Permittivity coupling across brain regions determines seizure recruitment in partial epilepsy

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.

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.

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.

Localizing epileptogenic zones with high-frequency oscillations and directed connectivity

PURPOSE

Precise localization of the epileptogenic zone (EZ) is essential for epilepsy surgery. Existing methods often fail to detect slow onset patterns or similar neural activities presented in the recorded signals. To address this issue, we propose a new measure to quantify epileptogenicity, i.e., the connectivity high-frequency epileptogenicity index (cHFEI).

METHODS

The cHFEI method combines directed connectivity and high-frequency oscillations (HFOs) to measure the epileptogenicity of regions involved in a brain network. By applying this method to stereoelectroencephalography (SEEG) recordings of 49 seizures in 20 patients, we calculated the accuracy, sensitivity, and precision with a visually identified epileptogenic zone as a reference. The performance was evaluated by the confusion matrix and the area under the receiver operating characteristic (ROC) curve.

RESULTS

Epileptic network estimation based on cHFEI successfully distinguished brain regions involved in seizure onset from the propagation network. Moreover, cHFEI outperformed other existing detection methods in the estimation of EZs in all patients, with an average area under the ROC curve of 0.88 and an accuracy of 0.85.

CONCLUSIONS

cHFEI can characterize EZ in a robust manner despite various seizure onset patterns and has potential application in epilepsy therapy.

Degeneracy in epilepsy: multiple routes to hyperexcitable brain circuits and their repair

Due to its complex and multifaceted nature, developing effective treatments for epilepsy is still a major challenge. To deal with this complexity we introduce the concept of degeneracy to the field of epilepsy research: the ability of disparate elements to cause an analogous function or malfunction. Here, we review examples of epilepsy-related degeneracy at multiple levels of brain organisation, ranging from the cellular to the network and systems level. Based on these insights, we outline new multiscale and population modelling approaches to disentangle the complex web of interactions underlying epilepsy and to design personalised multitarget therapies.

The distribution and heterogeneity of excitability in focal epileptic network potentially contribute to the seizure propagation

Introduction

Existing dynamical models can explain the transmigration mechanisms involved in seizures but are limited to a single modality. Combining models with networks can reproduce scaled epileptic dynamics. And the structure and coupling interactions of the network, as well as the heterogeneity of both the node and network activities, may influence the final state of the network model.

Methods

We built a fully connected network with focal nodes prominently interacting and established a timescale separated epileptic network model. The factors affecting epileptic network seizure were explored by varying the connectivity patterns of focal network nodes and modulating the distribution of network excitability.

Results

The whole brain network topology as the brain activity foundation affects the consistent delayed clustering seizure propagation. In addition, the network size and distribution heterogeneity of the focal excitatory nodes can influence seizure frequency. With the increasing of the network size and averaged excitability level of focal network, the seizure period decreases. In contrast, the larger heterogeneity of excitability for focal network nodes can lower the functional activity level (average degree) of focal network. There are also subtle effects of focal network topologies (connection patterns of excitatory nodes) that cannot be ignored along with non-focal nodes.

Discussion

Unraveling the role of excitatory factors in seizure onset and propagation can be used to understand the dynamic mechanisms and neuromodulation of epilepsy, with profound implications for the treatment of epilepsy and even for the understanding of the brain.

Amortized Bayesian inference on generative dynamical network models of epilepsy using deep neural density estimators

Whole-brain modeling of epilepsy combines personalized anatomical data with dynamical models of abnormal activities to generate spatio-temporal seizure patterns as observed in brain imaging data. Such a parametric simulator is equipped with a stochastic generative process, which itself provides the basis for inference and prediction of the local and global brain dynamics affected by disorders. However, the calculation of likelihood function at whole-brain scale is often intractable. Thus, likelihood-free algorithms are required to efficiently estimate the parameters pertaining to the hypothetical areas, ideally including the uncertainty. In this study, we introduce the simulation-based inference for the virtual epileptic patient model (SBI-VEP), enabling us to amortize the approximate posterior of the generative process from a low-dimensional representation of whole-brain epileptic patterns. The state-of-the-art deep learning algorithms for conditional density estimation are used to readily retrieve the statistical relationships between parameters and observations through a sequence of invertible transformations. We show that the SBI-VEP is able to efficiently estimate the posterior distribution of parameters linked to the extent of the epileptogenic and propagation zones from sparse intracranial electroencephalography recordings. The presented Bayesian methodology can deal with non-linear latent dynamics and parameter degeneracy, paving the way for fast and reliable inference on brain disorders from neuroimaging modalities.

Criticality in probabilistic models of spreading dynamics in brain networks: Epileptic seizures

The spread of seizures across brain networks is the main impairing factor, often leading to loss-of-consciousness, in people with epilepsy. Despite advances in recording and modeling brain activity, uncovering the nature of seizure spreading dynamics remains an important challenge to understanding and treating pharmacologically resistant epilepsy. To address this challenge, we introduce a new probabilistic model that captures the spreading dynamics in patient-specific complex networks. Network connectivity and interaction time delays between brain areas were estimated from white-matter tractography. The model's computational tractability allows it to play an important complementary role to more detailed models of seizure dynamics. We illustrate model fitting and predictive performance in the context of patient-specific Epileptor networks. We derive the phase diagram of spread size (order parameter) as a function of brain excitability and global connectivity strength, for different patient-specific networks. Phase diagrams allow the prediction of whether a seizure will spread depending on excitability and connectivity strength. In addition, model simulations predict the temporal order of seizure spread across network nodes. Furthermore, we show that the order parameter can exhibit both discontinuous and continuous (critical) phase transitions as neural excitability and connectivity strength are varied. Existence of a critical point, where response functions and fluctuations in spread size show power-law divergence with respect to control parameters, is supported by mean-field approximations and finite-size scaling analyses. Notably, the critical point separates two distinct regimes of spreading dynamics characterized by unimodal and bimodal spread-size distributions. Our study sheds new light on the nature of phase transitions and fluctuations in seizure spreading dynamics. We expect it to play an important role in the development of closed-loop stimulation approaches for preventing seizure spread in pharmacologically resistant epilepsy. Our findings may also be of interest to related models of spreading dynamics in epidemiology, biology, finance, and statistical physics.

Delineating epileptogenic networks using brain imaging data and personalized modeling in drug-resistant epilepsy

Precise estimates of epileptogenic zone networks (EZNs) are crucial for planning intervention strategies to treat drug-resistant focal epilepsy. Here, we present the virtual epileptic patient (VEP), a workflow that uses personalized brain models and machine learning methods to estimate EZNs and to aid surgical strategies. The structural scaffold of the patient-specific whole-brain network model is constructed from anatomical T1 and diffusion-weighted magnetic resonance imaging. Each network node is equipped with a mathematical dynamical model to simulate seizure activity. Bayesian inference methods sample and optimize key parameters of the personalized model using functional stereoelectroencephalography recordings of patients' seizures. These key parameters together with their personalized model determine a given patient's EZN. Personalized models were further used to predict the outcome of surgical intervention using virtual surgeries. We evaluated the VEP workflow retrospectively using 53 patients with drug-resistant focal epilepsy. VEPs reproduced the clinically defined EZNs with a precision of 0.6, where the physical distance between epileptogenic regions identified by VEP and the clinically defined EZNs was small. Compared with the resected brain regions of 25 patients who underwent surgery, VEP showed lower false discovery rates in seizure-free patients (mean, 0.028) than in non-seizure-free patients (mean, 0.407). VEP is now being evaluated in an ongoing clinical trial (EPINOV) with an expected 356 prospective patients with epilepsy.

