# Peristimulus time histogram

In neurophysiology, **peristimulus time histogram** and **poststimulus time histogram**, both abbreviated **PSTH** or **PST histogram**, are histograms of the times at which neurons fire. It is also sometimes called **pre event time histogram** or **PETH**. These histograms are used to visualize the rate and timing of neuronal spike discharges in relation to an external stimulus or event. The peristimulus time histogram is sometimes called **perievent time histogram**, and *post-stimulus* and *peri-stimulus* are often hyphenated.

The prefix *peri,* for *through,* is typically used in the case of periodic stimuli, in which case the PSTH show neuron firing times wrapped to one cycle of the stimulus. The prefix *post* is used when the PSTH shows the timing of neuron firings in response to a stimulus event or onset.^{[1]}

To make a PSTH, a spike train recorded from a single neuron is aligned with the onset, or a fixed phase point, of an identical stimulus repeatedly presented to an animal. The aligned sequences are superimposed in time, and then used to construct a histogram.^{[2]}

## Construction procedure[edit]

- Align spike sequences with the onset of a stimulus that is repeated
*n*times. For periodic stimuli, wrap the response sequence back to time zero after each time period*T*, and count*n*as the total number of periods of data. - Divide the stimulus period or observation period
*T*into*N*bins of size . - Count the number of spikes
*k*from all_{i}*n*sequences that fall in the bin*i*. - Draw a bar-graph histogram with the bar-height of bin
*i*given by in units of estimated spikes per second at time .

The optimal bin size (assuming an underlying Poisson point process) Δ is a minimizer of the formula, (2k-v)/Δ^{2},
where k and v are mean and variance of k_{i}.
^{[3]}

## References[edit]

**^**Franklin Bretschneider and Jan R. De Weille (2006).*Introduction to Electrophysiological Methods and Instrumentation*. Academic Press. ISBN 978-0-12-370588-4. Retrieved 2016-05-29.**^**Palm, G.; Aertsen, A. M.; Gerstein, G. L. (1988). "On the significance of correlations among neuronal spike trains".*Biological Cybernetics*.**59**(1): 1–11. doi:10.1007/BF00336885. PMID 3401513.**^**Shimazaki, H.; Shinomoto, S. (2007). "A method for selecting the bin size of a time histogram".*Neural Computation*.**19**(6): 1503–152. CiteSeerX 10.1.1.304.6404. doi:10.1162/neco.2007.19.6.1503. PMID 17444758.