Characterization of K-complexes and slow wave activity in a neural mass model

Altered sleep spindles and slow waves during space shuttle missions

Sleep deficiencies and associated performance decrements are common among astronauts during spaceflight missions. Previously, sleep in space was analyzed with a focus on global measures while the intricate structure of sleep oscillations remains largely unexplored. This study extends previous findings by analyzing how spaceflight affects characteristics of sleep spindles and slow waves, two sleep oscillations associated with sleep quality and quantity, in four astronauts before, during and after two Space Shuttle missions. Analysis of these oscillations revealed significantly increased fast spindle density, elevated slow spindle frequency, and decreased slow wave amplitude in space compared to on Earth. These results reflect sleep characteristics during spaceflight on a finer electrophysiological scale and provide an opportunity for further research on sleep in space.

Computational Modeling of Information Propagation during the Sleep–Waking Cycle

Simple Summary

During the deep phases of sleep we do not normally wake up by a thunder, but we nevertheless notice it when awake. The exact same sound gets to our ears and cortex through the thalamus and still, it triggers two very different responses. There is growing experimental evidence that these two states of the brain—sleep and wakefulness—distribute sensory information in different ways across the cortex. In particular, during sleep, neuronal responses remain local and do not spread out across distant synaptically connected regions. On the contrary, during wakefulness, stimuli are able to elicit a wider spatial response. We have used a computational model of coupled cortical columns to study how these two propagation modes arise. Moreover, the transition from sleep-like to waking-like dynamics occurs in agreement with the synaptic homeostasis hypothesis and only requires the increase of excitatory conductances. We have found that, in order to reproduce the aforementioned observations, this parameter change has to be selectively applied: synaptic conductances between distinct columns have to be potentiated over local ones.

Abstract

Non-threatening familiar sounds can go unnoticed during sleep despite the fact that they enter our brain by exciting the auditory nerves. Extracellular cortical recordings in the primary auditory cortex of rodents show that an increase in firing rate in response to pure tones during deep phases of sleep is comparable to those evoked during wakefulness. This result challenges the hypothesis that during sleep cortical responses are weakened through thalamic gating. An alternative explanation comes from the observation that the spatiotemporal spread of the evoked activity by transcranial magnetic stimulation in humans is reduced during non-rapid eye movement (NREM) sleep as compared to the wider propagation to other cortical regions during wakefulness. Thus, cortical responses during NREM sleep remain local and the stimulus only reaches nearby neuronal populations. We aim at understanding how this behavior emerges in the brain as it spontaneously shifts between NREM sleep and wakefulness. To do so, we have used a computational neural-mass model to reproduce the dynamics of the sensory auditory cortex and corresponding local field potentials in these two brain states. Following the synaptic homeostasis hypothesis, an increase in a single parameter, namely the excitatory conductance g¯AMPA, allows us to place the model from NREM sleep into wakefulness. In agreement with the experimental results, the endogenous dynamics during NREM sleep produces a comparable, even higher, response to excitatory inputs to the ones during wakefulness. We have extended the model to two bidirectionally connected cortical columns and have quantified the propagation of an excitatory input as a function of their coupling. We have found that the general increase in all conductances of the cortical excitatory synapses that drive the system from NREM sleep to wakefulness does not boost the effective connectivity between cortical columns. Instead, it is the inter-/intra-conductance ratio of cortical excitatory synapses that should raise to facilitate information propagation across the brain.

Canard solutions in neural mass models: consequences on critical regimes

Mathematical models at multiple temporal and spatial scales can unveil the fundamental mechanisms of critical transitions in brain activities. Neural mass models (NMMs) consider the average temporal dynamics of interconnected neuronal subpopulations without explicitly representing the underlying cellular activity. The mesoscopic level offered by the neural mass formulation has been used to model electroencephalographic (EEG) recordings and to investigate various cerebral mechanisms, such as the generation of physiological and pathological brain activities. In this work, we consider a NMM widely accepted in the context of epilepsy, which includes four interacting neuronal subpopulations with different synaptic kinetics. Due to the resulting three-time-scale structure, the model yields complex oscillations of relaxation and bursting types. By applying the principles of geometric singular perturbation theory, we unveil the existence of the canard solutions and detail how they organize the complex oscillations and excitability properties of the model. In particular, we show that boundaries between pathological epileptic discharges and physiological background activity are determined by the canard solutions. Finally we report the existence of canard-mediated small-amplitude frequency-specific oscillations in simulated local field potentials for decreased inhibition conditions. Interestingly, such oscillations are actually observed in intracerebral EEG signals recorded in epileptic patients during pre-ictal periods, close to seizure onsets.

