Figure - available from: Journal of Computational Neuroscience
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Phase diagram of the dominant frequency in parameter space. Color indicates the dominant frequency of ϕe at each point. Colorbar is in units of Hz. The white line indicates the theoretical boundary at which instability sets in as calculated from the system Jacobian. The stable zone is in the upper left quadrant. Parameters are as in Tables 1 and 2
Source publication
Epileptiform discharges on an isolated cortex are explored using neural field theory. A neural field model of the isolated cortex is used that consists of three neural populations, excitatory, inhibitory, and excitatory bursting. Mechanisms by which an isolated cortex gives rise to seizure-like waveforms thought to underly pathological EEG waveform...
Citations
This work presents a fractional-order Wilson-Cowan model derivation under Caputo’s formalism, considering an order of \(0<\alpha \le 1\). To that end, we propose memory-dependent response functions and average neuronal excitation functions that permit us to naturally arrive at a fractional-order model that incorporates past dynamics into the description of synaptically coupled neuronal populations’ activity. We then shift our focus on a particular example, aiming to analyze the fractional-order dynamics of the disinhibited cortex. This system mimics cortical activity observed during neurological disorders such as epileptic seizures, where an imbalance between excitation and inhibition is present, which allows brain dynamics to transition to a hyperexcited activity state. In the context of the first-order mathematical model, we recover traditional results showing a transition from a low-level activity state to a potentially pathological high-level activity state as an external factor modifies cortical inhibition. On the other hand, under the fractional-order formulation, we establish novel results showing that the system resists such transition as the order is decreased, permitting the possibility of staying in the low-activity state even with increased disinhibition. Furthermore, considering the memory index interpretation of the fractional-order model motivation here developed, our results establish that by increasing the memory index, the system becomes more resistant to transitioning towards the high-level activity state. That is, one possible effect of the memory index is to stabilize neuronal activity. Noticeably, this neuronal stabilizing effect is similar to homeostatic plasticity mechanisms. To summarize our results, we present a two-parameter structural portrait describing the system’s dynamics dependent on a proposed disinhibition parameter and the order. We also explore numerical model simulations to validate our results.
This work presents a fractional-order Wilson-Cowan model derivation under Caputo’s formalism, considering an order of 0 < α ≤ 1. To that end, we propose memory-dependent response functions and average neuronal excitation functions that permit us to naturally arrive to a fractional-order model that incorporates past dynamics into the description of synaptically coupled neuronal populations' activity. We then focus on a particular example to analyze the fractional-order dynamics of the disinhibited cortex. This system mimics cortical activity during neurological disorders such as epileptic seizures, which allows brain dynamics to transition to a hyperexcited activity state. In the first-order mathematical model, we recover traditional results showing a transition from a low-level activity state to a plausibly pathological high-level activity state as an external factor modifies cortical inhibition. On the other hand, under the fractional-order formulation, we establish novel results showing that the system resists such transition as the order is decreased, permitting the possibility of staying in the low-activity state even with increased disinhibition. Furthermore, considering the memory index interpretation of the fractional-order model motivation here developed, our results establish that by increasing the memory index, the system becomes more resistant to transitioning towards the high-level activity state. That is, a possible effect of the memory index is to stabilize neuronal activity. To summarize our results, we present a two-parameter structural portrait describing the system’s dynamics dependent on a proposed disinhibition parameter and the order. We also explore numerical model simulations to validate our results.
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.
