On the nature of seizure dynamics

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.

Modeling impairment of ionic regulation with extended Adaptive Exponential integrate-and-fire models

To model the dynamics of neuron membrane excitability many models can be considered, from the most biophysically detailed to the highest level of phenomenological description. Recent works at the single neuron level have shown the importance of taking into account the evolution of slow variables such as ionic concentration. A reduction of such a model to models of the integrate-and-fire family is interesting to then go to large network models. In this paper, we introduce a way to consider the impairment of ionic regulation by adding a third, slow, variable to the adaptive Exponential integrate-and-fire model (AdEx). We then implement and simulate a network including this model. We find that this network was able to generate normal and epileptic discharges. This model should be useful for the design of network simulations of normal and pathological states.

Advances in physiological and clinical relevance of hiPSC-derived brain models for precision medicine pipelines

Precision, or personalized, medicine aims to stratify patients based on variable pathogenic signatures to optimize the effectiveness of disease prevention and treatment. This approach is favorable in the context of brain disorders, which are often heterogeneous in their pathophysiological features, patterns of disease progression and treatment response, resulting in limited therapeutic standard-of-care. Here we highlight the transformative role that human induced pluripotent stem cell (hiPSC)-derived neural models are poised to play in advancing precision medicine for brain disorders, particularly emerging innovations that improve the relevance of hiPSC models to human physiology. hiPSCs derived from accessible patient somatic cells can produce various neural cell types and tissues; current efforts to increase the complexity of these models, incorporating region-specific neural tissues and non-neural cell types of the brain microenvironment, are providing increasingly relevant insights into human-specific neurobiology. Continued advances in tissue engineering combined with innovations in genomics, high-throughput screening and imaging strengthen the physiological relevance of hiPSC models and thus their ability to uncover disease mechanisms, therapeutic vulnerabilities, and tissue and fluid-based biomarkers that will have real impact on neurological disease treatment. True physiological understanding, however, necessitates integration of hiPSC-neural models with patient biophysical data, including quantitative neuroimaging representations. We discuss recent innovations in cellular neuroscience that can provide these direct connections through generative AI modeling. Our focus is to highlight the great potential of synergy between these emerging innovations to pave the way for personalized medicine becoming a viable option for patients suffering from neuropathologies, particularly rare epileptic and neurodegenerative disorders.

A New Perspective in Epileptic Seizure Classification: Applying the Taxonomy of Seizure Dynamotypes to Noninvasive EEG and Examining Dynamical Changes across Sleep Stages

Epilepsy, a neurological disorder characterized by recurrent unprovoked seizures, significantly impacts patient quality of life. Current classification methods focus primarily on clinical observations and electroencephalography (EEG) analysis, often overlooking the underlying dynamics driving seizures. This study uses surface EEG data to identify seizure transitions using a dynamical systems-based framework-the taxonomy of seizure dynamotypes-previously examined only in invasive data. We applied principal component and independent component (IC) analysis to surface EEG recordings from 1,177 seizures in 158 patients with focal epilepsy, decomposing the signals into ICs. The ICs were visually labeled for clear seizure transitions and bifurcation morphologies (BifMs), which were then examined using Bayesian multilevel modeling in the context of clinical factors. Our analysis reveals that certain onset bifurcations (saddle node on invariant circle and supercritical Hopf) are more prevalent during wakefulness compared with their reduced rate during nonrapid eye movement (NREM) sleep, particularly NREM3. We discuss the possible implications of our results in the context of modeling approaches and suggest additional avenues to continue this exploration. Furthermore, we demonstrate the feasibility of automating this classification process using machine learning, achieving high performance in identifying seizure-related ICs and classifying interspike interval changes. Our findings suggest that the noise in surface EEG may obscure certain BifMs, and we suggest technical improvements that could enhance detection accuracy. Expanding the dataset and incorporating long-term biological rhythms, such as circadian and multiday cycles, may provide a more comprehensive understanding of seizure dynamics and improve clinical decision-making.

Would you publish unrealistic models?

The theoretical neurosciences research community produces many models, of different natures, to capture activities or functions of the brain. Some of these models are presented as «realistic » models, often because variables and parameters have biophysical units, but not always. In this opinion article, I explain why this term can be misleading and I propose some elements that can be useful to characterize a model.

Computer-assisted analysis of routine EEG to identify hidden biomarkers of epilepsy: A systematic review

Background

Computational analysis of routine electroencephalogram (rEEG) could improve the accuracy of epilepsy diagnosis. We aim to systematically assess the diagnostic performances of computed biomarkers for epilepsy in individuals undergoing rEEG.

Methods

We searched MEDLINE, EMBASE, EBM reviews, IEEE Explore and the grey literature for studies published between January 1961 and December 2022. We included studies reporting a computational method to diagnose epilepsy based on rEEG without relying on the identification of interictal epileptiform discharges or seizures. Diagnosis of epilepsy as per a treating physician was the reference standard. We assessed the risk of bias using an adapted QUADAS-2 tool.

Results

We screened 10 166 studies, and 37 were included. The sample size ranged from 8 to 192 (mean=54). The computed biomarkers were based on linear (43%), non-linear (27%), connectivity (38%), and convolutional neural networks (10%) models. The risk of bias was high or unclear in all studies, more commonly from spectrum effect and data leakage. Diagnostic accuracy ranged between 64% and 100%. We observed high methodological heterogeneity, preventing pooling of accuracy measures.

Conclusion

The current literature provides insufficient evidence to reliably assess the diagnostic yield of computational analysis of rEEG.

Significance

We provide guidelines regarding patient selection, reference standard, algorithms, and performance validation.

Integration of partially observed multimodal and multiscale neural signals for estimating a neural circuit using dynamic causal modeling

Integrating multiscale, multimodal neuroimaging data is essential for a comprehensive understanding of neural circuits. However, this is challenging due to the inherent trade-offs between spatial coverage and resolution in each modality, necessitating a computational strategy that combines modality-specific information effectively. This study introduces a dynamic causal modeling (DCM) framework designed to address the challenge of combining partially observed, multiscale signals across a larger-scale neural circuit by employing a shared neural state model with modality-specific observation models. The proposed method achieves robust circuit inference by iteratively integrating parameter estimates from local microscale and global meso- or macroscale circuits, derived from signals across various scales and modalities. Parameters estimated from high-resolution data within specific regions inform global circuit estimation by constraining neural properties in unobserved regions, while large-scale circuit data help elucidate detailed local circuitry. Using a virtual ground truth system, we validated the method across diverse experimental settings, combining calcium imaging (CaI), voltage-sensitive dye imaging (VSDI), and blood-oxygen-level-dependent (BOLD) signals-each with distinct coverage and resolution. Our reciprocal and iterative parameter estimation approach markedly improves the accuracy of neural property and connectivity estimates compared to traditional one-step estimation methods. This iterative integration of local and global parameters presents a reliable approach to inferring extensive, complex neural circuits from partially observed, multimodal, and multiscale data, showcasing how information from different scales reciprocally enhances entire circuit parameter estimation.

