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Measuring spike train reliability
© Kreuz et al; licensee BioMed Central Ltd. 2008
Published: 11 July 2008
Measuring the degree of synchrony between two or more neuronal spike trains is an important tool in order to address issues such as neuronal coding, information transmission and model validation. Another prominent application is to measure the reliability of the response of individual neurons upon repeated presentations of the same stimulus. A number of both multivariate and bivariate measures have been proposed to address this issue. Multivariate approaches include the reliability measures by Hunter and Milton  and by Tiesinga , while bivariate approaches comprise the Victor-Purpura  and the van Rossum  distance, as well as the similarity measure proposed by Schreiber et al. , and, the most recent proposal, the ISI-distance , a method based on relative instantaneous firing rates. These approaches can be applied to multivariate data in a pairwise fashion, e.g., reliability can be defined as the average over all pairwise similarities.
Here, we extend the bivariate ISI-distance to a truly multivariate measure . This extension inherits the distinct properties of the ISI-distance, in particular, it is parameter free and time scale adaptive. In an application to in vitro recordings of cortical cells from rats we show that the multivariate ISI-distance serves as an excellent means to track relative firing patterns in the spike trains. The instantaneous degree of synchrony can be visualized easily, thus rendering this method a good choice for moving window applications on non-stationary neuronal dynamics. In particular, when estimating reliability this property allows the analyst to correlate intervals of high or low synchrony to the respective local stimulus features, which is desirable in many applications. Furthermore, we use a simulated network of Hindemarsh-Rose neurons with predefined clustering  as a controlled setting to evaluate the performance of the multivariate ISI-distance in distinguishing different sets consisting of a variable number of spike trains from different clusters. In a comparison with other multivariate approaches, as well as generalizations of several bivariate methods, the method presented here proves to be a very reliable indicator of set balance.
TK has been supported by the Marie Curie Individual Intra-European Fellowship "DEAN", project No 011434, DC by the I.U.E. Department of the Generalitat of Catalunya and the European Social Fund, and RGA by the Ramón y Cajal program. JSH acknowledges financial support by the San Diego Foundation.
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