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Stimulus-induced Epileptic Spike-Wave Discharges in Thalamocortical Model with Disinhibition

View Article: PubMed Central - PubMed

ABSTRACT

Epileptic absence seizure characterized by the typical 2–4 Hz spike-wave discharges (SWD) are known to arise due to the physiologically abnormal interactions within the thalamocortical network. By introducing a second inhibitory neuronal population in the cortical system, here we propose a modified thalamocortical field model to mathematically describe the occurrences and transitions of SWD under the mutual functions between cortex and thalamus, as well as the disinhibitory modulations of SWD mediated by the two different inhibitory interneuronal populations. We first show that stimulation can induce the recurrent seizures of SWD in the modified model. Also, we demonstrate the existence of various types of firing states including the SWD. Moreover, we can identify the bistable parametric regions where the SWD can be both induced and terminated by stimulation perturbations applied in the background resting state. Interestingly, in the absence of stimulation disinhibitory functions between the two different interneuronal populations can also both initiate and abate the SWD, which suggests that the mechanism of disinhibition is comparable to the effect of stimulation in initiating and terminating the epileptic SWD. Hopefully, the obtained results can provide theoretical evidences in exploring dynamical mechanism of epileptic seizures.

No MeSH data available.


Related in: MedlinePlus

Schematic plot of the attractors modified from Hauptmann et al.66 describing the dynamical model of epileptic absence seizure characterized by Spike (‘S’) and wave (‘W’) discharges (SWD) or normal background state.(a) kindling (green arrows) and (b) anti-kindling (red arrows) stimulation can drive the neuronal population indicated by the ball from one attractor beyond the critical position (pink triangles) to another. (c) Phase space portrait showing the bistable region between stable focus (fixed point, red ball) and SWD (stable limit cycle). In the bistable region there exists a separating manifold indicated by the sphere (analogous to the critical positions indicated by pink triangles in (a,b)) between the two states in five dimensional state space. State transitions between the non-seizure and SWD states can occur when the stimulus indicated by the green and red arrows beyond the separatrix occurs.
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f8: Schematic plot of the attractors modified from Hauptmann et al.66 describing the dynamical model of epileptic absence seizure characterized by Spike (‘S’) and wave (‘W’) discharges (SWD) or normal background state.(a) kindling (green arrows) and (b) anti-kindling (red arrows) stimulation can drive the neuronal population indicated by the ball from one attractor beyond the critical position (pink triangles) to another. (c) Phase space portrait showing the bistable region between stable focus (fixed point, red ball) and SWD (stable limit cycle). In the bistable region there exists a separating manifold indicated by the sphere (analogous to the critical positions indicated by pink triangles in (a,b)) between the two states in five dimensional state space. State transitions between the non-seizure and SWD states can occur when the stimulus indicated by the green and red arrows beyond the separatrix occurs.

Mentions: In particular, the stable focus can be considered as the resting state of background EEG, and the high amplitude oscillatory attractor is analogous to the various seizure states including the epileptic SWD discharges, simple tonic and clonic (slow-wave) oscillations. A mathematically simplified double-well potential diagrams (shown in Fig. 8(a,b), modified from Hauptmann et al.66) for the complex attractors by the first approximation is considered to illustrate the impact of a basin of attraction. The first bistable region between non-seizure state (background resting state) and spike and wave discharges (SWD) can be illustrated by considering a double-well potential, where each minimum corresponds to a stable attractor surrounded by a basin of attraction. The rhythmic SWD oscillations serving as a model for epileptic absence seizures is associated with two local minima representing the spike (‘S’) and wave (‘W’) phases of SWD oscillations, while the background saturated firings with a low amplitude and high frequency oscillation serves as the non-seizure state or healthy state. The ball in Fig. 8(a,b) is used as the neuronal population. Once the system, i.e., the ball, exceeds the critical position (pink triangle shown in Fig. 8(a,b)) and enters a particular basin of attraction, it will be attracted by the corresponding attractor and ultimately relaxes into the minimum of the corresponding potential.