A cortical field theory - dynamics and symmetries

We characterise cortical dynamics using partial differential equations (PDEs), analysing various connectivity patterns within the cortical sheet. This exploration yields diverse dynamics, encompassing wave equations and limit cycle activity. We presume balanced equations between excitatory and inhibitory neuronal units, reflecting the ubiquitous oscillatory patterns observed in electrophysiological measurements. Our derived dynamics comprise lowest-order wave equations (i.e., the Klein-Gordon model), limit cycle waves, higher-order PDE formulations, and transitions between limit cycles and near-zero states. Furthermore, we delve into the symmetries of the models using the Lagrangian formalism, distinguishing between continuous and discontinuous symmetries. These symmetries allow for mathematical expediency in the analysis of the model and could also be useful in studying the effect of symmetrical input from distributed cortical regions. Overall, our ability to derive multiple constraints on the fields - and predictions of the model - stems largely from the underlying assumption that the brain operates at a critical state. This assumption, in turn, drives the dynamics towards oscillatory or semi-conservative behaviour. Within this critical state, we can leverage results from the physics literature, which serve as analogues for neural fields, and implicit construct validity. Comparisons between our model predictions and electrophysiological findings from the literature - such as spectral power distribution across frequencies, wave propagation speed, epileptic seizure generation, and pattern formation over the cortical surface - demonstrate a close match. This study underscores the importance of utilizing symmetry preserving PDE formulations for further mechanistic insights into cortical activity.

Virtual resection evaluation based on sEEG propagation network for drug-resistant epilepsy

Drug-resistant epilepsy with frequent seizures are considered to undergo surgery to become seizure-free, but seizure-free rates have not dramatically improved, partly due to imprecise intervention locations. To address this clinical need, we construct effective connectivity to reveal epilepsy brain dynamics. Based on the propagation path captured by the high order effective connectivity, calculate the control centrality evaluation scheme of the excised area. We used three datasets: simulation dataset, clinical dataset, and public dataset. The epileptogenic propagation network was quantified by calculating high-order effective connection to obtain accurate propagation path, based on this, combined with the outdegree index for virtual resection. By removing electrodes and recalculating control centrality, we quantify each electrode or region's control centrality to evaluate the virtual resection scheme. Three datasets obtained consistent results. We track the accurate propagation path and find the obvious inflection points occurring during the excision process. The minimum intervention targets were obtained by comparing different schemes without recurrence. The clinical data with multiple seizures found that after resection, the brain reaches a stable state and is less likely to continue spreading. By quantitative analysis of control centrality to evaluate the possible excision scheme, finally we obtain the best intervention area for epilepsy, which assist in developing surgical plans.

Stationary correlation pattern in highly non-stationary MEG recordings of healthy subjects and its relation to former EEG studies

In this study, we analyze magnetoencephalographic (MEG) recordings from 48 clinically healthy subjects obtained from the Human Connectome Project (HCP) while they performed a working memory task and a motor task. Our results reveal a well-developed, stable interrelation pattern that spans the entire scalp and is nearly universal, being almost task- and subject-independent. Additionally, we demonstrate that this pattern closely resembles a stationary correlation pattern (SCP) observed in EEG signals under various physiological and pathological conditions (the distribution of Pearson correlations are centered at about 0.75). Furthermore, we identify the most effective EEG reference for studying the brain's functional network derived from lag-zero cross-correlations. We contextualize these findings within the theory of complex dynamical systems operating near a critical point of a phase transition.

Propagation of transient explosive synchronization in a mesoscale mouse brain network model of epilepsy

Generalized epileptic attacks, which exhibit widespread disruption of brain activity, are characterized by recurrent, spontaneous, and synchronized bursts of neural activity that self-initiate and self-terminate through critical transitions. Here we utilize the general framework of explosive synchronization (ES) from complex systems science to study the role of network structure and resource dynamics in the generation and propagation of seizures. We show that a combination of resource constraint and adaptive coupling in a Kuramoto network oscillator model can reliably generate seizure-like synchronization activity across different network topologies, including a biologically derived mesoscale mouse brain network. The model, coupled with a novel algorithm for tracking seizure propagation, provides mechanistic insight into the dynamics of transition to the synchronized state and its dependence on resources; and identifies key brain areas that may be involved in the initiation and spatial propagation of the seizure. The model, though minimal, efficiently recapitulates several experimental and theoretical predictions from more complex models and makes novel experimentally testable predictions.

Periodic forces combined with feedback induce quenching in a bistable oscillator

The coexistence of an abnormal rhythm and a normal steady state is often observed in nature (e.g., epilepsy). Such a system is modeled as a bistable oscillator that possesses both a limit cycle and a fixed point. Although bistable oscillators under several perturbations have been addressed in the literature, the mechanism of oscillation quenching, a transition from a limit cycle to a fixed point, has not been fully understood. In this study, we analyze quenching using the extended Stuart-Landau oscillator driven by periodic forces. Numerical simulations suggest that the entrainment to the periodic force induces the amplitude change of a limit cycle. By reducing the system with an averaging method, we investigate the bifurcation structures of the periodically driven oscillator. We find that oscillation quenching occurs by the homoclinic bifurcation when we use a periodic force combined with quadratic feedback. In conclusion, we develop a state-transition method in a bistable oscillator using periodic forces, which would have the potential for practical applications in controlling and annihilating abnormal oscillations. Moreover, we clarify the rich and diverse bifurcation structures behind periodically driven bistable oscillators, which we believe would contribute to further understanding the complex behaviors in non-autonomous systems.

Brain sodium MRI-derived priors support the estimation of epileptogenic zones using personalized model-based methods in epilepsy

Patients presenting with drug-resistant epilepsy are eligible for surgery aiming to remove the regions involved in the production of seizure activities, the so-called epileptogenic zone network (EZN). Thus the accurate estimation of the EZN is crucial. Data-driven, personalized virtual brain models derived from patient-specific anatomical and functional data are used in Virtual Epileptic Patient (VEP) to estimate the EZN via optimization methods from Bayesian inference. The Bayesian inference approach used in previous VEP integrates priors, based on the features of stereotactic-electroencephalography (SEEG) seizures' recordings. Here, we propose new priors, based on quantitative 23Na-MRI. The 23Na-MRI data were acquired at 7T and provided several features characterizing the sodium signal decay. The hypothesis is that the sodium features are biomarkers of neuronal excitability related to the EZN and will add additional information to VEP estimation. In this paper, we first proposed the mapping from 23Na-MRI features to predict the EZN via a machine learning approach. Then, we exploited these predictions as priors in the VEP pipeline. The statistical results demonstrated that compared with the results from current VEP, the result from VEP based on 23Na-MRI prior has better balanced accuracy, and the similar weighted harmonic mean of the precision and recall.

NeoCoMM: A neocortical neuroinspired computational model for the reconstruction and simulation of epileptiform events

BACKGROUND

Understanding the pathophysiological dynamics that underline Interictal Epileptiform Events (IEEs) such as epileptic spikes, spike-and-waves or High-Frequency Oscillations (HFOs) is of major importance in the context of neocortical refractory epilepsy, as it paves the way for the development of novel therapies. Typically, these events are detected in Local Field Potential (LFP) recordings obtained through depth electrodes during pre-surgical investigations. Although essential, the underlying pathophysiological mechanisms for the generation of these epileptic neuromarkers remain unclear. The aim of this paper is to propose a novel neurophysiologically relevant reconstruction of the neocortical microcircuitry in the context of epilepsy. This reconstruction intends to facilitate the analysis of a comprehensive set of parameters encompassing physiological, morphological, and biophysical aspects that directly impact the generation and recording of different IEEs.