Computational Evidence for a Competitive Thalamocortical Model of Spikes and Spindle Activity in Rolandic Epilepsy

Rolandic epilepsy (RE) is the most common idiopathic focal childhood epilepsy syndrome, characterized by sleep-activated epileptiform spikes and seizures and cognitive deficits in school age children. Recent evidence suggests that this disease may be caused by disruptions to the Rolandic thalamocortical circuit, resulting in both an abundance of epileptiform spikes and a paucity of sleep spindles in the Rolandic cortex during non-rapid eye movement sleep (NREM); electrographic features linked to seizures and cognitive symptoms, respectively. The neuronal mechanisms that support the competitive shared thalamocortical circuitry between pathological epileptiform spikes and physiological sleep spindles are not well-understood. In this study we introduce a computational thalamocortical model for the sleep-activated epileptiform spikes observed in RE. The cellular and neuronal circuits of this model incorporate recent experimental observations in RE, and replicate the electrophysiological features of RE. Using this model, we demonstrate that: (1) epileptiform spikes can be triggered and promoted by either a reduced NMDA current or h-type current; and (2) changes in inhibitory transmission in the thalamic reticular nucleus mediates an antagonistic dynamic between epileptiform spikes and spindles. This work provides the first computational model that both recapitulates electrophysiological features and provides a mechanistic explanation for the thalamocortical switch between the pathological and physiological electrophysiological rhythms observed during NREM sleep in this common epileptic encephalopathy.

Reversed and increased functional connectivity in non-REM sleep suggests an altered rather than reduced state of consciousness relative to wake

Sleep resting state network (RSN) functional connectivity (FC) is poorly understood, particularly for rapid eye movement (REM), and in non-sleep deprived subjects. REM and non-REM (NREM) sleep involve competing drives; towards hypersynchronous cortical oscillations in NREM; and towards wake-like desynchronized oscillations in REM. This study employed simultaneous electroencephalography-functional magnetic resonance imaging (EEG-fMRI) to explore whether sleep RSN FC reflects these opposing drives. As hypothesized, this was confirmed for the majority of functional connections modulated by sleep. Further, changes were directional: e.g., positive wake correlations trended towards negative correlations in NREM and back towards positive correlations in REM. Moreover, the majority did not merely reduce magnitude, but actually either reversed and strengthened in the opposite direction, or increased in magnitude during NREM. This finding supports the notion that NREM is best expressed as having altered, rather than reduced FC. Further, as many of these functional connections comprised “higher-order” RSNs (which have been previously linked to cognition and consciousness), such as the default mode network, this finding is suggestive of possibly concomitant alterations to cognition and consciousness.

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.

Effects of Cholinergic Neuromodulation on Thalamocortical Rhythms During NREM Sleep: A Model Study

It has been suggested that cholinergic neurons shape the oscillatory activity of the thalamocortical (TC) network in behavioral and electrophysiological experiments. However, theoretical modeling demonstrating how cholinergic neuromodulation of thalamocortical rhythms during non-rapid eye movement (NREM) sleep might occur has been lacking. In this paper, we first develop a novel computational model (TC-ACH) by incorporating a cholinergic neuron population (CH) into the classical thalamo-cortical circuitry, where connections between populations are modeled in accordance with existing knowledge. The neurotransmitter acetylcholine (ACH) released by neurons in CH, which is able to change the discharge activity of thalamocortical neurons, is the primary focus of our work. Simulation results with our TC-ACH model reveal that the cholinergic projection activity is a key factor in modulating oscillation patterns in three ways: (1) transitions between different patterns of thalamocortical oscillations are dramatically modulated through diverse projection pathways; (2) the model expresses a stable spindle oscillation state with certain parameter settings for the cholinergic projection from CH to thalamus, and more spindles appear when the strength of cholinergic input from CH to thalamocortical neurons increases; (3) the duration of oscillation patterns during NREM sleep including K-complexes, spindles, and slow oscillations is longer when cholinergic input from CH to thalamocortical neurons becomes stronger. Our modeling results provide insights into the mechanisms by which the sleep state is controlled, and provide a theoretical basis for future experimental and clinical studies.

NREM sleep in the rodent neocortex and hippocampus reflects excitable dynamics

During non-rapid eye movement (NREM) sleep, neuronal populations in the mammalian forebrain alternate between periods of spiking and inactivity. Termed the slow oscillation in the neocortex and sharp wave-ripples in the hippocampus, these alternations are often considered separately but are both crucial for NREM functions. By directly comparing experimental observations of naturally-sleeping rats with a mean field model of an adapting, recurrent neuronal population, we find that the neocortical alternations reflect a dynamical regime in which a stable active state is interrupted by transient inactive states (slow waves) while the hippocampal alternations reflect a stable inactive state interrupted by transient active states (sharp waves). We propose that during NREM sleep in the rodent, hippocampal and neocortical populations are excitable: each in a stable state from which internal fluctuations or external perturbation can evoke the stereotyped population events that mediate NREM functions.

