Recurrence network analysis of EEG signals: A Geometric Approach

Understanding the neuronal dynamics of dynamical diseases like epilepsy is of fundamental importance. For instance, establishing the presence of deterministic chaos can open up possibilities that can lead to potential medical applications, including timely prevention of seizures. Additionally, understanding the dynamics of interictal activity can greatly aid the localization of epileptic foci without the need for recording seizures. Recurrences, a fundamental property of dynamical systems, are useful for characterizing nonlinear systems. Recurrence networks, which are obtained by reinterpreting the recurrence matrix as an adjacency matrix of a complex network, are useful in characterizing the structural or geometric properties of the underlying system. Recurrence network analysis has established itself as a versatile tool in the field of nonlinear time series analysis and its applicability in investigating neural dynamics remains unexplored. Certain recurrence network measures are particularly sensitive to the presence of unstable periodic orbits (UPOs), which are important for detecting determinism and are the backbone of chaotic attractors.In this thesis, we introduce recurrence network analysis as a tool for nonlinear time series analysis of epileptic electroencephalographic (EEG) signals. We present novel results based on the application of recurrence network analysis combined with surrogate testing to intracranial and extracranial epileptic EEG signals. In addition, using paradigmatic examples of dynamical systems, we present theoretical results exploring the effect of increasing noise levels on recurrence network measures.Using paradigmatic model systems, we first demonstrate that recurrence network measures can distinguish between deterministic (chaos) and stochastic processes, even at short data lengths (≈ 200 samples). In particular, our results from theoretical simulations show that recurrence network measures, particularly transitivity, local clustering coefficient, assortativity, and betweenness centrality can successfully distinguish between deterministic chaotic and stochastic processes (after additional embedding) due to their sensitivity to the presence of UPOs. Our results also show that recurrence network measures like transitivity and average path length are robust against noise and perform better than the Complexity-Entropy plane method at short data lengths. Furthermore, our results show that the effect of noise on the recurrence network measures can be minimized by increasing the recurrence rate.For the analysis of real-world data such as EEG signals, we combined the recurrence network approach with surrogate data to test for the structural complexity in healthy and epileptic EEG signals. Here our results point to an increasing complexity of EEG recordings when moving from healthy to epileptic conditions. Furthermore, we used both univariate network measure and bivariate cross-network measure to distinguish between the structural properties of interictal EEG signals recorded from epileptic and nonepileptic brain areas. Here, our results clearly demonstrated that interictal EEG signals recorded from epileptic areas are more deterministic and interdependent compared to interictal activity recorded from nonepileptic areas. Finally, we show that recurrence network analysis can be applied to uncover the dynamical transitions in neural signals using short segments of data (≈ 150 to 500 samples). To demonstrate this, we used two kinds of neural data - epileptic EEG data and local field potential (LFP) signals recorded during a visuomotor task. We observed that the temporal fluctuations observed in the recurrence network measures are consistent with the dynamical transitions underlying the epileptic and task-based LFP signals.To conclude, recurrence network analysis analysis can capture the complexity in the organization of EEG data in different dynamical states in a more elaborated fashion compared to other approaches such as nonlinear prediction error or correlation dimension. By means of the recurrence network measures, this difference can be assessed not only qualitatively (as when using as tests for nonlinearity), but also quantitatively. Thus, coupled with its ability to operate on short-window sizes and robustness to noise, recurrence network analysis can be a powerful tool to analyze the dynamics of multi-scale neural signals

Editorial : Data science in neuro- and onco-biology

publishedVersionNon peer reviewe

Causal coupling inference from multivariate time series based on ordinal partition transition networks

Identifying causal relationships is a challenging yet crucial problem in many fields of science like epidemiology, climatology, ecology, genomics, economics and neuroscience, to mention only a few. Recent studies have demonstrated that ordinal partition transition networks (OPTNs) allow inferring the coupling direction between two dynamical systems. In this work, we generalize this concept to the study of the interactions among multiple dynamical systems and we propose a new method to detect causality in multivariate observational data. By applying this method to numerical simulations of coupled linear stochastic processes as well as two examples of interacting nonlinear dynamical systems (coupled Lorenz systems and a network of neural mass models), we demonstrate that our approach can reliably identify the direction of interactions and the associated coupling delays. Finally, we study real-world observational microelectrode array electrophysiology data from rodent brain slices to identify the causal coupling structures underlying epileptiform activity. Our results, both from simulations and real-world data, suggest that OPTNs can provide a complementary and robust approach to infer causal effect networks from multivariate observational data

Tracking of dynamic functional connectivity from MEG data with Kalman filtering

Owing to their millisecond-scale temporal resolution, magnetoencephalography (MEG) and electroencephalography (EEG) are well-suited tools to study dynamic functional connectivity between regions in the human brain. However, current techniques to estimate functional connectivity from MEG/EEG are based on a two-step approach; first, the MEG/EEG inverse problem is solved to estimate the source activity, and second, connectivity is estimated between the sources. In this work, we propose a method for simultaneous estimation of source activities and their dynamic functional connectivity using a Kalman filter. Based on simulations, our approach can reliably estimate source activities and resolve their time-varying interactions even at low SNR (< 1). When applied on empirical MEG responses to simple visual stimuli, our approach could capture the dynamic patterns of the underlying functional connectivity changes between the lower (pericalcarine) and higher (fusiform and parahippocampal) visual areas. In conclusion, wedemonstrate that our approach is capable of tracking changes in functional connectivity at the millisecond resolution of MEG/EEG and thus making it suitable for real-time tracking of functional connectivity, which none of the current techniques are capable of.Peer reviewe