METHOD

a novel microscale computational model of an epileptic neocortical column was introduced. This model incorporates the intricate multilayered structure of the cortex and allows for the simulation of realistic interictal epileptic signals. The proposed model was validated through comparisons with real IEEs recorded using intracranial stereo-electroencephalography (SEEG) signals from both humans and animals. Using the model, the user can recreate epileptiform patterns observed in different species (human, rodent, and mouse) and study the intracellular activity associated with these patterns.

RESULTS

Our model allowed us to unravel the relationship between glutamatergic and GABAergic synaptic transmission of the epileptic neural network and the type of generated IEE. Moreover, sensitivity analyses allowed for the exploration of the pathophysiological parameters responsible for the transitions between these events. Finally, the presented modeling framework also provides an Electrode Tissue Model (ETI) that adds realism to the simulated signals and offers the possibility of studying their sensitivity to the electrode characteristics.

CONCLUSION

The model (NeoCoMM) presented in this work can be of great use in different applications since it offers an in silico framework for sensitivity analysis and hypothesis testing. It can also be used as a starting point for more complex studies.

Predicting radiofrequency thermocoagulation surgical outcomes in refractory focal epilepsy patients using functional coupled neural mass model

Objective

The success rate of achieving seizure freedom after radiofrequency thermocoagulation surgery for patients with refractory focal epilepsy is about 20-40%. This study aims to enhance the prediction of surgical outcomes based on preoperative decisions through network model simulation, providing a reference for clinicians to validate and optimize surgical plans.

Methods

Twelve patients with epilepsy who underwent radiofrequency thermocoagulation were retrospectively reviewed in this study. A coupled model based on model subsets of the neural mass model was constructed by calculating partial directed coherence as the coupling matrix from stereoelectroencephalography (SEEG) signals. Multi-channel time-varying model parameters of excitation and inhibitions were identified by fitting the real SEEG signals with the coupled model. Further incorporating these model parameters, the coupled model virtually removed contacts destroyed in radiofrequency thermocoagulation or selected randomly. Subsequently, the coupled model after virtual surgery was simulated.

Results

The identified excitatory and inhibitory parameters showed significant difference before and after seizure onset (p < 0.05), and the trends of parameter changes aligned with the seizure process. Additionally, excitatory parameters of epileptogenic contacts were higher than that of non-epileptogenic contacts, and opposite findings were noticed for inhibitory parameters. The simulated signals of postoperative models to predict surgical outcomes yielded an area under the curve (AUC) of 83.33% and an accuracy of 91.67%.

Conclusion

The multi-channel coupled model proposed in this study with physiological characteristics showed a desirable performance for preoperatively predicting patients' prognoses.

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.

Effects of baicalin pre-treatment on pentylenetetrazole-induced seizures: Insights from zebrafish larvae locomotor behavior and neuronal calcium imaging

Natural compounds are increasingly being studied for their potential neuroprotective effects against inflammatory neurological diseases. Epilepsy is a common neurological disease associated with inflammatory processes, and around 30% of people with epilepsy do not respond to traditional treatments. Some flavonoids, when taken along with antiseizure medications can help reduce the likelihood of drug-resistant epilepsy. Baicalin, a plant-based compound, has been shown to possess pharmacological properties such as anti-inflammatory, neuroprotective, anticonvulsant, and antioxidant activities. In this study, we tested the effect of baicalin on an established model of pharmacologically induced seizure in zebrafish using measures of both locomotor behavior and calcium imaging of neuronal activity. The results of our study showed that, at the tested concentration, and contrary to other studies in rodents, baicalin did not have an anti-seizure effect in zebrafish larvae. However, given its known properties, other concentrations and approaches should be explored to determine if it could potentially have other beneficial effects, either alone or when administered in combination with classic antiseizure medications.

Morphological and Functional Alterations in the CA1 Pyramidal Neurons of the Rat Hippocampus in the Chronic Phase of the Lithium-Pilocarpine Model of Epilepsy

Epilepsy is known to cause alterations in neural networks. However, many details of these changes remain poorly understood. The objective of this study was to investigate changes in the properties of hippocampal CA1 pyramidal neurons and their synaptic inputs in a rat lithium-pilocarpine model of epilepsy. In the chronic phase of the model, we found a marked loss of pyramidal neurons in the CA1 area. However, the membrane properties of the neurons remained essentially unaltered. The results of the electrophysiological and morphological studies indicate that the direct pathway from the entorhinal cortex to CA1 neurons is reinforced in epileptic animals, whereas the inputs to them from CA3 are either unaltered or even diminished. In particular, the dendritic spine density in the str. lacunosum moleculare, where the direct pathway from the entorhinal cortex terminates, was found to be 2.5 times higher in epileptic rats than in control rats. Furthermore, the summation of responses upon stimulation of the temporoammonic pathway was enhanced by approximately twofold in epileptic rats. This enhancement is believed to be a significant contributing factor to the heightened epileptic activity observed in the entorhinal cortex of epileptic rats using an ex vivo 4-aminopyridine model.

Recent Progress in Brain Network Models for Medical Applications: A Review

Importance: Pathological perturbations of the brain often spread via connectome to fundamentally alter functional consequences. By integrating multimodal neuroimaging data with mathematical neural mass modeling, brain network models (BNMs) enable to quantitatively characterize aberrant network dynamics underlying multiple neurological and psychiatric disorders. We delved into the advancements of BNM-based medical applications, discussed the prevalent challenges within this field, and provided possible solutions and future directions. Highlights: This paper reviewed the theoretical foundations and current medical applications of computational BNMs. Composed of neural mass models, the BNM framework allows to investigate large-scale brain dynamics behind brain diseases by linking the simulated functional signals to the empirical neurophysiological data, and has shown promise in exploring neuropathological mechanisms, elucidating therapeutic effects, and predicting disease outcome. Despite that several limitations existed, one promising trend of this research field is to precisely guide clinical neuromodulation treatment based on individual BNM simulation. Conclusion: BNM carries the potential to help understand the mechanism underlying how neuropathology affects brain network dynamics, further contributing to decision-making in clinical diagnosis and treatment. Several constraints must be addressed and surmounted to pave the way for its utilization in the clinic.

Parameter estimation in a whole-brain network model of epilepsy: Comparison of parallel global optimization solvers

The Virtual Epileptic Patient (VEP) refers to a computer-based representation of a patient with epilepsy that combines personalized anatomical data with dynamical models of abnormal brain activities. It is capable of generating spatio-temporal seizure patterns that resemble those recorded with invasive methods such as stereoelectro EEG data, allowing for the evaluation of clinical hypotheses before planning surgery. This study highlights the effectiveness of calibrating VEP models using a global optimization approach. The approach utilizes SaCeSS, a cooperative metaheuristic algorithm capable of parallel computation, to yield high-quality solutions without requiring excessive computational time. Through extensive benchmarking on synthetic data, our proposal successfully solved a set of different configurations of VEP models, demonstrating better scalability and superior performance against other parallel solvers. These results were further enhanced using a Bayesian optimization framework for hyperparameter tuning, with significant gains in terms of both accuracy and computational cost. Additionally, we added a scalable uncertainty quantification phase after model calibration, and used it to assess the variability in estimated parameters across different problems. Overall, this study has the potential to improve the estimation of pathological brain areas in drug-resistant epilepsy, thereby to inform the clinical decision-making process.

