Oscillations and neuronal synchronization in epilepsy: an approach based on oscillation theory and statistical mechanics.

openIn questo lavoro si propone di studiare i processi di sincronizzazione neuronale dal punto di vista dei sistemi dinamici, in particolare, della teoria delle oscillazioni. Si può dimostrare che esistono oscillazioni macroscopiche nel sistema talamocorticale dei topi epilettici. Questo fatto permette di modellare gli attacchi epilettici come processi di sincronizzazione di uno o due oscillatori auto-sostenuti, i cui parametri vengono ricavati dalle funzioni di risposta di fase ottenute sperimentalmente. Si osservano anche le cosiddette lingue di Arnold e i plateau di sincronizzazione, caratteristici della risposta di fase dei processi con un ciclo limite. Inoltre, utilizzando metodi della fisica statistica e la teoria di informazione, si ricava un rapporto fra la sincronizzazione e la quantità di informazione contenuta nelle rette funzionali del cervello. Si osserva che questa quantità di informazione è massima a livelli intermedi di sincronizzazione, in stati normali di veglia, e molto più bassa durante gli attacchi epiletticiIn this work we propose to study the neuronal synchronization processes from the point of view of the dynamical systems, in particular of the oscillations theory. It can be demonstrated that there are macroscopic oscillations in the thalamocortical network in epileptic rats. So we are able to model the epileptic seizures as synchronization processes of one or two self-sustained oscillator, whose parameters are extracted from the phase response functions obtained experimentally. We observe also the Arnold tongues and the synchronization plateau that are typical pf the phase response processes with a limit cycle. Moreover, using statistical physics and information theory methods, we obtain a relation between synchronization and quantity of information contained in the brain functional lines. This quantity of information has a peak at intermediate synchronization levels, as in conscious awareness states, and it is lower during epileptic seizures

Computer modelling of connectivity change suggests epileptogenesis mechanisms in idiopathic generalised epilepsy

Patients with idiopathic generalised epilepsy (IGE) typically have normal conventional magnetic resonance imaging (MRI), hence MRI based diagnosis is challenging. Anatomical abnormalities underlying brain dysfunctions in IGE are unclear and their relation to the pathomechanisms of epileptogenesis is poorly understood. In this study, we applied connectometry, an advanced quantitative neuroimaging technique for investigating localised changes in white-matter tissue. Analysing white matter structures of 32 subjects we incorporated our findings in a computational model of seizure dynamics to suggest a plausible mechanism of epileptogenesis. Patients with IGE have significant bilateral alterations in major white-matter fascicles. In the cingulum, fornix, and superior longitudinal fasciculus, tract integrity is compromised, whereas in specific parts of tracts between thalamus and the precentral gyrus, tract integrity is enhanced in patients. Combining these alterations in a logistic regression model, we computed the decision boundary that discriminated patients and controls. The computational model, informed with the findings on the tract abnormalities, specifically highlighted the importance of enhanced cortico-reticular connections along with impaired cortico-cortical connections in inducing pathological seizure-like dynamics. We emphasise taking directionality of brain connectivity into consideration towards understanding the pathological mechanisms; this is possible by combining neuroimaging and computational modelling. Our imaging evidence of structural alterations suggest the loss of cortico-cortical and enhancement of cortico-thalamic fibre integrity in IGE. We further suggest that impaired connectivity from cortical regions to the thalamic reticular nucleus offers a therapeutic target for selectively modifying the brain circuit for reversing the mechanisms leading to epileptogenesis

Interacting Turing-Hopf Instabilities Drive Symmetry-Breaking Transitions in a Mean-Field Model of the Cortex: A Mechanism for the Slow Oscillation

