No evidence for critical slowing down prior to human epileptic seizures

Transitions in intensive care: Investigating critical slowing down post extubation

Complex biological systems undergo sudden transitions in their state, which are often preceded by a critical slowing down of dynamics. This results in longer recovery times as systems approach transitions, quantified as an increase in measures such as the autocorrelation and variance. In this study, we analysed paediatric patients in intensive care for whom mechanical ventilation was discontinued through removal of the endotracheal tube (extubation). Some patients failed extubation, and required a re-intubation within 48 hours. We investigated whether critical slowing down could be observed post failed extubations, prior to re-intubation. We tested for significant increases (p <.05) between extubation and re-intubation, in the variance and autocorrelation, over the time series data of heart rate, respiratory rate and mean blood pressure. The autocorrelation of the heart rate showed a significantly higher proportion of increases in the group that failed extubation, compared who those who did not. It also showed a significantly higher magnitude of increase for the failed extubation group in a t-test. Moreover, incorporating these magnitudes significantly improved the fit of a logistic regression model when compared to a model that solely used the mean and standard deviation of the vital signs. While immediate clinical utility is limited, the work marks an important first step towards using dynamical systems theory to understand the dynamics of signals measured at the bedside during intensive care.

The critical dynamics of hippocampal seizures

Epilepsy is defined by the abrupt emergence of harmful seizures, but the nature of these regime shifts remains enigmatic. From the perspective of dynamical systems theory, such critical transitions occur upon inconspicuous perturbations in highly interconnected systems and can be modeled as mathematical bifurcations between alternative regimes. The predictability of critical transitions represents a major challenge, but the theory predicts the appearance of subtle dynamical signatures on the verge of instability. Whether such dynamical signatures can be measured before impending seizures remains uncertain. Here, we verified that predictions on bifurcations applied to the onset of hippocampal seizures, providing concordant results from in silico modeling, optogenetics experiments in male mice and intracranial EEG recordings in human patients with epilepsy. Leveraging pharmacological control over neural excitability, we showed that the boundary between physiological excitability and seizures can be inferred from dynamical signatures passively recorded or actively probed in hippocampal circuits. Of importance for the design of future neurotechnologies, active probing surpassed passive recording to decode underlying levels of neural excitability, notably when assessed from a network of propagating neural responses. Our findings provide a promising approach for predicting and preventing seizures, based on a sound understanding of their dynamics.

Time-series-analysis-based detection of critical transitions in real-world non-autonomous systems

Real-world non-autonomous systems are open, out-of-equilibrium systems that evolve in and are driven by temporally varying environments. Such systems can show multiple timescale and transient dynamics together with transitions to very different and, at times, even disastrous dynamical regimes. Since such critical transitions disrupt the systems' intended or desired functionality, it is crucial to understand the underlying mechanisms, to identify precursors of such transitions, and to reliably detect them in time series of suitable system observables to enable forecasts. This review critically assesses the various steps of investigation involved in time-series-analysis-based detection of critical transitions in real-world non-autonomous systems: from the data recording to evaluating the reliability of offline and online detections. It will highlight pros and cons to stimulate further developments, which would be necessary to advance understanding and forecasting nonlinear behavior such as critical transitions in complex systems.

Application of early warning signs to physiological contexts: a comparison of multivariate indices in patients on long-term hemodialysis

Early warnings signs (EWSs) can anticipate abrupt changes in system state, known as "critical transitions," by detecting dynamic variations, including increases in variance, autocorrelation (AC), and cross-correlation. Numerous EWSs have been proposed; yet no consensus on which perform best exists. Here, we compared 15 multivariate EWSs in time series of 763 hemodialyzed patients, previously shown to present relevant critical transition dynamics. We calculated five EWSs based on AC, six on variance, one on cross-correlation, and three on AC and variance. We assessed their pairwise correlations, trends before death, and mortality predictive power, alone and in combination. Variance-based EWSs showed stronger correlations (r = 0.663 ± 0.222 vs. 0.170 ± 0.205 for AC-based indices) and a steeper increase before death. Two variance-based EWSs yielded HR95 > 9 (HR95 standing for a scale-invariant metric of hazard ratio), but combining them did not improve the area under the receiver-operating curve (AUC) much compared to using them alone (AUC = 0.798 vs. 0.796 and 0.791). Nevertheless, the AUC reached 0.825 when combining 13 indices. While some indicators did not perform overly well alone, their addition to the best performing EWSs increased the predictive power, suggesting that indices combination captures a broader range of dynamic changes occurring within the system. It is unclear whether this added benefit reflects measurement error of a unified phenomenon or heterogeneity in the nature of signals preceding critical transitions. Finally, the modest predictive performance and weak correlations among some indices call into question their validity, at least in this context.