Impaired brain-heart axis in focal epilepsy: Alterations in information flow and implications for seizure dynamics

This study delves into functional brain-heart interplay (BHI) dynamics during interictal periods before and after seizure events in focal epilepsy. Our analysis focuses on elucidating the causal interaction between cortical and autonomic nervous system (ANS) oscillations, employing electroencephalography and heart rate variability series. The dataset for this investigation comprises 47 seizure events from 14 independent subjects, obtained from the publicly available Siena Dataset. Our findings reveal an impaired brain-heart axis especially in the heart-to-brain functional direction. This is particularly evident in bottom-up oscillations originating from sympathovagal activity during the transition between preictal and postictal periods. These results indicate a pivotal role of the ANS in epilepsy dynamics. Notably, the brain-to-heart information flow targeting cardiac oscillations in the low-frequency band does not display significant changes. However, there are noteworthy changes in cortical oscillations, primarily originating in central regions, influencing heartbeat oscillations in the high-frequency band. Our study conceptualizes seizures as a state of hyperexcitability and a network disease affecting both cortical and peripheral neural dynamics. Our results pave the way for a deeper understanding of BHI in epilepsy, which holds promise for the development of advanced diagnostic and therapeutic approaches also based on bodily neural activity for individuals living with epilepsy.

Individualized epidemic spreading models predict epilepsy surgery outcomes: A pseudo-prospective study

Epilepsy surgery is the treatment of choice for drug-resistant epilepsy patients, but up to 50% of patients continue to have seizures one year after the resection. In order to aid presurgical planning and predict postsurgical outcome on a patient-by-patient basis, we developed a framework of individualized computational models that combines epidemic spreading with patient-specific connectivity and epileptogeneity maps: the Epidemic Spreading Seizure and Epilepsy Surgery framework (ESSES). ESSES parameters were fitted in a retrospective study (N = 15) to reproduce invasive electroencephalography (iEEG)-recorded seizures. ESSES reproduced the iEEG-recorded seizures, and significantly better so for patients with good (seizure-free, SF) than bad (nonseizure-free, NSF) outcome. We illustrate here the clinical applicability of ESSES with a pseudo-prospective study (N = 34) with a blind setting (to the resection strategy and surgical outcome) that emulated presurgical conditions. By setting the model parameters in the retrospective study, ESSES could be applied also to patients without iEEG data. ESSES could predict the chances of good outcome after any resection by finding patient-specific model-based optimal resection strategies, which we found to be smaller for SF than NSF patients, suggesting an intrinsic difference in the network organization or presurgical evaluation results of NSF patients. The actual surgical plan overlapped more with the model-based optimal resection, and had a larger effect in decreasing modeled seizure propagation, for SF patients than for NSF patients. Overall, ESSES could correctly predict 75% of NSF and 80.8% of SF cases pseudo-prospectively. Our results show that individualised computational models may inform surgical planning by suggesting alternative resections and providing information on the likelihood of a good outcome after a proposed resection. This is the first time that such a model is validated with a fully independent cohort and without the need for iEEG recordings.

Treatment effects in epilepsy: a mathematical framework for understanding response over time

Epilepsy is a neurological disorder characterized by recurrent seizures, affecting over 65 million people worldwide. Treatment typically commences with the use of anti-seizure medications, including both mono- and poly-therapy. Should these fail, more invasive therapies such as surgery, electrical stimulation and focal drug delivery are often considered in an attempt to render the person seizure free. Although a significant portion ultimately benefit from these treatment options, treatment responses often fluctuate over time. The physiological mechanisms underlying these temporal variations are poorly understood, making prognosis a significant challenge when treating epilepsy. Here we use a dynamic network model of seizure transition to understand how seizure propensity may vary over time as a consequence of changes in excitability. Through computer simulations, we explore the relationship between the impact of treatment on dynamic network properties and their vulnerability over time that permit a return to states of high seizure propensity. For small networks we show vulnerability can be fully characterised by the size of the first transitive component (FTC). For larger networks, we find measures of network efficiency, incoherence and heterogeneity (degree variance) correlate with robustness of networks to increasing excitability. These results provide a set of potential prognostic markers for therapeutic interventions in epilepsy. Such markers could be used to support the development of personalized treatment strategies, ultimately contributing to understanding of long-term seizure freedom.

Exploration of interictal to ictal transition in epileptic seizures using a neural mass model

An epileptic seizure can usually be divided into three stages: interictal, preictal, and ictal. However, the seizure underlying the transition from interictal to ictal activities in the brain involves complex interactions between inhibition and excitation in groups of neurons. To explore this mechanism at the level of a single population, this paper employed a neural mass model, named the complete physiology-based model (cPBM), to reconstruct electroencephalographic (EEG) signals and to infer the changes in excitatory/inhibitory connections related to excitation-inhibition (E-I) balance based on an open dataset recorded for ten epileptic patients. Since epileptic signals display spectral characteristics, spectral dynamic causal modelling (DCM) was applied to quantify these frequency characteristics by maximizing the free energy in the framework of power spectral density (PSD) and estimating the cPBM parameters. In addition, to address the local maximum problem that DCM may suffer from, a hybrid deterministic DCM (H-DCM) approach was proposed, with a deterministic annealing-based scheme applied in two directions. The H-DCM approach adjusts the temperature introduced in the objective function by gradually decreasing the temperature to obtain relatively good initialization and then gradually increasing the temperature to search for a better estimation after each maximization. The results showed that (i) reconstructed EEG signals belonging to the three stages together with their PSDs can be reproduced from the estimated parameters of the cPBM; (ii) compared to DCM, traditional D-DCM and anti D-DCM, the proposed H-DCM shows higher free energies and lower root mean square error (RMSE), and it provides the best performance for all stages (e.g., the RMSEs between the reconstructed PSD computed from the reconstructed EEG signal and the sample PSD obtained from the real EEG signal are 0.33 ± 0.08, 0.67 ± 0.37 and 0.78 ± 0.57 in the interictal, preictal and ictal stages, respectively); and (iii) the transition from interictal to ictal activity can be explained by an increase in the connections between pyramidal cells and excitatory interneurons and between pyramidal cells and fast inhibitory interneurons, as well as a decrease in the self-loop connection of the fast inhibitory interneurons in the cPBM. Moreover, the E-I balance, defined as the ratio between the excitatory connection from pyramidal cells to fast inhibitory interneurons and the inhibitory connection with the self-loop of fast inhibitory interneurons, is also significantly increased during the epileptic seizure transition.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-023-09976-6.

Early and widespread engagement of the cerebellum during hippocampal epileptiform activity Format: Brief Communication

Despite research illustrating the cerebellum may be a critical circuit element in the epilepsies, remarkably little is known about cerebellar engagement during seizures. We therefore implemented a novel method for repeated imaging of the cerebellum in awake, chronically epileptic animals. We found widespread changes in cerebellar calcium signals during behavioral seizures and during hippocampal seizures that remained electrographic only, arguing against cerebellar modulation simply reflecting motor components. Moreover, even brief interictal spikes produced widespread alterations in cerebellar activity. Changes were noted in the anterior and posterior cerebellum, along the midline, and both ipsilaterally and contralaterally to the seizure focus. Remarkably, changes in the cerebellum also occurred prior to any noticeable change in the hippocampal electrographic recordings, suggesting a special relationship between the cerebellum and hippocampal epileptiform activity. Together these results underscore the importance of the cerebellum in epilepsy, warranting a more consistent consideration of the cerebellum when evaluating epilepsy patients.