Interictal Functional Connectivity in Focal Refractory Epilepsies Investigated by Intracranial EEG

Introduction: Focal epilepsies are diseases of neuronal excitability affecting macroscopic networks of cortical and subcortical neural structures. These networks ("epileptogenic networks") can generate pathological electrophysiological activities during seizures, and also between seizures (interictal period). Many works attempt to describe these networks by using quantification methods, particularly based on the estimation of statistical relationships between signals produced by brain regions, namely functional connectivity (FC). Results: FC has been shown to be greatly altered during seizures and in the immediate peri-ictal period. An increasing number of studies have shown that FC is also altered during the interictal period depending on the degree of epileptogenicity of the structures. Furthermore, connectivity values could be correlated with other clinical variables including surgical outcome. Significance: This leads to a conceptual change and to consider epileptic areas as both hyperexcitable and abnormally connected. These data open the door to the use of interictal FC as a marker of epileptogenicity and as a complementary tool for predicting the effect of surgery. Aim: In this article, we review the available data concerning interictal FC estimated from intracranial electroencephalograhy (EEG) in focal epilepsies and discuss it in the light of data obtained from other modalities (EEG imaging) and modeling studies.

Estimating the Parameters of the Epileptor Model for Epileptic Seizure Suppression

Epilepsy is one of the most common brain disorders worldwide, affecting millions of people every year. Given the partially successful existing treatments for epileptiform activity suppression, dynamic mathematical models have been proposed with the purpose of better understanding the factors that might trigger an epileptic seizure and how to mitigate it, among which Epileptor stands out, due to its relative simplicity and consistency with experimental observations. Recent studies using this model have provided evidence that establishing a feedback-based control approach is possible. However, for this strategy to work properly, Epileptor's parameters, which describe the dynamic characteristics of a seizure, must be known beforehand. Therefore, this work proposes a methodology for estimating such parameters based on a successive optimization technique. The results show that it is feasible to approximate their values as they converge to reference values based on different initial conditions, which are modeled by an uncertainty factor or noise addition. Also, interictal (healthy) and ictal (ongoing seizure) conditions, as well as time resolution, must be taken into account for an appropriate estimation. At last, integrating such a parameter estimation approach with observers and controllers for purposes of seizure suppression is carried out, which might provide an interesting alternative for seizure suppression in practice in the future.

Fully Bayesian estimation of virtual brain parameters with self-tuning Hamiltonian Monte Carlo

Virtual brain models are data-driven patient-specific brain models integrating individual brain imaging data with neural mass modeling in a single computational framework, capable of autonomously generating brain activity and its associated brain imaging signals. Along the example of epilepsy, we develop an efficient and accurate Bayesian methodology estimating the parameters linked to the extent of the epileptogenic zone. State-of-the-art advances in Bayesian inference using Hamiltonian Monte Carlo (HMC) algorithms have remained elusive for large-scale differential-equations based models due to their slow convergence. We propose appropriate priors and a novel reparameterization to facilitate efficient exploration of the posterior distribution in terms of computational time and convergence diagnostics. The methodology is illustrated for in-silico dataset and then, applied to infer the personalized model parameters based on the empirical stereotactic electroencephalography (SEEG) recordings of retrospective patients. This improved methodology may pave the way to render HMC methods sufficiently easy and efficient to use, thus applicable in personalized medicine.

Fully Closed Loop Test Environment for Adaptive Implantable Neural Stimulators Using Computational Models

Implantable brain stimulation devices continue to be developed to treat and monitor brain conditions. As the complexity of these devices grows to include adaptive neuromodulation therapy, validating the operation and verifying the correctness of these systems becomes more complicated. The new complexities lie in the functioning of the device being dependent on the interaction with the patient and environmental factors such as noise and artifacts. Here, we present a hardware-in-the-loop (HIL) testing framework that employs computational models of pathological neural dynamics to test adaptive deep brain stimulation (DBS) devices prior to animal or human testing. A brain stimulation and recording electrode array is placed in the saline tank and connected to an adaptive neuromodulation system that measures and processes the synthetic signals and delivers stimulation back into the saline tank. A data acquisition system is used to detect the stimulation and provide feedback to the computational model in order to simulate the effects of stimulation on the neural dynamics. In this study, we used real-time computational models to emulate the dynamics of epileptic seizures observed in the anterior nucleus of the thalamus (ANT) in epilepsy patients and beta band (11-35 Hz) oscillations observed in the subthalamic nucleus (STN) of Parkinson's disease (PD) patients. These models simulated neuronal responses to electrical stimulation pulses and the saline tank tested hardware interactions between the detection algorithms and stimulation interference. We tested and validated the operation of adaptive DBS algorithms for seizure and beta band power suppression embedded in an implantable DBS system (Medtronic Summit RC+S). This study highlights the utility of the proposed hardware-in-the-loop framework to systematically test the adaptive DBS systems in the presence of system aggressors such as environmental noise and stimulation-induced electrical artifacts. This testing procedure can help ensure correctness and robustness of adaptive DBS devices prior to animal and human testing.

Critical dynamics in the spread of focal epileptic seizures: Network connectivity, neural excitability and phase transitions

Focal epileptic seizures can remain localized or, alternatively, spread across brain areas, often resulting in impairment of cognitive function and loss of consciousness. Understanding the factors that promote spread is important for developing better therapeutic approaches. Here, we show that: (1) seizure spread undergoes “critical” phase transitions in models (epileptor-networks) that capture the neural dynamics of spontaneous seizures while incorporating patient-specific brain network connectivity, axonal delays and identified epileptogenic zones (EZs). We define a collective variable for the spreading dynamics as the spread size, i.e. the number of areas or nodes in the network to which a seizure has spread. Global connectivity strength and excitability in the surrounding non-epileptic areas work as phase-transition control parameters for this collective variable. (2) Phase diagrams are predicted by stability analysis of the network dynamics. (3) In addition, the components of the Jacobian’s leading eigenvector, which tend to reflect the connectivity strength and path lengths from the EZ to surrounding areas, predict the temporal order of network-node recruitment into seizure. (4) However, stochastic fluctuations in spread size in a near-criticality region make predictability more challenging. Overall, our findings support the view that within-patient seizure-spread variability can be characterized by phase-transition dynamics under transient variations in network connectivity strength and excitability across brain areas. Furthermore, they point to the potential use and limitations of model-based prediction of seizure spread in closed-loop interventions for seizure control.

Cerebral Cavernous Malformation: Immune and Inflammatory Perspectives

Cerebral cavernous malformation (CCM) is a type of vascular anomaly that arises due to the dyshomeostasis of brain capillary networks. In the past two decades, many advances have been made in this research field. Notably, as a more reasonable current view, the CCM lesions should be attributed to the results of a great number of additional events related to the homeostasis disorder of the endothelial cell. Indeed, one of the most fascinating concerns in the research field is the inflammatory perturbation in the immune microenvironment, which would affect the disease progression as well as the patients’ outcomes. In this work, we focused on this topic, and underlined the immune-related factors’ contribution to the CCM pathologic progression.

