Continuous carry-over, fMRI experiments should present stimuli in a sequence that is at least first-order counterbalanced, meaning every stimulus precedes and follows every other. Certain orderings of stimuli are optimal, given a particular similarity matrix that is sought and a hemodynamic response function.

To assist in finding appropriate sequences, we have created a tool for the selection of efficient sequences for fMRI carry-over experiments.

The python source code is available as well.

The following information is entered:

• Email - Optional. We like to know who is using the tool so we can let you know about updates or fixes.
• Form of counterbalanced sequence - Choose a type of counterbalanced sequence from the drop-down menu. Currently, only type 1, index 1 sequences are supported.
• Trial duration - The duration (in seconds) of each trial in the experiment. This includes the stimulus and any inter-stimulus interval.
• Double blanks? - [Yes or No] The efficiency of a continuous carry-over experiment for detection of the “direct effect” of a stimulus as compared to a null-trial is markedly improved by increasing the duration of the null-trial label each time it appears. Choosing “yes” doubles the length of null (zero) events.
• Use a target stimulus? - [Yes or No] In some experiments, a target stimulus may be used for an attention task. This target stimulus may have a distant or undefined similarity relationship to the other stimuli. If this option is selected, an additional label will be included in the sequence for the presentation of targets, but the similarity of the target to the other stimuli will not be considered in the identification of an optimal sequence.
• Number of sequences to return - This many of the most efficient sequences found will be returned.
• Permutations - The number of label permutations to search for the optimal sequence. More is better but 1000 should identify a sequence with near-optimal efficiency. If more permutations are desired, we suggest you run the python source code locally.
• Dissimilarity structure 1 - A comma separated list of the assumed or hypothesized dissimilarity matrix for the stimuli. The optimal sequence is the one that provides the greatest efficiency for detecting the pattern of neural activity induced by fMRI signal habituation that is proportional to the defined similarity. More information regarding construction of this matrix is provided below.
• Dissimilarity structure 2/3 - Optional. If two or more structures are provided, the sequence that provides the best overall (sum of squares) efficiency for the detection of the structures is sought.

After pressing the Submit button, there will be a brief (1-2 minute) period of processing. A results page will then appear which first summarizes the inputs you have provided, then lists the top efficient sequences that were found. Each sequence is given as a comma-separated list of labels. Note that label 0 is always presumed to be a blank (null) trial that has no defined similarity to the remainder of the stimuli. If a target stimulus was selected, it will be indicated by the largest label value.

For each sequence, a calculated Efficiency is also provided.

You need to create a symmetric matrix which defines the dissimilarity relationships between your stimuli. Given n stimuli, the matrix is an n x n matrix which is symmetric about the diagonal. Each cell contains the dissimilarity (i.e., distance) of one stimulus from another. The dissimilarity of each stimulus from itself is defined as zero along the diagonal.

For example, consider a set of stimuli composed of 6 bars of different orientation, which are labeled as stimuli 1 through 6:

1	2	3	4	5	6

We may choose to define the dissimilarity of one stimulus from the other as the difference in angle between any given stimulus pair. This would yield the following dissimilarity matrix:

To be entered into the sequence search routine, this matrix is expressed as a vector, using only the lower triangle, columns first:

Yielding:

18,36,54,72,90,18,36,54,72,18,36,54,18,36,18

Consider an experiment that presented the 6 lines of different orientations during fMRI scanning. To monitor subject attention, the design might have an occasional target stimulus (e.g., a fixation dot) appear to which the subject would make a button press response.

The following would be a possible set of parameters for such a study:

The dissimilarity structure would be the one described above in terms of displacement of angle in degrees between possible pairings of the lines:

18,36,54,72,90,18,36,54,72,18,36,54,18,36,18

The generator will return an n=8 sequence, with the labels 0..7. The label zero indicates a blank trial, the label 7 indicates a target trial, and the other labels correspond to the six levels of the stimulus. The Efficiency reported for the sequence indicates the proportion of neural variance induced by the hypothetical experiment (assuming neural adaptation proportional to sequential stimulus dissimilarity) that would be reflected in BOLD signal.

One possible output sequence is:

6,1,4,5,0,0,7,3,2,2,3,6,4,1,5,7,0,0,0,0,1,7,5,4,2,6,3,3,4,6,0,0,5,2,7,1,1,2,0,0,6,7,4,3,5,5,6,2,1,3,0,0,4,7,7,6,5,3,1,0,0,2,4,4,0,0,3,7,2,5,1,6

[Note that the zero trials are doubled at each occurrence, and that the final item of the sequence is the same as the first]

This sequence implies the following stimulus presentation stream to the subject (1500 msecs per stimulus):

											etcetera
6	1	4	5	0	0	7	3	2	2	3	…

1. The general approach of searching for optimal carry-over designs is described in Appendix A of:
   • GK Aguirre (2007) Continuous carry-over designs for fMRI. Neuroimage, 35, 1480-1494.
2. The rationale and approach for optimizing for multiple possible similarity structures is considered in:
   • DM Drucker, WT Kerr, GK Aguirre. (2009) Distinguishing conjoint and independent neural tuning for stimulus features with fMRI adaptation. Journal of Neurophysiology. June;101(6):3310-24
   • See in particular Figure 7, which shows that for some similarity matrices optimization for each matrix is independent.
3. The search optimizes for the detection of a composite neural response in which the magnitude of neural signal change from one stimulus to the next is proportional to the dissimilarity of the stimuli. One neural mechanism which could provide for such a signal change is habituation of a neural population code for stimulus identity, although other mechanisms are possible.
4. The web-based implementation is limited to searching for dissimilarity matrices which are symmetric across stimulus transitions. This is not a necessary feature of carry-over designs or their analysis, but is assumed here for ease of implementation.
5. Calculation of Efficiency is conducted for a particular assumed hemodynamic response function. We used the first Eigenvector (essentially the across subject average) reported here:
   • GK Aguirre, E Zarahn, M D'Esposito. (1998). The variability of human BOLD hemodynamic responses. NeuroImage, 8, 360-369.
   • This empirical, across-subject HRF is nearly identical to the canonical HRF included in the SPM distribution.

1. A usage log may be found in:

   ~/html/webseq/visitors.txt