Heart rate variability as a preictal marker for determining the laterality of seizure onset zone in frontal lobe epilepsy

Determining the laterality of the seizure onset zone is challenging in frontal lobe epilepsy (FLE) due to the rapid propagation of epileptic discharges to the contralateral hemisphere. There is hemispheric lateralization of autonomic control, and heart rate is modulated by interactions between the sympathetic and parasympathetic nervous systems. Based on this notion, the laterality of seizure foci in FLE might be determined using heart rate variability (HRV) parameters. We explored preictal markers for differentiating the laterality of seizure foci in FLE using HRV parameters. Twelve patients with FLE (6 right FLE and 6 left FLE) were included in the analyzes. A total of 551 (460 left FLE and 91 right FLE) 1-min epoch electrocardiography data were used for HRV analysis. We found that most HRV parameters differed between the left and right FLE groups. Among the machine learning algorithms applied in this study, the light gradient boosting machine was the most accurate, with an AUC value of 0.983 and a classification accuracy of 0.961. Our findings suggest that HRV parameter-based laterality determination models can be convenient and effective tools in clinical settings. Considering that heart rate can be easily measured in real time with a wearable device, our proposed method can be applied to a closed-loop device as a real-time monitoring tool for determining the side of stimulation.

Virtual brain twins: from basic neuroscience to clinical use

Virtual brain twins are personalized, generative and adaptive brain models based on data from an individual's brain for scientific and clinical use. After a description of the key elements of virtual brain twins, we present the standard model for personalized whole-brain network models. The personalization is accomplished using a subject's brain imaging data by three means: (1) assemble cortical and subcortical areas in the subject-specific brain space; (2) directly map connectivity into the brain models, which can be generalized to other parameters; and (3) estimate relevant parameters through model inversion, typically using probabilistic machine learning. We present the use of personalized whole-brain network models in healthy ageing and five clinical diseases: epilepsy, Alzheimer's disease, multiple sclerosis, Parkinson's disease and psychiatric disorders. Specifically, we introduce spatial masks for relevant parameters and demonstrate their use based on the physiological and pathophysiological hypotheses. Finally, we pinpoint the key challenges and future directions.

Optimal input reverberation and homeostatic self-organization toward the edge of synchronization

Transient or partial synchronization can be used to do computations, although a fully synchronized network is sometimes related to the onset of epileptic seizures. Here, we propose a homeostatic mechanism that is capable of maintaining a neuronal network at the edge of a synchronization transition, thereby avoiding the harmful consequences of a fully synchronized network. We model neurons by maps since they are dynamically richer than integrate-and-fire models and more computationally efficient than conductance-based approaches. We first describe the synchronization phase transition of a dense network of neurons with different tonic spiking frequencies coupled by gap junctions. We show that at the transition critical point, inputs optimally reverberate through the network activity through transient synchronization. Then, we introduce a local homeostatic dynamic in the synaptic coupling and show that it produces a robust self-organization toward the edge of this phase transition. We discuss the potential biological consequences of this self-organization process, such as its relation to the Brain Criticality hypothesis, its input processing capacity, and how its malfunction could lead to pathological synchronization and the onset of seizure-like activity.

Multi-scale modelling of the epileptic brain: advantages of computational therapy exploration

Objective: Epilepsy is a complex disease spanning across multiple scales, from ion channels in neurons to neuronal circuits across the entire brain. Over the past decades, computational models have been used to describe the pathophysiological activity of the epileptic brain from different aspects. Traditionally, each computational model can aid in optimizing therapeutic interventions, therefore, providing a particular view to design strategies for treating epilepsy. As a result, most studies are concerned with generating specific models of the epileptic brain that can help us understand the certain machinery of the pathological state. Those specific models vary in complexity and biological accuracy, with system-level models often lacking biological details.Approach: Here, we review various types of computational model of epilepsy and discuss their potential for different therapeutic approaches and scenarios, including drug discovery, surgical strategies, brain stimulation, and seizure prediction. We propose that we need to consider an integrated approach with a unified modelling framework across multiple scales to understand the epileptic brain. Our proposal is based on the recent increase in computational power, which has opened up the possibility of unifying those specific epileptic models into simulations with an unprecedented level of detail.Main results: A multi-scale epilepsy model can bridge the gap between biologically detailed models, used to address molecular and cellular questions, and brain-wide models based on abstract models which can account for complex neurological and behavioural observations.Significance: With these efforts, we move toward the next generation of epileptic brain models capable of connecting cellular features, such as ion channel properties, with standard clinical measures such as seizure severity.

Linking fast and slow: The case for generative models

A pervasive challenge in neuroscience is testing whether neuronal connectivity changes over time due to specific causes, such as stimuli, events, or clinical interventions. Recent hardware innovations and falling data storage costs enable longer, more naturalistic neuronal recordings. The implicit opportunity for understanding the self-organised brain calls for new analysis methods that link temporal scales: from the order of milliseconds over which neuronal dynamics evolve, to the order of minutes, days, or even years over which experimental observations unfold. This review article demonstrates how hierarchical generative models and Bayesian inference help to characterise neuronal activity across different time scales. Crucially, these methods go beyond describing statistical associations among observations and enable inference about underlying mechanisms. We offer an overview of fundamental concepts in state-space modeling and suggest a taxonomy for these methods. Additionally, we introduce key mathematical principles that underscore a separation of temporal scales, such as the slaving principle, and review Bayesian methods that are being used to test hypotheses about the brain with multiscale data. We hope that this review will serve as a useful primer for experimental and computational neuroscientists on the state of the art and current directions of travel in the complex systems modelling literature.

Dynamical modulation of hypersynchronous seizure onset with transcranial magneto-acoustic stimulation in a hippocampal computational model

Hypersynchronous (HYP) seizure onset is one of the frequently observed seizure-onset patterns in temporal lobe epileptic animals and patients, often accompanied by hippocampal sclerosis. However, the exact mechanisms and ion dynamics of the transition to HYP seizures remain unclear. Transcranial magneto-acoustic stimulation (TMAS) has recently been proposed as a novel non-invasive brain therapy method to modulate neurological disorders. Therefore, we propose a biophysical computational hippocampal network model to explore the evolution of HYP seizure caused by changes in crucial physiological parameters and design an effective TMAS strategy to modulate HYP seizure onset. We find that the cooperative effects of abnormal glial uptake strength of potassium and excessive bath potassium concentration could produce multiple discharge patterns and result in transitions from the normal state to the HYP seizure state and ultimately to the depolarization block state. Moreover, we find that the pyramidal neuron and the PV+ interneuron in HYP seizure-onset state exhibit saddle-node-on-invariant-circle/saddle homoclinic (SH) and saddle-node/SH at onset/offset bifurcation pairs, respectively. Furthermore, the response of neuronal activities to TMAS of different ultrasonic waveforms revealed that lower sine wave stimulation can increase the latency of HYP seizures and even completely suppress seizures. More importantly, we propose an ultrasonic parameter area that not only effectively regulates epileptic rhythms but also is within the safety limits of ultrasound neuromodulation therapy. Our results may offer a more comprehensive understanding of the mechanisms of HYP seizure and provide a theoretical basis for the application of TMAS in treating specific types of seizures.

