Dynamic origin of spike and wave discharges in the brain
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:
Here, is bias, is Gaussian white noise with zero mean and standard deviation, and and 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
References (94)
- et al.
How does stochastic resonance work within the human brain? - psychophysics of internal and external noise
Chem. Phys.
(2010) - et al.
From stochastic resonance to brain waves
Phys. Lett.
(2000) - et al.
Dependence of absence seizure dynamics on physiological parameter evolution
J. Theor. Biol.
(2018) Corticothalamic feedback
Network models of absence seizures
- et al.
Human brain alpha rhythm: nonlinear oscillation or filtered noise?
Brain Res.
(1999) - et al.
Intermittent spike-wave dynamics in a heterogeneous, spatially extended neural mass model
Neuroimage
(2011) - et al.
Self-organised transients in a neural mass model of epileptogenic tissue dynamics
Neuroimage
(2012) - et al.
Entrainment of brain oscillations by transcranial alternating current stimulation
Curr. Biol.
(2014) - et al.
Thalamo-cortical mechanisms underlying changes in amplitude and frequency of human alpha oscillations
Neuroimage
(2013)
Dynamics underlying spontaneous human alpha oscillations: a data-driven approach
Neuroimage
Dynamics of epileptic seizures: evolution, spreading, and suppression
J. Theor. Biol.
Transition to seizure in photosensitive epilepsy
Epilepsy Res.
Models of neuronal populations: the basic mechanisms of rhythmicity
Prog. Brain Res.
Alpha rhythms: noise, dynamics and models
Int. J. Psychophysiol.
Modeling spike-wave discharges by a complex network of neuronal oscillators
Neural Network.
Evaluating the entrainment of the alpha rhythm during stroboscopic flash stimulation by means of coherence analysis
Med. Eng. Phys.
Photoparoxysmal responses in children: their characteristics and clinical correlates
Pediatr. Neurol.
Modeling absence seizure dynamics: implications for basic mechanisms and measurement of thalamocortical and corticothalamic latencies
J. Theor. Biol.
Out of thin air: hyperventilation-triggered seizures
Brain Res.
Dynamics of the human alpha rhythm: evidence for non-linearity?
Clin. Neurophysiol.
Interneuronal epileptic discharges related to spike-and-wave cortical seizures in behaving monkeys
Electroencephalogr. Clin. Neurophysiol.
Spike-and-wave afterdischarges in cortical somatosensory neurons of cat
Electroencephalogr. Clin. Neurophysiol.
Computational model of thalamo-cortical networks: dynamical control of alpha rhythms in relation to focal attention
Int. J. Psychophysiol.
Dynamics of non-convulsive epileptic phenomena modeled by a bistable neuronal network
Neuroscience
Effects of flash frequency and repetition of intermittent photic stimulation on photoparoxysmal responses
Seizure
Cortical firing and sleep homeostasis
Neuron
The different patterns of the photoparoxysmal response - a genetic study
Electroencephalogr. Clin. Neurophysiol.
Computational models of epileptiform activity
J. Neurosci. Methods
Bifurcation analysis of two coupled Jansen-Rit neural mass models
PLoS One
Dynamics of pattern formation in lateral-inhibition type neural fields
Biol. Cybern.
A brief history on the oscillating roles of thalamus and cortex in absence seizures
Epilepsia
The importance of modeling epileptic seizure dynamics as spatio-temporal patterns
Front. Physiol.
Cellular and network mechanisms of spike-wave seizures
Epilepsia
A unifying explanation of primary generalized seizures through nonlinear brain modeling and bifurcation analysis
Cerebr. Cortex
A stochastic limit cycle oscillator model of the EEG
Biol. Cybern.
Genetic animal models for absence epilepsy: a review of the WAG/Rij strain of rats
Behav. Genet.
Childhood absence epilepsy: genes, channels, neurons and networks
Nat. Rev. Neurosci.
Can GABA A conductances explain the fast oscillation frequency of absence seizures in rodents?
Eur. J. Neurosci.
Photic- and pattern-induced seizures: a review for the epilepsy foundation of America working group
Epilepsia
Network bistability mediates spontaneous transitions between normal and pathological brain states
J. Neurosci.
The electro-encephalogram in epilepsy and in conditions of impaired consciousness
Arch. Neurol. Psychiatr.
Bifurcation analysis of Jansen's neural mass model
Neural Comput.
α-Oscillations in the monkey sensorimotor network influence discrimination performance by rhythmical inhibition of neuronal spiking
Proc. Natl. Acad. Sci. Unit. States Am.
Are absence epilepsy and nocturnal frontal lobe epilepsy system epilepsies of the sleep/wake system?
Behav. Neurol.
Human EEG responses to 1-100 Hz flicker: resonance phenomena in visual cortex and their potential correlation to cognitive phenomena
Exp. Brain Res.
Shaping intrinsic neural oscillations with periodic stimulation
J. Neurosci.
Cited by (14)
Initiation and termination of epilepsy induced by Lévy noise: A view from the cortical neural mass model
2023, Chaos, Solitons and FractalsThe hidden, period-adding, mixed-mode oscillations and control in a HR neuron under electromagnetic induction
2021, Chaos, Solitons and FractalsCitation Excerpt :The purpose of establishment of neuron model is to use mathematical language to represent the complex discharge activities. Currently, various neurons and simplified models have been established [2-5]. Since the Hindmarsh-Rose (HR) neuron model was established in 1982, the model has been widely used to study the discharge activity and bifurcation behavior of neurons.
Characterization of information processing in the subthalamic area of Parkinson's patients
2020, NeuroImageCitation Excerpt :One possibility is that afferent noise from the periphery, transmitted via the hyperdirect pathway, increases the baseline beta-activity of subthalamic populations, thereby effectively lowering the threshold for spike generations. Such an effect of noise on subthreshold oscillations is known as stochastic resonance (for a review see (McDonnell and Abbott, 2009)) and has been observed e.g. in hippocampal neurons (Stacey and Durand, 2000), computational models for epilepsy (Sohanian Haghighi and Markazi 2019), muscle spindles (Cordo et al., 1996) and the auditory system (Zeng et al., 2000). Another computational study assumes stochastic resonance to be a major mechanism of the basal ganglia to initiate movements (Chakravarthy, 2013).
Resonance transmission of multiple independent signals in cortical networks
2020, NeurocomputingCitation Excerpt :It is shown that the ability of neurons and neural circuits to process weak input signal can be significantly enhanced by adding noise to the system [28-30]. Besides, cellular diversity, synaptic coupling mode and the structure of the underlying network can enhance the resonance of neural network, while in turn resonance can be used as amplification of information transmission in excitable systems [31-34]. It is therefore suggested that stochastic resonance is of great importance for understanding the weak signal detection and information propagation in neural system [35].
Dynamic effect of electromagnetic induction on epileptic waveform
2022, BMC Neuroscience