Deconvolution Analysis for
Rapid Event-Related Designs
Background
Experimental fMRI designs with closely spaced stimuli became more and more popular in
the last years because of several advantages over blocked designs and slow event-related
designs. These advantages include a more natural presentation rate of stimuli without the
need to wait ca. 15 seconds between event presentations, as well as a randomized
presentation order. Closely spaced stimuli appear to be difficult to analyze because the
elongated hemodynamic responses overlap substantially and seem to be impossible to
attribute to the correct conditions. Deconvolution analysis allows to separate the overlapping
responses if the stimuli are closely spaced and separated with a variable ISI from each
other.
Note that rapid event-related designs can be analyzed appropriately with standard General
Linear Models, i.e. by defining one predictor per condition with an expected
hemodynamically convolved time course for each event. This approach has the advantage
of high statistical power since only one (or a few) predictors are used per condition.
Furthermore, this strategy can be applied for protocols with millisecond resolution, which can
not be analyzed (at present) with the deconvolution approach in BrainVoyager QX. The
deconvolution approach, on the other hand, is much more flexible than a standard GLM
because the shape of the hemodynamic response is not predetermined but delivered as a
result of the analysis. The deconvolution analysis requires, however, many predictors per
condition (typically 10-20) which reduces the statistical power of the analysis. Since an
expected time course is not provided, the mapping results are typically also more “noisy”
because they reveal also non-BOLD like time courses.
Because of the close spacing of the events, standard event-related averaging will normally
not produce useful results. A strength of the deconvolution analysis is that it can not only be
used for voxel-wise brain mapping but also for averaged the time courses of regions-ofinterest. As opposed to event-related averaging, the ROI deconvolution analysis produces
correct hemodynamic response curves for each condition (under the assumption of linearity).
Exercise
In this exercise, we will analyzie a rapid event-related design first using a standard GLM
followed by a deconvolution GLM. We will then demonstrate that event-related averages will
not produce useful results and then show that ROI deconvolution analysis can take the role
of event-related averaging for rapid event-related designs.
The example experiment comes from a sensory-motor mapping experiment kindly provided
by Alard Roebroeck. In this experiment, subjects are presented with a sequence of stimuli,
houses, faces and objects presented for 120 ms. If subjects saw a face, they had to respond
with one index finger and if they saw a house, they had to respond with another finger. If
they see other objects, they should not respond (no-go condition). As an additional stimulus
a cue was presented from time-to-time, which indicated a switch in the sensory-motor
mapping rule for the subsequent trials. This cue indicated, for example, that subjects should
use another finger for faces than before or that they had not to press a button when seeing a
certain stimulus category.
A. Running a standard GLM analysis
1) From the “BVQXSampleData/Deconvolution” folder, load the structural data set
“CP3_SenMot7_MPRAGE_inh_TAL.vmr”.
2) In the folder are the functional data (VTCs) of three subjects. Link the file
“FV4_SenMot7_Run1_3DMC_SCSAI_LTR_THP4c_TAL.vtc” to the VMR by using the
“Link 3D Volume Time Course (VTC)” dialog.
3) Enter the “Single Study General Linear Model” dialog. You see now a visualization of the
protocol with vertical lines coding events of the conditions “cue”, “face”, “house”, and
“object”.
4) You could define four predictors by clicking on events with the right mouse button or,
more convenient, by clicking on the names of the conditions in the legend on the right.
The easiest way to define the predictors is, however, to use the “Define predictors”
function. Click “Options…” to enter the “Single Study GLM Options” dialog.
5) In most designs, a fixation or rest condition is defined and this condition should usually
not defined as a predictor to avoid overdetermined design matrices. In the example data
set, the “rest” condition is not defined and corresponds to the spaces between the
events. We thus should not exclude any condition. Deselect the “Exclude first condition
(Rest)” option, which is turned on as default. Now click “Define predictors”. You will now
see the defined predictors. Note that even for a single predictor, the expected
hemodynamic responses overlap in various regions. The combined (summed) expected
hemodynamic response, thus, will be - at each time point - a value reflecting different
predictors to different degrees at each time point. This can be seen in a visualization of
the design matrix showing all predictors in a set of columns. To get this display, enter the
“Single Study GLM Options” dialog again and click the “Design matrix” button.
6) Click the “GO” button in the “Single Study General Linear Model” dialog to run the
standard GLM. Inspect the overall GLM result. Observe the “Voxel Beta Plot” window
while moving the mouse over the volume map.
7) Enter the “Overlay GLM Contrasts and Contribution Maps” dialog and specify a “faces [+]
houses [-]” contrast. Click OK to visualize the contrast. Lower the threshold until you see
the face and house areas. Use the “Voxel Beta Plot” window to inspect the differential
response in these areas (see below).
B. Running a deconvolution GLM analysis
1) The deconvolution analysis only works at present with a volume resolution protocol but
the current protocol attached to the VTC file is defined in milliseconds. Since the stimulus
presentation was triggered with volume onset times, it is possible to convert the protocol
to volume resolution without loosing temporal information. Enter the “Stimulation
Protocol” dialog. Within the dialog, click the “Intervals” button to expand the dialog. To
convert the protocol, click the “Volumes” option in the lower part of the dialog. To save
the converted protocol, click the “Save .PRT” button and enter the name
“FV4_SenMot7_Run1_2.prt”. Note that you could permanently link this protocol to the
VTC using the “VTC Properties” dialog, which is available from the “File” menu.
2) Enter the “Single Study General Linear Model” dialog. Click the “Options…” button to
switch to the “Single Study GLM Options” dialog. Click the “Deconvolution design” tab.
