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We start by generating an artificial stimulus. Inter-stimulus
intervals (ISI) between single-events were drawn at random from a
Poisson distribution with mean 8 seconds. ISIs were discarded if
less than 4 seconds or greater than 16 seconds. Events were then
randomly assigned as being stimulus or rest with equal
probability.
We then generated two artificial datasets, using two different
HRFs. The first HRF is shown in
figure 4(a) and has a post stimulus
undershoot. The second HRF, shown in
figure 3(a), is the same except it
has no post stimulus undershoot.
The artificial stimulus was then convolved (at 0.5 second
resolution) with the two different HRFs to give the two different
artificial signals shown in figures 4(b)
and 3(b). The signals were then
added to 100 voxels in a
square section of a slice of
a null/rest dataset, to generate two
artificial datasets. The null/rest dataset data was obtained with
the subject performing no specific task using echo planar images
(EPI) acquired using a 3 Tesla system with TR=3 seconds, time to
echo (TE) = 30ms, in-plane resolution 4mm and slice thickness 7mm.
The first 4 scans were discarded to leave scans and the
data was motion corrected using MCFLIRT (31) and
high-pass filtered as described in (43).
We can then use the full model (including the best noise model) in two forms on the two datasets. One with the ARD prior on the undershoot size parameter, , and one with a
non-informative prior.
Figure 3:
(a) the HRF used to generate the artificial signal
without undershoot (, , , , , ) (b) artificial signal used in the artificial
data generated from convolving the stimulus with the HRF in
(a).
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Figure 4:
(a) the HRF used to generate the artificial signal with
undershoot (, , , , , ), (b) artificial signal used in the artificial data
generated from convolving the stimulus with the HRF in
(a).
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