Emerging or diminishing nonlinear interactions in the evolution of a complex system may signal a possible structural change in its underlying mechanism. This type of structural break may exist in many applications, such as in climate and finance, and standard methods for change-point detection may not be sensitive to it. In this article, we present a novel scheme for detecting structural breaks through the occurrence or vanishing of nonlinear causal relationships in a complex system. A significance resampling test was developed for the null hypothesis (H₀) of no nonlinear causal relationships using (a) an appropriate Gaussian instantaneous transform and vector autoregressive (VAR) process to generate the resampled multivariate time series consistent with H₀; (b) the modelfree Granger causality measure of partial mutual information from mixed embedding (PMIME) to estimate all causal relationships; and (c) a characteristic of the network formed by PMIME as test statistic. The significance test was applied to sliding windows on the observed multivariate time series, and the change from rejection to no-rejection of H₀, or the opposite, signaled a non-trivial change of the underlying dynamics of the observed complex system. Different network indices that capture different characteristics of the PMIME networks were used as test statistics. The test was evaluated on multiple synthetic complex and chaotic systems, as well as on linear and nonlinear stochastic systems, demonstrating that the proposed methodology is capable of detecting nonlinear causality. Furthermore, the scheme was applied to different records of financial indices regarding the global financial crisis of 2008, the two commodity crises of 2014 and 2020, the Brexit referendum of 2016, and the outbreak of COVID-19, accurately identifying the structural breaks at the identified times.

Accurate epileptogenic focus localization is required prior to surgical resection of brain tissue for treatment of patients with antiepileptic drug resistant (intractable) epilepsy. This clinical need is only partially fulfilled through a subjective, and at times inconclusive, evaluation of the recorded electroence-phalogram (EEG) at seizures’ onset (the so-called gold standard for focus localization in epilepsy). We herein present a novel method of multivariate analysis of the EEG that appears to be very promising for an objective and robust localization of the epileptogenic focus at seizures’ onset. Using the measure of Generalized Partial Directed Coherence (GPDC), combined with surrogate data analysis, we first estimated from multichannel intracranial EEG the statistically significant causal interactions between brain regions at the onset of 92 clinical seizures from 9 patients with temporal lobe intractable epilepsy. From the networks that were formed based on the thus derived interactions, a set of centrality metrics was estimated per network node (brain site). Brain sites located anatomically within the epileptogenic focus were shown to be associated with greater inward centrality values than non-focal brain regions at high frequencies (.. band), and particular inward centrality metrics accurately localized the focus in all 9 patients. In addition to focus localization from seizure (ictal) onset, the developed novel framework for analysis of EEG could be employed to identify the changes of the focal network over time, peri-ictally and interictally, and thus shed light onto the dynamics of ictogenesis, which could then have a significant impact on automated prediction and closed-loop control of seizures by neuromodulation.

Instantaneous phases extracted from multivariate time series can retain information about the relationships between the underlying mechanisms that generate the series. Although phases have been widely used in the study of nondirectional coupling and connectivity, they have not found similar appeal in the study of causality. Herein, we present a new method for phase-based causality analysis, which combines ideas from the mixed embedding technique and the information-theoretic approach to causality in coupled oscillatory systems. We then use the introduced method to investigate causality in simulated datasets of bivariate, unidirectionally paired systems from combinations of Rössler, Lorenz, van der Pol, and Mackey–Glass equations. We observe that causality analysis using the phases can capture the true causal relation for coupling strength smaller than the analysis based on the amplitudes can capture. On the other hand, the causality estimation based on the phases tends to have larger variability, which is attributed more to the phase extraction process than the actual phase-based causality method. In addition, an application on real electroencephalographic data from an experiment on elicited human emotional states reinforces the usefulness of phases in causality identification.

Transcranial magnetic stimulation (TMS) in humans induces electric fields (E-fields, EF) that perturb and modulate the brain’s endogenous neuronal activity and result in the generation of TMS-evoked potentials (TEPs). The exact relation of the characteristics of the induced E-field and the intensity of the brains’ response, as measured by electroencephalography (EEG), is presently unclear. In this pilot study, conducted on three healthy subjects and two patients with generalized epilepsy (total: 3 males, 2 females, mean age of 26 years; healthy: 2 males, 1 female, mean age of 25.7 years; patients: 1 male, 1 female, mean age of 26.5 years), we investigated the temporal and spatial relations of the E-field, induced by single-pulse stimuli, and the brain’s response to TMS. Brain stimulation was performed with a deep TMS device (BrainsWay Ltd., Jerusalem, Israel) and an H7 coil placed over the central area. The induced EF was computed on personalized anatomical models of the subjects through magneto quasi-static simulations. We identified specific time instances and brain regions that exhibit high positive or negative associations of the E-field with brain activity. In addition, we identified significant correlations of the brain’s response intensity with the strength of the induced E-field and finally prove that TEPs are better correlated with E-field characteristics than with the stimulator’s output. These observations provide further insight in the relation between E-field and the ensuing cortical activation, validate in a clinically relevant manner the results of E-field modeling and reinforce the view that personalized approaches should be adopted in the field of non-invasive brain stimulation.