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

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

Spontaneous transitions to focal-onset epileptic seizures: A dynamical study

Given the complex temporal evolution of epileptic seizures, understanding their dynamic nature might be beneficial for clinical diagnosis and treatment. Yet, the mechanisms behind, for instance, the onset of seizures are still unknown. According to an existing classification, two basic types of dynamic onset patterns plus a number of more complex onset waveforms can be distinguished. Here, we introduce a basic three-variable model with two time scales to study potential mechanisms of spontaneous seizure onset. We expand the model to demonstrate how coupling of oscillators leads to more complex seizure onset waveforms. Finally, we test the response to pulse perturbation as a potential biomarker of interictal changes. Focal epileptic seizures are characterized by complex spatiotemporal rhythms of electric brain activity. Phenomenologically, there are different types of rhythms, namely, fast-small oscillations, slow-large spiking, and complex waveforms of the voltage. The dynamics of these types are, however, still poorly understood and their clinical characterization is, therefore, mostly descriptive. We use computational modeling of macro-level electrical brain activity to study the spontaneous onset and evolution of major clinical seizure rhythms. Looking at principal models of one and two coupled oscillators with a slow driving population, we show the dynamical characteristics and relationships between basic seizure onset types. In addition, we show that pulse perturbations of background activity can serve as a biomarker for seizure onset

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

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

Mechanisms explaining transitions between tonic and phasic firing in neuronal populations as predicted by a low dimensional firing rate model

Several firing patterns experimentally observed in neural populations have been successfully correlated to animal behavior. Population bursting, hereby regarded as a period of high firing rate followed by a period of quiescence, is typically observed in groups of neurons during behavior. Biophysical membrane-potential models of single cell bursting involve at least three equations. Extending such models to study the collective behavior of neural populations involves thousands of equations and can be very expensive computationally. For this reason, low dimensional population models that capture biophysical aspects of networks are needed. \noindent The present paper uses a firing-rate model to study mechanisms that trigger and stop transitions between tonic and phasic population firing. These mechanisms are captured through a two-dimensional system, which can potentially be extended to include interactions between different areas of the nervous system with a small number of equations. The typical behavior of midbrain dopaminergic neurons in the rodent is used as an example to illustrate and interpret our results. \noindent The model presented here can be used as a building block to study interactions between networks of neurons. This theoretical approach may help contextualize and understand the factors involved in regulating burst firing in populations and how it may modulate distinct aspects of behavior.Comment: 25 pages (including references and appendices); 12 figures uploaded as separate file

The Hippocampus Participates in a Pharmacological Rat Model of Absence Seizures

The thalamocortical network is responsible for the generation of spike-and-wave discharges (SWDs) in absence epilepsy. Recent studies suggest a potential involvement of the hippocampus, which may explain the variability in the extent of cognitive deficits among patients with absence epilepsy. I hypothesize that the hippocampus may become entrained in spike-and-wave discharges following thalamocortical activation. The gamma-butyrolactone (GBL) rat model of absence seizures was used in this thesis. Following GBL injection, SWDs of 4 to 6 Hz developed in the spontaneous local field potentials (LFPs) recorded by depth electrodes in the thalamus, neocortex and hippocampus. Synchronization of hippocampal, thalamic and neocortical SWDs was revealed by coherence analysis of the LFPs, and multiple unit activity of hippocampal neurons occurred within 250 msec prior to the negative peak of thalamic SWDs. Functional magnetic resonance imaging (fMRI) demonstrated functional connectivity between the hippocampus and the thalamocortical network. Thus, electrophysiological and fMRI activity of the hippocampus were shown to be time-locked to the thalamocortical SWDs, suggesting functional connectivity of the hippocampus and thalamocortical network during GBL-induced absence seizures

Development and application of inhibitory luminopsins for the treatment of epilepsy

Optogenetics has shown great promise as a direct neuromodulatory tool for halting seizure activity in various animal models of epilepsy. However, light delivery into the brain is still a major practical challenge that needs to be addressed before future clinical translation is feasible. Not only does light delivery into the brain require surgically implanted hardware that can be both invasive and restrictive, but it is also difficult to illuminate large or complicated structures in the brain due to light scatter and attenuation. We have bypassed the challenges of external light delivery by directly coupling a bioluminescent light source (a genetically encoded Renilla luciferase) to an inhibitory opsin (Natronomonas halorhodopsin) as a single fusion protein, which we term an inhibitory luminopsin (iLMO). iLMOs were developed and characterized in vitro and in vivo using intracellular recordings, multielectrode arrays, and behavioral testing. iLMO2 was shown to generate hyperpolarizing outward currents in response to both external light and luciferase substrate, which was sufficient to suppress action potential firing and synchronous bursting activity in vitro. iLMO2 was further shown to suppress single-unit firing rate and local field potentials in the hippocampus of anesthetized and awake animals. Finally, expression of iLMO was scaled up to multiple structures of the basal ganglia to modulate rotational behavior of freely moving animals in a hardware-independent fashion. iLMO2 was further utilized to acutely suppress focal epileptic discharges induced by intracerebral injection of bicuculline and generalized seizures resulting from systemic administration of pentylenetetrazol. Inhibitory luminopsins have enabled the possibility of optogenetic inhibition of neural activity in a non-invasive and hardware-independent fashion. This work increases the versatility, scalability, and practicality of utilizing optogenetic approaches for halting seizure activity in vivo.Ph.D