Limits...
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.


The time series for the mean of neural populations PY and IN1, with linearly increasing k4 from 0 to 2 and corresponding to the Fig. 4(a,b).The close-ups of the different phases of (a) shown in the panels (a1)-(a4): simple tonic oscillation (a1), SWD discharges (a2), simple slow-wave (clonic) oscillations (a3) and the evolution into the saturated firing from the simple slow-wave oscillations (a4). The pink, red, yellow and green solid circles represent the bifurcation critical timings of different firing states, corresponding to t = 80, 126.5, 136 and 167.5, respectively. The grey region corresponds to the bistable region where stimulus can induce the onsets of SWD as shown in the inset of (a).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC5120301&req=5

f6: The time series for the mean of neural populations PY and IN1, with linearly increasing k4 from 0 to 2 and corresponding to the Fig. 4(a,b).The close-ups of the different phases of (a) shown in the panels (a1)-(a4): simple tonic oscillation (a1), SWD discharges (a2), simple slow-wave (clonic) oscillations (a3) and the evolution into the saturated firing from the simple slow-wave oscillations (a4). The pink, red, yellow and green solid circles represent the bifurcation critical timings of different firing states, corresponding to t = 80, 126.5, 136 and 167.5, respectively. The grey region corresponds to the bistable region where stimulus can induce the onsets of SWD as shown in the inset of (a).

Mentions: It should be noted that during the bifurcation simulations (Fig. 4 and Fig. 5) same initial conditions are used for all parameters to be scanned. However, from the electrophysiological standpoint, k4 and k10, i.e., the mutual interactions between the cortex and subcortical thalamus, change continuously over time. In order to justify the bifurcation diagrams in Fig. 4 and Fig. 5 and their stability, numerical calculations should be carried out by incrementing the parameter value slightly and using the end values from the previous simulation as initial conditions for the next simulation. However, instead of being somewhat redundant, we only provide the result corresponding to the Fig. 4(a,b). And particularly for convenience and without the loss of generality, we scan k4 forwards from 0 to 2 with linear growth. As shown in Fig. 6, we first suppose that k4 is time-dependent and linearly increase over time (Fig. 6(b)). The time series can be obtained with k4 linearly increasing, shown in Fig. 6(a), where four different timings indicated by four colored circles segregate the time series into several distinct firing states. From the close-ups of the different phases of the time series, shown in the right panels of the figure (a1-a4), we can see that when t < ≈ 80 s the system displays simple tonic oscillations. In time intervals, 126.5 s < ≈ t < ≈ 136 s and 136 s < ≈ t < ≈ 167.5 s, the system displays SWD and clonic oscillations, respectively. For the rest of intervals, without the single-pulse stimulations, the system consistently shows the saturated firings. However, when the stimulation introduced, it is shown that in the grey region of Fig. 6(a), corresponding to the bistable states of the system, the SWD discharges can be induced by the single-pulse stimulation perturbations. As a whole, with k4 linearly increasing and under the single-pulse stimulus, the system shows the transitions from tonic oscillation, low saturated firing, stimulus-induced SWD, spontaneous SWD, clonic oscillations and to the high saturated firing, which is qualitatively consistent with the bifurcation diagram in Fig. 4(a,b). In addition, in order to illustrate the robustness of bifurcation dynamics in Fig. 4(a,b), we also repeat a backward scan from 2 to 0 of k4 with a linear decline. Transitions of various firings states can be typically and sequentially inversed, which somewhat reveals the bistability of system.


Stimulus-induced Epileptic Spike-Wave Discharges in Thalamocortical Model with Disinhibition
The time series for the mean of neural populations PY and IN1, with linearly increasing k4 from 0 to 2 and corresponding to the Fig. 4(a,b).The close-ups of the different phases of (a) shown in the panels (a1)-(a4): simple tonic oscillation (a1), SWD discharges (a2), simple slow-wave (clonic) oscillations (a3) and the evolution into the saturated firing from the simple slow-wave oscillations (a4). The pink, red, yellow and green solid circles represent the bifurcation critical timings of different firing states, corresponding to t = 80, 126.5, 136 and 167.5, respectively. The grey region corresponds to the bistable region where stimulus can induce the onsets of SWD as shown in the inset of (a).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f6: The time series for the mean of neural populations PY and IN1, with linearly increasing k4 from 0 to 2 and corresponding to the Fig. 4(a,b).The close-ups of the different phases of (a) shown in the panels (a1)-(a4): simple tonic oscillation (a1), SWD discharges (a2), simple slow-wave (clonic) oscillations (a3) and the evolution into the saturated firing from the simple slow-wave oscillations (a4). The pink, red, yellow and green solid circles represent the bifurcation critical timings of different firing states, corresponding to t = 80, 126.5, 136 and 167.5, respectively. The grey region corresponds to the bistable region where stimulus can induce the onsets of SWD as shown in the inset of (a).
Mentions: It should be noted that during the bifurcation simulations (Fig. 4 and Fig. 5) same initial conditions are used for all parameters to be scanned. However, from the electrophysiological standpoint, k4 and k10, i.e., the mutual interactions between the cortex and subcortical thalamus, change continuously over time. In order to justify the bifurcation diagrams in Fig. 4 and Fig. 5 and their stability, numerical calculations should be carried out by incrementing the parameter value slightly and using the end values from the previous simulation as initial conditions for the next simulation. However, instead of being somewhat redundant, we only provide the result corresponding to the Fig. 4(a,b). And particularly for convenience and without the loss of generality, we scan k4 forwards from 0 to 2 with linear growth. As shown in Fig. 6, we first suppose that k4 is time-dependent and linearly increase over time (Fig. 6(b)). The time series can be obtained with k4 linearly increasing, shown in Fig. 6(a), where four different timings indicated by four colored circles segregate the time series into several distinct firing states. From the close-ups of the different phases of the time series, shown in the right panels of the figure (a1-a4), we can see that when t < ≈ 80 s the system displays simple tonic oscillations. In time intervals, 126.5 s < ≈ t < ≈ 136 s and 136 s < ≈ t < ≈ 167.5 s, the system displays SWD and clonic oscillations, respectively. For the rest of intervals, without the single-pulse stimulations, the system consistently shows the saturated firings. However, when the stimulation introduced, it is shown that in the grey region of Fig. 6(a), corresponding to the bistable states of the system, the SWD discharges can be induced by the single-pulse stimulation perturbations. As a whole, with k4 linearly increasing and under the single-pulse stimulus, the system shows the transitions from tonic oscillation, low saturated firing, stimulus-induced SWD, spontaneous SWD, clonic oscillations and to the high saturated firing, which is qualitatively consistent with the bifurcation diagram in Fig. 4(a,b). In addition, in order to illustrate the robustness of bifurcation dynamics in Fig. 4(a,b), we also repeat a backward scan from 2 to 0 of k4 with a linear decline. Transitions of various firings states can be typically and sequentially inversed, which somewhat reveals the bistability of system.

View Article: PubMed Central - PubMed

ABSTRACT

Epileptic absence seizure characterized by the typical 2&ndash;4&thinsp;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.