A novel method for quantifying periodicity and time delay in dynamic neural networks using unstable subaction potential threshold depolarizations

Abstract

Techniques to identify and correlate the propagation of electrical signals (like action potentials) along neural networks are well described, using multisite recordings. In these cases, the waveform of action potentials is usually relatively stable and discriminating relevant electrical signals straightforward. However, problems can arise when attempting to identify and correlate the propagation of signals when their waveforms are unstable (e.g., fluctuations in amplitude or time course). This makes correlation of the degree of synchronization and time lag between propagating electrical events across two or more recording sites problematic. Here, we present novel techniques for the determination of the periodicity of electrical signals at individual sites. When recording from two independent sites, we present novel analytical techniques for joint determination of periodicity and time delay. The techniques presented exploit properties of the cross-correlation function, rather than utilizing the time lag at which the cross-correlation function is maximized. The approach allows determination of directionality of the spread of excitation along a neural network based on measurements of the time delay between recording sites. This new method is particularly applicable to analysis of signals in other biological systems that have unstable characteristics in waveform that show dynamic variability. NEW & NOTEWORTHY The determination of frequency(s) at which two sources are synchronized, and relative time delay between them, is a fundamental problem for a wide a range of signalprocessing applications. In this methodology paper, we present novel procedures for periodicity estimation for single time series and joint periodicity and time delay estimation for two time series. The methods use properties of the cross-correlation function rather than the crosscorrelation function explicitly.