Plasticity-modulated seizure dynamics for seizure termination in realistic neuronal models

Glial Modulation of Electrical Rhythms in a Neuroglial Network Model of Epilepsy

OBJECTIVE

An important EEG-based biomarker for epilepsy is the phase-amplitude cross-frequency coupling (PAC) of electrical rhythms; however, the underlying pathways of these pathologic markers are not always clear. Since glial cells have been shown to play an active role in neuroglial networks, it is likely that some of these PAC markers are modulated via glial effects.

METHODS

We developed a 4-unit hybrid model of a neuroglial network, consisting of 16 sub-units, that combines a mechanistic representation of neurons with an oscillator-based Cognitive Rhythm Generator (CRG) representation of glial cells-astrocytes and microglia. The model output was compared with recorded generalized tonic-clonic patient data, both in terms of PAC features, and state classification using an unsupervised hidden Markov model (HMM).

RESULTS

The neuroglial model output showed PAC features similar to those observed in epileptic seizures. These generated PAC features were able to accurately identify spontaneous epileptiform discharges (SEDs) as seizure-like states, as well as a postictal-like state following the long-duration SED, when applied to the HMM machine learning algorithm trained on patient data. The evolution profile of the maximal PAC during the SED compared well with patient data, showing similar association with the duration of the postictal state.

CONCLUSION

The hybrid neuroglial network model was able to generate PAC features similar to those observed in ictal and postictal epileptic states, which has been used for state classification and postictal state duration prediction.

SIGNIFICANCE

Since PAC biomarkers are important for epilepsy research and postictal state duration has been linked with risk of sudden unexplained death in epilepsy, this model suggests glial synaptic effects as potential targets for further analysis and treatment.

Dynamics of convulsive seizure termination and postictal generalized EEG suppression

It is not fully understood how seizures terminate and why some seizures are followed by a period of complete brain activity suppression, postictal generalized EEG suppression. This is clinically relevant as there is a potential association between postictal generalized EEG suppression, cardiorespiratory arrest and sudden death following a seizure. We combined human encephalographic seizure data with data of a computational model of seizures to elucidate the neuronal network dynamics underlying seizure termination and the postictal generalized EEG suppression state. A multi-unit computational neural mass model of epileptic seizure termination and postictal recovery was developed. The model provided three predictions that were validated in EEG recordings of 48 convulsive seizures from 48 subjects with refractory focal epilepsy (20 females, age range 15-61 years). The duration of ictal and postictal generalized EEG suppression periods in human EEG followed a gamma probability distribution indicative of a deterministic process (shape parameter 2.6 and 1.5, respectively) as predicted by the model. In the model and in humans, the time between two clonic bursts increased exponentially from the start of the clonic phase of the seizure. The terminal interclonic interval, calculated using the projected terminal value of the log-linear fit of the clonic frequency decrease was correlated with the presence and duration of postictal suppression. The projected terminal interclonic interval explained 41% of the variation in postictal generalized EEG suppression duration (P < 0.02). Conversely, postictal generalized EEG suppression duration explained 34% of the variation in the last interclonic interval duration. Our findings suggest that postictal generalized EEG suppression is a separate brain state and that seizure termination is a plastic and autonomous process, reflected in increased duration of interclonic intervals that determine the duration of postictal generalized EEG suppression.

Preventive and Abortive Strategies for Stimulation Based Control of Epilepsy: A Computational Model Study

Epilepsy is a condition in which periods of ongoing normal EEG activity alternate with periods of oscillatory behavior characteristic of epileptic seizures. The dynamics of the transitions between the two states are still unclear. Computational models provide a powerful tool to explore the underlying mechanisms of such transitions, with the purpose of eventually finding therapeutic interventions for this debilitating condition. In this study, the possibility to postpone seizures elicited by a decrease of inhibition is investigated by using external stimulation in a realistic bistable neuronal model consisting of two interconnected neuronal populations representing pyramidal cells and interneurons. In the simulations, seizures are induced by slowly decreasing the conductivity of GABA[Formula: see text] synaptic channels over time. Since the model is bistable, the system will change state from the initial steady state (SS) to the limit cycle (LS) state because of internal noise, when the inhibition falls below a certain threshold. Several state-independent stimulations paradigms are simulated. Their effectiveness is analyzed for various stimulation frequencies and intensities in combination with periodic and random stimulation sequences. The distributions of the time to first seizure in the presence of stimulation are compared with the situation without stimulation. In addition, stimulation protocols targeted to specific subsystems are applied with the objective of counteracting the baseline shift due to decreased inhibition in the system. Furthermore, an analytical model is used to investigate the effects of random noise. The relation between the strength of random noise stimulation, the control parameter of the system and the transitions between steady state and limit cycle are investigated. The study shows that it is possible to postpone epileptic activity by targeted stimulation in a realistic neuronal model featuring bistability and that it is possible to stop seizures by random noise in an analytical model.