Prediction and control of focal seizure spread: Random walk with restart on heterogeneous brain networks

Whole-brain models offer a promising method of predicting seizure spread, which is critical for successful surgical treatment of focal epilepsy. Existing methods are largely based on structural connectome, which ignores the effects of heterogeneity within the regional excitability of brains. In this study we used a whole-brain model to show that heterogeneity in nodal excitability had a significant impact on seizure propagation in the networks and compromised the prediction accuracy with structural connections. We then addressed this problem with an algorithm based on random walk with restart on graphs. We demonstrated that by establishing a relationship between the restarting probability and the excitability for each node, this algorithm could significantly improve the seizure spread prediction accuracy in heterogeneous networks and was more robust against the extent of heterogeneity. We also strategized surgical seizure control as a process to identify and remove the key nodes (connections) responsible for the early spread of seizures from the focal region. Compared to strategies based on structural connections, virtual surgery with a strategy based on a modified random walk with extended restart generated outcomes with a high success rate while maintaining low damage to the brain by removing fewer anatomical connections. These findings may have potential applications in developing personalized surgery strategies for epilepsy.

Neuronal Electrical Ongoing Activity as Cortical Areas Signature: An Insight from MNI Intracerebral Recording Atlas

The time course of the neuronal activity in the brain network, the neurodynamics, reflects the structure and functionality of the generating neuronal pools. Here, using the intracranial stereo-electroencephalographic (sEEG) recordings of the public Montreal Neurological Institute (MNI) atlas, we investigated the neurodynamics of primary motor (M1), somatosensory (S1) and auditory (A1) cortices measuring power spectral densities (PSD) and Higuchi fractal dimension (HFD) in the same subject (M1 vs. S1 in 16 subjects, M1 vs. A1 in 9, S1 vs. A1 in 6). We observed specific spectral features in M1, which prevailed above beta band, S1 in the alpha band, and A1 in the delta band. M1 HFD was higher than S1, both higher than A1. A clear distinction of neurodynamics properties of specific primary cortices supports the efforts in cortical parceling based on this expression of the local cytoarchitecture and connectivity. In this perspective, we selected within the MNI intracortical database a first set of primary motor, somatosensory and auditory cortices' representatives to query in recognizing ongoing patterns of neuronal communication. Potential clinical impact stands primarily in exploiting such exchange patterns to enhance the efficacy of neuromodulation intervention to cure symptoms secondary to neuronal activity unbalances.

Identifying spatio-temporal seizure propagation patterns in epilepsy using Bayesian inference

Focal drug resistant epilepsy is a neurological disorder characterized by seizures caused by abnormal activity originating in one or more regions together called as epileptogenic zone. Treatment for such patients involves surgical resection of affected regions. Epileptogenic zone is typically identified using stereotactic EEG recordings from the electrodes implanted into the patient's brain. Identifying the epileptogenic zone is a challenging problem due to the spatial sparsity of electrode implantation. We propose a probabilistic hierarchical model of seizure propagation patterns, based on a phenomenological model of seizure dynamics called Epileptor. Using Bayesian inference, the Epileptor model is optimized to build patient specific virtual models that best fit to the log power of intracranial recordings. First, accuracy of the model predictions and identifiability of the model are investigated using synthetic data. Then, model predictions are evaluated against a retrospective patient cohort of 25 patients with varying surgical outcomes. In the patients who are seizure free after surgery, model predictions showed good match with the clinical hypothesis. In patients where surgery failed to achieve seizure freedom model predictions showed a strong mismatch. Our results demonstrate that proposed probabilistic model could be a valuable tool to aid the clinicians in identifying the seizure focus.

Patient-Specific Network Connectivity Combined With a Next Generation Neural Mass Model to Test Clinical Hypothesis of Seizure Propagation

Dynamics underlying epileptic seizures span multiple scales in space and time, therefore, understanding seizure mechanisms requires identifying the relations between seizure components within and across these scales, together with the analysis of their dynamical repertoire. In this view, mathematical models have been developed, ranging from single neuron to neural population. In this study, we consider a neural mass model able to exactly reproduce the dynamics of heterogeneous spiking neural networks. We combine mathematical modeling with structural information from non invasive brain imaging, thus building large-scale brain network models to explore emergent dynamics and test the clinical hypothesis. We provide a comprehensive study on the effect of external drives on neuronal networks exhibiting multistability, in order to investigate the role played by the neuroanatomical connectivity matrices in shaping the emergent dynamics. In particular, we systematically investigate the conditions under which the network displays a transition from a low activity regime to a high activity state, which we identify with a seizure-like event. This approach allows us to study the biophysical parameters and variables leading to multiple recruitment events at the network level. We further exploit topological network measures in order to explain the differences and the analogies among the subjects and their brain regions, in showing recruitment events at different parameter values. We demonstrate, along with the example of diffusion-weighted magnetic resonance imaging (dMRI) connectomes of 20 healthy subjects and 15 epileptic patients, that individual variations in structural connectivity, when linked with mathematical dynamic models, have the capacity to explain changes in spatiotemporal organization of brain dynamics, as observed in network-based brain disorders. In particular, for epileptic patients, by means of the integration of the clinical hypotheses on the epileptogenic zone (EZ), i.e., the local network where highly synchronous seizures originate, we have identified the sequence of recruitment events and discussed their links with the topological properties of the specific connectomes. The predictions made on the basis of the implemented set of exact mean-field equations turn out to be in line with the clinical pre-surgical evaluation on recruited secondary networks.

On the influence of prior information evaluated by fully Bayesian criteria in a personalized whole-brain model of epilepsy spread

Individualized anatomical information has been used as prior knowledge in Bayesian inference paradigms of whole-brain network models. However, the actual sensitivity to such personalized information in priors is still unknown. In this study, we introduce the use of fully Bayesian information criteria and leave-one-out cross-validation technique on the subject-specific information to assess different epileptogenicity hypotheses regarding the location of pathological brain areas based on a priori knowledge from dynamical system properties. The Bayesian Virtual Epileptic Patient (BVEP) model, which relies on the fusion of structural data of individuals, a generative model of epileptiform discharges, and a self-tuning Monte Carlo sampling algorithm, is used to infer the spatial map of epileptogenicity across different brain areas. Our results indicate that measuring the out-of-sample prediction accuracy of the BVEP model with informative priors enables reliable and efficient evaluation of potential hypotheses regarding the degree of epileptogenicity across different brain regions. In contrast, while using uninformative priors, the information criteria are unable to provide strong evidence about the epileptogenicity of brain areas. We also show that the fully Bayesian criteria correctly assess different hypotheses about both structural and functional components of whole-brain models that differ across individuals. The fully Bayesian information-theory based approach used in this study suggests a patient-specific strategy for epileptogenicity hypothesis testing in generative brain network models of epilepsy to improve surgical outcomes.

Modeling seizures: From single neurons to networks

Dynamical system tools offer a complementary approach to detailed biophysical seizure modeling, with a high potential for clinical applications. This review describes the theoretical framework that provides a basis for theorizing certain properties of seizures and for their classification according to their dynamical properties at onset and offset. We describe various modeling approaches spanning different scales, from single neurons to large-scale networks. This narrative review provides an accessible overview of this field, including non-exhaustive examples of key recent works.