Sleep Modelling across Physiological Levels

Sleep and circadian rhythms are regulated across multiple functional, spatial and temporal levels: from genes to networks of coupled neurons and glial cells, to large scale brain dynamics and behaviour. The dynamics at each of these levels are complex and the interaction between the levels is even more so, so research have mostly focused on interactions within the levels to understand the underlying mechanisms—the so-called reductionist approach. Mathematical models were developed to test theories of sleep regulation and guide new experiments at each of these levels and have become an integral part of the field. The advantage of modelling, however, is that it allows us to simulate and test the dynamics of complex biological systems and thus provides a tool to investigate the connections between the different levels and study the system as a whole. In this paper I review key models of sleep developed at different physiological levels and discuss the potential for an integrated systems biology approach for sleep regulation across these levels. I also highlight the necessity of building mechanistic connections between models of sleep and circadian rhythms across these levels.

Classifying dynamic transitions in high dimensional neural mass models: A random forest approach

Neural mass models (NMMs) are increasingly used to uncover the large-scale mechanisms of brain rhythms in health and disease. The dynamics of these models is dependent upon the choice of parameters, and therefore it is crucial to be able to understand how dynamics change when parameters are varied. Despite being considered low dimensional in comparison to micro-scale, neuronal network models, with regards to understanding the relationship between parameters and dynamics, NMMs are still prohibitively high dimensional for classical approaches such as numerical continuation. Therefore, we need alternative methods to characterise dynamics of NMMs in high dimensional parameter spaces. Here, we introduce a statistical framework that enables the efficient exploration of the relationship between model parameters and selected features of the simulated, emergent model dynamics of NMMs. We combine the classical machine learning approaches of trees and random forests to enable studying the effect that varying multiple parameters has on the dynamics of a model. The method proceeds by using simulations to transform the mathematical model into a database. This database is then used to partition parameter space with respect to dynamic features of interest, using random forests. This allows us to rapidly explore dynamics in high dimensional parameter space, capture the approximate location of qualitative transitions in dynamics and assess the relative importance of all parameters in the model in all dimensions simultaneously. We apply this method to a commonly used NMM in the context of transitions to seizure dynamics. We find that the inhibitory sub-system is most crucial for the generation of seizure dynamics, confirm and expand previous findings regarding the ratio of excitation and inhibition, and demonstrate that previously overlooked parameters can have a significant impact on model dynamics. We advocate the use of this method in future to constrain high dimensional parameter spaces enabling more efficient, person-specific, model calibration.

A Thalamocortical Neural Mass Model of the EEG during NREM Sleep and Its Response to Auditory Stimulation

Few models exist that accurately reproduce the complex rhythms of the thalamocortical system that are apparent in measured scalp EEG and at the same time, are suitable for large-scale simulations of brain activity. Here, we present a neural mass model of the thalamocortical system during natural non-REM sleep, which is able to generate fast sleep spindles (12–15 Hz), slow oscillations (<1 Hz) and K-complexes, as well as their distinct temporal relations, and response to auditory stimuli. We show that with the inclusion of detailed calcium currents, the thalamic neural mass model is able to generate different firing modes, and validate the model with EEG-data from a recent sleep study in humans, where closed-loop auditory stimulation was applied. The model output relates directly to the EEG, which makes it a useful basis to develop new stimulation protocols.

Sleep plays a pivotal role for the consolidation of memory. While REM sleep had originally been the focus of research due to its similarity with wakefulness, more recent studies suggest that different sleep stages are responsible for the consolidation of different types of memory. To better understand the changes in neuronal dynamics between the different sleep stages, neural mass models are a valuable tool, as they relate directly to the large-scale dynamics measured by an EEG. Here, we present a model of the sleeping thalamocortical system. We first show that the isolated thalamic submodule is able to generate different oscillatory behavior found in vivo. Furthermore, the full thalamocortical model reproduces the EEG of sleep stages N2 and N3 and preserves the temporal relationship between cortical K-complexes/slow oscillations and thalamic sleep spindles. A comparison with event related potential data from a recent sleep study in humans demonstrates its possible application in predicting the outcome of external stimulation on EEG rhythms. Our study shows, that a neural mass model incorporating few key mechanisms is sufficient to reproduce the complex brain dynamics observed during sleep.

Timing matters: open-loop stimulation does not improve overnight consolidation of word pairs in humans

The application of auditory clicks during non‐rapid eye movement (NREM) sleep phase‐locked to the up state of the slow oscillation (closed‐loop stimulation) has previously been shown to enhance the consolidation of declarative memories. We designed and applied sequences of three clicks during deep NREM sleep to achieve a quasi‐phase‐dependent open‐loop stimulation. This stimulation was successful in eliciting slow oscillation power in the stimulation period. Although fast and slow spindle power were markedly decreased during the stimulation period, memory consolidation did not differ from control. During putative up states fast spindle power remained, however, at control levels. We conclude that concurrence of slow oscillations and fast spindles suffices to maintain memory consolidation at control levels despite an overall decreased spindle activity.