Bifurcations and bursting in the Epileptor

The Epileptor is a phenomenological model for seizure activity that is used in a personalized large-scale brain modeling framework, the Virtual Epileptic Patient, with the aim of improving surgery outcomes for drug-resistant epileptic patients. Transitions between interictal and ictal states are modeled as bifurcations, enabling the definition of seizure classes in terms of onset/offset bifurcations. This establishes a taxonomy of seizures grounded in their essential underlying dynamics and the Epileptor replicates the activity of the most common class, as observed in patients with focal epilepsy, which is characterized by square-wave bursting properties. The Epileptor also encodes an additional mechanism to account for interictal spikes and spike and wave discharges. Here we use insights from a more generic model for square-wave bursting, based on the Unfolding Theory approach, to guide the bifurcation analysis of the Epileptor and gain a deeper understanding of the model and the role of its parameters. We show how the Epileptor's parameters can be modified to produce activities for other seizures classes of the taxonomy, as observed in patients, so that the large-scale brain models could be further personalized. Some of these classes have already been described in the literature in the Epileptor, others, predicted by the generic model, are new. Finally, we unveil how the interaction with the additional mechanism for spike and wave discharges alters the bifurcation structure of the main burster.

The time-evolving epileptic brain network: concepts, definitions, accomplishments, perspectives

Epilepsy is now considered a network disease that affects the brain across multiple levels of spatial and temporal scales. The paradigm shift from an epileptic focus-a discrete cortical area from which seizures originate-to a widespread epileptic network-spanning lobes and hemispheres-considerably advanced our understanding of epilepsy and continues to influence both research and clinical treatment of this multi-faceted high-impact neurological disorder. The epileptic network, however, is not static but evolves in time which requires novel approaches for an in-depth characterization. In this review, we discuss conceptual basics of network theory and critically examine state-of-the-art recording techniques and analysis tools used to assess and characterize a time-evolving human epileptic brain network. We give an account on current shortcomings and highlight potential developments towards an improved clinical management of epilepsy.

Stimulation to probe, excite, and inhibit the epileptic brain

Direct cortical stimulation has been applied in epilepsy for nearly a century and has experienced a renaissance, given unprecedented opportunities to probe, excite, and inhibit the human brain. Evidence suggests stimulation can increase diagnostic and therapeutic utility in patients with drug-resistant epilepsies. However, choosing appropriate stimulation parameters is not a trivial issue, and is further complicated by epilepsy being characterized by complex brain state dynamics. In this article derived from discussions at the ICTALS 2022 Conference (International Conference on Technology and Analysis for Seizures), we succinctly review the literature on cortical stimulation applied acutely and chronically to the epileptic brain for localization, monitoring, and therapeutic purposes. In particular, we discuss how stimulation is used to probe brain excitability, discuss evidence on the usefulness of stimulation to trigger and stop seizures, review therapeutic applications of stimulation, and finally discuss how stimulation parameters are impacted by brain dynamics. Although research has advanced considerably over the past decade, there are still significant hurdles to optimizing use of this technique. For example, it remains unclear to what extent short timescale diagnostic biomarkers can predict long-term outcomes and to what extent these biomarkers add information to already existing biomarkers from passive electroencephalographic recordings. Further questions include the extent to which closed loop stimulation offers advantages over open loop stimulation, what the optimal closed loop timescales may be, and whether biomarker-informed stimulation can lead to seizure freedom. The ultimate goal of bioelectronic medicine remains not just to stop seizures but rather to cure epilepsy and its comorbidities.

