrary
multiple of the columns of F (i.e., V = V0 + F G, where G is
an arbitrary q x p matrix); the solution above is the solution
that is orthogonal to the columns of F.
-- RWCox - March 2006 - purely for experimental purposes!
===================== EXAMPLE USAGE =====================================
** Step 1: From a training dataset, generate activation map.
The input dataset has 4 runs, each 108 time points long. 3dDeconvolve
is used on the first 3 runs (time points 0..323) to generate the
activation map. There are two visual stimuli (Complex and Simple).
3dDeconvolve -x1D xout_short_two.1D -input rall_vr+orig'[0..323]' \
-num_stimts 2 \
-stim_file 1 hrf_complex.1D -stim_label 1 Complex \
-stim_file 2 hrf_simple.1D -stim_label 2 Simple \
-concat '1D:0,108,216' \
-full_first -fout -tout \
-bucket func_ht2_short_two -cbucket cbuc_ht2_short_two
N.B.: You may want to de-spike, smooth, and register the 3D+time
dataset prior to the analysis (as usual). These steps are not
shown here -- I'm presuming you know how to use AFNI already.
** Step 2: Create a mask of highly activated voxels.
The F statistic threshold is set to 30, corresponding to a voxel-wise
p = 1e-12 = very significant. The mask is also lightly clustered, and
restricted to brain voxels.
3dAutomask -prefix Amask rall_vr+orig
3dcalc -a 'func_ht2_short+orig[0]' -b Amask+orig -datum byte \
-nscale -expr 'step(a-30)*b' -prefix STmask300
3dmerge -dxyz=1 -1clust 1.1 5 -prefix STmask300c STmask300+orig
** Step 3: Run 3dInvFMRI to estimate the stimulus functions in run #4.
Run #4 is time points 324..431 of the 3D+time dataset (the -data
input below). The -map input is the beta weights extracted from
the -cbucket output of 3dDeconvolve.
3dInvFMRI -mask STmask300c+orig \
-data rall_vr+orig'[324..431]' \
-map cbuc_ht2_short_two+orig'[6..7]' \
-polort 1 -alpha 0.01 -median5 -method K \
-out ii300K_short_two.1D
3dInvFMRI -mask STmask300c+orig \
-data rall_vr+orig'[324..431]' \
-map cbuc_ht2_short_two+orig'[6..7]' \
-polort 1 -alpha 0.01 -median5 -method C \
-out ii300C_short_two.1D
** Step 4: Plot the results, and get confused.
1dplot -ynames VV KK CC -xlabel Run#4 -ylabel ComplexStim \
hrf_complex.1D'{324..432}' \
ii300K_short_two.1D'[0]' \
ii300C_short_two.1D'[0]'
1dplot -ynames VV KK CC -xlabel Run#4 -ylabel SimpleStim \
hrf_simple.1D'{324..432}' \
ii300K_short_two.1D'[1]' \
ii300C_short_two.1D'[1]'
N.B.: I've found that method K works better if MORE voxels are
included in the mask (lower threshold) and method C if
FEWER voxels are included. The above threshold gave 945
voxels being used to determine the 2 output time series.
=========================================================================
++ Compile date = May 30 2023 {AFNI_23.1.07:linux_ubuntu_16_64}
```