Dependence of absence seizure dynamics on physiological parameter evolution

Kir4.1 channel and voltage-gated calcium channel of astrocyte account for the transition dynamics of seizures

Astrocytes have an important role in the indirect regulation of neuronal excitability. The abnormalities of their ion channels cause neurons to discharge abnormally, which may induce seizures. The inwardly rectifying potassium channel 4.1 (Kir4.1 channel) and the voltage-gated calcium channel (VGCC) of an astrocyte play important roles in maintaining the homeostasis of these potassium and calcium ions, and have been found to be associated with seizures. However, the underlying mechanisms by which they induce seizures remain unclear. This paper established a neuron-astrocyte network model, which is a model consisting of a neuron and an astrocyte, to explore some mechanisms of epileptic seizures. Through a series of simulations based on this model, the results showed that low conductance of Kir4.1 channel can induce spontaneous periodic epileptic activity (SPEA) whereas higher conductance results in spontaneous periodic bursting event (SPBE) and high-frequency tonic discharges (HFTD). The abnormalities of VGCC also lead to the generation of SPEA and SPBE. As the changes of potassium concentration in the largest nearby reservoir which is analogous to a bath solution that contains a specific concentration of potassium, SPEA can undergo a process from appearance to disappearance. Thus, the research findings showed that the transitions of seizure-like discharges provide further theoretical analyses to clarify the complex mechanism of seizures.

Sleep and circadian rhythms modeling: From hypothalamic regulatory networks to cortical dynamics and behavior

Sleep and circadian rhythms are regulated by dynamic physiologic processes that operate across multiple spatial and temporal scales. These include, but are not limited to, genetic oscillators, clearance of waste products from the brain, dynamic interplay among brain regions, and propagation of local dynamics across the cortex. The combination of these processes, modulated by environmental cues, such as light-dark cycles and work schedules, represents a complex multiscale system that regulates sleep-wake cycles and brain dynamics. Physiology-based mathematical models have successfully explained the mechanisms underpinning dynamics at specific scales and are a useful tool to investigate interactions across multiple scales. They can help answer questions such as how do electroencephalographic (EEG) features relate to subthalamic neuron activity? Or how are local cortical dynamics regulated by the homeostatic and circadian mechanisms? In this chapter, we review two types of models that are well-positioned to consider such interactions. Part I of the chapter focuses on the subthalamic sleep regulatory networks and a model of arousal dynamics capable of predicting sleep, circadian rhythms, and cognitive outputs. Part II presents a model of corticothalamic circuits, capable of predicting spatial and temporal EEG features. We then discuss existing approaches and unsolved challenges in developing unified multiscale models.

Criticality, Connectivity, and Neural Disorder: A Multifaceted Approach to Neural Computation

It has been hypothesized that the brain optimizes its capacity for computation by self-organizing to a critical point. The dynamical state of criticality is achieved by striking a balance such that activity can effectively spread through the network without overwhelming it and is commonly identified in neuronal networks by observing the behavior of cascades of network activity termed "neuronal avalanches." The dynamic activity that occurs in neuronal networks is closely intertwined with how the elements of the network are connected and how they influence each other's functional activity. In this review, we highlight how studying criticality with a broad perspective that integrates concepts from physics, experimental and theoretical neuroscience, and computer science can provide a greater understanding of the mechanisms that drive networks to criticality and how their disruption may manifest in different disorders. First, integrating graph theory into experimental studies on criticality, as is becoming more common in theoretical and modeling studies, would provide insight into the kinds of network structures that support criticality in networks of biological neurons. Furthermore, plasticity mechanisms play a crucial role in shaping these neural structures, both in terms of homeostatic maintenance and learning. Both network structures and plasticity have been studied fairly extensively in theoretical models, but much work remains to bridge the gap between theoretical and experimental findings. Finally, information theoretical approaches can tie in more concrete evidence of a network's computational capabilities. Approaching neural dynamics with all these facets in mind has the potential to provide a greater understanding of what goes wrong in neural disorders. Criticality analysis therefore holds potential to identify disruptions to healthy dynamics, granted that robust methods and approaches are considered.

Neuroproteomics in Epilepsy: What Do We Know so Far?

