Hello Andy:

Yes, Sally is correct. Since the stimuli are being presented at 2 per TR,
the individual impulses have different phase relationships relative to the fMRI
data. Specifically, the even impulses can only contribute to estimation of the
even IRF coefs., and the odd impulses can only contribute to estimation of the
odd IRF coefs.

This can be illustrated with a simple example. The command:

RSFgen -nt 40 -num_stimts 1 -nreps 1 10 -seed 957821451 \
-one_file -prefix myStim

will generate the following 40 pt. input stimulus function:

1 1 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0
0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0

Now, analyze this using the 3dDeconvolve "-nodata" option, with NPTR = 2:

3dDeconvolve \
-nodata -nfirst 0 -num_stimts 1 \
-stim_file 1 "myStim.1D[0]" -stim_maxlag 1 5 -stim_nptr 1 2 \
-xout

The X matrix is written to the screen:

X matrix:
1.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000
1.0000 1.0000 1.0000 1.0000 1.0000 0.0000 0.0000 0.0000
1.0000 2.0000 0.0000 1.0000 1.0000 1.0000 1.0000 0.0000
1.0000 3.0000 0.0000 0.0000 0.0000 1.0000 1.0000 1.0000
1.0000 4.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000
1.0000 5.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
1.0000 6.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000
1.0000 7.0000 0.0000 1.0000 1.0000 0.0000 0.0000 0.0000
1.0000 8.0000 0.0000 0.0000 0.0000 1.0000 1.0000 0.0000
1.0000 9.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000
1.0000 10.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
1.0000 11.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
1.0000 12.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000
1.0000 13.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000
1.0000 14.0000 1.0000 0.0000 0.0000 0.0000 1.0000 0.0000
1.0000 15.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000
1.0000 16.0000 1.0000 0.0000 0.0000 0.0000 1.0000 0.0000
1.0000 17.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000
1.0000 18.0000 0.0000 1.0000 0.0000 0.0000 1.0000 0.0000
1.0000 19.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000

Inspecting the X matrix, you will see that the columns corresponding to the
IRF h[0], h[2], and h[4] coefficients are time-lagged versions of the even
numbered input stim. fn. bits, and the columns corresponding to the IRF
h[1], h[3], and h[5] coefs. are time-lagged versions of the odd numbered
input bits.

Note that if the "ON" bits are somewhat sparse, then the parameter estimation
accuracy is roughly inversely proportional to the square root of the number
of "ON" bits. (Do not carry this crude approx. too far; see the 3dDeconvolve
output for the actual numbers.) In this particular example, there are more
even numbered "ON" bits than odd numbered "ON" bits; hence, the norm. std. devs.
for the even IRF coefs. are smaller than the norm. std. devs. for the odd coefs.
as indicated below:

Stimulus: Stim #1
h[ 0] norm. std. dev. = 0.6330
h[ 1] norm. std. dev. = 0.7485
h[ 2] norm. std. dev. = 0.6287
h[ 3] norm. std. dev. = 0.7511
h[ 4] norm. std. dev. = 0.6672
h[ 5] norm. std. dev. = 0.7895

This simple example illustrates, for the case of TR/2 stimulus presentation,
why the even numbered IRF coef. estimation accuracies tend to agree, and the
odd numbered IRF coef. estimation accuracies tend to agree, although the
evens and odds may differ.

See Section 1.4.8 of the 3dDeconvolve documentation for more details.


>>> This seems to be a trade-off issue increased temporal resolution but a
>>> more "variable" estimate. Is this accurate?

I think, yes. You can't get something for nothing. Holding the number of
fMRI data points constant, increasing the number of estimated parameters will
decrease the accuracy of the estimates. However, there are other considerations,
such as the accuracy of the model itself. There may not be a general answer.
Using sub-TR intervals (for the input stim. functions) does not increase the
sampling of the hemodynamic response (which is still once per TR). However,
using sub-TR intervals does allow estimation of the hemodynamic response at
a higher resolution.

Regarding placement of one "blank" trial between every condition:
After you have created the file TEST2.1D containing the stimuli with block
length 2, next convert the columns into rows:

1dtranspose TEST2.1D TEST2.1D.trans

Then, use a text editor to replace each occurrence of
"1 1" with "1 0"

Finally, convert the rows back to columns:
rm -f TEST2.1D
1dtranspose TEST2.1D.trans TEST2.1D
rm -f TEST2.1D.trans


I hope the skies are clear over Roswell.

Doug Ward
BRI/MCW/WI/USA/SOL3/MWG/LGG/VSC/MOG