Measuring synchronisation

Collaborators:

Ralph G. Andrzejak, Henri D.I. Abarbanel, Peter Grassberger, Julie Haas, Alexander Kraskov, Klaus Lehnertz, Alice Morelli, Florian Mormann, Antonio Politi, Rodrigo Quian Quiroga, Harald Stoegbauer.

Description:

This includes the development, analysis and comparison of different approaches to quantify the synchronization between two time series. In more recent works particular attention was paid to measures that estimate the synchronization between discrete events within the time series (such as spikes). Both coupled model systems as well as electrophysiological data were analysed.

The figures below show two examples in which a new measure of spike train synchrony, the ISI-Distance, is applied to both very similar and rather different neuronal time series (for details see Ref. [6] below, the Matlab source code of this method can be found here).

Publications:

[1] Quian Quiroga R, Kraskov A, Kreuz T, and Grassberger P:
     Performance of different synchronization measures in real data: A case study on electroencephalographic signals.
     Phys. Rev. E, 65, 041903 (2002).

[2] Quian Quiroga R, Kreuz T, and Grassberger P:
     Event Synchronization: A simple and fast method to measure synchronicity and time delay patterns.
     Phys.Rev. E, 66, 041904 (2002).

[3] Quian Quiroga R, Kraskov A, Kreuz T, and Grassberger P:
     Reply to "Comment on 'Performance of different synchronization measures in real data: A case study on
     electroencephalographic signals.'".
     Phys. Rev. E 67, 063902 (2003).

[4] Kreuz T:
     Measuring synchronization in model systems and electroencephalographic time series from epilepsy patients.
     Interdisciplinary PhD thesis in physics, University of Wuppertal, Research Center Juelich (2003).
     Supervisors: Prof. P. Grassberger, Research Center Juelich, Germany; Dr. K. Lehnertz, University of Bonn, Germany [PDF].

Abstract: The main aim of this dissertation is the comparative investigation of different measures of synchronization derived from various approaches and concepts. These include both measures for estimating the degree of dependence between two time series as well as measures which quantify the directionality of this dependence. The first group comprises the linear cross correlation, mutual information, six different indices for phase synchronization (based either on the Hilbert or on the wavelet transform) as well as symmetrized variants of two nonlinear interdependence measures and of event synchronization. The anti-symmetrized variants of the last three measures form the group of measures of directionality.

In the first part of this dissertation the symmetric measures are tested in a controlled setting by means of various model systems. Using the coupling strength as a first control parameter it is investigated to which extent the different measures are able to distinguish between different degrees of dependence. Furthermore, the robustness of the measures against external noise is estimated by varying the signal-to-noise ratio as the second control parameter.

Subsequently, all measures are employed to analyze electroencephalographic recordings from epilepsy patients. This application part consists of two single studies. First a comprehensive comparison on the predictability of epileptic seizures is carried out. Object of investigation is the capability of the different measures to reliably distinguish between the intervals preceding epileptic seizures and the intervals far away from any seizure activity. Already in this study a great deal of attention is paid to the statistical validation of seizure predictions. This issue is particularly addressed in the last part of this dissertation in which the method of measure profile surrogates is introduced as an appropriate tool to distinguish between measures and algorithms unsuited for the prediction of epileptic seizures, and more promising approaches. Two of the measures of synchronization are used to illustrate this new approach.

[5] Kreuz T, Mormann F, Andrzejak RG, Kraskov A, Lehnertz K, Grassberger P:
     Measuring synchronization in coupled model systems: A comparison of different approaches.
     Phys D 225, 29 (2007) [PDF].

Abstract: The investigation of synchronization phenomena on measured experimental data such as biological time series has recently become an increasing focus of interest. Different approaches for measuring synchronization have been proposed that rely on certain characteristic features of the dynamical system under investigation. For experimental data the underlying dynamics are usually not completely known, therefore it is difficult to decide a priori which synchronization measure is most suitable for an analysis. In this study we use three different coupled model systems to create a controlled setting for a comparison of six different measures of synchronization. All measures are compared to each other with respect to their ability to distinguish between different levels of coupling and their robustness against noise. Results show that the measure to be applied to a certain task can not be chosen according to a fixed criterion but rather pragmatically as the measure which most reliably yields plausible information in test applications, although certain dynamical features of a system under investigation (e.g., power spectra, dimension) may render certain measures more suitable than others.

[6] Kreuz T, Haas JS, Morelli A, Abarbanel HDI, Politi A:
     Measuring spike train synchrony.
     J Neurosci Methods 165, 151 (2007) [PDF].

Abstract: Estimating the degree of synchrony or reliability between two or more spike trains is a frequent task in both experimental and computational neuroscience. In recent years, many different methods have been proposed that typically compare the timing of spikes on a certain time scale to be optimized by the analyst. Here, we propose the ISI-distance, a simple complementary approach that extracts information from the interspike intervals by evaluating the ratio of the instantaneous firing rates. The method is parameter free, time scale independent and easy to visualize as illustrated by an application to real neuronal spike trains obtained in vitro from rat slices. In a comparison with existing approaches on spike trains extracted from a simulated Hindemarsh-Rose network, the ISI-distance performs as well as the best time-scale-optimized measure based on spike timing.