An Integrative View of Mechanisms Underlying Generalized Spike-and-Wave Epileptic Seizures and Its Implication on Optimal Therapeutic Treatments

Many types of epileptic seizures are characterized by generalized spike-and-wave discharges. In the past, notable effort has been devoted to understanding seizure dynamics and various hypotheses have been proposed to explain the underlying mechanisms. In this paper, by taking an integrative view of the underlying mechanisms, we demonstrate that epileptic seizures can be generated by many different combinations of synaptic strengths and intrinsic membrane properties. This integrative view has important medical implications: the specific state of a patient characterized by a set of biophysical characteristics ultimately determines the optimal therapeutic treatment. Through the same view, we further demonstrate the potentiation effect of rational polypharmacy in the treatment of epilepsy and provide a new angle to resolve the debate on polypharmacy. Our results underscore the need for personalized medicine and demonstrate that computer modeling and simulation may play an important role in assisting the clinicians in selecting the optimal treatment on an individual basis

Understanding Epileptiform After-Discharges as Rhythmic Oscillatory Transients

Electro-cortical activity in patients with epilepsy may show abnormal rhythmic transients in response to stimulation. Even when using the same stimulation parameters in the same patient, wide variability in the duration of transient response has been reported. These transients have long been considered important for the mapping of the excitability levels in the epileptic brain but their dynamic mechanism is still not well understood. To understand the occurrence of abnormal transients dynamically, we use a thalamo-cortical neural population model of epileptic spike-wave activity and study the interaction between slow and fast subsystems. In a reduced version of the thalamo-cortical model, slow wave oscillations arise from a fold of cycles (FoC) bifurcation. This marks the onset of a region of bistability between a high amplitude oscillatory rhythm and the background state. In vicinity of the bistability in parameter space, the model has excitable dynamics, showing prolonged rhythmic transients in response to suprathreshold pulse stimulation. We analyse the state space geometry of the bistable and excitable states, and find that the rhythmic transient arises when the impending FoC bifurcation deforms the state space and creates an area of locally reduced attraction to the fixed point. This area essentially allows trajectories to dwell there before escaping to the stable steady state, thus creating rhythmic transients. In the full thalamo-cortical model, we find a similar FoC bifurcation structure. Based on the analysis, we propose an explanation of why stimulation induced epileptiform activity may vary between trials, and predict how the variability could be related to ongoing oscillatory background activity.Comment: http://journal.frontiersin.org/article/10.3389/fncom.2017.00025/ful

Modeling extracellular field potentials and the frequency-filtering properties of extracellular space

Extracellular local field potentials (LFP) are usually modeled as arising from a set of current sources embedded in a homogeneous extracellular medium. Although this formalism can successfully model several properties of LFPs, it does not account for their frequency-dependent attenuation with distance, a property essential to correctly model extracellular spikes. Here we derive expressions for the extracellular potential that include this frequency-dependent attenuation. We first show that, if the extracellular conductivity is non-homogeneous, there is induction of non-homogeneous charge densities which may result in a low-pass filter. We next derive a simplified model consisting of a punctual (or spherical) current source with spherically-symmetric conductivity/permittivity gradients around the source. We analyze the effect of different radial profiles of conductivity and permittivity on the frequency-filtering behavior of this model. We show that this simple model generally displays low-pass filtering behavior, in which fast electrical events (such as Na$^+$-mediated action potentials) attenuate very steeply with distance, while slower (K$^+$-mediated) events propagate over larger distances in extracellular space, in qualitative agreement with experimental observations. This simple model can be used to obtain frequency-dependent extracellular field potentials without taking into account explicitly the complex folding of extracellular space.Comment: text (LaTeX), 6 figs. (ps

Model for a cortical circuit associated with childhood absence epilepsy

Childhood absence epilepsy is suspected to result from mutations in genes which encode ion channels including sodium channels. Our purpose in this thesis is to explore some of the factors that alter the function of neurons in the cerebral cortex. In particular, we investigate the consequence of these alterations on neuronal network activity associated with this disorder. In this regard, we create a small network consisting of deep layer cortical pyramidal neurons and an interneuron, each described by a single-compartment Hodgkin-Huxley style model. We investigate factors that convert a normal network into a hyperexcitable one, including impairment of $GABA_A$ synapses and sodium channel defects resulting from mutations in Scn genes. Our model agrees with experimental results indicating the role of GABA impairment in generating a hyperexcitable network. In particular, our cortical network is capable of generating its own spike-and-wave oscillations analogous to those in a thalamocortical network. Our results also suggest that the co-existence of multiple $Na^{+}$- channel mutations alters individual neuronal function to increase or decrease the likelihood of the network exhibiting seizure-like behaviour