Variation in environmental stochasticity dramatically affects viability and extinction time in a predator-prey system with high prey group cohesion

Understanding how tipping points arise is critical for population protection and ecosystem robustness. This work evaluates the impact of environmental stochasticity on the emergence of tipping points in a predator-prey system subject to the Allee effect and Holling type IV functional response, modeling an environment in which the prey has high group cohesion. We analyze the relationship between stochasticity and the probability and time that predator and prey populations in our model tip between different steady states. We evaluate the safety from extinction of different population values for each species, and accordingly assign extinction warning levels to these population values. Our analysis suggests that the effects of environmental stochasticity on tipping phenomena are scenario-dependent but follow a few interpretable trends. The probability of tipping towards a steady state in which one or both species go extinct generally monotonically increased with noise intensity, while the probability of tipping towards a more favorable steady state (in which more species were viable) usually peaked at intermediate noise intensity. For tipping between two equilibria where a given species was at risk of extinction in one equilibrium but not the other, noise affecting that species had greater impact on tipping probability than noise affecting the other species. Noise in the predator population facilitated quicker tipping to extinction equilibria, whereas prey noise instead often slowed down extinction. Changes in warning level for initial population values due to noise were most apparent near attraction basin boundaries, but noise of sufficient magnitude (especially in the predator population) could alter risk even far away from these boundaries. Our model provides critical theoretical insights for the conservation of population diversity: management criteria and early warning signals can be developed based on our results to keep populations away from destructive critical thresholds.

Personalized dynamic network models of the human brain as a future tool for planning and optimizing epilepsy therapy

Epilepsy is a common neurological disorder, with one third of patients not responding to currently available antiepileptic drugs. The proportion of pharmacoresistant epilepsies has remained unchanged for many decades. To cure epilepsy and control seizures requires a paradigm shift in the development of new approaches to epilepsy diagnosis and treatment. Contemporary medicine has benefited from the exponential growth of computational modeling, and the application of network dynamics theory to understanding and treating human brain disorders. In epilepsy, the introduction of these approaches has led to personalized epileptic network modeling that can explore the patient's seizure genesis and predict the functional impact of resection on its individual network's propensity to seize. The application of the dynamic systems approach to neurostimulation therapy of epilepsy allows designing stimulation strategies that consider the patient's seizure dynamics and long-term fluctuations in the stability of their epileptic networks. In this article, we review, in a nontechnical fashion suitable for a broad neuroscientific audience, recent progress in personalized dynamic brain network modeling that is shaping the future approach to the diagnosis and treatment of epilepsy.

Systematic analysis and optimization of early warning signals for critical transitions using distribution data

Abrupt shifts between alternative regimes occur in complex systems, from cell regulation to brain functions to ecosystems. Several model-free early warning signals (EWS) have been proposed to detect impending transitions, but failure or poor performance in some systems have called for better investigation of their generic applicability. Notably, there are still ongoing debates whether such signals can be successfully extracted from data in particular from biological experiments. In this work, we systematically investigate properties and performance of dynamical EWS in different deteriorating conditions, and we propose an optimized combination to trigger warnings as early as possible, eventually verified on experimental data from microbiological populations. Our results explain discrepancies observed in the literature between warning signs extracted from simulated models and from real data, provide guidance for EWS selection based on desired systems and suggest an optimized composite indicator to alert for impending critical transitions using distribution data.

Classification of Epileptic and Psychogenic Non-Epileptic Seizures Using Electroencephalography and Electrocardiography

Patients with psychogenic non-epileptic seizures (PNES) may exhibit similar clinical features to patients with epileptic seizures (ES). Misdiagnosis of PNES and ES can lead to inappropriate treatment and significant morbidity. This study investigates the use of machine learning techniques for classification of PNES and ES based on electroencephalography (EEG) and electrocardiography (ECG) data. Video-EEG-ECG of 150 ES events from 16 patients and 96 PNES from 10 patients were analysed. Four preictal periods (time before event onset) in EEG and ECG data were selected for each PNES and ES event (60-45 min, 45-30 min, 30-15 min, 15-0 min). Time-domain features were extracted from each preictal data segment in 17 EEG channels and 1 ECG channel. The classification performance using k-nearest neighbour, decision tree, random forest, naive Bayes, and support vector machine classifiers were evaluated. The results showed the highest classification accuracy was 87.83% using the random forest on 15-0 min preictal period of EEG and ECG data. The performance was significantly higher using 15-0 min preictal period data than 30-15 min, 45-30 min, and 60-45 min preictal periods ( [Formula: see text]). The classification accuracy was improved from 86.37% to 87.83% by combining ECG data with EEG data ( [Formula: see text]). The study provided an automated classification algorithm for PNES and ES events using machine learning techniques on preictal EEG and ECG data.

