Elsevier

NeuroImage

Volume 197, 15 August 2019, Pages 69-79
NeuroImage

Dynamic origin of spike and wave discharges in the brain

https://doi.org/10.1016/j.neuroimage.2019.04.047Get rights and content

Highlights

  • A revised version of Jansen-Rit neural mass model is introduced.

  • 3 Hz Spike-wave discharges can be interpreted as a resonance in a bistable system.

  • A new computational model is developed to simulate spontaneous spike-wave seizures.

Abstract

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.

Introduction

In 1935, a few short years after the discovery of the electroencephalogram (EEG) by Hans Berger, Gibbs and his colleagues presented a clear description of brain electrical activity during clinical seizures (Gibbs et al., 1935). They found large amplitude 3 Hz approximately sinusoidal waves including sharp negative spikes in EEGs from twelve patients with petit mal (absence) epilepsy. Since that time, spike-wave complexes are known as characteristic oscillatory patterns that can be observed in EEG signals during absence seizures. Absence seizures are often found in children typically between 4 and 10 years of age and cause lapses in consciousness (Stafstrom and Carmant, 2015). These seizures usually last 5–20 s and the frequency of occurrence varies from a few to hundreds per day. Seizures commonly start and end abruptly and the amplitude of complexes increases and the repetition frequency decreases during the ictal phase. SWDs are also associated with photosensitive epilepsy, a type of epilepsy induced by visual stimuli e.g. flashing or flickering lights (Fisher et al., 2005). Finding spike and wave pattern in EEG during intermittent photic stimulation is a common examination for the diagnosis of photosensitive epilepsy. Additionally, SWDs can be found in some other types of epilepsy such as Lennox-Gastaut syndrome and juvenile myoclonic epilepsy with a little difference in recurrence frequency of discharges (Stafstrom and Carmant, 2015).

Absence epilepsy is considered to be a brain disorder with a genetic aetiology (Crunelli and Leresche, 2002). There is a hot debate whether the location of SWD generators is in the cortex or the thalamus (Avoli, 2012). Experimental findings seem to be controversial (Blumenfeld, 2005) but more evidence support the cortical origin theory (Meeren et al., 2005, 2002) for human subjects (Moeller et al., 2010; Seneviratne et al., 2014). A fundamental question is whether the SWDs can be generated only in the cortex (or thalamus) or the interaction between cortical and sub-cortical areas is necessary.

Mathematical neural models are useful tools to study effects of various parameters and dynamic mechanisms underlying the brain state variations. Computational models of SWD could be divided into two main groups: thalamocortical models and network models (Wendling et al., 2016). Thalamocortical models consider the interactions of cortical and thalamic neuronal populations. Usually, both excitatory and inhibitory populations in cortex module and reticular nucleus and relay nuclei in thalamic module are modeled in a thalamocortical network. In order to develop such a thalamocortical model, Lopes da Silva and his group (Lopes da Silva et al., 2003) extended the alpha rhythm model (Lopes da Silva et al., 1974) and then showed that the extended model has a bistable regime (coexistence of a fixed point and a limit cycle). So, the model was used to simulate spontaneous transitions between normal and epileptic states in a noisy environment (Suffczynski et al., 2004). In the same years, Robinson and his colleagues developed another corticothalamic model (Robinson et al., 2003, 2002). The model is sensitive to its parameters and depending to the parameters values, various dynamical regimes including 3 Hz spike and wave limit cycle can be found in the model (Breakspear et al., 2006; Deeba et al., 2018; Kim et al., 2009; Roberts and Robinson, 2008; Rodrigues et al., 2009; Yang and Robinson, 2017). Another group of researchers extended Amari neural field model (Amari, 1977) in order to develop another thalamocortical model (Taylor et al., 2013a) based on previous models of SWD (Taylor and Baier, 2011; Wang et al., 2012). It was shown that the model is excitable and so a seizure can be simulated as a transient response to stimulation. The model can also work in a bistable regime (Taylor et al., 2015) and in this case and in the absence of noise, if a second stimulus is not applied the SWD will never end. Besides these thalamocortical models, a number of network models are also available. Network models usually constructed by making networks of neuronal oscillators such as Hodgkin-Huxley model or Fitzhugh-Nagumo neural model in order to simulate SWDs in the brain (Destexhe, 2014, 2008; Medvedeva et al., 2018). However, studies of networks of neural mass models are also available in the literature (Goodfellow et al., 2012; Peter Neal Taylor et al., 2013a,b). Based on analysis of a network of coupled neural population models (Goodfellow et al., 2011) the authors introduced intermittency (spontaneous bursting behavior) as another possible dynamic mechanism of SWD.

