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# regularity of spike series

Matt Jones jonesmat at physiology.wisc.edu
Tue Jan 27 14:26:28 EST 2004

mats_trash at hotmail.com (mat) wrote in message news:<43525ce3.0401220431.67b6948f at posting.google.com>...
> Can anyone direct me to literature on useful metrics of regularity in
> spike series.  I've plotted autocorrelograms to see if any whopping
> peaks appear but to no avail.  On cursory reading I came accros papers
> on 'Approximate Entropy' but I don't think my datasets contain enough
> spikes to make this a valid measure.
>
> Many thanks

Hi,

I guess it depends on what you mean by regularity. The autocorrelegram
should reveal periodicity, but if there's a lot of "background"
spiking (i.e., scattered spikes that don't follow the periodicity of
the other spikes) that'll produce a large fuzzy baseline in the
autocorrelogram, upon which peaks might be difficult to detect.

I agree that the first step ought to be visual inspection of the ISI
distribution. However, it is not correct, as someone else suggested,
that a peaked ISI distribution wouldn't produce periodicity. In fact,
drawing spikes randomly from a gaussian distribution is a good way to
synthesize a periodic spiketrain that has a peaky autocorrelogram
(depending on the width of the gaussian, of course).

A good graphical way of observing regularity (not just periodicity,
but higher order regularity too) is to construct what's known as a
"first return plot" (sometimes also called a Poincare plot). This is
easy, you make a 2D scatter plot of each ISI versus the ISI that
immediately followed it (i.e., plot ISI(n) vs ISI(n+1), where n goes
from 1 through the total number of spikes).

If there is significant "regularity", this will show up as clusters of
points in the return plot. For example, if the spiketrain highly
periodic, there would be a single dense cluster somewhere on the line
of identity (ISI(n) = ISI(n+1)).  If there were a multiperiodic orbit,
say, where the system oscillates short interval -> long interval ->
short interval -> long interval, then there would be two clusters of
points symmetrically opposite each other across the line of identity.

Unfortunately many systems (including the one you're studying) display
orbits that are even more complex than the examples above, where
visual inspection isn't quite good enough to detect the underlying
structure. The "clusters" become to diffuse and overlapping to

There have been several papers about detecting higher order structure
in neuronal time series that you might find useful. You may want to
check out these papers, which use return plots to study dynamics in
slices under "epileptic" conditions:

Schiff SJ, Jerger K, Duong DH, Chang T, Spano ML, Ditto WL.
Controlling chaos in the brain.
Nature. 1994 Aug 25; 370(6491): 615-20.

Aitken PG, Sauer T, Schiff SJ.
Looking for chaos in brain slices.
J Neurosci Methods. 1995 Jun; 59(1): 41-8.

Slutzky MW, Cvitanovic P, Mogul DJ.
Manipulating epileptiform bursting in the rat hippocampus using chaos
IEEE Trans Biomed Eng. 2003 May; 50(5): 559-70.

Slutzky MW, Cvitanovic P, Mogul DJ.
Deterministic chaos and noise in three in vitro hippocampal models of
epilepsy.
Ann Biomed Eng. 2001; 29(7): 607-18.

Cheers,

Matt