Epileptic-network-based prediction and control of seizures in humans

Epilepsy is now conceptualized as a network disease. The epileptic brain network comprises structurally and functionally connected cortical and subcortical brain regions - spanning lobes and hemispheres -, whose connections and dynamics evolve in time. With this concept, focal and generalized seizures as well as other related pathophysiological phenomena are thought to emerge from, spread via, and be terminated by network vertices and edges that also generate and sustain normal, physiological brain dynamics. Research over the last years has advanced concepts and techniques to identify and characterize the evolving epileptic brain network and its constituents on various spatial and temporal scales. Network-based approaches further our understanding of how seizures emerge from the evolving epileptic brain network, and they provide both novel insights into pre-seizure dynamics and important clues for success or failure of measures for network-based seizure control and prevention. In this review, we summarize the current state of knowledge and address several important challenges that would need to be addressed to move network-based prediction and control of seizures closer to clinical translation.

Quantifying resilience and the risk of regime shifts under strong correlated noise

Early warning indicators often suffer from the shortness and coarse-graining of real-world time series. Furthermore, the typically strong and correlated noise contributions in real applications are severe drawbacks for statistical measures. Even under favourable simulation conditions the measures are of limited capacity due to their qualitative nature and sometimes ambiguous trend-to-noise ratio. In order to solve these shortcomings, we analyze the stability of the system via the slope of the deterministic term of a Langevin equation, which is hypothesized to underlie the system dynamics close to the fixed point. The open-source available method is applied to a previously studied seasonal ecological model under noise levels and correlation scenarios commonly observed in real world data. We compare the results to autocorrelation, standard deviation, skewness, and kurtosis as leading indicator candidates by a Bayesian model comparison with a linear and a constant model. We show that the slope of the deterministic term is a promising alternative due to its quantitative nature and high robustness against noise levels and types. The commonly computed indicators apart from the autocorrelation with deseasonalization fail to provide reliable insights into the stability of the system in contrast to a previously performed study in which the standard deviation was found to perform best. In addition, we discuss the significant influence of the seasonal nature of the data to the robust computation of the various indicators, before we determine approximately the minimal amount of data per time window that leads to significant trends for the drift slope estimations.

Epileptic seizure prediction in intracranial EEG using critical nucleus based on phase transition

BACKGROUND AND OBJECTIVE

Epilepsy is the second most prevalent neurological disorder of brain activity, affecting about seventy million people, or nearly 1% of the world population. Epileptic seizures prediction is extremely important for improving the epileptic patients' life. This paper proposed a novel method to predict seizures by detecting the critical transition of brain activities with intracranial EEG (iEEG) signals.

METHODS

This article used three key measures of fluctuation, correlation and percolation to quantify pre-ictal states of epilepsy. Based on these measures, a ritical nucleus of iEEG signals was constructed and a composite index was introduced to detect the likelihood of impending seizures. In addition, we analyzed the dynamical mechanism of seizures at the tipping point from the perspective of spatial diffusion and temporal fluctuation.

RESULTS

The empirical results supported that the seizures are self-initiated via a critical transition in pre-ictal state and showed that the proposed model can achieve a good prediction performance. The average accuracy, sensitivity, specificity and false-positive rate (FPR) attain 87.96%, 82.93%, 89.33% and 0.11/h respectively. The results also suggest that the temporal and spatial factors have strong synergistic effect on triggering seizures. For those seizures consistent with critical transition, the predictive performance was greatly improved with sensitivity up to 96.88%.

CONCLUSIONS

This article proposed a critical nucleus model combined with spatial and temporal features of iEEG signals capable of seizure prediction. The proposed model brings insight from phase transition into epileptic iEEG signals analysis and quantifies the transition of the state to predict epileptic seizures with high accuracy.

What Models and Tools can Contribute to a Better Understanding of Brain Activity?