Electrical recordings of brain activity during the transition from wake to anesthetic coma show temporal and spectral alterations that are correlated with gross changes in the underlying brain state. Entry into anesthetic unconsciousness is signposted by the emergence of large, slow oscillations of electrical activity (≲1  Hz) similar to the slow waves observed in natural sleep. Here we present a two-dimensional mean-field model of the cortex in which slow spatiotemporal oscillations arise spontaneously through a Turing (spatial) symmetry-breaking bifurcation that is modulated by a Hopf (temporal) instability. In our model, populations of neurons are densely interlinked by chemical synapses, and by interneuronal gap junctions represented as an inhibitory diffusive coupling. To demonstrate cortical behavior over a wide range of distinct brain states, we explore model dynamics in the vicinity of a general-anesthetic-induced transition from “wake” to “coma.” In this region, the system is poised at a codimension-2 point where competing Turing and Hopf instabilities coexist. We model anesthesia as a moderate reduction in inhibitory diffusion, paired with an increase in inhibitory postsynaptic response, producing a coma state that is characterized by emergent low-frequency oscillations whose dynamics is chaotic in time and space. The effect of long-range axonal white-matter connectivity is probed with the inclusion of a single idealized point-to-point connection. We find that the additional excitation from the long-range connection can provoke seizurelike bursts of cortical activity when inhibitory diffusion is weak, but has little impact on an active cortex. Our proposed dynamic mechanism for the origin of anesthetic slow waves complements—and contrasts with—conventional explanations that require cyclic modulation of ion-channel conductances. We postulate that a similar bifurcation mechanism might underpin the slow waves of natural sleep and comment on the possible consequences of chaotic dynamics for memory processing and learning

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

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

Implementing the cellular mechanisms of synaptic transmission in a neural mass model of the thalamocortical circuitry

A novel direction to existing neural mass modeling technique is proposed where the commonly used “alpha function” for representing synaptic transmission is replaced by a kinetic framework of neurotransmitter and receptor dynamics. The aim is to underpin neuro-transmission dynamics associated with abnormal brain rhythms commonly observed in neurological and psychiatric disorders. An existing thalamocortical neural mass model is modified by using the kinetic Q1 framework for modeling synaptic transmission mediated by glutamatergic and GABA (gamma-aminobutyric-acid)-ergic receptors. The model output is compared qualitatively with existing literature on in vitro experimental studies of ferret thalamic slices, as well as on single-neuron-level model based studies of neuro-receptor and transmitter dynamics in the thalamocortical tissue. The results are consistent with these studies: the activation of ligand-gated GABA receptors is essential for generation of spindle waves in the model, while blocking this pathway leads to low-frequency synchronized oscillations such as observed in slow-wave sleep; the frequency of spindle oscillations increase with increased levels of post-synaptic membrane conductance for AMPA (alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic-acid) receptors, and blocking this pathway effects a quiescent model output. In terms of computational efficiency, the simulation time is improved by a factor of 10 compared to a similar neural mass model based on alpha functions. This implies a dramatic improvement in computational resources for large-scale network simulation using this model. Thus, the model provides a platform for correlating high-level brain oscillatory activity with low-level synaptic attributes, and makes a significant contribution toward advancements in current neural mass modeling paradigm as a potential computational tool to better the understanding of brain oscillations in sickness and in health

Modulation of intrinsic and synaptic excitability during sleep oscillations and electrographic seizures