Perturbations both trigger and delay seizures due to generic properties of slow-fast relaxation oscillators

The mechanisms underlying the emergence of seizures are one of the most important unresolved issues in epilepsy research. In this paper, we study how perturbations, exogenous or endogenous, may promote or delay seizure emergence. To this aim, due to the increasingly adopted view of epileptic dynamics in terms of slow-fast systems, we perform a theoretical analysis of the phase response of a generic relaxation oscillator. As relaxation oscillators are effectively bistable systems at the fast time scale, it is intuitive that perturbations of the non-seizing state with a suitable direction and amplitude may cause an immediate transition to seizure. By contrast, and perhaps less intuitively, smaller amplitude perturbations have been found to delay the spontaneous seizure initiation. By studying the isochrons of relaxation oscillators, we show that this is a generic phenomenon, with the size of such delay depending on the slow flow component. Therefore, depending on perturbation amplitudes, frequency and timing, a train of perturbations causes an occurrence increase, decrease or complete suppression of seizures. This dependence lends itself to analysis and mechanistic understanding through methods outlined in this paper. We illustrate this methodology by computing the isochrons, phase response curves and the response to perturbations in several epileptic models possessing different slow vector fields. While our theoretical results are applicable to any planar relaxation oscillator, in the motivating context of epilepsy they elucidate mechanisms of triggering and abating seizures, thus suggesting stimulation strategies with effects ranging from mere delaying to full suppression of seizures.

Despite its simplicity, the modelling of epileptic dynamics as a slow-fast transition between low and high activity states mediated by some slow feedback variable is a relatively novel albeit fruitful approach. This study is the first, to our knowledge, characterizing the response of such slow-fast models of epileptic brain to perturbations by computing its isochrons. Besides its numerical computation, we theoretically determine which factors shape the geometry of isochrons for planar slow-fast oscillators. As a consequence, we introduce a theoretical approach providing a clear understanding of the response of perturbations of slow-fast oscillators. Within the epilepsy context, this elucidates the origin of the contradictory role of interictal epileptiform discharges in the transition to seizure, manifested by both pro-convulsive and anti-convulsive effect depending on the amplitude, frequency and timing. More generally, this paper provides theoretical framework highlighting the role of the slow flow component on the response to perturbations in relaxation oscillators, pointing to the general phenomena in such slow-fast oscillators ubiquitous in biological systems.

In silico exploration of mouse brain dynamics by focal stimulation reflects the organization of functional networks and sensory processing

Resting-state functional networks such as the default mode network (DMN) dominate spontaneous brain dynamics. To date, the mechanisms linking brain structure and brain dynamics and functions in cognition, perception, and action remain unknown, mainly due to the uncontrolled and erratic nature of the resting state. Here we used a stimulation paradigm to probe the brain’s resting behavior, providing insights on state-space stability and multiplicity of network trajectories after stimulation. We performed explorations on a mouse model to map spatiotemporal brain dynamics as a function of the stimulation site. We demonstrated the emergence of known functional networks in brain responses. Several responses heavily relied on the DMN and were suggestive of the DMN playing a mechanistic role between functional networks. We probed the simulated brain responses to the stimulation of regions along the information processing chains of sensory systems from periphery up to primary sensory cortices. Moreover, we compared simulated dynamics against in vivo brain responses to optogenetic stimulation. Our results underwrite the importance of anatomical connectivity in the functional organization of brain networks and demonstrate how functionally differentiated information processing chains arise from the same system.

We demonstrate how functionally differentiated information processing chains arise from the same anatomical network. The main result of the in-silico mouse brain simulations is the emergence of specific functional networks based on structural data from the mouse brain. When the brain is stimulated, for example, by sensory inputs or direct electrical stimulation, the brain initially responds with activities in specific regions. The brain’s anatomical connectivity constrains the subsequent pattern formation. We built a high-resolution mouse brain network model. The model structure originated from experimental data. We systematically explored the mouse model and investigated the simulated brain dynamics after stimulation. Known functional networks emerged in the simulated brain responses. The default mode network occurred in almost all characteristic response patterns. Simulated brain response dynamics and in-vivo response dynamics of the mouse brain to optogenetic stimulation showed similarities even without parameter tuning. Anatomical connectivity and dynamics shape the functional organization of brain networks.

Measuring the Coupling Direction between Neural Oscillations with Weighted Symbolic Transfer Entropy

Neural oscillations reflect rhythmic fluctuations in the synchronization of neuronal populations and play a significant role in neural processing. To further understand the dynamic interactions between different regions in the brain, it is necessary to estimate the coupling direction between neural oscillations. Here, we developed a novel method, termed weighted symbolic transfer entropy (WSTE), that combines symbolic transfer entropy (STE) and weighted probability distribution to measure the directionality between two neuronal populations. The traditional STE ignores the degree of difference between the amplitude values of a time series. In our proposed WSTE method, this information is picked up by utilizing a weighted probability distribution. The simulation analysis shows that the WSTE method can effectively estimate the coupling direction between two neural oscillations. In comparison with STE, the new method is more sensitive to the coupling strength and is more robust against noise. When applied to epileptic electrocorticography data, a significant coupling direction from the anterior nucleus of thalamus (ANT) to the seizure onset zone (SOZ) was detected during seizures. Considering the superiorities of the WSTE method, it is greatly advantageous to measure the coupling direction between neural oscillations and consequently characterize the information flow between different brain regions.

Neural mass modeling of slow-fast dynamics of seizure initiation and abortion

Epilepsy is a dynamic and complex neurological disease affecting about 1% of the worldwide population, among which 30% of the patients are drug-resistant. Epilepsy is characterized by recurrent episodes of paroxysmal neural discharges (the so-called seizures), which manifest themselves through a large-amplitude rhythmic activity observed in depth-EEG recordings, in particular in local field potentials (LFPs). The signature characterizing the transition to seizures involves complex oscillatory patterns, which could serve as a marker to prevent seizure initiation by triggering appropriate therapeutic neurostimulation methods. To investigate such protocols, neurophysiological lumped-parameter models at the mesoscopic scale, namely neural mass models, are powerful tools that not only mimic the LFP signals but also give insights on the neural mechanisms related to different stages of seizures. Here, we analyze the multiple time-scale dynamics of a neural mass model and explain the underlying structure of the complex oscillations observed before seizure initiation. We investigate population-specific effects of the stimulation and the dependence of stimulation parameters on synaptic timescales. In particular, we show that intermediate stimulation frequencies (>20 Hz) can abort seizures if the timescale difference is pronounced. Those results have the potential in the design of therapeutic brain stimulation protocols based on the neurophysiological properties of tissue.

VEP atlas: An anatomic and functional human brain atlas dedicated to epilepsy patients

BACKGROUND

Several automated parcellation atlases of the human brain have been developed over the past decades, based on various criteria, and have been applied in basic and clinical research.

NEW METHOD

Here we present the Virtual Epileptic Patient (VEP) atlas that offers a new automated brain region parcellation and labeling, which has been developed for the specific use in the domains of epileptology and functional neurosurgery and is able to apply at individual patient's level.

RESULTS

It comprises 162 brain regions, including 73 cortical and 8 subcortical regions per hemisphere. We demonstrate the successful application of the VEP atlas in a cohort of 50 retrospective patients. The structural organization is complemented by the functional variation of stereotactic intracerebral EEG (SEEG) signal data features establishing brain region-specific 3d-maps.

COMPARISON WITH EXISTING METHODS

The VEP atlas integrates both anatomical and functional definitions in the same atlas, adapted to applications for epilepsy patients and individualizable.

CONCLUSION

The covariation of structural and functional organization is the basis for current efforts of patient-specific large-scale brain network modeling exploiting virtual brain technologies for the identification of the epileptogenic regions in an ongoing prospective clinical trial EPINOV.