Seizure Pathways Changes at the Subject-Specific Level via Dynamic Step Effective Network Analysis

The variability in the propagation pathway in epilepsy is a main factor contributing to surgical treatment failure. Ways to accurately capture the brain propagation network and quantitatively assess its evolution remain poorly described. This work aims to develop a dynamic step effective network (dSTE) to obtain the propagation path network of multiple seizures in the same patient and explore the degree of dissimilarity. Multichannel stereo-electroencephalography (sEEG) signals were acquired with ictal processes involving continuous changes in information propagation. We utilized high-order dynamic brain networks to obtain propagation networks through different levels of linking steps. We proposed a dissimilarity index based on singular value decomposition to quantitatively compare seizure pathways. Simulated data were generated through The Virtual Brain, and the reliability of this method was verified through ablation experiments. By applying the proposed method to two datasets consisting of 29 patients total, the evolution processes of each patient's seizure networks was obtained, and the within-patient dissimilarities were quantitatively compared. Finally, three types of brain network connectivity patterns were found. Type I patients have a good prognosis, while type III patients are prone to postoperative recurrence. This method captures the evolution of seizure propagation networks and assesses their dissimilarity more reliably than existing methods, demonstrating good robustness for studying the propagation path differences for multiple seizures in epilepsy patients. The three different patterns will be important considerations when planning epilepsy surgery under sEEG guidance.

Concurrent functional ultrasound imaging with graphene-based DC-coupled electrophysiology as a platform to study slow brain signals and cerebral blood flow under control and pathophysiological brain states

Current methodology used to investigate how shifts in brain states associated with regional cerebral blood volume (CBV) change in deep brain areas, are limited by either the spatiotemporal resolution of the CBV techniques, and/or compatibility with electrophysiological recordings; particularly in relation to spontaneous brain activity and the study of individual events. Additionally, infraslow brain signals (<0.1 Hz), including spreading depolarisations, DC-shifts and infraslow oscillations (ISO), are poorly captured by traditional AC-coupled electrographic recordings; yet these very slow brain signals can profoundly change CBV. To gain an improved understanding of how infraslow brain signals couple to CBV we present a new method for concurrent CBV with wide bandwidth electrophysiological mapping using simultaneous functional ultrasound imaging (fUS) and graphene-based field effect transistor (gFET) DC-coupled electrophysiological acquisitions. To validate the feasibility of this methodology visually-evoked neurovascular coupling (NVC) responses were examined. gFET recordings are not affected by concurrent fUS imaging, and epidural placement of gFET arrays within the imaging window did not deteriorate fUS signal quality. To examine directly the impact of infra-slow potential shifts on CBV, cortical spreading depolarisations (CSDs) were induced. A biphasic pattern of decreased, followed by increased CBV, propagating throughout the ipsilateral cortex, and a delayed decrease in deeper subcortical brain regions was observed. In a model of acute seizures, CBV oscillations were observed prior to seizure initiation. Individual seizures occurred on the rising phase of both infraslow brain signal and CBV oscillations. When seizures co-occurred with CSDs, CBV responses were larger in amplitude, with delayed CBV decreases in subcortical structures. Overall, our data demonstrate that gFETs are highly compatible with fUS and allow concurrent examination of wide bandwidth electrophysiology and CBV. This graphene-enabled technological advance has the potential to improve our understanding of how infraslow brain signals relate to CBV changes in control and pathological brain states.

Generalisability of epileptiform patterns across time and patients

The complexity of localising the epileptogenic zone (EZ) contributes to surgical resection failures in achieving seizure freedom. The distinct patterns of epileptiform activity during interictal and ictal phases, varying across patients, often lead to suboptimal localisation using electroencephalography (EEG) features. We posed two key questions: whether neural signals reflecting epileptogenicity generalise from interictal to ictal time windows within each patient, and whether epileptiform patterns generalise across patients. Utilising an intracranial EEG dataset from 55 patients, we extracted a large battery of simple to complex features from stereo-EEG (SEEG) and electrocorticographic (ECoG) neural signals during interictal and ictal windows. Our features (n = 34) quantified many aspects of the signals including statistical moments, complexities, frequency-domain and cross-channel network attributes. Decision tree classifiers were then trained and tested on distinct time windows and patients to evaluate the generalisability of epileptogenic patterns across time and patients, respectively. Evidence strongly supported generalisability from interictal to ictal time windows across patients, particularly in signal power and high-frequency network-based features. Consistent patterns of epileptogenicity were observed across time windows within most patients, and signal features of epileptogenic regions generalised across patients, with higher generalisability in the ictal window. Signal complexity features were particularly contributory in cross-patient generalisation across patients. These findings offer insights into generalisable features of epileptic neural activity across time and patients, with implications for future automated approaches to supplement other EZ localisation methods.

Electroencephalographic microstates as a potential neurophysiological marker differentiating bilateral from unilateral temporal lobe epilepsy

OBJECTIVE

Electroencephalographic (EEG) microstate abnormalities have been documented in different neurological disorders. We aimed to assess whether EEG microstates are altered also in patients with temporal epilepsy (TLE) and whether they show different activations in patients with unilateral TLE (UTLE) and bilateral TLE (BTLE).

METHODS

Nineteen patients with UTLE, 12 with BTLE, and 15 healthy controls were enrolled. Resting state high-density electroencephalography (128 channels) was recorded for 15 min with closed eyes. We obtained a set of stable scalp maps representing the EEG activity, named microstates, from which we acquired the following variables: global explained variance (GEV), mean duration (MD), time coverage (TC), and frequency of occurrence (FO). Two-way repeated measures analysis of variance was used to compare groups, and Spearman correlation was performed to study the maps in association with the clinical and neuropsychological data.

RESULTS

Patients with BTLE and UTLE showed differences in most of the parameters (GEV, MD, TC, FO) of the four microstate maps (A-D) compared to controls. Patients with BTLE showed a significant increase in all parameters for the microstates in Map-A and a decrease in Map-D compared to UTLE and controls. We observed a correlation between Map-A, disease duration, and spatial short-term memory, whereas microstate Map-D was correlated with the global intelligence score and short-term memory performance.

SIGNIFICANCE

A global alteration of the neural dynamics was observed in patients with TLE compared to controls. A different pattern of EEG microstate abnormalities was identified in BTLE compared to UTLE, which might represent a distinctive biomarker.

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.

Epileptic seizure suppression: A computational approach for identification and control using real data

Epilepsy affects millions of people worldwide every year and remains an open subject for research. Current development on this field has focused on obtaining computational models to better understand its triggering mechanisms, attain realistic descriptions and study seizure suppression. Controllers have been successfully applied to mitigate epileptiform activity in dynamic models written in state-space notation, whose applicability is, however, restricted to signatures that are accurately described by them. Alternatively, autoregressive modeling (AR), a typical data-driven tool related to system identification (SI), can be directly applied to signals to generate more realistic models, and since it is inherently convertible into state-space representation, it can thus be used for the artificial reconstruction and attenuation of seizures as well. Considering this, the first objective of this work is to propose an SI approach using AR models to describe real epileptiform activity. The second objective is to provide a strategy for reconstructing and mitigating such activity artificially, considering non-hybrid and hybrid controllers - designed from ictal and interictal events, respectively. The results show that AR models of relatively low order represent epileptiform activities fairly well and both controllers are effective in attenuating the undesired activity while simultaneously driving the signal to an interictal condition. These findings may lead to customized models based on each signal, brain region or patient, from which it is possible to better define shape, frequency and duration of external stimuli that are necessary to attenuate seizures.

