Phase-locked cluster oscillations in periodically forced integrate-and-fire-or-burst neuronal populations

Cross-Frequency Slow Oscillation–Spindle Coupling in a Biophysically Realistic Thalamocortical Neural Mass Model

Sleep manifests itself by the spontaneous emergence of characteristic oscillatory rhythms, which often time-lock and are implicated in memory formation. Here, we analyze a neural mass model of the thalamocortical loop in which the cortical node can generate slow oscillations (approximately 1 Hz) while its thalamic component can generate fast sleep spindles of σ-band activity (12–15 Hz). We study the dynamics for different coupling strengths between the thalamic and cortical nodes, for different conductance values of the thalamic node's potassium leak and hyperpolarization-activated cation-nonselective currents, and for different parameter regimes of the cortical node. The latter are listed as follows: (1) a low activity (DOWN) state with noise-induced, transient excursions into a high activity (UP) state, (2) an adaptation induced slow oscillation limit cycle with alternating UP and DOWN states, and (3) a high activity (UP) state with noise-induced, transient excursions into the low activity (DOWN) state. During UP states, thalamic spindling is abolished or reduced. During DOWN states, the thalamic node generates sleep spindles, which in turn can cause DOWN to UP transitions in the cortical node. Consequently, this leads to spindle-induced UP state transitions in parameter regime (1), thalamic spindles induced in some but not all DOWN states in regime (2), and thalamic spindles following UP to DOWN transitions in regime (3). The spindle-induced σ-band activity in the cortical node, however, is typically the strongest during the UP state, which follows a DOWN state “window of opportunity” for spindling. When the cortical node is parametrized in regime (3), the model well explains the interactions between slow oscillations and sleep spindles observed experimentally during Non-Rapid Eye Movement sleep. The model is computationally efficient and can be integrated into large-scale modeling frameworks to study spatial aspects like sleep wave propagation.

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.

Transitions in information processing dynamics at the whole-brain network level are driven by alterations in neural gain

A key component of the flexibility and complexity of the brain is its ability to dynamically adapt its functional network structure between integrated and segregated brain states depending on the demands of different cognitive tasks. Integrated states are prevalent when performing tasks of high complexity, such as maintaining items in working memory, consistent with models of a global workspace architecture. Recent work has suggested that the balance between integration and segregation is under the control of ascending neuromodulatory systems, such as the noradrenergic system, via changes in neural gain (in terms of the amplification and non-linearity in stimulus-response transfer function of brain regions). In a previous large-scale nonlinear oscillator model of neuronal network dynamics, we showed that manipulating neural gain parameters led to a 'critical' transition in phase synchrony that was associated with a shift from segregated to integrated topology, thus confirming our original prediction. In this study, we advance these results by demonstrating that the gain-mediated phase transition is characterized by a shift in the underlying dynamics of neural information processing. Specifically, the dynamics of the subcritical (segregated) regime are dominated by information storage, whereas the supercritical (integrated) regime is associated with increased information transfer (measured via transfer entropy). Operating near to the critical regime with respect to modulating neural gain parameters would thus appear to provide computational advantages, offering flexibility in the information processing that can be performed with only subtle changes in gain control. Our results thus link studies of whole-brain network topology and the ascending arousal system with information processing dynamics, and suggest that the constraints imposed by the ascending arousal system constrain low-dimensional modes of information processing within the brain.

Cluster burst synchronization in a scale-free network of inhibitory bursting neurons

We consider a scale-free network of inhibitory Hindmarsh-Rose (HR) bursting neurons, and make a computational study on coupling-induced cluster burst synchronization by varying the average coupling strength J 0 . For sufficiently small J 0 , non-cluster desynchronized states exist. However, when passing a critical point J c ∗ ( ≃ 0.16 ) , the whole population is segregated into 3 clusters via a constructive role of synaptic inhibition to stimulate dynamical clustering between individual burstings, and thus 3-cluster desynchronized states appear. As J 0 is further increased and passes a lower threshold J l ∗ ( ≃ 0.78 ) , a transition to 3-cluster burst synchronization occurs due to another constructive role of synaptic inhibition to favor population synchronization. In this case, HR neurons in each cluster make burstings every 3rd cycle of the instantaneous burst rate R w ( t ) of the whole population, and exhibit burst synchronization. However, as J 0 passes an intermediate threshold J m ∗ ( ≃ 5.2 ) , HR neurons fire burstings intermittently at a 4th cycle of R w ( t ) via burst skipping rather than at its 3rd cycle, and hence they begin to make intermittent hoppings between the 3 clusters. Due to such intermittent intercluster hoppings via burst skippings, the 3 clusters become broken up (i.e., the 3 clusters are integrated into a single one). However, in spite of such break-up (i.e., disappearance) of the 3-cluster states, (non-cluster) burst synchronization persists in the whole population, which is well visualized in the raster plot of burst onset times where bursting stripes (composed of burst onset times and indicating burst synchronization) appear successively. With further increase in J 0 , intercluster hoppings are intensified, and bursting stripes also become dispersed more and more due to a destructive role of synaptic inhibition to spoil the burst synchronization. Eventually, when passing a higher threshold J h ∗ ( ≃ 17.8 ) a transition to desynchronization occurs via complete overlap between the bursting stripes. Finally, we also investigate the effects of stochastic noise on both 3-cluster burst synchronization and intercluster hoppings.

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.

Synchronization-desynchronization transitions in complex networks: an interplay of distributed time delay and inhibitory nodes

We investigate the combined effects of distributed delay and the balance between excitatory and inhibitory nodes on the stability of synchronous oscillations in a network of coupled Stuart-Landau oscillators. To this end a symmetric network model is proposed for which the stability can be investigated analytically. It is found that beyond a critical inhibition ratio, synchronization tends to be unstable. However, increasing distributional widths can counteract this trend, leading to multiple resynchronization transitions at relatively high inhibition ratios. The extended applicability of the results is confirmed by numerical studies on asymmetrically perturbed network topologies. All investigations are performed on two distribution types, a uniform distribution and a Γ distribution.