Domino-like transient dynamics at seizure onset in epilepsy

The International League Against Epilepsy (ILAE) groups seizures into "focal", "generalized" and "unknown" based on whether the seizure onset is confined to a brain region in one hemisphere, arises in several brain region simultaneously, or is not known, respectively. This separation fails to account for the rich diversity of clinically and experimentally observed spatiotemporal patterns of seizure onset and even less so for the properties of the brain networks generating them. We consider three different patterns of domino-like seizure onset in Idiopathic Generalized Epilepsy (IGE) and present a novel approach to classification of seizures. To understand how these patterns are generated on networks requires understanding of the relationship between intrinsic node dynamics and coupling between nodes in the presence of noise, which currently is unknown. We investigate this interplay here in the framework of domino-like recruitment across a network. In particular, we use a phenomenological model of seizure onset with heterogeneous coupling and node properties, and show that in combination they generate a range of domino-like onset patterns observed in the IGE seizures. We further explore the individual contribution of heterogeneous node dynamics and coupling by interpreting in-vitro experimental data in which the speed of onset can be chemically modulated. This work contributes to a better understanding of possible drivers for the spatiotemporal patterns observed at seizure onset and may ultimately contribute to a more personalized approach to classification of seizure types in clinical practice.

Feasibility of focal brain cooling for partial epilepsy with secondary generalization: A computational study. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2020;2020:2532-2535. [PMID: 33018522 DOI: 10.1109/embc44109.2020.9175157] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

Experiments with animal models of epilepsy have consistently shown that focal cooling of epilepsy-induced brain region reversibly suppresses or terminates epileptic discharge activity. Recently, we formulated a physiologically plausible temperature dependence in a neural mass model that can reproduce the effect of focal cooling on epileptic discharge activity. This can be used to implement a temperature control in an implantable cooling device for thermal neuromodulation of the epileptogenic zone in patients with partial epilepsy when seizure activity is detected. However, there have been no experiments that looked into the effect of focal cooling in animal models of epilepsy with secondary generalization in which the seizure activity spreads from the pathologic region to other regions of the brain. Using the temperature-dependent neural mass model and a physiological coupling model, we show that focal cooling stops the propagation of low-frequency discharge activity; on the other hand, it increases the amount of coupling required to propagate high-frequency discharge activity. Moreover, discharge activities that are propagated with cooling are lower in both magnitude and frequency compared to those propagated without cooling. These results suggest the feasibility of focal cooling as an effective alternative therapeutic treatment for medically intractable partial epilepsy even with secondary generalization.Clinical Relevance- The computational study establishes focal cooling of the brain region with partial epilepsy not only suppresses epileptic discharges but can also prevent its generalization to other brain regions.

Artificial Intelligence and Computational Approaches for Epilepsy

Studies on treatment of epilepsy have been actively conducted in multiple avenues, but there are limitations in improving its efficacy due to between-subject variability in which treatment outcomes vary from patient to patient. Accordingly, there is a growing interest in precision medicine that provides accurate diagnosis for seizure types and optimal treatment for an individual epilepsy patient. Among these approaches, computational studies making this feasible are rapidly progressing in particular and have been widely applied in epilepsy. These computational studies are being conducted in two main streams: 1) artificial intelligence-based studies implementing computational machines with specific functions, such as automatic diagnosis and prognosis prediction for an individual patient, using machine learning techniques based on large amounts of data obtained from multiple patients and 2) patient-specific modeling-based studies implementing biophysical in-silico platforms to understand pathological mechanisms and derive the optimal treatment for each patient by reproducing the brain network dynamics of the particular patient per se based on individual patient's data. These computational approaches are important as it can integrate multiple types of data acquired from patients and analysis results into a single platform. If these kinds of methods are efficiently operated, it would suggest a novel paradigm for precision medicine.

Dynamical Mechanisms of Interictal Resting-State Functional Connectivity in Epilepsy

Drug-resistant focal epilepsy is a large-scale brain networks disorder characterized by altered spatiotemporal patterns of functional connectivity (FC), even during interictal resting state (RS). Although RS-FC-based metrics can detect these changes, results from RS functional magnetic resonance imaging (RS-fMRI) studies are unclear and difficult to interpret, and the underlying dynamical mechanisms are still largely unknown. To better capture the RS dynamics, we phenomenologically extended the neural mass model of partial seizures, the Epileptor, by including two neuron subpopulations of epileptogenic and nonepileptogenic type, making it capable of producing physiological oscillations in addition to the epileptiform activity. Using the neuroinformatics platform The Virtual Brain, we reconstructed 14 epileptic and 5 healthy human (of either sex) brain network models (BNMs), based on individual anatomical connectivity and clinically defined epileptogenic heatmaps. Through systematic parameter exploration and fitting to neuroimaging data, we demonstrated that epileptic brains during interictal RS are associated with lower global excitability induced by a shift in the working point of the model, indicating that epileptic brains operate closer to a stable equilibrium point than healthy brains. Moreover, we showed that functional networks are unaffected by interictal spikes, corroborating previous experimental findings; additionally, we observed higher excitability in epileptogenic regions, in agreement with the data. We shed light on new dynamical mechanisms responsible for altered RS-FC in epilepsy, involving the following two key factors: (1) a shift of excitability of the whole brain leading to increased stability; and (2) a locally increased excitability in the epileptogenic regions supporting the mixture of hyperconnectivity and hypoconnectivity in these areas.

SIGNIFICANCE STATEMENT Advances in functional neuroimaging provide compelling evidence for epilepsy-related brain network alterations, even during the interictal resting state (RS). However, the dynamical mechanisms underlying these changes are still elusive. To identify local and network processes behind the RS-functional connectivity (FC) spatiotemporal patterns, we systematically manipulated the local excitability and the global coupling in the virtual human epileptic patient brain network models (BNMs), complemented by the analysis of the impact of interictal spikes and fitting to the neuroimaging data. Our results suggest that a global shift of the dynamic working point of the brain model, coupled with locally hyperexcitable node dynamics of the epileptogenic networks, provides a mechanistic explanation of the epileptic processes during the interictal RS period. These, in turn, are associated with the changes in FC.

The Bayesian Virtual Epileptic Patient: A probabilistic framework designed to infer the spatial map of epileptogenicity in a personalized large-scale brain model of epilepsy spread

Despite the importance and frequent use of Bayesian frameworks in brain network modeling for parameter inference and model prediction, the advanced sampling algorithms implemented in probabilistic programming languages to overcome the inference difficulties have received relatively little attention in this context. In this technical note, we propose a probabilistic framework, namely the Bayesian Virtual Epileptic Patient (BVEP), which relies on the fusion of structural data of individuals to infer the spatial map of epileptogenicity in a personalized large-scale brain model of epilepsy spread. To invert the individualized whole-brain model employed in this study, we use the recently developed algorithms known as No-U-Turn Sampler (NUTS) as well as Automatic Differentiation Variational Inference (ADVI). Our results indicate that NUTS and ADVI accurately estimate the degree of epileptogenicity of brain regions, therefore, the hypothetical brain areas responsible for the seizure initiation and propagation, while the convergence diagnostics and posterior behavior analysis validate the reliability of the estimations. Moreover, we illustrate the efficiency of the transformed non-centered parameters in comparison to centered form of parameterization. The Bayesian framework used in this work proposes an appropriate patient-specific strategy for estimating the epileptogenicity of the brain regions to improve outcome after epilepsy surgery.