Le présente mémoire fournit des nouvelles évidences montrant la modulation de l’excitabilité neuronale intrinsèque et synaptique, et la conséquence de cette modulation sur l’activité neuronale durant à la fois, les oscillations lentes du sommeil, et les crises électrographiques in vivo chez des animaux anesthésiés. Nous effectuons des enregistrements intracellulaires simultanés de neurones corticaux et des potentiels de champs locaux au niveau du gyrus suprasylvien à l’intérieur du cortex associatif pariétal (aires : 5, 7 et 21). Nous suggérons que la fluctuation de la concentration extracellulaire du calcium durant les oscillations lentes du sommeil module à la fois, l’excitabilité intrinsèque et synaptique des neurones corticaux, ainsi par conséquent, elle module affecte la relation d’input-output de ces neurones. L’apparition durant les oscillations lentes du sommeil, des crises de type Lennex-Gastaut qui sont générées corticalement, nous a permet d’étudier les propriétés spatio-temporelles des ondes paroxysmiques rapides associées avec ce type de crises. Nous suggérons que les ondes paroxysmiques rapides apparaissent comme des oscillations quasi-indépendantes même dans les localisations corticales voisines, suggérant leur origine focal.The present memoir provides new evidences showing the modulation of intrinsic and synaptic excitability of cortical neurons, and the consequence of this modulation on neuronal activity during both slow sleep oscillations and electrographic seizures in vivo in anaesthetized animals. We performed simultaneous recordings of cortical neurons with local field potentials in suprasylvian gyrus within parietal associative cortex (area 5, 7 and 21). We suggest that the fluctuation of extacellular calcium concentration during slow sleep oscillations, modulates both intrinsic and synaptic excitability cortical neurons, thus by consequence modulates the input-output relationship of these neurons. The occurrence during slow-wave sleep of cortically generated Lennox-Gastaut type of seizures admits us to study the spatio-temporal properties of paroxysmal fast runs associated with this type of seizures. We suggest that fast runs appeared as quasi-independent oscillations even in neighbouring cortical locations suggesting their focal origin

Dynamics and precursor signs for phase transitions in neural systems

This thesis investigates neural state transitions associated with sleep, seizure and anaesthesia. The aim is to address the question: How does a brain traverse the critical threshold between distinct cortical states, both healthy and pathological? Specifically we are interested in sub-threshold neural behaviour immediately prior to state transition. We use theoretical neural modelling (single spiking neurons, a network of these, and a mean-field continuum limit) and in vitro experiments to address this question. Dynamically realistic equations of motion for thalamic relay neuron, reticular nuclei, cortical pyramidal and cortical interneuron in different vigilance states are developed, based on the Izhikevich spiking neuron model. A network of cortical neurons is assembled to examine the behaviour of the gamma-producing cortical network and its transition to lower frequencies due to effect of anaesthesia. Then a three-neuron model for the thalamocortical loop for sleep spindles is presented. Numerical simulations of these networks confirms spiking consistent with reported in vivo measurement results, and provides supporting evidence for precursor indicators of imminent phase transition due to occurrence of individual spindles. To complement the spiking neuron networks, we study the Wilson–Cowan neural mass equations describing homogeneous cortical columns and a 1D spatial cluster of such columns. The abstract representation of cortical tissue by a pair of coupled integro-differential equations permits thorough linear stability, phase plane and bifurcation analyses. This model shows a rich set of spatial and temporal bifurcations marking the boundary to state transitions: saddle-node, Hopf, Turing, and mixed Hopf–Turing. Close to state transition, white-noise-induced subthreshold fluctuations show clear signs of critical slowing down with prolongation and strengthening of autocorrelations, both in time and space, irrespective of bifurcation type. Attempts at in vitro capture of these predicted leading indicators form the last part of the thesis. We recorded local field potentials (LFPs) from cortical and hippocampal slices of mouse brain. State transition is marked by the emergence and cessation of spontaneous seizure-like events (SLEs) induced by bathing the slices in an artificial cerebral spinal fluid containing no magnesium ions. Phase-plane analysis of the LFP time-series suggests that distinct bifurcation classes can be responsible for state change to seizure. Increased variance and growth of spectral power at low frequencies (f < 15 Hz) was observed in LFP recordings prior to initiation of some SLEs. In addition we demonstrated prolongation of electrically evoked potentials in cortical tissue, while forwarding the slice to a seizing regime. The results offer the possibility of capturing leading temporal indicators prior to seizure generation, with potential consequences for understanding epileptogenesis. Guided by dynamical systems theory this thesis captures evidence for precursor signs of phase transitions in neural systems using mathematical and computer-based modelling as well as in vitro experiments