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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

Bifurcation diagram showing the extrema of the mean of excitatory and inhibitory neuronal populations, PY and IN1.Inhibition-induced SWD discharges without stimulation. Corresponding to the Fig. 4(a), as the coupling strength k4 varies in the region [0, 2] with k10 = 3, with the inhibition function k6 increasing from (a) k6 = 1.05, (b) k6 = 1.063, (c) k6 = 1.078, (d) k6 = 1.095, and to (e) k6 = 1.106, the low saturated firings on the right short regions of k4 = 1 can be gradually disturbed into the SWD discharges. In addition, compared to the Fig. 4(a), after the introducing of inhibition function performed by the k6, as the increasing of k4, the system displays richer dynamical transition behaviors, showing the larger regions of saturated firings. Particularly, the small k4 can terminate the epileptic tonic seizures.
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f10: Bifurcation diagram showing the extrema of the mean of excitatory and inhibitory neuronal populations, PY and IN1.Inhibition-induced SWD discharges without stimulation. Corresponding to the Fig. 4(a), as the coupling strength k4 varies in the region [0, 2] with k10 = 3, with the inhibition function k6 increasing from (a) k6 = 1.05, (b) k6 = 1.063, (c) k6 = 1.078, (d) k6 = 1.095, and to (e) k6 = 1.106, the low saturated firings on the right short regions of k4 = 1 can be gradually disturbed into the SWD discharges. In addition, compared to the Fig. 4(a), after the introducing of inhibition function performed by the k6, as the increasing of k4, the system displays richer dynamical transition behaviors, showing the larger regions of saturated firings. Particularly, the small k4 can terminate the epileptic tonic seizures.

Mentions: However, in contrast to the abatement effect of IN2 on the stimulus-induced SWD, we further wonder if the output from IN2 can also induce the onsets of SWD in the absence of stimulation, comparable to the effect of single-pulse stimulation. This may be beneficial for us to biologically understand the inner mechanisms underlying the spontaneous epileptic SWD and search the biological therapies instead of the clinical stimulation control. Therefore, in the following section we will investigate the initiation effect of IN2 on the SWD oscillation. Here, we take k10 = 3 with k4 varying in the interval [0, 2] and k4 = 1 with k10 varying in the interval [0, 8], respectively. As shown in the Fig. 10(a), without the impact of stimulation, i.e., as the k4 varies in [0, 2] with fixing k10 = 3, the system has a good robustness against the relatively weak inhibitory regulation function of second inhibitory neuronal population as k6 is lower around k6 = 1.05. And, on this occasion, within the right short parameter interval of k4 = 1 the system always displays the background low saturated firings (i.e., the low-amplitude and high-frequency tonic oscillations as shown in the inset of Fig. 2(a)). However, as the k6 is increased into k6 = 1.063 (Fig. 10(b)), similar to the single-point stimulation, inhibition can also induce the occurrence of SWD. With the further increasing of inhibitory function, i.e., k6 becomes larger, the larger parameter intervals can be found, where inhibition-induced SWD occurs. Compared to Fig. 10(b), as k6 is increased into k6 = 1.106 (Fig. 10(e)), enough large inhibition function can induce the occurrence of SWD on the whole parameter interval of stimulus-induced SWD. In addition, we can also see that inhibition can terminate the epileptic tonic seizures on the parameter intervals of small k4 with k10 = 3. Particularly, during the increasing of k6 saturated firing states can be repeatedly induced by the inhibition, which results in the recurrent onsets of various epileptic seizures including the simple tonic oscillations, SWD discharges and simple clonic (slow-wave) oscillations.


Stimulus-induced Epileptic Spike-Wave Discharges in Thalamocortical Model with Disinhibition
Bifurcation diagram showing the extrema of the mean of excitatory and inhibitory neuronal populations, PY and IN1.Inhibition-induced SWD discharges without stimulation. Corresponding to the Fig. 4(a), as the coupling strength k4 varies in the region [0, 2] with k10 = 3, with the inhibition function k6 increasing from (a) k6 = 1.05, (b) k6 = 1.063, (c) k6 = 1.078, (d) k6 = 1.095, and to (e) k6 = 1.106, the low saturated firings on the right short regions of k4 = 1 can be gradually disturbed into the SWD discharges. In addition, compared to the Fig. 4(a), after the introducing of inhibition function performed by the k6, as the increasing of k4, the system displays richer dynamical transition behaviors, showing the larger regions of saturated firings. Particularly, the small k4 can terminate the epileptic tonic seizures.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f10: Bifurcation diagram showing the extrema of the mean of excitatory and inhibitory neuronal populations, PY and IN1.Inhibition-induced SWD discharges without stimulation. Corresponding to the Fig. 4(a), as the coupling strength k4 varies in the region [0, 2] with k10 = 3, with the inhibition function k6 increasing from (a) k6 = 1.05, (b) k6 = 1.063, (c) k6 = 1.078, (d) k6 = 1.095, and to (e) k6 = 1.106, the low saturated firings on the right short regions of k4 = 1 can be gradually disturbed into the SWD discharges. In addition, compared to the Fig. 4(a), after the introducing of inhibition function performed by the k6, as the increasing of k4, the system displays richer dynamical transition behaviors, showing the larger regions of saturated firings. Particularly, the small k4 can terminate the epileptic tonic seizures.
Mentions: However, in contrast to the abatement effect of IN2 on the stimulus-induced SWD, we further wonder if the output from IN2 can also induce the onsets of SWD in the absence of stimulation, comparable to the effect of single-pulse stimulation. This may be beneficial for us to biologically understand the inner mechanisms underlying the spontaneous epileptic SWD and search the biological therapies instead of the clinical stimulation control. Therefore, in the following section we will investigate the initiation effect of IN2 on the SWD oscillation. Here, we take k10 = 3 with k4 varying in the interval [0, 2] and k4 = 1 with k10 varying in the interval [0, 8], respectively. As shown in the Fig. 10(a), without the impact of stimulation, i.e., as the k4 varies in [0, 2] with fixing k10 = 3, the system has a good robustness against the relatively weak inhibitory regulation function of second inhibitory neuronal population as k6 is lower around k6 = 1.05. And, on this occasion, within the right short parameter interval of k4 = 1 the system always displays the background low saturated firings (i.e., the low-amplitude and high-frequency tonic oscillations as shown in the inset of Fig. 2(a)). However, as the k6 is increased into k6 = 1.063 (Fig. 10(b)), similar to the single-point stimulation, inhibition can also induce the occurrence of SWD. With the further increasing of inhibitory function, i.e., k6 becomes larger, the larger parameter intervals can be found, where inhibition-induced SWD occurs. Compared to Fig. 10(b), as k6 is increased into k6 = 1.106 (Fig. 10(e)), enough large inhibition function can induce the occurrence of SWD on the whole parameter interval of stimulus-induced SWD. In addition, we can also see that inhibition can terminate the epileptic tonic seizures on the parameter intervals of small k4 with k10 = 3. Particularly, during the increasing of k6 saturated firing states can be repeatedly induced by the inhibition, which results in the recurrent onsets of various epileptic seizures including the simple tonic oscillations, SWD discharges and simple clonic (slow-wave) oscillations.

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