Unified dynamics of interictal events and absence seizures

The dynamics of interictal events between absence seizures and their relationship to seizures themselves are investigated by employing a neural field model of the corticothalamic system. Interictal events are modeled as being due to transient parameter excursions beyond the seizure threshold, in the present case by sufficiently temporally varying the connection strength between the cerebral cortex and the thalamus. Increasing connection strength drives the system into ∼3-Hz seizure oscillations via a supercritical Hopf bifurcation once the linear instability threshold is passed. Depending on the time course of the excursion above threshold, different interictal activity event dynamics are seen in the time series of corticothalamic fields. These resemble experimental interictal time series observed via electroencephalography. It is found that the morphology of these events depends on the magnitude and duration of the excursion above threshold. For a large-amplitude excursion of short duration, events resemble interictal spikes, where one large spike is seen, followed by small damped oscillations. For a short excursion with long duration, events like observed interictal periodic sharp waves are seen. When both amplitude and duration above threshold are large, seizure oscillations are seen. Using these outcomes, proximity to seizure can be estimated and tracked.

Interictal stereotactic-EEG functional connectivity in refractory focal epilepsies

Drug-refractory focal epilepsies are network diseases associated with functional connectivity alterations both during ictal and interictal periods. A large majority of studies on the interictal/resting state have focused on functional MRI-based functional connectivity. Few studies have used electrophysiology, despite its high temporal capacities. In particular, stereotactic-EEG is highly suitable to study functional connectivity because it permits direct intracranial electrophysiological recordings with relative large-scale sampling. Most previous studies in stereotactic-EEG have been directed towards temporal lobe epilepsy, which does not represent the whole spectrum of drug-refractory epilepsies. The present study aims at filling this gap, investigating interictal functional connectivity alterations behind cortical epileptic organization and its association with post-surgical prognosis. To this purpose, we studied a large cohort of 59 patients with malformation of cortical development explored by stereotactic-EEG with a wide spatial sampling (76 distinct brain areas were recorded, median of 13.2 per patient). We computed functional connectivity using non-linear correlation. We focused on three zones defined by stereotactic-EEG ictal activity: the epileptogenic zone, the propagation zone and the non-involved zone. First, we compared within-zone and between-zones functional connectivity. Second, we analysed the directionality of functional connectivity between these zones. Third, we measured the associations between functional connectivity measures and clinical variables, especially post-surgical prognosis. Our study confirms that functional connectivity differs according to the zone under investigation. We found: (i) a gradual decrease of the within-zone functional connectivity with higher values for epileptogenic zone and propagation zone, and lower for non-involved zones; (ii) preferential coupling between structures of the epileptogenic zone; (iii) preferential coupling between epileptogenic zone and propagation zone; and (iv) poorer post-surgical outcome in patients with higher functional connectivity of non-involved zone (within- non-involved zone, between non-involved zone and propagation zone functional connectivity). Our work suggests that, even during the interictal state, functional connectivity is reinforced within epileptic cortices (epileptogenic zone and propagation zone) with a gradual organization. Moreover, larger functional connectivity alterations, suggesting more diffuse disease, are associated with poorer post-surgical prognosis. This is consistent with computational studies suggesting that connectivity is crucial in order to model the spatiotemporal dynamics of seizures.10.1093/brain/awy214_video1awy214media15833456182001.

Optimization of surgical intervention outside the epileptogenic zone in the Virtual Epileptic Patient (VEP)

Studies to improve the efficacy of epilepsy surgery have focused on better refining the localization of the epileptogenic zone (EZ) with the aim of effectively resecting it. However, in a considerable number of patients, EZs are distributed across multiple brain regions and may involve eloquent areas that cannot be removed due to the risk of neurological complications. There is a clear need for developing alternative approaches to induce seizure relief, but minimal impact on normal brain functions. Here, we develop a personalized in-silico network approach, that suggests effective and safe surgical interventions for each patient. Based on the clinically identified EZ, we employ modularity analysis to identify target brain regions and fiber tracts involved in seizure propagation. We then construct and simulate a patient-specific brain network model comprising phenomenological neural mass models at the nodes, and patient-specific structural brain connectivity using the neuroinformatics platform The Virtual Brain (TVB), in order to evaluate effectiveness and safety of the target zones (TZs). In particular, we assess safety via electrical stimulation for pre- and post-surgical condition to quantify the impact on the signal transmission properties of the network. We demonstrate the existence of a large repertoire of efficient surgical interventions resulting in reduction of degree of seizure spread, but only a small subset of them proves safe. The identification of novel surgical interventions through modularity analysis and brain network simulations may provide exciting solutions to the treatment of inoperable epilepsies.

We propose a personalized in-silico surgical approach able to suggest effective and safe surgical options for each epilepsy patient. In particular, we focus on deriving effective alternative methods for those cases where EZs are inoperable because of issues related with neurological complications. Based on modularity analysis using structural brain connectivity from each patient, TZs that would be considered as surgical sites are obtained. The acquired TZs are evaluated by personalized brain network simulations in terms of effectiveness and safety. Through the feedback approach combining modularity analysis and brain network simulations, the optimized TZ options that minimize seizure propagation while not affecting normal brain functions are obtained. Our study has a great importance in that it demonstrates the possibility of computational neuroscience field being able to construct a paradigm for personalized medicine by deriving innovative surgical options suitable for each patient and predicting the surgical outcomes.

A fingerprint of the epileptogenic zone in human epilepsies

Defining a bio-electrical marker for the brain area responsible for initiating a seizure remains an unsolved problem. Fast gamma activity has been identified as the most specific marker for seizure onset, but conflicting results have been reported. In this study, we describe an alternative marker, based on an objective description of interictal to ictal transition, with the aim of identifying a time-frequency pattern or ‘fingerprint’ that can differentiate the epileptogenic zone from areas of propagation. Seventeen patients who underwent stereoelectroencephalography were included in the study. Each had seizure onset characterized by sustained gamma activity and were seizure-free after tailored resection or laser ablation. We postulated that the epileptogenic zone was always located inside the resection region based on seizure freedom following surgery. To characterize the ictal frequency pattern, we applied the Morlet wavelet transform to data from each pair of adjacent intracerebral electrode contacts. Based on a visual assessment of the time-frequency plots, we hypothesized that a specific time-frequency pattern in the epileptogenic zone should include a combination of (i) sharp transients or spikes; preceding (ii) multiband fast activity concurrent; with (iii) suppression of lower frequencies. To test this hypothesis, we developed software that automatically extracted each of these features from the time-frequency data. We then used a support vector machine to classify each contact-pair as being within epileptogenic zone or not, based on these features. Our machine learning system identified this pattern in 15 of 17 patients. The total number of identified contacts across all patients was 64, with 58 localized inside the resected area. Subsequent quantitative analysis showed strong correlation between maximum frequency of fast activity and suppression inside the resection but not outside. We did not observe significant discrimination power using only the maximum frequency or the timing of fast activity to differentiate contacts either between resected and non-resected regions or between contacts identified as epileptogenic versus non-epileptogenic. Instead of identifying a single frequency or a single timing trait, we observed the more complex pattern described above that distinguishes the epileptogenic zone. This pattern encompasses interictal to ictal transition and may extend until seizure end. Its time-frequency characteristics can be explained in light of recent models emphasizing the role of fast inhibitory interneurons acting on pyramidal cells as a prominent mechanism in seizure triggering. The pattern clearly differentiates the epileptogenic zone from areas of propagation and, as such, represents an epileptogenic zone ‘fingerprint’.