An exploratory computational analysis in mice brain networks of widespread epileptic seizure onset locations along with potential strategies for effective intervention and propagation control

Mean-field models have been developed to replicate key features of epileptic seizure dynamics. However, the precise mechanisms and the role of the brain area responsible for seizure onset and propagation remain incompletely understood. In this study, we employ computational methods within The Virtual Brain framework and the Epileptor model to explore how the location and connectivity of an Epileptogenic Zone (EZ) in a mouse brain are related to focal seizures (seizures that start in one brain area and may or may not remain localized), with a specific focus on the hippocampal region known for its association with epileptic seizures. We then devise computational strategies to confine seizures (prevent widespread propagation), simulating medical-like treatments such as tissue resection and the application of an anti-seizure drugs or neurostimulation to suppress hyperexcitability. Through selectively removing (blocking) specific connections informed by the structural connectome and graph network measurements or by locally reducing outgoing connection weights of EZ areas, we demonstrate that seizures can be kept constrained around the EZ region. We successfully identified the minimal connections necessary to prevent widespread seizures, with a particular focus on minimizing surgical or medical intervention while simultaneously preserving the original structural connectivity and maximizing brain functionality.

The seizure classification of focal epilepsy based on the network motif analysis

Due to the complexity of focal epilepsy and its risk for transiting to the generalized epilepsy, the development of reliable classification methods to accurately predict and classify focal and generalized seizures is critical for the clinical management of patients with epilepsy. In order to holistically understand the seizure propagation behavior of focal epilepsy, we propose a three-node motif reduced network by respectively simplifying the focal region, surrounding healthy region and their critical regions as the single node. Because three-node motif can richly characterize information evolutions, the motif analysis method could comprehensively investigate the seizure behavior of focal epilepsy. Firstly, we define a new seizure propagation marker value to capture the seizure onsets and intensity. Based on the three-node motif analysis, it is shown that the focal seizure and spreading can be categorized as inhibitory seizure, focal seizure, focal-critical seizure and generalized seizures, respectively. The four types of seizures correspond to specific modal types respectively, reflecting the strong correlation between seizure behavior and information flow evolution. In addition, it is found that the intensity difference of outflow and inflow information from the critical node (connection heterogeneity) and the excitability of the critical node significantly affected the distribution and transition of the four seizure types. In particular, the method of local linear stability analysis also verifies the effectiveness of four types of seizures classification. In sum, this paper computationally confirms the complex dynamic behavior of focal seizures, and the study of criticality is helpful to propose novel seizure control strategies.

Weakly nonlinear analysis on synchronization and oscillation quenching of coupled mechanical oscillators

Various oscillatory phenomena occur in the world. Because some are associated with abnormal states (e.g. epilepsy), it is important to establish ways to terminate oscillations by external stimuli. However, despite the prior development of techniques for stabilizing unstable oscillations, relatively few studies address the transition from oscillatory to resting state in nonlinear dynamics. This study mainly analyzes the oscillation-quenching of metronomes on a platform as an example of such transitions. To facilitate the analysis, we describe the impulsive force (escapement mechanism) of a metronome by a fifth-order polynomial. By performing both averaging approximation and numerical simulation, we obtain a phase diagram for synchronization and oscillation quenching. We find that quenching occurs when the feedback to the oscillator increases, which will help explore the general principle regarding the state transition from oscillatory to resting state. We also numerically investigate the bifurcation of out-of-phase synchronization and beat-like solution. Despite the simplicity, our model successfully reproduces essential phenomena in interacting mechanical clocks, such as the bistability of in-phase and anti-phase synchrony and oscillation quenching occurring for a large mass ratio between the oscillator and the platform. We believe that our simple model will contribute to future analyses of other dynamics of mechanical clocks.

Response to photic stimulation as a measure of cortical excitability in epilepsy patients

Studying states and state transitions in the brain is challenging due to nonlinear, complex dynamics. In this research, we analyze the brain's response to non-invasive perturbations. Perturbation techniques offer a powerful method for studying complex dynamics, though their translation to human brain data is under-explored. This method involves applying small inputs, in this case via photic stimulation, to a system and measuring its response. Sensitivity to perturbations can forewarn a state transition. Therefore, biomarkers of the brain's perturbation response or "cortical excitability" could be used to indicate seizure transitions. However, perturbing the brain often involves invasive intracranial surgeries or expensive equipment such as transcranial magnetic stimulation (TMS) which is only accessible to a minority of patient groups, or animal model studies. Photic stimulation is a widely used diagnostic technique in epilepsy that can be used as a non-invasive perturbation paradigm to probe brain dynamics during routine electroencephalography (EEG) studies in humans. This involves changing the frequency of strobing light, sometimes triggering a photo-paroxysmal response (PPR), which is an electrographic event that can be studied as a state transition to a seizure state. We investigate alterations in the response to these perturbations in patients with genetic generalized epilepsy (GGE), with (n = 10) and without (n = 10) PPR, and patients with psychogenic non-epileptic seizures (PNES; n = 10), compared to resting controls (n = 10). Metrics of EEG time-series data were evaluated as biomarkers of the perturbation response including variance, autocorrelation, and phase-based synchrony measures. We observed considerable differences in all group biomarker distributions during stimulation compared to controls. In particular, variance and autocorrelation demonstrated greater changes in epochs close to PPR transitions compared to earlier stimulation epochs. Comparison of PPR and spontaneous seizure morphology found them indistinguishable, suggesting PPR is a valid proxy for seizure dynamics. Also, as expected, posterior channels demonstrated the greatest change in synchrony measures, possibly reflecting underlying PPR pathophysiologic mechanisms. We clearly demonstrate observable changes at a group level in cortical excitability in epilepsy patients as a response to perturbation in EEG data. Our work re-frames photic stimulation as a non-invasive perturbation paradigm capable of inducing measurable changes to brain dynamics.

Kindling in humans: Does secondary epileptogenesis occur?

The relevance of secondary epileptogenesis for human epilepsy remains a controversial subject decades after it was first described in animal models. Whether or not a previously normal brain region can become independently epileptogenic through a kindling-like process has not, and cannot, be definitely proven in humans. Rather than reliance on direct experimental evidence, attempts to answering this question must depend on observational data. In this review, observations based largely upon contemporary surgical series will advance the case for secondary epileptogenesis in humans. As will be argued, hypothalamic hamartoma-related epilepsy provides the strongest case for this process; all the stages of secondary epileptogenesis can be observed. Hippocampal sclerosis (HS) is another pathology where the question of secondary epileptogenesis frequently arises, and observations from bitemporal and dual pathology series are explored. The verdict here is far more difficult to reach, in large part because of the scarcity of longitudinal cohorts; moreover, recent experimental data have challenged the claim that HS is acquired consequent to recurrent seizures. Synaptic plasticity more than seizure-induced neuronal injury is the likely mechanism of secondary epileptogenesis. Postoperative running-down phenomenon provides the best evidence that a kindling-like process occurs in some patients, evidenced by its reversal. Finally, a network perspective of secondary epileptogenesis is considered, as well as the possible role for subcortical surgical interventions.

Bistable spiral wave dynamics in electrically excitable media

We show that a positive feedback loop between sodium current inactivation and wave-front ramp-up speed causes a saddle-node bifurcation to result in bistable planar and spiral waves in electrically excitable media, in which both slow and fast waves are triggered by different stimulation protocols. Moreover, the two types of spiral wave conduction may interact to give rise to more complex spiral wave dynamics. The transitions between different spiral wave behaviors via saddle-node bifurcation can be a candidate mechanism for transitions widely seen in cardiac arrhythmias and neural diseases.