Suppressing epileptic activity in a neural mass model using a closed-loop proportional-integral controller

Closed-loop control is a promising deep brain stimulation (DBS) strategy that could be used to suppress high-amplitude epileptic activity. However, there are currently no analytical approaches to determine the stimulation parameters for effective and safe treatment protocols. Proportional-integral (PI) control is the most extensively used closed-loop control scheme in the field of control engineering because of its simple implementation and perfect performance. In this study, we took Jansen's neural mass model (NMM) as a test bed to develop a PI-type closed-loop controller for suppressing epileptic activity. A graphical stability analysis method was employed to determine the stabilizing region of the PI controller in the control parameter space, which provided a theoretical guideline for the choice of the PI control parameters. Furthermore, we established the relationship between the parameters of the PI controller and the parameters of the NMM in the form of a stabilizing region, which provided insights into the mechanisms that may suppress epileptic activity in the NMM. The simulation results demonstrated the validity and effectiveness of the proposed closed-loop PI control scheme.

A neural mass model of spontaneous burst suppression and epileptic seizures

The paper presents a neural mass model that is capable of simulating the transition to and from various forms of paroxysmal activity such as burst suppression and epileptic seizure-like waveforms. These events occur without changing parameters in the model. The model is based on existing neural mass models, with the addition of feedback of fast dynamics to create slowly time varying parameters, or slow states. The goal of this research is to establish a link between system properties that modulate neural activity and the fast changing dynamics, such as membrane potentials and firing rates that can be manipulated using electrical stimulation. Establishing this link is likely to be a necessary component of a closed-loop system for feedback control of pathological neural activity.

Gap Junctions as Common Cause of High-Frequency Oscillations and Epileptic Seizures in a Computational Cascade of Neuronal Mass and Compartmental Modeling

High frequency oscillations (HFO) appear to be a promising marker for delineating the seizure onset zone (SOZ) in patients with localization related epilepsy. It remains, however, a purely observational phenomenon and no common mechanism has been proposed to relate HFOs and seizure generation. In this work we show that a cascade of two computational models, one on detailed compartmental scale and a second one on neural mass scale can explain both the autonomous generation of HFOs and the presence of epileptic seizures as emergent properties. To this end we introduce axonal–axonal gap junctions on a microscopic level and explore their impact on the higher level neural mass model (NMM). We show that the addition of gap junctions can generate HFOs and simultaneously shift the operational point of the NMM from a steady state network into bistable behavior that can autonomously generate epileptic seizures. The epileptic properties of the system, or the probability to generate epileptic type of activity, increases gradually with the increase of the density of axonal–axonal gap junctions. We further demonstrate that ad hoc HFO detectors used in previous studies are applicable to our simulated data.

MULTIPLE OSCILLATORY STATES IN MODELS OF COLLECTIVE NEURONAL DYNAMICS

In our previous studies, we showed that the both realistic and analytical computational models of neural dynamics can display multiple sustained states (attractors) for the same values of model parameters. Some of these states can represent normal activity while other, of oscillatory nature, may represent epileptic types of activity. We also showed that a simplified, analytical model can mimic this type of behavior and can be used instead of the realistic model for large scale simulations. The primary objective of the present work is to further explore the phenomenon of multiple stable states, co-existing in the same operational model, or phase space, in systems consisting of large number of interconnected basic units. As a second goal, we aim to specify the optimal method for state control of the system based on inducing state transitions using appropriate external stimulus. We use here interconnected model units that represent the behavior of neuronal populations as an effective dynamic system. The model unit is an analytical model (S. Kalitzin et al., Epilepsy Behav. 22 (2011) S102–S109) and does not correspond directly to realistic neuronal processes (excitatory–inhibitory synaptic interactions, action potential generation). For certain parameter choices however it displays bistable dynamics imitating the behavior of realistic neural mass models. To analyze the collective behavior of the system we applied phase synchronization analysis (PSA), principal component analysis (PCA) and stability analysis using Lyapunov exponent (LE) estimation. We obtained a large variety of stable states with different dynamic characteristics, oscillatory modes and phase relations between the units. These states can be initiated by appropriate initial conditions; transitions between them can be induced stochastically by fluctuating variables (noise) or by specific inputs. We propose a method for optimal reactive control, allowing forced transitions from one state (attractor) into another.

DYNAMICS OF COLLECTIVE MULTI-STABILITY IN MODELS OF MULTI-UNIT NEURONAL SYSTEMS

In this study, we investigate the correspondence between dynamic patterns of behavior in two types of computational models of neuronal activity. The first model type is the realistic neuronal model; the second model type is the phenomenological or analytical model. In the simplest model set-up of two interconnected units, we define a parameter space for both types of systems where their behavior is similar. Next we expand the analytical model to two sets of 90 fully interconnected units with some overlap, which can display multi-stable behavior. This system can be in three classes of states: (i) a class consisting of a single resting state, where all units of a set are in steady state, (ii) a class consisting of multiple preserving states, where subsets of the units of a set participate in limit cycle, and (iii) a class consisting of a single saturated state, where all units of a set are recruited in a global limit cycle. In the third and final part of the work, we demonstrate that phase synchronization of units can be detected by a single output unit.

