Research - Measuring synchronization


Collaborators:

Henri D.I. Abarbanel, Ralph G. Andrzejak, Daniel Chicharro, 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 continuous time series. The measures are applied to coupled model systems as well as electrophysiological data (mostly EEG). This is complemented by measures that estimate the synchronization between discrete events within the time series (such as spikes in neuronal recordings). In particular, the ISI-Distance and its extensions are introduced as simple, fast and time-resolved measures that quantify the similarity between two or more spike trains. This family of measures is parameter free, time scale independent and easy to visualize.

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


Publications:

[7] Kreuz T, Chicharro D, Andrzejak RG, Haas JS, Abarbanel HDI:
Measuring multiple spike train synchrony.
J Neurosci Methods 183, 287 (2009) [PDF].

Abstract: Measures of multiple spike train synchrony are essential in order to study issues such as spike timing reliability, network synchronization, and neuronal coding. These measures can broadly be divided in multivariate measures and averages over bivariate measures. One of the most recent bivariate approaches, the ISI-distance, employs the ratio of instantaneous interspike intervals. In this study we propose two extensions of the ISI-distance, the straightforward averaged bivariate ISI-distance and the multivariate ISI-diversity based on the coeffcient of variation. Like the original measure these extensions combine many properties desirable in applications to real data. In particular, they are parameter free, time scale independent, and easy to visualize in a time-resolved manner, as we illustrate with in vitro recordings from a cortical neuron. Using a simulated network of Hindemarsh-Rose neurons as a controlled configuration we compare the performance of our methods in distinguishing different levels of multi-neuron spike train synchrony to the performance of six other previously published measures. We show and explain why the averaged bivariate
measures perform better than the multivariate ones and why the multivariate ISI-diversity is the best performer among the multivariate methods. Finally, in a comparison against standard methods that rely on moving window estimates, we use single-unit monkey data to demonstrate the advantages of the instantaneous nature of our methods.

[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.

[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.

[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.

[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).

[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).

[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).