Despite impressive scientific advances in understanding the structure and function of the human brain, big challenges remain. A deep understanding of healthy and aberrant brain activity at a wide range of temporal and spatial scales is needed. Here we discuss, from an interdisciplinary network perspective, the advancements in physical and mathematical modeling as well as in data analysis techniques that, in our opinion, have potential to further advance our understanding of brain structure and function.

Towards a Data-Driven Estimation of Resilience in Networked Dynamical Systems: Designing a Versatile Testbed

Estimating resilience of adaptive, networked dynamical systems remains a challenge. Resilience refers to a system's capacity "to absorb exogenous and/or endogenous disturbances and to reorganize while undergoing change so as to still retain essentially the same functioning, structure, and feedbacks." The majority of approaches to estimate resilience requires exact knowledge of the underlying equations of motion; the few data-driven approaches so far either lack appropriate strategies to verify their suitability or remain subject of considerable debate. We develop a testbed that allows one to modify resilience of a multistable networked dynamical system in a controlled manner. The testbed also enables generation of multivariate time series of system observables to evaluate the suitability of data-driven estimators of resilience. We report first findings for such an estimator.

The Challenging Path to Developing a Mobile Health Device for Epilepsy: The Current Landscape and Where We Go From Here

Seizure detection, and more recently seizure forecasting, represent important avenues of clinical development in epilepsy, promoted by progress in wearable devices and mobile health (mHealth), which might help optimizing seizure control and prevention of seizure-related mortality and morbidity in persons with epilepsy. Yet, very long-term continuous monitoring of seizure-sensitive biosignals in the ambulatory setting presents a number of challenges. We herein provide an overview of these challenges and current technological landscape of mHealth devices for seizure detection. Specifically, we display, which types of sensor modalities and analytical methods are available, and give insight into current clinical practice guidelines, main outcomes of clinical validation studies, and discuss how to evaluate device performance at point-of-care facilities. We then address pitfalls which may arise in patient compliance and the need to design solutions adapted to user experience.

Time in Brain: How Biological Rhythms Impact on EEG Signals and on EEG-Derived Brain Networks

Electroencephalography (EEG) is a widely employed tool for exploring brain dynamics and is used extensively in various domains, ranging from clinical diagnosis via neuroscience, cognitive science, cognitive psychology, psychophysiology, neuromarketing, neurolinguistics, and pharmacology to research on brain computer interfaces. EEG is the only technique that enables the continuous recording of brain dynamics over periods of time that range from a few seconds to hours and days and beyond. When taking long-term recordings, various endogenous and exogenous biological rhythms may impinge on characteristics of EEG signals. While the impact of the circadian rhythm and of ultradian rhythms on spectral characteristics of EEG signals has been investigated for more than half a century, only little is known on how biological rhythms influence characteristics of brain dynamics assessed with modern EEG analysis techniques. At the example of multiday, multichannel non-invasive and invasive EEG recordings, we here discuss the impact of biological rhythms on temporal changes of various characteristics of human brain dynamics: higher-order statistical moments and interaction properties of multichannel EEG signals as well as local and global characteristics of EEG-derived evolving functional brain networks. Our findings emphasize the need to take into account the impact of biological rhythms in order to avoid erroneous statements about brain dynamics and about evolving functional brain networks.

Prediction of Seizure Recurrence. A Note of Caution

Great strides have been made recently in documenting that machine-learning programs can predict seizure occurrence in people who have epilepsy. Along with this progress have come claims that appear to us to be a bit premature. We anticipate that many people will benefit from seizure prediction. We also doubt that all will benefit. Although machine learning is a useful tool for aiding discovery, we believe that the greatest progress will come from deeper understanding of seizures, epilepsy, and the EEG features that enable seizure prediction. In this essay, we lay out reasons for optimism and skepticism.

