Biomedical Engineering Reference
In-Depth Information
In above code, random data are generated. The loops then
increments through the random data to find matches and to
generate the raw JPSTH matrix. An optimized version of this
approach would avoid for loops; this code is only used for clarity.
Also, in order interpret the results, one must subtract a shift-
predicted matrix, and divide by the product of standard devia-
tions of PSTHs to normalize the matrix and compare between
pairs.
A thorny problem is determination of significance of JPSTH
arrays. Established approaches
(27)
assess significance either by
determining if the modulation can be assessed by chance using
a metric referred to as 'surprise'. We prefer a statistical approach
with trial-shuffled data. In this approach, the CTH is calculated
both for neurons of interest and for several iterations of trial-
shuffled data. One can then investigate whether CTH values
observed over a time epoch can be expected due to chance at
a p value of 0.05.
A example of neurons with a significant JPST interaction is
shown in
Fig. 7.5C
. This pair of motor cortex neurons reveals
strong negative interactions both along the diagonal as well
negative interactions before presentation of the stimulus (mean-
ing that if the horizontal unit is firing, the vertical unit is not),
and then a switch during the delay period when the vertical unit
fires up to 2 s after delay activity in the horizontal unit. The cross-
correlation reveals slow interactions on the order of 50-100 ms,
suggesting that there are slow functional interactions between
neurons.
We applied this analysis to the neurons in dmPFC and motor
cortex in our example data set. In trial-shuffled data, JPSTH val-
ues of greater than
|
|
<
0. 05
(20)
. Pairs
of neurons in which one neuron did not have enough spikes
(
0. 2
corresponded to p
10 times the number of trials) and from the same wires
were excluded. Of 78 potential pairs, 15 (19%) had significant
JPST interactions around the time of the stimulus (
Fig. 7.5D),
9
in motor cortex, 2 in dmPFC, and 4 between motor and
dmPFC.
Several potential pitfalls must be considered when using
JPSTH. Foremost, all of the concerns of cross-correlation, includ-
ing sufficient spikes and non-stationarity, apply when considering
JPSTH. Non-stationarities become even more relevant because
a confounding variable such as behavioral motivation may cre-
ate spurious trial-by-trial relationships. The influence of such
non-stationarities on JPSTH analysis is unknown. Our experi-
ence has been that the JPSTH should be normalized to facili-
tate comparisons with other neuronal pairs and that bin size is
critical, and should be thoroughly explored for each data set of
interest.
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