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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

The abatement effect of the introduced neuronal population, IN2, on stimulation-induced SWD, mediated by the k3 and k6 parameters.The stimulus-induced ~3 Hz SWD seizure state (bottom of the figure) can be adjusted by the combined function of (k3, k6) to return into the normal background resting state (top of the figure).
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f9: The abatement effect of the introduced neuronal population, IN2, on stimulation-induced SWD, mediated by the k3 and k6 parameters.The stimulus-induced ~3 Hz SWD seizure state (bottom of the figure) can be adjusted by the combined function of (k3, k6) to return into the normal background resting state (top of the figure).

Mentions: In the previous sections, we have set k3 and k6, i.e., the output of the introduced second neuronal population, IN2, to much small values regardless of the impact from IN2. However, in this section, we will first investigate the abatement effect of IN2 on the stimulus-initiated SWD by strengthening the output of IN2, i.e., increasing the values of k3 and k6, which correspond to the inputs of IN2 into PY and IN1 of cortex, respectively. Without loss of generality, we take (k4, k10) = (1, 3) from the bistable region (see the region ‘III’ in Fig. 5(a)). After the initiation of SWD, we investigate the abatement effect of IN2 on the 2D plane of (k3, k6) ∈ [0.5, 1.5] × [0.5, 1.5], by mediating the inputs into PY and IN1. As shown in Fig. 9, for the small values of k3 (e.g. k3 < ≈ 1), i.e., the weak input into PY from IN2, the stimulus-induced SWD can always not be effectively terminated by mediating the input to IN1 from IN2 for k6 ∈ [0.5, 1.5]. However, for the values of k3 larger than k3 ≈ 1, weak input into IN1 (e.g. k6 < ≈ 1) can start to shift the system from ~3 Hz SWD oscillation into background resting state, inducing the abatement of SWD. Particularly, as k3 getting larger, the window of SWD abatement mediated by the k6 is also gradually being enlarged. In addition, for the much large values of k3 (e.g. k3 > ≈ 1.15), the stimulus-induced SWD has been totally abated by the input into PY of IN2 (i.e., k3), immune to the impact of input into IN1 from IN2, with k6 ∈ [0.5, 1.5]. In sum, under the combined mediation of outputs from IN2 (i.e., k3 and k6) the SWD abatement effect of IN2 can be specifically revealed. From the mathematical standpoint, the SWD abatement effect of the IN2 output may be due to the shift of separatrix between the non-seizure and SWD states towards the attraction basin of stable focus, mediated by k3 and k6 in the model, with enlarging the attraction basin of stable focus and reducing the attraction basin of limit cycle symbolizing SWD. Then the initial values of the system enter the attraction basin of stable focus and the system ultimately relaxes into the background resting state.


Stimulus-induced Epileptic Spike-Wave Discharges in Thalamocortical Model with Disinhibition
The abatement effect of the introduced neuronal population, IN2, on stimulation-induced SWD, mediated by the k3 and k6 parameters.The stimulus-induced ~3 Hz SWD seizure state (bottom of the figure) can be adjusted by the combined function of (k3, k6) to return into the normal background resting state (top of the figure).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f9: The abatement effect of the introduced neuronal population, IN2, on stimulation-induced SWD, mediated by the k3 and k6 parameters.The stimulus-induced ~3 Hz SWD seizure state (bottom of the figure) can be adjusted by the combined function of (k3, k6) to return into the normal background resting state (top of the figure).
Mentions: In the previous sections, we have set k3 and k6, i.e., the output of the introduced second neuronal population, IN2, to much small values regardless of the impact from IN2. However, in this section, we will first investigate the abatement effect of IN2 on the stimulus-initiated SWD by strengthening the output of IN2, i.e., increasing the values of k3 and k6, which correspond to the inputs of IN2 into PY and IN1 of cortex, respectively. Without loss of generality, we take (k4, k10) = (1, 3) from the bistable region (see the region ‘III’ in Fig. 5(a)). After the initiation of SWD, we investigate the abatement effect of IN2 on the 2D plane of (k3, k6) ∈ [0.5, 1.5] × [0.5, 1.5], by mediating the inputs into PY and IN1. As shown in Fig. 9, for the small values of k3 (e.g. k3 < ≈ 1), i.e., the weak input into PY from IN2, the stimulus-induced SWD can always not be effectively terminated by mediating the input to IN1 from IN2 for k6 ∈ [0.5, 1.5]. However, for the values of k3 larger than k3 ≈ 1, weak input into IN1 (e.g. k6 < ≈ 1) can start to shift the system from ~3 Hz SWD oscillation into background resting state, inducing the abatement of SWD. Particularly, as k3 getting larger, the window of SWD abatement mediated by the k6 is also gradually being enlarged. In addition, for the much large values of k3 (e.g. k3 > ≈ 1.15), the stimulus-induced SWD has been totally abated by the input into PY of IN2 (i.e., k3), immune to the impact of input into IN1 from IN2, with k6 ∈ [0.5, 1.5]. In sum, under the combined mediation of outputs from IN2 (i.e., k3 and k6) the SWD abatement effect of IN2 can be specifically revealed. From the mathematical standpoint, the SWD abatement effect of the IN2 output may be due to the shift of separatrix between the non-seizure and SWD states towards the attraction basin of stable focus, mediated by k3 and k6 in the model, with enlarging the attraction basin of stable focus and reducing the attraction basin of limit cycle symbolizing SWD. Then the initial values of the system enter the attraction basin of stable focus and the system ultimately relaxes into the background resting state.

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.


Related in: MedlinePlus