Assessing criticality in pre-seizure single-neuron activity of human epileptic cortex

Epileptic seizures are characterized by abnormal and excessive neural activity, where cortical network dynamics seem to become unstable. However, most of the time, during seizure-free periods, cortex of epilepsy patients shows perfectly stable dynamics. This raises the question of how recurring instability can arise in the light of this stable default state. In this work, we examine two potential scenarios of seizure generation: (i) epileptic cortical areas might generally operate closer to instability, which would make epilepsy patients generally more susceptible to seizures, or (ii) epileptic cortical areas might drift systematically towards instability before seizure onset. We analyzed single-unit spike recordings from both the epileptogenic (focal) and the nonfocal cortical hemispheres of 20 epilepsy patients. We quantified the distance to instability in the framework of criticality, using a novel estimator, which enables an unbiased inference from a small set of recorded neurons. Surprisingly, we found no evidence for either scenario: Neither did focal areas generally operate closer to instability, nor were seizures preceded by a drift towards instability. In fact, our results from both pre-seizure and seizure-free intervals suggest that despite epilepsy, human cortex operates in the stable, slightly subcritical regime, just like cortex of other healthy mammalians.

Criticality, Connectivity, and Neural Disorder: A Multifaceted Approach to Neural Computation

It has been hypothesized that the brain optimizes its capacity for computation by self-organizing to a critical point. The dynamical state of criticality is achieved by striking a balance such that activity can effectively spread through the network without overwhelming it and is commonly identified in neuronal networks by observing the behavior of cascades of network activity termed "neuronal avalanches." The dynamic activity that occurs in neuronal networks is closely intertwined with how the elements of the network are connected and how they influence each other's functional activity. In this review, we highlight how studying criticality with a broad perspective that integrates concepts from physics, experimental and theoretical neuroscience, and computer science can provide a greater understanding of the mechanisms that drive networks to criticality and how their disruption may manifest in different disorders. First, integrating graph theory into experimental studies on criticality, as is becoming more common in theoretical and modeling studies, would provide insight into the kinds of network structures that support criticality in networks of biological neurons. Furthermore, plasticity mechanisms play a crucial role in shaping these neural structures, both in terms of homeostatic maintenance and learning. Both network structures and plasticity have been studied fairly extensively in theoretical models, but much work remains to bridge the gap between theoretical and experimental findings. Finally, information theoretical approaches can tie in more concrete evidence of a network's computational capabilities. Approaching neural dynamics with all these facets in mind has the potential to provide a greater understanding of what goes wrong in neural disorders. Criticality analysis therefore holds potential to identify disruptions to healthy dynamics, granted that robust methods and approaches are considered.

Noise amplification precedes extreme epileptic events on human EEG

Extreme events are rare and sudden abnormal deviations of the system's behavior from a typical state. Statistical analysis reveals that if the time series contains extreme events, its distribution has a heavy tail. In dynamical systems, extreme events often occur due to developing instability preceded by noise amplification. Here, we apply this theory to analyze generalized epileptic seizures in the human brain. First, we demonstrate that the time series of electroencephalogram (EEG) spectral power in a frequency band of 1-5 Hz obeys a heavy-tailed distribution, confirming the presence of extreme events. Second, we report that noise on EEG signals gradually increases before the seizure onset. Thus, we hypothesize that generalized epileptic seizures in humans are the extreme events emerging from instability accompanied by preictal noise amplification similar to other dynamical systems.

Effect of rate of change of parameter on early warning signals for critical transitions

Many dynamical systems exhibit abrupt transitions or tipping as the control parameter is varied. In scenarios where the parameter is varied continuously, the rate of change of the control parameter greatly affects the performance of early warning signals (EWS) for such critical transitions. We study the impact of variation of the control parameter with a finite rate on the performance of EWS for critical transitions in a thermoacoustic system (a horizontal Rijke tube) exhibiting subcritical Hopf bifurcation. There is a growing interest in developing early warning signals for tipping in real systems. First, we explore the efficacy of early warning signals based on critical slowing down and fractal characteristics. From this study, lag-1 autocorrelation (AC) and Hurst exponent (H) are found to be good measures to predict the transition well before the tipping point. The warning time, obtained using AC and H, reduces with an increase in the rate of change of the control parameter following an inverse power law relation. Hence, for very fast rates, the warning time may be too short to perform any control action. Furthermore, we report the observation of a hyperexponential scaling relation between the AC and the variance of fluctuations during such a dynamic Hopf bifurcation. We construct a theoretical model for noisy Hopf bifurcation wherein the control parameter is continuously varied at different rates to study the effect of rate of change of the parameter on EWS. Similar results, including the hyperexponential scaling, are observed in the model as well.