The mentioned studies used various mathematical models and proposed different dynamic mechanisms such as bistability, bifurcation, excitability or intermittency (Baier et al., 2012) to describe transitions between ictal and interictal states. However, most of them have a common characteristic: at least one limit cycle attractor exists in the model. Noise, variation of parameters, perturbation or internal dynamics may push the dynamics into this limit cycle. Since more than one single mechanism may contribute to initiation and propagation of epileptic seizures in different cases, alternative descriptive mechanisms of transitions between normal and abnormal epileptic states should be taken into account. Moreover, there are a number of clinical and experimental observations that could not be explained straightforwardly when a limit cycle attractor is considered as the origin of SWDs. For example, initial studies by Steriade and colleagues showed that 3 Hz SWDs can be induced by 10 Hz electrical stimulation of the brain, in both the monkey (Steriade, 1974) and the cat (Steriade and Yossif, 1974). A recent study also revealed a causal relationship between rhythmic stimulation and seizure initiation in WAG/Rij rats using intracortical optogenetic stimulation (Wagner et al., 2015). The study also showed seizures were induced more effectively when the stimulation frequency is around 10 Hz. In addition, generalized 3 Hz spike and waves are the most common pattern in photoparoxysmal response to rhythmic visual stimulations (Fisher et al., 2005; Waltz et al., 1992). In general, there exists a lack of knowledge about the underlying dynamic mechanism responsible for such abnormal EEG response to visual stimulations at certain frequencies.

Here, and in line with our previous work (Sohanian Haghighi and Markazi, 2017), we hypothesis that epileptic seizures could be considered as a resonance phenomenon rather than a limit cycle behavior. To provide some computational evidence for this hypothesis, the well-known Jansen-Rit neural mass model is used. The model is first described and revised by a change in one of its parameters. Next, frequency responses of the revised model are obtained to find out possibility of spike and wave like response due to harmonic excitations. Finally, based on the obtained results, we try to explain some related clinical and experimental findings from a dynamical system point of view.

Section snippets

Model description

One of the earliest neural mass models which many other neural population models are developed based upon this model, is presented by Lopes da Silva (Lopes da Silva et al., 1974). The model contains of two kinds of neural populations, an excitatory population, representing pyramidal neurons and an inhibitory cell population, representing inhibitory interneurons. The two populations are connected via a feedback loop with two coupling constants that enables the model to simulate rhythmical

Results

In order to explore the model dynamics in monostable region of Fig. 2b, a sinusoidal waveform signal is added to input of the model, which was originally a biased white noise:p(t)=p0+pn+pssin(2πfst)

Here, p0 is bias, pn is Gaussian white noise with zero mean and standard deviation, σn and ps and fs are amplitude and frequency of the sinusoidal component. The Gaussian noise is generated with 40 Hz constant sampling frequency. Frequency responses of the model are obtained in the absence of the

Discussion

The current study was based on the hypothesis that the brain works like a resonator, which can be excited by either internal or external sources. This hypothesis is supported by findings of brain stimulation experiments with different techniques including sensory stimulation (Herrmann, 2001; Spiegler et al., 2011; Zaehle et al., 2010), transcranial magnetic stimulation (Rosanova et al., 2009) and transcranial alternating current stimulation (Helfrich et al., 2014). The brain response to a

Conclusion

In this study, we tried to explain underling dynamic mechanism of spike and wave discharges in the brain. The well-known Jansen-Rit neural mass model was first refreshed by revising the connectivity constant parameter. Bifurcation analysis showed the revised model has two distinct regions for constant inputs: a monostable region with a fixed point (wake state) and a bistable region with two stable fixed points (sleep state). Frequency response of the model in the monostable regime subjected to

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