Controlling seizure propagation in large-scale brain networks

Information transmission in the human brain is a fundamentally dynamic network process. In partial epilepsy, this process is perturbed and highly synchronous seizures originate in a local network, the so-called epileptogenic zone (EZ), before recruiting other close or distant brain regions. We studied patient-specific brain network models of 15 drug-resistant epilepsy patients with implanted stereotactic electroencephalography (SEEG) electrodes. Each personalized brain model was derived from structural data of magnetic resonance imaging (MRI) and diffusion tensor weighted imaging (DTI), comprising 88 nodes equipped with region specific neural mass models capable of demonstrating a range of epileptiform discharges. Each patient's virtual brain was further personalized through the integration of the clinically hypothesized EZ. Subsequent simulations and connectivity modulations were performed and uncovered a finite repertoire of seizure propagation patterns. Across patients, we found that (i) patient-specific network connectivity is predictive for the subsequent seizure propagation pattern; (ii) seizure propagation is characterized by a systematic sequence of brain states; (iii) propagation can be controlled by an optimal intervention on the connectivity matrix; (iv) the degree of invasiveness can be significantly reduced via the proposed seizure control as compared to traditional resective surgery. To stop seizures, neurosurgeons typically resect the EZ completely. We showed that stability analysis of the network dynamics, employing structural and dynamical information, estimates reliably the spatiotemporal properties of seizure propagation. This suggests novel less invasive paradigms of surgical interventions to treat and manage partial epilepsy.

Adaptation and Inhibition Control Pathological Synchronization in a Model of Focal Epileptic Seizure

Pharmacoresistant epilepsy is a common neurological disorder in which increased neuronal intrinsic excitability and synaptic excitation lead to pathologically synchronous behavior in the brain. In the majority of experimental and theoretical epilepsy models, epilepsy is associated with reduced inhibition in the pathological neural circuits, yet effects of intrinsic excitability are usually not explicitly analyzed. Here we present a novel neural mass model that includes intrinsic excitability in the form of spike-frequency adaptation in the excitatory population. We validated our model using local field potential (LFP) data recorded from human hippocampal/subicular slices. We found that synaptic conductances and slow adaptation in the excitatory population both play essential roles for generating seizures and pre-ictal oscillations. Using bifurcation analysis, we found that transitions towards seizure and back to the resting state take place via Andronov-Hopf bifurcations. These simulations therefore suggest that single neuron adaptation as well as synaptic inhibition are responsible for orchestrating seizure dynamics and transition towards the epileptic state.

Calcium imaging and dynamic causal modelling reveal brain-wide changes in effective connectivity and synaptic dynamics during epileptic seizures

Pathophysiological explanations of epilepsy typically focus on either the micro/mesoscale (e.g. excitation-inhibition imbalance), or on the macroscale (e.g. network architecture). Linking abnormalities across spatial scales remains difficult, partly because of technical limitations in measuring neuronal signatures concurrently at the scales involved. Here we use light sheet imaging of the larval zebrafish brain during acute epileptic seizure induced with pentylenetetrazole. Spectral changes of spontaneous neuronal activity during the seizure are then modelled using neural mass models, allowing Bayesian inference on changes in effective network connectivity and their underlying synaptic dynamics. This dynamic causal modelling of seizures in the zebrafish brain reveals concurrent changes in synaptic coupling at macro- and mesoscale. Fluctuations of both synaptic connection strength and their temporal dynamics are required to explain observed seizure patterns. These findings highlight distinct changes in local (intrinsic) and long-range (extrinsic) synaptic transmission dynamics as a possible seizure pathomechanism and illustrate how our Bayesian model inversion approach can be used to link existing neural mass models of seizure activity and novel experimental methods.

Minimal model of interictal and ictal discharges "Epileptor-2"

Seizures occur in a recurrent manner with intermittent states of interictal and ictal discharges (IIDs and IDs). The transitions to and from IDs are determined by a set of processes, including synaptic interaction and ionic dynamics. Although mathematical models of separate types of epileptic discharges have been developed, modeling the transitions between states remains a challenge. A simple generic mathematical model of seizure dynamics (Epileptor) has recently been proposed by Jirsa et al. (2014); however, it is formulated in terms of abstract variables. In this paper, a minimal population-type model of IIDs and IDs is proposed that is as simple to use as the Epileptor, but the suggested model attributes physical meaning to the variables. The model is expressed in ordinary differential equations for extracellular potassium and intracellular sodium concentrations, membrane potential, and short-term synaptic depression variables. A quadratic integrate-and-fire model driven by the population input current is used to reproduce spike trains in a representative neuron. In simulations, potassium accumulation governs the transition from the silent state to the state of an ID. Each ID is composed of clustered IID-like events. The sodium accumulates during discharge and activates the sodium-potassium pump, which terminates the ID by restoring the potassium gradient and thus polarizing the neuronal membranes. The whole-cell and cell-attached recordings of a 4-AP-based in vitro model of epilepsy confirmed the primary model assumptions and predictions. The mathematical analysis revealed that the IID-like events are large-amplitude stochastic oscillations, which in the case of ID generation are controlled by slow oscillations of ionic concentrations. The IDs originate in the conditions of elevated potassium concentrations in a bath solution via a saddle-node-on-invariant-circle-like bifurcation for a non-smooth dynamical system. By providing a minimal biophysical description of ionic dynamics and network interactions, the model may serve as a hierarchical base from a simple to more complex modeling of seizures.

In pathological conditions of epilepsy, the functioning of the neural network crucially depends on the ionic concentrations inside and outside neurons. A number of factors that affect neuronal activity is large. That is why the development of a minimal model that reproduces typical seizures could structure further experimental and analytical studies of the pathological mechanisms. Here, on a base of known biophysical models, we present a simple population-type model that includes only four principal variables, the extracellular potassium concentration, the intracellular sodium concentration, the membrane potential and the synaptic resource diminishing due to short-term synaptic depression. A simple modeled neuron is used as an observer of the population activity. We validate the model assumptions with in vitro experiments. Our model reproduces ictal and interictal events, where the latter result in bursts of spikes in single neurons, and the former represent the cluster of spike bursts. Mathematical analysis reveals that the bursts are spontaneous large-amplitude oscillations, which may cluster after a saddle-node on invariant circle bifurcation in the pro-epileptic conditions. Our consideration has significant bearing in understanding pathological neuronal network dynamics.

Dependence of absence seizure dynamics on physiological parameter evolution

A neural field model of the corticothalamic system is applied to investigate the temporal and spectral characteristics of absence seizures in the presence of a temporally varying connection strength between the cerebral cortex and thalamus. Increasing connection strength drives the system into an absence seizure-like state once a threshold is passed and a supercritical Hopf bifurcation occurs. The dynamics and spectral characteristics of the resulting model seizures are explored as functions of maximum connection strength, time above threshold, and the rate at which the connection strength increases (ramp rate). Our results enable spectral and temporal characteristics of seizures to be related to changes in the underlying physiological evolution of connections via nonlinear dynamics and neural field theory. Spectral analysis reveals that the power of the harmonics and the duration of the oscillations increase as the maximum connection strength and the time above threshold increase. It is also found that the time to reach the stable limit-cycle seizure oscillation from the instability threshold decreases with the square root of the ramp rate.