Active probing to highlight approaching transitions to ictal states in coupled neural mass models

The extraction of electrophysiological features that reliably forecast the occurrence of seizures is one of the most challenging goals in epilepsy research. Among possible approaches to tackle this problem is the use of active probing paradigms in which responses to stimuli are used to detect underlying system changes leading up to seizures. This work evaluates the theoretical and mechanistic underpinnings of this strategy using two coupled populations of the well-studied Wendling neural mass model. Different model settings are evaluated, shifting parameters (excitability, slow inhibition, or inter-population coupling gains) from normal towards ictal states while probing stimuli are applied every 2 seconds to the input of either one or both populations. The correlation between the extracted features and the ictogenic parameter shifting indicates if the impending transition to the ictal state may be identified in advance. Results show that not only can the response to the probing stimuli forecast seizures but this is true regardless of the altered ictogenic parameter. That is, similar feature changes are highlighted by probing stimuli responses in advance of the seizure including: increased response variance and lag-1 autocorrelation, decreased skewness, and increased mutual information between the outputs of both model subsets. These changes were mostly restricted to the stimulated population, showing a local effect of this perturbational approach. The transition latencies from normal activity to sustained discharges of spikes were not affected, suggesting that stimuli had no pro-ictal effects. However, stimuli were found to elicit interictal-like spikes just before the transition to the ictal state. Furthermore, the observed feature changes highlighted by probing the neuronal populations may reflect the phenomenon of critical slowing down, where increased recovery times from perturbations may signal the loss of a systems' resilience and are common hallmarks of an impending critical transition. These results provide more evidence that active probing approaches highlight information about underlying system changes involved in ictogenesis and may be able to play a role in assisting seizure forecasting methods which can be incorporated into early-warning systems that ultimately enable closing the loop for targeted seizure-controlling interventions.

Seizure forecasting and cyclic control of seizures

Epilepsy is a unique neurologic condition characterized by recurrent seizures, where causes, underlying biomarkers, triggers, and patterns differ across individuals. The unpredictability of seizures can heighten fear and anxiety in people with epilepsy, making it difficult to take part in day-to-day activities. Epilepsy researchers have prioritized developing seizure prediction algorithms to combat episodic seizures for decades, but the utility and effectiveness of prediction algorithms has not been investigated thoroughly in clinical settings. In contrast, seizure forecasts, which theoretically provide the probability of a seizure at any time (as opposed to predicting the next seizure occurrence), may be more feasible. Many advances have been made over the past decade in the field of seizure forecasting, including improvements in algorithms as a result of machine learning and exploration of non-EEG-based measures of seizure susceptibility, such as physiological biomarkers, behavioral changes, environmental drivers, and cyclic seizure patterns. For example, recent work investigating periodicities in individual seizure patterns has determined that more than 90% of people have circadian rhythms in their seizures, and many also experience multiday, weekly, or longer cycles. Other potential indicators of seizure susceptibility include stress levels, heart rate, and sleep quality, all of which have the potential to be captured noninvasively over long time scales. There are many possible applications of a seizure-forecasting device, including improving quality of life for people with epilepsy, guiding treatment plans and medication titration, optimizing presurgical monitoring, and focusing scientific research. To realize this potential, it is vital to better understand the user requirements of a seizure-forecasting device, continue to advance forecasting algorithms, and design clear guidelines for prospective clinical trials of seizure forecasting.

Autonomic nervous system changes detected with peripheral sensors in the setting of epileptic seizures

A better understanding of the early detection of seizures is highly desirable as identification of an impending seizure may afford improved treatments, such as antiepileptic drug chronotherapy, or timely warning to patients. While epileptic seizures are known to often manifest also with autonomic nervous system (ANS) changes, it is not clear whether ANS markers, if recorded from a wearable device, are also informative about an impending seizure with statistically significant sensitivity and specificity. Using statistical testing with seizure surrogate data and a unique dataset of continuously recorded multi-day wristband data including electrodermal activity (EDA), temperature (TEMP) and heart rate (HR) from 66 people with epilepsy (9.9 ± 5.8 years; 27 females; 161 seizures) we investigated differences between inter- and preictal periods in terms of mean, variance, and entropy of these signals. We found that signal mean and variance do not differentiate between inter- and preictal periods in a statistically meaningful way. EDA signal entropy was found to be increased prior to seizures in a small subset of patients. Findings may provide novel insights into the pathophysiology of epileptic seizures with respect to ANS function, and, while further validation and investigation of potential causes of the observed changes are needed, indicate that epilepsy-related state changes may be detectable using peripheral wearable devices. Detection of such changes with wearable devices may be more feasible for everyday monitoring than utilizing an electroencephalogram.

