RAPID COMMUNICATION On the Detection and Measurement of Synchrony in Neural Populations by Coherence Analysis

Christakos, Constantinos N. On the detection and measurement (Christakos 1994; also see the appendix in Christakos et al. of synchrony in large neural populations by coherence analysis. 1991). This approach uses as a tool the coherence function J. Neurophysiol. 78: 3453–3459, 1997. This study considers the between unitary and population-aggregate activity (UTA copossibility of using coherence analysis for detection and measureherence). In the following, the term aggregate activity reprement of synchrony (correlations) in large neural populations, apsents the sum of the individual units’ activities in the populaplied to activities that are relatively easy to record in parallel. tion, such as the electrical activity recorded from a nerve. Mathematical analysis and computer simulations are used to examOn the basis of theoretical considerations and computer ine the behavior of the coherence function between both unitary and simulations of a uniform population, that study revealed a population-aggregate activity (UTA coherence) and the aggregate dual property of the UTA coherence function. Unless the activities of two populations (ATA coherence). The results indicate that for a large population showing partial correlations, the population is small in numerical size (up to a few tens of UTA coherence function is almost zero at all frequencies for the units) , this function is almost zero at all frequencies for the uncorrelated units. However, unless the synchrony is very reuncorrelated units. However, it is nonzero at the frequencies stricted, its value is nonzero (i.e., statistically significant by comwhere there is synchrony for the units that are correlated to mon criteria) at each frequency of synchrony for the units that other units. As the results indicated, the value of this nonzero show correlations to other units. Moreover, this value is indicative coherence at each frequency reflects the three features of of the strength of synchrony for any given unit. These properties synchrony: 1) its extent, i.e., the proportion of correlated enable the identification of the correlated units in a sample of units in the population; 2) its strength, i.e., the strength of unit /population activities simultaneously recorded in a series of the unitary correlations; and 3) the degree of similarity of experiments, and hence the detection of synchrony. The extent of synchrony can then be estimated as the fraction of such units in the phases of the correlated units. The value of the UTA the sample, whereas the values of the UTA coherences in the coherence also reflects the numerical size of the population, sample can be used to estimate the strength and its distribution i.e., a parameter that is not related to synchrony. Finally, within the population. Similarly, the ATA coherence function is this coherence stays substantial within very wide ranges of generally nonzero (significant) at the frequencies where there are values of these four parameters. correlations between members of two large populations. This enThe properties of the UTA coherence function, as revealed ables the easy detection of such correlations from simultaneously by the simulations, suggested using this function as a tool recorded population activities. However, this function is a very for 1) identifying the correlated units in a sample of unit / sensitive index of synchrony and even shows saturation effects. It may therefore be used as a general measure of synchrony only population activities recorded in parallel in a series of experunder restricted conditions. iments, and thus detecting population synchrony and estimating its extent; and 2) obtaining information on the strengths of the unitary correlations. I N T R O D U C T I O N Subsequent mathematical analysis confirmed the results of the simulations and also furnished detailed predictions on The detection of synchrony (unitary correlations) within, the behavior of this function as a tool for detection and or between, neural populations and the estimation of its exquantification of population synchrony. In addition, this tent and strength are important tasks in the study of many analysis was extended to the behavior of the coherence funcneural systems. However they present great difficulties when tion between the activities of two (sub)populations, i.e., of performed with traditional unit-to-unit (UTU) correlation the aggregate-to-aggregate (ATA) coherence function. ATA analysis (Perkel et al. 1967), particularly if the populations coherence computations have often been used in certain are large in numerical size. The main difficulties relate to the areas of Neurophysiology (e.g., the EEG area) as a simple simultaneous and independent recording of a large number of means of assessing population synchrony. However, detailed pairs of unitary activities, as required, and the appropriate studies of the behavior and dependencies of this function and economical representation of the results of such analysis were lacking. In other words, essential information for the (which are originally in the form of a large number of crosscorrect interpretation of coherence estimates was not availcorrelograms) for the quantification of synchrony. However, able. there is a more recent technique that deals with the latter In the case of large populations (several hundred or difficulty (Gerstein and Aertsen 1985). more) , the results of the mathematical analysis are simple A different approach for analysis of population synchrony has been suggested by the results of a recent study and compact. A summary of these results is presented below,