A spatially extended model for macroscopic spike-wave discharges

Spike-wave discharges are a distinctive feature of epileptic seizures. So far, they have not been reported in spatially extended neural field models. We study a space-independent version of the Amari neural field model with two competing inhibitory populations. We show that this competition leads to robust spike-wave dynamics if the inhibitory populations operate on different time-scales. The spike-wave oscillations present a fold/homoclinic type bursting. From this result we predict parameters of the extended Amari system where spike-wave oscillations produce a spatially homogeneous pattern. We propose this mechanism as a prototype of macroscopic epileptic spike-wave discharges. To our knowledge this is the first example of robust spike-wave patterns in a spatially extended neural field model

A unifying explanation of primary generalized seizures through nonlinear brain modeling and bifurcation analysis

The aim of this paper is to explain critical features of the human primary generalized epilepsies by investigating the dynamical bifurcations of a nonlinear model of the brain’s mean field dynamics. The model treats the cortex as a medium for the propagation of waves of electrical activity, incorporating key physiological processes such as propagation delays, membrane physiology and corticothalamic feedback. Previous analyses have demonstrated its descriptive validity in a wide range of healthy states and yielded specific predictions with regards to seizure phenomena. We show that mapping the structure of the nonlinear bifurcation set predicts a number of crucial dynamic processes, including the onset of periodic and chaotic dynamics as well as multistability. Quantitative study of electrophysiological data supports the validity of these predictions and reveals processes unique to the global bifurcation set. Specifically, we argue that the core electrophysiological and cognitive differences between tonic-clonic and absence seizures are predicted by the global bifurcation diagram of the model’s dynamics. The present study is the first to present a unifying explanation of these generalized seizures using the bifurcation analysis of a dynamical model of the brain

A computational neurogenetic model of a spiking neuron

The paper presents a novel, biologically plausible spiking neuronal model that includes a dynamic gene network. Interactions of genes in neurons affect the dynamics of the neurons and the whole network through neuronal parameters that change as a function of gene expression. The proposed model is used to build a spiking neural network (SNN) illustrated on a real EEC data case study problem. The paper also presents a novel computational approach to brain neural network modeling that integrates dynamic gene networks with a neural network model. Interaction of genes in neurons affects the dynamics of the whole neural network through neuronal parameters, which are no longer constant, but change as a function of gene expression. Through optimization of the gene interaction network, initial gene/protein expression values and ANN parameters, particular target states of the neural network operation can be achieved, and statistics about gene intercation matrix can be extracted. It is illustrated by means of a simple neurogenetic model of a spiking neural network (SNN). The behavior of SNN is evaluated by means of the local field potential, thus making it possible to attempt modeling the role of genes in different brain states, where EEC data is available to test the model. We use standard signal processing techniques like FFT to evaluate the SNN output to compare it with real human EEC data. © 2005 IEEE

Computational neurogenetic modeling: a methodology to study gene interactions underlying neural oscillations

We present new results from Computational Neurogenetic Modeling to aid discoveries of complex gene interactions underlying oscillations in neural systems. Interactions of genes in neurons affect the dynamics of the whole neural network model through neuronal parameters, which change their values as a function of gene expression. Through optimization of the gene interaction network, initial gene/protein expression values and neuronal parameters, particular target states of the neural network operation can be achieved, and statistics about gene interaction matrix can be extracted. In such a way it is possible to model the role of genes and their interactions in different brain states and conditions. Experiments with human EEG data are presented as an illustration of this methodology and also, as a source for the discovery of unknown interactions between genes in relation to their impact on brain activity. © 2006 IEEE

Simplest relationship between local field potential and intracellular signals in layered neural tissue.

The relationship between the extracellularly measured electric field potential resulting from synaptic activity in an ensemble of neurons and intracellular signals in these neurons is an important but still open question. Based on a model neuron with a cylindrical dendrite and lumped soma, we derive a formula that substantiates a proportionality between the local field potential and the total somatic transmembrane current that emerges from the difference between the somatic and dendritic membrane potentials. The formula is tested by intra- and extracellular recordings of evoked synaptic responses in hippocampal slices. Additionally, the contribution of different membrane currents to the field potential is demonstrated in a two-population mean-field model. Our formalism, which allows for a simple estimation of unknown dendritic currents directly from somatic measurements, provides an interpretation of the local field potential in terms of intracellularly measurable synaptic signals. It is also applicable to the study of cortical activity using two-compartment neuronal population models