Sleep, oscillations, and epilepsy

Sleep and wake are defined through physiological and behavioral criteria and can be typically separated into non-rapid eye movement (NREM) sleep stages N1, N2, and N3, rapid eye movement (REM) sleep, and wake. Sleep and wake states are not homogenous in time. Their properties vary during the night and day cycle. Given that brain activity changes as a function of NREM, REM, and wake during the night and day cycle, are seizures more likely to occur during NREM, REM, or wake at a specific time? More generally, what is the relationship between sleep-wake cycles and epilepsy? We will review specific examples from clinical data and results from experimental models, focusing on the diversity and heterogeneity of these relationships. We will use a top-down approach, starting with the general architecture of sleep, followed by oscillatory activities, and ending with ionic correlates selected for illustrative purposes, with respect to seizures and interictal spikes. The picture that emerges is that of complexity; sleep disruption and pathological epileptic activities emerge from reorganized circuits. That different circuit alterations can occur across patients and models may explain why sleep alterations and the timing of seizures during the sleep-wake cycle are patient-specific.

Critical-like Brain Dynamics in a Continuum from Second- to First-Order Phase Transition

The classic brain criticality hypothesis postulates that the brain benefits from operating near a continuous second-order phase transition. Slow feedback regulation of neuronal activity could, however, lead to a discontinuous first-order transition and thereby bistable activity. Observations of bistability in awake brain activity have nonetheless remained scarce and its functional significance unclear. Moreover, there is no empirical evidence to support the hypothesis that the human brain could flexibly operate near either a first- or second-order phase transition despite such a continuum being common in models. Here, using computational modeling, we found bistable synchronization dynamics to emerge through elevated positive feedback and occur exclusively in a regimen of critical-like dynamics. We then assessed bistability in vivo with resting-state MEG in healthy adults (7 females, 11 males) and stereo-electroencephalography in epilepsy patients (28 females, 36 males). This analysis revealed that a large fraction of the neocortices exhibited varying degrees of bistability in neuronal oscillations from 3 to 200 Hz. In line with our modeling results, the neuronal bistability was positively correlated with classic assessment of brain criticality across narrow-band frequencies. Excessive bistability was predictive of epileptic pathophysiology in the patients, whereas moderate bistability was positively correlated with task performance in the healthy subjects. These empirical findings thus reveal the human brain as a one-of-a-kind complex system that exhibits critical-like dynamics in a continuum between continuous and discontinuous phase transitions.SIGNIFICANCE STATEMENT In the model, while synchrony per se was controlled by connectivity, increasing positive local feedback led to gradually emerging bistable synchrony with scale-free dynamics, suggesting a continuum between second- and first-order phase transitions in synchrony dynamics inside a critical-like regimen. In resting-state MEG and SEEG, bistability of ongoing neuronal oscillations was pervasive across brain areas and frequency bands and was observed only with concurring critical-like dynamics as the modeling predicted. As evidence for functional relevance, moderate bistability was positively correlated with executive functioning in the healthy subjects, and excessive bistability was associated with epileptic pathophysiology. These findings show that critical-like neuronal dynamics in vivo involves both continuous and discontinuous phase transitions in a frequency-, neuroanatomy-, and state-dependent manner.

Optimization of ictal aborting stimulation using the dynamotype taxonomy

Electrical stimulation is an increasingly popular method to terminate epileptic seizures, yet it is not always successful. A potential reason for inconsistent efficacy is that stimuli are applied empirically without considering the underlying dynamical properties of a given seizure. We use a computational model of seizure dynamics to show that different bursting classes have disparate responses to aborting stimulation. This model was previously validated in a large set of human seizures and led to a description of the Taxonomy of Seizure Dynamics and the dynamotype, which is the clinical analog of the bursting class. In the model, the stimulation is realized as an applied input, which successfully aborts the burst when it forces the system from a bursting state to a quiescent state. This transition requires bistability, which is not present in all bursters. We examine how topological and geometric differences in the bistable state affect the probability of termination as the burster progresses from onset to offset. We find that the most significant determining factors are the burster class (dynamotype) and whether the burster has a DC (baseline) shift. Bursters with a baseline shift are far more likely to be terminated due to the necessary structure of their state space. Furthermore, we observe that the probability of termination varies throughout the burster's duration, is often dependent on the phase when it was applied, and is highly correlated to dynamotype. Our model provides a method to predict the optimal method of termination for each dynamotype. These results lead to the prediction that optimization of ictal aborting stimulation should account for seizure dynamotype, the presence of a DC shift, and the timing of the stimulation.

Reconstructing computational system dynamics from neural data with recurrent neural networks

Computational models in neuroscience usually take the form of systems of differential equations. The behaviour of such systems is the subject of dynamical systems theory. Dynamical systems theory provides a powerful mathematical toolbox for analysing neurobiological processes and has been a mainstay of computational neuroscience for decades. Recently, recurrent neural networks (RNNs) have become a popular machine learning tool for studying the non-linear dynamics of neural and behavioural processes by emulating an underlying system of differential equations. RNNs have been routinely trained on similar behavioural tasks to those used for animal subjects to generate hypotheses about the underlying computational mechanisms. By contrast, RNNs can also be trained on the measured physiological and behavioural data, thereby directly inheriting their temporal and geometrical properties. In this way they become a formal surrogate for the experimentally probed system that can be further analysed, perturbed and simulated. This powerful approach is called dynamical system reconstruction. In this Perspective, we focus on recent trends in artificial intelligence and machine learning in this exciting and rapidly expanding field, which may be less well known in neuroscience. We discuss formal prerequisites, different model architectures and training approaches for RNN-based dynamical system reconstructions, ways to evaluate and validate model performance, how to interpret trained models in a neuroscience context, and current challenges.

Can in vitro studies aid in the development and use of antiseizure therapies? A report of the ILAE/AES Joint Translational Task Force

In vitro preparations (defined here as cultured cells, brain slices, and isolated whole brains) offer a variety of approaches to modeling various aspects of seizures and epilepsy. Such models are particularly amenable to the application of anti-seizure compounds, and consequently are a valuable tool to screen the mechanisms of epileptiform activity, mode of action of known anti-seizure medications (ASMs), and the potential efficacy of putative new anti-seizure compounds. Despite these applications, all disease models are a simplification of reality and are therefore subject to limitations. In this review, we summarize the main types of in vitro models that can be used in epilepsy research, describing key methodologies as well as notable advantages and disadvantages of each. We argue that a well-designed battery of in vitro models can form an effective and potentially high-throughput screening platform to predict the clinical usefulness of ASMs, and that in vitro models are particularly useful for interrogating mechanisms of ASMs. To conclude, we offer several key recommendations that maximize the potential value of in vitro models in ASM screening. This includes the use of multiple in vitro tests that can complement each other, carefully combined with in vivo studies, the use of tissues from chronically epileptic (rather than naïve wild-type) animals, and the integration of human cell/tissue-derived preparations.

Nonequilibrium indicator for the onset of epileptic seizure

The occurrence of spontaneous bursts of uncontrolled electrical activity between neurons can disrupt normal brain function and lead to epileptic seizures. Despite extensive research, the mechanisms underlying seizure onset remain unclear. This study investigates the onset of seizures from the perspective of nonequilibrium statistical physics. By analyzing the probability flux within the framework of the nonequilibrium potential-flux landscape, we establish a connection between seizure dynamics and nonequilibrium. Our findings demonstrate that the degree of nonequilibrium is sensitive to the onset of epileptic seizures. This result offers an alternative perspective on assessing seizure onset in epilepsy.

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.