Stimulus-induced Epileptic Spike-Wave Discharges in Thalamocortical Model with Disinhibition
Schematic plot of the attractors modified from Hauptmann et al.66 describing the dynamical model of epileptic absence seizure characterized by Spike (‘S’) and wave (‘W’) discharges (SWD) or normal background state.(a) kindling (green arrows) and (b) anti-kindling (red arrows) stimulation can drive the neuronal population indicated by the ball from one attractor beyond the critical position (pink triangles) to another. (c) Phase space portrait showing the bistable region between stable focus (fixed point, red ball) and SWD (stable limit cycle). In the bistable region there exists a separating manifold indicated by the sphere (analogous to the critical positions indicated by pink triangles in (a,b)) between the two states in five dimensional state space. State transitions between the non-seizure and SWD states can occur when the stimulus indicated by the green and red arrows beyond the separatrix occurs.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5120301&req=5

f8: Schematic plot of the attractors modified from Hauptmann et al.66 describing the dynamical model of epileptic absence seizure characterized by Spike (‘S’) and wave (‘W’) discharges (SWD) or normal background state.(a) kindling (green arrows) and (b) anti-kindling (red arrows) stimulation can drive the neuronal population indicated by the ball from one attractor beyond the critical position (pink triangles) to another. (c) Phase space portrait showing the bistable region between stable focus (fixed point, red ball) and SWD (stable limit cycle). In the bistable region there exists a separating manifold indicated by the sphere (analogous to the critical positions indicated by pink triangles in (a,b)) between the two states in five dimensional state space. State transitions between the non-seizure and SWD states can occur when the stimulus indicated by the green and red arrows beyond the separatrix occurs.
Mentions: In particular, the stable focus can be considered as the resting state of background EEG, and the high amplitude oscillatory attractor is analogous to the various seizure states including the epileptic SWD discharges, simple tonic and clonic (slow-wave) oscillations. A mathematically simplified double-well potential diagrams (shown in Fig. 8(a,b), modified from Hauptmann et al.66) for the complex attractors by the first approximation is considered to illustrate the impact of a basin of attraction. The first bistable region between non-seizure state (background resting state) and spike and wave discharges (SWD) can be illustrated by considering a double-well potential, where each minimum corresponds to a stable attractor surrounded by a basin of attraction. The rhythmic SWD oscillations serving as a model for epileptic absence seizures is associated with two local minima representing the spike (‘S’) and wave (‘W’) phases of SWD oscillations, while the background saturated firings with a low amplitude and high frequency oscillation serves as the non-seizure state or healthy state. The ball in Fig. 8(a,b) is used as the neuronal population. Once the system, i.e., the ball, exceeds the critical position (pink triangle shown in Fig. 8(a,b)) and enters a particular basin of attraction, it will be attracted by the corresponding attractor and ultimately relaxes into the minimum of the corresponding potential.

View Article: PubMed Central - PubMed

ABSTRACT

Epileptic absence seizure characterized by the typical 2–4 Hz spike-wave discharges (SWD) are known to arise due to the physiologically abnormal interactions within the thalamocortical network. By introducing a second inhibitory neuronal population in the cortical system, here we propose a modified thalamocortical field model to mathematically describe the occurrences and transitions of SWD under the mutual functions between cortex and thalamus, as well as the disinhibitory modulations of SWD mediated by the two different inhibitory interneuronal populations. We first show that stimulation can induce the recurrent seizures of SWD in the modified model. Also, we demonstrate the existence of various types of firing states including the SWD. Moreover, we can identify the bistable parametric regions where the SWD can be both induced and terminated by stimulation perturbations applied in the background resting state. Interestingly, in the absence of stimulation disinhibitory functions between the two different interneuronal populations can also both initiate and abate the SWD, which suggests that the mechanism of disinhibition is comparable to the effect of stimulation in initiating and terminating the epileptic SWD. Hopefully, the obtained results can provide theoretical evidences in exploring dynamical mechanism of epileptic seizures.

No MeSH data available.


Related in: MedlinePlus