Critical slowing down as a biomarker for seizure susceptibility

The human brain has the capacity to rapidly change state, and in epilepsy these state changes can be catastrophic, resulting in loss of consciousness, injury and even death. Theoretical interpretations considering the brain as a dynamical system suggest that prior to a seizure, recorded brain signals may exhibit critical slowing down, a warning signal preceding many critical transitions in dynamical systems. Using long-term intracranial electroencephalography (iEEG) recordings from fourteen patients with focal epilepsy, we monitored key signatures of critical slowing down prior to seizures. The metrics used to detect critical slowing down fluctuated over temporally long scales (hours to days), longer than would be detectable in standard clinical evaluation settings. Seizure risk was associated with a combination of these signals together with epileptiform discharges. These results provide strong validation of theoretical models and demonstrate that critical slowing down is a reliable indicator that could be used in seizure forecasting algorithms.

Critical slowing (associated with increased variance and autocorrelation) can precede critical state transitions. Here, the authors show critical slowing can be used as a marker in seizure forecasting algorithms.

Flickering of cardiac state before the onset and termination of atrial fibrillation

Complex dynamical systems can shift abruptly from a stable state to an alternative stable state at a tipping point. Before the critical transition, the system either slows down in its recovery rate or flickers between the basins of attraction of the alternative stable states. Whether the heart critically slows down or flickers before it transitions into and out of paroxysmal atrial fibrillation (PAF) is still an open question. To address this issue, we propose a novel definition of cardiac states based on beat-to-beat (RR) interval fluctuations derived from electrocardiogram data. Our results show the cardiac state flickers before PAF onset and termination. Prior to onset, flickering is due to a "tug-of-war" between the sinus node (the natural pacemaker) and atrial ectopic focus/foci (abnormal pacemakers), or the pacing by the latter interspersed among the pacing by the former. It may also be due to an abnormal autonomic modulation of the sinus node. This abnormal modulation may be the sole cause of flickering prior to termination since atrial ectopic beats are absent. Flickering of the cardiac state could potentially be used as part of an early warning or screening system for PAF and guide the development of new methods to prevent or terminate PAF. The method we have developed to define system states and use them to detect flickering can be adapted to study critical transition in other complex systems.

Controversies on the network theory of epilepsy: Debates held during the ICTALS 2019 conference

Debates on six controversial topics on the network theory of epilepsy were held during two debate sessions, as part of the International Conference for Technology and Analysis of Seizures, 2019 (ICTALS 2019) convened at the University of Exeter, UK, September 2-5 2019. The debate topics were (1) From pathologic to physiologic: is the epileptic network part of an existing large-scale brain network? (2) Are micro scale recordings pertinent for defining the epileptic network? (3) From seconds to years: do we need all temporal scales to define an epileptic network? (4) Is it necessary to fully define the epileptic network to control it? (5) Is controlling seizures sufficient to control the epileptic network? (6) Does the epileptic network want to be controlled? This article, written by the organizing committee for the debate sessions and the debaters, summarizes the arguments presented during the debates on these six topics.

Mitigation of tipping point transitions by time-delay feedback control

In stochastic multistable systems driven by the gradient of a potential, transitions between equilibria are possible because of noise. We study the ability of linear delay feedback control to mitigate these transitions, ensuring that the system stays near a desirable equilibrium. For small delays, we show that the control term has two effects: (i) a stabilizing effect by deepening the potential well around the desirable equilibrium and (ii) a destabilizing effect by intensifying the noise by a factor of (1-τα)^-1/2, where τ and α denote the delay and the control gain, respectively. As a result, successful mitigation depends on the competition between these two factors. We also derive analytical results that elucidate the choice of the appropriate control gain and delay that ensure successful mitigations. These results eliminate the need for any Monte Carlo simulations of the stochastic differential equations and, therefore, significantly reduce the computational cost of determining the suitable control parameters. We demonstrate the application of our results on two examples.