Burst Analysis

This analysis identifies bursts in spike trains. Burst start and end times, duration of each burst and other burst statistics are calculated.

For each neuronal variable, a new interval variable can also be created that would contain the time intervals corresponding to bursts.

Parameters

Parameter	Description
Algorithm	Selection of MaxInterval, Surprise or Firing Rate Based algorithms.
Max Interval	Maximum interspike interval to start the burst (in seconds, MaxInterval method).
Max End Interval	Maximum interspike interval to end the burst (in seconds, MaxInterval method).
Min Interburst Interval	Minimum interval between bursts (in seconds, MaxInterval method).
Min Burst Duration	Minimum burst duration (in seconds, MaxInterval method).
Min Number of Spikes	Minimum number of spikes in the burst (MaxInterval method).
Min Surprise	Minimum surprise of the burst (Surprise method).
Surprise Method Min. Num. Spikes	Minimum number of spikes in the burst (Surprise method).
Surprise Method Min. Duration	Minimum burst duration (Surprise method).
Surprise Merge Bursts	Merge bursts (Surprise method).
Surprise Min. Interburst Interval (sec)	Merge bursts if interburst interval is less than this parameter (Surprise method).
Firing Rate Method Bin	Firing Rate Method Bin (seconds).
Firing Rate Method Smooth Width	Width of the Gaussian filter used in Firing Rate Method.
Firing Rate Method Threshold	Firing Rate Method Threshold (number of standard deviations).
Firing Rate Method Minimum Number of Spikes in Burst	Firing Rate Method Minimum Number of Spikes in Burst.
Display	Specifies what burst statistics to display.
Add Burst Interval Vars.	An option to create interval variables containing time intervals corresponding to bursts.
Select Data	If Select Data is From Time Range, only the data from the specified (by Select Data From and Select Data To parameters) time range will be used in analysis. See also Data Selection Options .
Select Data From	Start of the time range in seconds.
Select Data To	End of the time range in seconds.
Interval filter	Specifies the interval filter(s) that will be used to preselect data before analysis. See also Data Selection Options.
Send to Excel	An option to send numerical results or summary of numerical results to Excel. See also Excel Options .
Sheet Name	The name of the worksheet in Excel where to copy the numerical results.
TopLeft	Specifies the Excel cell where the results are copied. Should be in the form CR where C is Excel column name, R is the row number. For example, A1 is the top-left cell in the worksheet.

Summary of Numerical Results

The following information is available in the Summary of Numerical Results

Column	Description
Variable	Variable name.
YMin	Burst rate histogram minimum.
YMax	Burst rate histogram maximum.
Spikes	The number of spikes used in spectrum calculation.
Filter Length	The length of all the intervals of the interval filter (if a filter was used) or the length or the recording session (in seconds).
Mean Frequency	Mean firing rate (Spikes/Filter_Length).
Num Bursts	Number of bursts.
Bursts Per Second	Burst rate in bursts per second.
Bursts Per Minute	Burst rate in bursts per minute.
% of Spikes in Bursts	Percent of spikes in bursts.
Mean Burst Duration	Mean duration of burst (in seconds).
St. Dev. of Burst Duration	Standard deviation of burst duration.
Mean Spikes in Burst	Average number of spikes in burst.
St. Dev. of Spikes in Burst	Standard deviation of the number of spikes in burst.
Mean ISI Burst	Mean interspike interval in burst.
St. Dev of ISI in Burst	Standard deviation of interspike intervals in burst.
Mean Freq. in Burst	Mean firing rate `(1/interspike_interval)` in burst.
St. Dev. of Freq. in Burst	Standard deviation of `(1/interspike_interval)` in burst.
Mean Peak Frequency in Burst	Mean of `(1/min_interspike_interval)`, where `min_interspike_interval` is the minimum interspike interval in a burst.
St. Dev. Peak Frequency in Burst	Standard deviation of `(1/min_interspike_interval)`, where `min_interspike_interval` is the minimum interspike interval in a burst.
Mean Interburst Interval	Average length (in seconds) of interburst interval. Interburst interval is the interval from the end of the previous burst to the start of the current burst.
St. Dev. of Interburst Interval	Standard deviation of the interburst intervals.
Mean Burst Surprise	Average burst surprise.
St. Dev. Burst Surprise	Standard deviation of burst surprise.

Algorithm

For each spike train, NeuroExplorer identifies bursts and calculates burst start and end times, burst duration, number of spikes in burst, mean ISI in burst and peak frequency (1/min_interspike_interval) in burst. Optionally, creates a new Interval variable and stores all the burst intervals in this variable.

MaxInterval Method

Find all the bursts using the following algorithm:

Scan the spike train until an interspike interval is found that is less than or equal to Max. Interval.
While the interspike intervals are less than Max. End Interval, they are included in the burst.
If the interspike interval is more than Max. End Interval, the burst ends.
Merge all the bursts that are less than Min. Interval Between Bursts apart.
Remove the bursts that have duration less than Min. Duration of Burst or have fewer spikes than Min. Number of Spikes.

Surprise Method

First, the mean firing rate (Freq) and mean interspike interval (MeanISI) of the neuron are calculated.

Freq = NumberOfSpikes / (FileEndTime - FileStartTime)
MeanISI = 1 / Freq
ISIToStartBurst = MeanISI / 2
ISIToEndBurst = MeanISI

NeuroExplorer scans the spike train until it finds two sequential ISI’s so that each of those ISIs is less than ISIToStartBurst. The surprise of the resulting 3-spike sequence is calculated:

If we assume that a random variable P has a Poisson distribution with parameter Freq and we also assume that the burst has N spikes and the distance from the first to the last spike of the burst is T, then the surprise of the burst is:
```
S = - log10 (Probability that P has at least N points in time interval of length T)
```
NeuroExplorer adds the spikes to the end of the burst until the first ISI that is more than ISIToEndBurst and calculates surprise for each of the bursts (with 3 initial spikes, 4 spikes, 5 spikes, etc.). The burst with maximum surprise Smax is then selected.
NeuroExplorer removes the spikes from the beginning of the burst and calculates the surprise for each of the reduced bursts. The burst with maximum surprise Smax is then selected.
If Smax is more than MinSurprise and the number of spikes in the burst is more than Surprise Method Min. Num. Spikes, NeuroExplorer adds the burst to the result.

Firing Rate Based Method

Firing rate histogram with the specified bin size is calculated.
Rate histogram is smoothed using Gaussian smooth filter of the specified width. See Post-Processing Options for details of filter design.
Mean and Standard Deviation (STD) of the smoothed rate histogram are calculated.
Bins that have smooth histogram values of more than Mean+STD*Firing_Rate_Method_Threshold are considered to be in the burst. Burst start is the first spike in the burst bins, burst end is the last spike in the burst bins.
Bursts that have fewer spikes than the specified Firing Rate Method Minimum Number of Spikes in Burst are removed.

Reference

Legendy C.R. and Salcman M. (1985): Bursts and recurrences of bursts in the spike trains of spontaneously active striate cortex neurons. J. Neurophysiology, 53(4):926-39.