The role of stereoelectroencephalography (SEEG) in reevaluation of epilepsy surgery failures

Management of patients after initial epilepsy surgical failure is challenging. In this study, we report our experience in using the stereoelectroencephalography (SEEG) method in the reevaluation of patients after initial epilepsy surgical failure. We selected 28 patients examined through SEEG in our department for drug-resistant focal epilepsy following initial epilepsy surgical failure. For each patient, the residual seizure onset zone (rSOZ) as defined by SEEG was classified as either contiguous if the seizure onset zone (SOZ) was focal and close to the surgical cavity (same lobe) or noncontiguous in cases where the SOZ included site(s) distant from the surgical cavity. The rSOZ was defined according to visual analysis of SEEG traces completed by an estimation of the epileptogenicity index (EI). A second surgical procedure was performed in 12 patients (45%). A favorable outcome (Engel class I or II) was obtained in 9/12 patients (6 in Engel class I, 50%). The proportion of patients that had reoperation was higher in the contiguous group (80%) than in the noncontiguous group (22%) (p=0.02). A rSOZ localized in close relation to the initial surgical resection zone (contiguous group) was found in 10 patients (35%). Among them, 8 have since undergone reoperation, and a good outcome (Engel class I) was achieved in 5/8 (63%). A rSOZ involving a distant region from the first surgery was observed in 18 patients (65%) (noncontiguous group). Among them, only 4 have undergone reoperation, leading to a failure in 2 (Engel class III or IV) and a good outcome in 2 (IA). Ten patients had a first standard temporal lobectomy, and in 50% of these cases, the insula was involved in the rSOZ. Stereoelectroencephalography offers a unique way to evaluate the rSOZ at the individual level and thus guide further surgical decision-making. The best results are observed in patients having a focal rSOZ close to the site of the surgical resection in the first surgery.

Predicting the spatiotemporal diversity of seizure propagation and termination in human focal epilepsy

Recent studies have shown that seizures can spread and terminate across brain areas via a rich diversity of spatiotemporal patterns. In particular, while the location of the seizure onset area is usually invariant across seizures in an individual patient, the source of traveling (2–3 Hz) spike-and-wave discharges during seizures can either move with the slower propagating ictal wavefront or remain stationary at the seizure onset area. Furthermore, although many focal seizures terminate synchronously across brain areas, some evolve into distinct ictal clusters and terminate asynchronously. Here, we introduce a unifying perspective based on a new neural field model of epileptic seizure dynamics. Two main mechanisms, the co-existence of wave propagation in excitable media and coupled-oscillator dynamics, together with the interaction of multiple time scales, account for the reported diversity. We confirm our predictions in seizures and tractography data obtained from patients with pharmacologically resistant epilepsy. Our results contribute toward patient-specific seizure modeling.

A major goal of epilepsy research is understanding the spatiotemporal dynamics of seizure. Here, the authors extend the Epileptor neural mass model into a neural field model, in order to provide a unified and patient-specific model of seizure initiation, propagation, and termination.

Network dynamics in the healthy and epileptic developing brain

Electroencephalography (EEG) allows recording of cortical activity at high temporal resolution. EEG recordings can be summarized along different dimensions using network-level quantitative measures, such as channel-to-channel correlation, or band power distributions across channels. These reveal network patterns that unfold over a range of different timescales and can be tracked dynamically. Here we describe the dynamics of network state transitions in EEG recordings of spontaneous brain activity in normally developing infants and infants with severe early infantile epileptic encephalopathies (n = 8, age: 1–8 months). We describe differences in measures of EEG dynamics derived from band power, and correlation-based summaries of network-wide brain activity. We further show that EEGs from different patient groups and controls may be distinguishable on a small set of the novel quantitative measures introduced here, which describe dynamic network state switching. Quantitative measures related to the sharpness of switching from one correlation pattern to another show the largest differences between groups. These findings reveal that the early epileptic encephalopathies are associated with characteristic dynamic features at the network level. Quantitative network-based analyses like the one presented here may in the future inform the clinical use of quantitative EEG for diagnosis.

The Energy Landscape of Neurophysiological Activity Implicit in Brain Network Structure

A critical mystery in neuroscience lies in determining how anatomical structure impacts the complex functional dynamics of the brain. How does large-scale brain circuitry constrain states of neuronal activity and transitions between those states? We address these questions using a maximum entropy model of brain dynamics informed by white matter tractography. We demonstrate that the most probable brain states - characterized by minimal energy - display common activation profiles across brain areas: local spatially-contiguous sets of brain regions reminiscent of cognitive systems are co-activated frequently. The predicted activation rate of these systems is highly correlated with the observed activation rate measured in a separate resting state fMRI data set, validating the utility of the maximum entropy model in describing neurophysiological dynamics. This approach also offers a formal notion of the energy of activity within a system, and the energy of activity shared between systems. We observe that within- and between-system energies cleanly separate cognitive systems into distinct categories, optimized for differential contributions to integrated versus segregated function. These results support the notion that energetic and structural constraints circumscribe brain dynamics, offering insights into the roles that cognitive systems play in driving whole-brain activation patterns.

Commonalities in epileptogenic processes from different acute brain insults: Do they translate?

The most common forms of acquired epilepsies arise following acute brain insults such as traumatic brain injury, stroke, or central nervous system infections. Treatment is effective for only 60%-70% of patients and remains symptomatic despite decades of effort to develop epilepsy prevention therapies. Recent preclinical efforts are focused on likely primary drivers of epileptogenesis, namely inflammation, neuron loss, plasticity, and circuit reorganization. This review suggests a path to identify neuronal and molecular targets for clinical testing of specific hypotheses about epileptogenesis and its prevention or modification. Acquired human epilepsies with different etiologies share some features with animal models. We identify these commonalities and discuss their relevance to the development of successful epilepsy prevention or disease modification strategies. Risk factors for developing epilepsy that appear common to multiple acute injury etiologies include intracranial bleeding, disruption of the blood-brain barrier, more severe injury, and early seizures within 1 week of injury. In diverse human epilepsies and animal models, seizures appear to propagate within a limbic or thalamocortical/corticocortical network. Common histopathologic features of epilepsy of diverse and mostly focal origin are microglial activation and astrogliosis, heterotopic neurons in the white matter, loss of neurons, and the presence of inflammatory cellular infiltrates. Astrocytes exhibit smaller K+ conductances and lose gap junction coupling in many animal models as well as in sclerotic hippocampi from temporal lobe epilepsy patients. There is increasing evidence that epilepsy can be prevented or aborted in preclinical animal models of acquired epilepsy by interfering with processes that appear common to multiple acute injury etiologies, for example, in post-status epilepticus models of focal epilepsy by transient treatment with a trkB/PLCγ1 inhibitor, isoflurane, or HMGB1 antibodies and by topical administration of adenosine, in the cortical fluid percussion injury model by focal cooling, and in the albumin posttraumatic epilepsy model by losartan. Preclinical studies further highlight the roles of mTOR1 pathways, JAK-STAT3, IL-1R/TLR4 signaling, and other inflammatory pathways in the genesis or modulation of epilepsy after brain injury. The wealth of commonalities, diversity of molecular targets identified preclinically, and likely multidimensional nature of epileptogenesis argue for a combinatorial strategy in prevention therapy. Going forward, the identification of impending epilepsy biomarkers to allow better patient selection, together with better alignment with multisite preclinical trials in animal models, should guide the clinical testing of new hypotheses for epileptogenesis and its prevention.

The Virtual Mouse Brain: A Computational Neuroinformatics Platform to Study Whole Mouse Brain Dynamics

Connectome-based modeling of large-scale brain network dynamics enables causal in silico interrogation of the brain’s structure-function relationship, necessitating the close integration of diverse neuroinformatics fields. Here we extend the open-source simulation software The Virtual Brain (TVB) to whole mouse brain network modeling based on individual diffusion magnetic resonance imaging (dMRI)-based or tracer-based detailed mouse connectomes. We provide practical examples on how to use The Virtual Mouse Brain (TVMB) to simulate brain activity, such as seizure propagation and the switching behavior of the resting state dynamics in health and disease. TVMB enables theoretically driven experimental planning and ways to test predictions in the numerous strains of mice available to study brain function in normal and pathological conditions.