A deconvolution design matrix is defined by a set of shifted “stick” predictors. It is very
tedious to manually code these predictors. The “Define predictors” function in the
“Deconvolution design” tab will define these predictors automatically. As in the standard
GLM, we deselect the “Exclude first condition” option since there is no “Rest” condition
defined. The “Data points:” spin box contains the number of stick predictors defined for
each condition. Since the stick predictors should capture the duration of the
hemodynamic response to the stimuli, they should cover about 12 – 20 seconds for short
stimulus presentations as used in this example experiment. The number of data points to
enter depends also on the TR used in the experiment. Since in our experiment the TR
has a value of 1 second, the number of data points will correspond to the number of
seconds. If, for example, a TR of 2 seconds would have been used, the number of data
points would be set to half the number used with a TR of 1 second (CoveredTime =
NrOfDataPoints*TR). Note that one should try to minimize the number of data points in
order to get a powerful statistical analysis (without loosing too many degrees of
freedom). We will use a value of “14” for the “Data points:” value. To get experience with
the deconvolution analysis, you should rerun the analysis with a different value (i.e. 10 or
20) and compare the results.
3) Click the “Define predictors” button to define a set of 14 stick predictors for each
condition. The predictors belonging to one condition are named as
“<ConditionName>_D<Shift>”. The first predictor of condition “face” will be labeled, for
example, as “face_D0”, the second as “face_D1” and so on. The first predictor is always
defined at the event onset time, the second predictor is shifted one TR from the onset
time, the third predictor is shifted two TR and so on. Since we have four conditions, we
will have a design matrix of 4*14 = 56 predictors of interest. Re-enter the “Single Study
GLM Options” dialog and click the “Design matrix” button. The obtained visualization
clearly shows the set of fourteen stick predictors for each of the four conditions (see
snapshot). Close the design matrix dialog. Save the created design matrix by clicking the
“Save…” button in the “Single Study General Linear Model” dialog. Name the file
“FV4_SenMot7_Deconv14_DM.rtc”.
4) Now run the deconvolution GLM by clicking the “GO” button in the “Single Study General
Linear Model” dialog. Observe the “Voxel Beta Plot” window while moving the mouse
over the volume map. It nicely shows now the deconvolved hemodynamic responses for
all four conditions in relevant visual regions. You may increase the size of the window to
see the time courses better. You can also adjust plotting parameters, such as decreasing
the range of values or reducing the size of the plot symbols. A respective “Options”
dialog appears after clicking at any point within the window.
5) The overall deconvolution GLM result is normally not as “clean” as with the standard
GLM since the stick predictors “capture” not only BOLD-like response curves but any
time course fluctuation. It is thus important to specify appropriate contrasts. Enter the
“Overlay Contrasts and Contribution Maps” dialog. Set the predictors “D0” – “D2” to
“minus”, the predictors “D5” – “D8” to “plus” and the predictors “D11” – “D13” to “minus”
for one condition (i.e. for faces). Click the “Balance” button and then “OK”. Observe the
resulting clusters in the map using the “Voxel Beta Plot” window. Re-enter the dialog and
try other conditions and other contrasts.
Further exercises. Run the same analysis for the data of the other two subjects (two more
VTC files available in the sample data set folder). Do not forget to create volume resolution
protocols from the provided millisecond resolution protocols as described above. Then
create multi-subject (MDM) design matrices and run a) a standard GLM across the three
subjects and then a deconvolution analysis over all subjects. Inspect the results.
C. Running a ROI deconvolution analysis
1) Deconvolution analysis can be also applied to regions-of-interest. Before doing so it is
instructive to learn that standard event-related analysis does not work well with rapid
event-related designs due to the variable, close spacing of the events. Load the provided
VMR file and link the file “FV4_SenMot7_Run1_3DMC_SCSAI_LTR_THP4c_TAL.vtc”
2) Create an event-related averaging file for all conditions of subject “FV4”. Select the
“FV4_SenMot7_Run1_3DMC_SCSAI_LTR_THP4c_TAL.vtc” file and all four conditions.
Save the “.AVG” file using all default parameters.
3) Use the volume resolution protocol. First run (or load it in case you saved it) the GLM
with four predictors (cue, houses, faces, objects) and specify a “face[+] – house[-]”
contrast. Select a region of interest and show its time course (CTRL-click). Then select
the AVG file created in the previous step. Depending on the area chosen, you will see a
plot similar to the one above. Note that it is difficult to see the event-related responses in
the time course. While the event-related averaging plot shows an increase in some
conditions, they normally show only a weak response and the ordering of conditions are
not suited for statistical analysis.
4) In the time course window click the “ROI GLM” button. Click “Browse…” and select the
previously saved deconvolution design matrix file “FV4_SenMot7_Deconv14_DM.rtc”,
then click the “Fit GLM” button. You will obtain an “event-related deconvolution plot”
showing the estimated beta values of the 4*16 stick predictors. You will also receive a
table showing the numerical details. Compare the event-related averaging with the
deconvolution plot for several other areas (overlay also other contrasts, i.e. for the “cue”
condition). While the two plots might look similar in many cases (the ordering of events
were very well balanced so that the history around each event are quite similar), the
deconvolution results are normally better because they represent an unbiased estimate
of the time course of the different conditions while the event-related averages are biased
by the overlapping hemodynamic responses from close-by conditions.
Remarks
Note that deconvolution analysis can also be used for events with a longer duration. It can
also be applied to slow event-related designs and even for block designs. In the latter cases,
the estimated beta values describe the shape of the fMRI response in various conditions
(events or blocks). Note that for long-lasting events or block designs you have to adjust the
number of data points accordingly.