Characterization of seizure-like events recorded in vivo in a mouse model of Rett syndrome

Rett syndrome is a neurodevelopmental disorder caused by mutations in the X-linked gene encoding methyl-CpG-binding protein 2 (MECP2). Spontaneous recurrent discharge episodes are displayed in Rett-related seizures as in other types of epilepsies. The aim of this paper is to investigate the seizure-like event (SLE) and inter-SLE states in a female MeCP2-deficient mouse model of Rett syndrome and compare them to those found in other spontaneous recurrent epilepsy models. The study was performed on a small population of female MeCP2-deficient mice using telemetric local field potential (LFP) recordings over a 24 h period. Durations of SLEs and inter-SLEs were extracted using a rule-based automated SLE detection system for both daytime and nighttime, as well as high and low power levels of the delta frequency range (0.5-4 Hz) of the recorded LFPs. The results suggest SLE occurrences are not influenced by circadian rhythms, but had a significantly greater association with delta power. Investigating inter-SLE and SLE states by fitting duration histograms to the gamma distribution showed that SLE initiation and termination were associated with random and deterministic mechanisms, respectively. These findings when compared to reported studies on epilepsy suggest that Rett-related seizures share many similarities with absence epilepsy.

Connectivity and phase coherence in neural network models of interconnected Z(4)-bi-stable units

A phenomenological neural network model with bi-stable oscillatory units is used to model up- and down-states. These states have been observed in vivo in biological neuronal systems and feature oscillatory, limit cycle type of behavior in the up-states. A network is formed by a set of interconnected units. Two different types of network layouts are considered in this work: networks with hierarchical connections and hubs and networks with random connections. The phase coherence between the different units is analyzed and compared to the connectivity distance between nodes. In addition the connectivity degree of a node is associated to the average phase coherence with all other units. The results show that we may be able to identify the set of hubs in a network based on the phase coherence estimates between the different nodes. If the network is very dense or randomly connected, the underlying network structure, however, can not be derived uniquely from the phase coherence.

REACTIVE CONTROL OF EPILEPTIFORM DISCHARGES IN REALISTIC COMPUTATIONAL NEURONAL MODELS WITH BISTABILITY

We aim to derive fully autonomous seizure suppression paradigms based on reactive control of neuronal dynamics. A previously derived computational model of seizure generation describing collective degrees of freedom and featuring bistable dynamics is used. A novel technique for real-time control of epileptogenicity is introduced. The reactive control reduces practically all seizures in the model. The study indicates which parameters provide the maximal seizure reduction with minimal intervention. An adaptive scheme is proposed that optimizes the stimulation parameters in nonstationary situations.

Human seizures self-terminate across spatial scales via a critical transition

Why seizures spontaneously terminate remains an unanswered fundamental question of epileptology. Here we present evidence that seizures self-terminate via a discontinuous critical transition or bifurcation. We show that human brain electrical activity at various spatial scales exhibits common dynamical signatures of an impending critical transition--slowing, increased correlation, and flickering--in the approach to seizure termination. In contrast, prolonged seizures (status epilepticus) repeatedly approach, but do not cross, the critical transition. To support these results, we implement a computational model that demonstrates that alternative stable attractors, representing the ictal and postictal states, emulate the observed dynamics. These results suggest that self-terminating seizures end through a common dynamical mechanism. This description constrains the specific biophysical mechanisms underlying seizure termination, suggests a dynamical understanding of status epilepticus, and demonstrates an accessible system for studying critical transitions in nature.

Computational model prospective on the observation of proictal states in epileptic neuronal systems

Epilepsy is a pathological condition of the human central nervous system in which normal brain functions are impaired by unexpected transitions to states called seizures. We developed a lumped neuronal model that has the property of switching between two states as a result of intrinsic or extrinsic perturbations, such as noisy fluctuations. In one version of the model, seizure risk is controlled by a single connectivity parameter representing excitatory couplings between two model lumps. We show that this risk can be reconstructed from calculation of the cross-covariance between the activities of the two neural populations during the nonictal phase. In a second simulation sequence, we use a system of 10 interconnected lumps with randomly generated connectivity matrices. We show again that the tendency to develop seizures can be inferred from the cross-covariances calculated during the nonictal states. Our conclusion is that the risk of epileptic transitions in biological systems can be objectively quantified. This article is part of a Supplemental Special Issue entitled The Future of Automated Seizure Detection and Prediction.