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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.


Bifurcation diagram showing the extrema of the mean of excitatory and inhibitory neuronal populations, PY and IN1, and their corresponding dominant frequencies.As the coupling strengths, k4, varies in the region [0, 2] with k10 = 3 (a,b), or k10 varies in the region [0, 8] with k4 = 1 (c,d), the system successively transits from the high-frequency and low-amplitude tonic oscillations (~15 Hz) to the low saturated firings, SWD discharges (~3 Hz) (shaded area), low-frequency but high-amplitude clonic oscillations (~3 Hz) and to the high saturated firing, respectively (see the illustrations in upper panels of (a)). Particularly, before stimulation (a,c) the system lies in the low saturated firings on the right short regions of k4 = 1 (a) and k10 = 3 (c). After stimulation (b,d), SWD can be induced from these stable low saturated firings, and the parameter regions of SWD is enlarged. The red and blue lines represent the maxima and minima, repectively. Numbered pink circles indicate the accurate bifurcation points. SWD can be typically initiated by stimulation perturbations in the regions indicated by the vertical lines.
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f4: Bifurcation diagram showing the extrema of the mean of excitatory and inhibitory neuronal populations, PY and IN1, and their corresponding dominant frequencies.As the coupling strengths, k4, varies in the region [0, 2] with k10 = 3 (a,b), or k10 varies in the region [0, 8] with k4 = 1 (c,d), the system successively transits from the high-frequency and low-amplitude tonic oscillations (~15 Hz) to the low saturated firings, SWD discharges (~3 Hz) (shaded area), low-frequency but high-amplitude clonic oscillations (~3 Hz) and to the high saturated firing, respectively (see the illustrations in upper panels of (a)). Particularly, before stimulation (a,c) the system lies in the low saturated firings on the right short regions of k4 = 1 (a) and k10 = 3 (c). After stimulation (b,d), SWD can be induced from these stable low saturated firings, and the parameter regions of SWD is enlarged. The red and blue lines represent the maxima and minima, repectively. Numbered pink circles indicate the accurate bifurcation points. SWD can be typically initiated by stimulation perturbations in the regions indicated by the vertical lines.

Mentions: Results of Fig. 4 show that without (Fig. 4(a,c)) and with (Fig. 4(b,d)) single-point stimulations or little perturbations projected into the system, the modified Taylor model can display rich dynamics as the coupling strength, k4 or k10, i.e., the projecting function of TC on to the PY or the feedback projecting function of PY onto the TC, varies. In particular, before stimulation, it can be seen from the upper panel of Fig. 4(a) (the bottom illustrations of the figure) that the modified Taylor model firstly transits from the simple tonic oscillation to the low saturated firing as the parameter k4 changes with fixing k10 = 3. Successively, transition to the periodic spike-wave discharges (SWD) can be found with k4 increasing to around k4 = 1.14. Afterwards, with k4 further increasing the system can transit from the SWD to the simple clonic oscillation. Finally, for the large value of k4, the system transits into the high saturated firing, which occurs around k4 = 1.64. Similarly, when we take k4 = 1, bifurcation scenario of the modified model is plotted in Fig. 4(c) as the parameter k10 varies in [0, 8]. Obviously, similar to the Fig. 4(a), rich dynamic transitions successively from simple tonic oscillation to low saturated firing, spike-wave discharge (SWD), simple clonic oscillation and to the high saturated firing can also be found in the upper panel of the Fig. 4(c). Particularly, from Fig. 4(c) we can see that as k10 increases into around k10 = 3.28, the SWD discharge can be induced. The SWD can also be terminated as k10 further increases to around k10 = 4.44, and simultaneously the systems transfer into the simple clonic oscillation.


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, and their corresponding dominant frequencies.As the coupling strengths, k4, varies in the region [0, 2] with k10 = 3 (a,b), or k10 varies in the region [0, 8] with k4 = 1 (c,d), the system successively transits from the high-frequency and low-amplitude tonic oscillations (~15 Hz) to the low saturated firings, SWD discharges (~3 Hz) (shaded area), low-frequency but high-amplitude clonic oscillations (~3 Hz) and to the high saturated firing, respectively (see the illustrations in upper panels of (a)). Particularly, before stimulation (a,c) the system lies in the low saturated firings on the right short regions of k4 = 1 (a) and k10 = 3 (c). After stimulation (b,d), SWD can be induced from these stable low saturated firings, and the parameter regions of SWD is enlarged. The red and blue lines represent the maxima and minima, repectively. Numbered pink circles indicate the accurate bifurcation points. SWD can be typically initiated by stimulation perturbations in the regions indicated by the vertical lines.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f4: Bifurcation diagram showing the extrema of the mean of excitatory and inhibitory neuronal populations, PY and IN1, and their corresponding dominant frequencies.As the coupling strengths, k4, varies in the region [0, 2] with k10 = 3 (a,b), or k10 varies in the region [0, 8] with k4 = 1 (c,d), the system successively transits from the high-frequency and low-amplitude tonic oscillations (~15 Hz) to the low saturated firings, SWD discharges (~3 Hz) (shaded area), low-frequency but high-amplitude clonic oscillations (~3 Hz) and to the high saturated firing, respectively (see the illustrations in upper panels of (a)). Particularly, before stimulation (a,c) the system lies in the low saturated firings on the right short regions of k4 = 1 (a) and k10 = 3 (c). After stimulation (b,d), SWD can be induced from these stable low saturated firings, and the parameter regions of SWD is enlarged. The red and blue lines represent the maxima and minima, repectively. Numbered pink circles indicate the accurate bifurcation points. SWD can be typically initiated by stimulation perturbations in the regions indicated by the vertical lines.
Mentions: Results of Fig. 4 show that without (Fig. 4(a,c)) and with (Fig. 4(b,d)) single-point stimulations or little perturbations projected into the system, the modified Taylor model can display rich dynamics as the coupling strength, k4 or k10, i.e., the projecting function of TC on to the PY or the feedback projecting function of PY onto the TC, varies. In particular, before stimulation, it can be seen from the upper panel of Fig. 4(a) (the bottom illustrations of the figure) that the modified Taylor model firstly transits from the simple tonic oscillation to the low saturated firing as the parameter k4 changes with fixing k10 = 3. Successively, transition to the periodic spike-wave discharges (SWD) can be found with k4 increasing to around k4 = 1.14. Afterwards, with k4 further increasing the system can transit from the SWD to the simple clonic oscillation. Finally, for the large value of k4, the system transits into the high saturated firing, which occurs around k4 = 1.64. Similarly, when we take k4 = 1, bifurcation scenario of the modified model is plotted in Fig. 4(c) as the parameter k10 varies in [0, 8]. Obviously, similar to the Fig. 4(a), rich dynamic transitions successively from simple tonic oscillation to low saturated firing, spike-wave discharge (SWD), simple clonic oscillation and to the high saturated firing can also be found in the upper panel of the Fig. 4(c). Particularly, from Fig. 4(c) we can see that as k10 increases into around k10 = 3.28, the SWD discharge can be induced. The SWD can also be terminated as k10 further increases to around k10 = 4.44, and simultaneously the systems transfer into the simple clonic oscillation.

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.