Epilepsies are chronic neurological diseases that affect approximately 2% of the world population. In addition to being one of the most frequent neurological disorders, treatment for patients with epilepsy remains a challenge, because a proportion of patients do not respond to the antiseizure medications that are currently available. This results in a severe economic and social burden for patients, families, and the healthcare system. A characteristic common to all forms of epilepsy is the occurrence of epileptic seizures that are caused by abnormal neuronal discharges, leading to a clinical manifestation that is dependent on the affected brain region. It is generally accepted that an imbalance between neuronal excitation and inhibition generates the synchronic electrical activity leading to seizures. However, it is still unclear how a normal neural circuit becomes susceptible to the generation of seizures or how epileptogenesis is induced. Herein, we review the results of recent proteomic studies applied to investigate the underlying mechanisms leading to epilepsies and how these findings may impact research and treatment for these disorders.

Effects of physiological parameter evolution on the dynamics of tonic-clonic seizures

The temporal and spectral characteristics of tonic-clonic seizures are investigated using a neural field model of the corticothalamic system in the presence of a temporally varying connection strength between the cerebral cortex and thalamus. Increasing connection strength drives the system into ∼ 10 Hz seizure oscillations once a threshold is passed and a subcritical Hopf bifurcation occurs. In this study, the spectral and temporal characteristics of tonic-clonic seizures are explored as functions of the relevant properties of physiological connection strengths, such as maximum strength, time above threshold, and the ramp rate at which the strength increases or decreases. Analysis shows that the seizure onset time decreases with the maximum connection strength and time above threshold, but increases with the ramp rate. Seizure duration and offset time increase with maximum connection strength, time above threshold, and rate of change. Spectral analysis reveals that the power of nonlinear harmonics and the duration of the oscillations increase as the maximum connection strength and the time above threshold increase. A secondary limit cycle at ∼ 18 Hz, termed a saddle-cycle, is also seen during seizure onset and becomes more prominent and robust with increasing ramp rate. If the time above the threshold is too small, the system does not reach the 10 Hz limit cycle, and only exhibits 18 Hz saddle-cycle oscillations. It is also seen that the time to reach the saturated large amplitude limit-cycle seizure oscillation from both the instability threshold and from the end of the saddle-cycle oscillations is inversely proportional to the square root of the ramp rate.

Unified dynamics of interictal events and absence seizures

The dynamics of interictal events between absence seizures and their relationship to seizures themselves are investigated by employing a neural field model of the corticothalamic system. Interictal events are modeled as being due to transient parameter excursions beyond the seizure threshold, in the present case by sufficiently temporally varying the connection strength between the cerebral cortex and the thalamus. Increasing connection strength drives the system into ∼3-Hz seizure oscillations via a supercritical Hopf bifurcation once the linear instability threshold is passed. Depending on the time course of the excursion above threshold, different interictal activity event dynamics are seen in the time series of corticothalamic fields. These resemble experimental interictal time series observed via electroencephalography. It is found that the morphology of these events depends on the magnitude and duration of the excursion above threshold. For a large-amplitude excursion of short duration, events resemble interictal spikes, where one large spike is seen, followed by small damped oscillations. For a short excursion with long duration, events like observed interictal periodic sharp waves are seen. When both amplitude and duration above threshold are large, seizure oscillations are seen. Using these outcomes, proximity to seizure can be estimated and tracked.

Dynamic origin of spike and wave discharges in the brain

Spike and wave discharges are the main electrographic characteristic of a number of epileptic brain disorders including childhood absence epilepsy and photosensitive epilepsy. The basic dynamic mechanism that underlies the occurrence of these abnormal electrical patterns in the brain is not well understood. The current paper aims to provide a dynamic explanation for features and generation mechanism of spike and wave discharges in the brain. The main proposition of this study is that epileptic seizures could be interpreted as a resonance phenomenon rather than a limit cycle behavior. To shows this, a revised version of Jansen-Rit neural mass model is employed. The system can switch between monostable and bistable regimes, which are considered in this paper as wake and sleep states of the brain, respectively. In particular, it is shown that, in monostable region, the model can depict the alpha rhythm and alpha rhythm suppression due to mental activity. Frequency responses of the model near the bistable regime demonstrate that high amplitude harmonic excitation may lead to spike and wave like oscillations. Based on the computational results and the concept of stochastic resonance, a model for absence epilepsy is presented which can simulate spontaneous transitions between ictal and interictal states. Finally, it is shown that spike and wave discharges during epileptic seizures can be explained as a resonance phenomenon in a nonlinear system.