Background and Objective

Epilepsy is a dynamic disease of neuronal networks and epileptic activity in the brain should be suppressed quickly in the shortest possible time with minimum control signal. Thus, a closed-loop feedback control by using the fixed-time integral super-twisting sliding-mode controller via an optogenetic method is employed for suppressing seizures in the Pinsky–Rinzel (PR) model as a dynamic model of the hippocampus CA3 region where epileptic seizures occur. The control signal is applied to the PR model through the ChR2 channel model in the form of light photons using the optogenetic method. The present study aimed to determine the controller robustness against parameter changes and disturbances in order to reduce the control time, approach the zero tracking error of the normal desired state in a fixed time, and finally, converge the epileptic state to the normal desired state.

Method

In order to apply the control signal to the Pinsky–Rinzel model in the optogenetic method, the dynamic model of the ion current generated by channelrhodopsin 2 (ChR2) as a light-sensitive protein model in the optogenetic method was first applied to the PR model. Then, a fixed-time integral super-twisting sliding-mode controller was designed for the system, which is the combination of PR and ChR2 models.

Results

After applying the proposed controller, the simulation results indicated that the control signal was −0.7 mV, the tracking error of the normal desired state could reach zero within 1.5 milliseconds, and the problems of singularity and chattering were solved.

Conclusions

A reduction occurred in the control signal reduced regarding the objectives of the study and comparing the proposed controller with the classical sliding-mode controller. Thus, this method can produce a safe control input for brain. In addition, both types of sliding mode controllers are robust against the parameters variations and external disturbances. Thus, they are superior to non-robust and simple controllers. Finally, based on the results, the validity of the fixed-time integral super-twisting sliding mode controller is confirmed for epilepsy control.

中文翻译：

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使用光遗传学方法通过离子通道对 Pinsky-Rinzel 锥体模型进行固定时间积分超扭曲滑模控制的癫痫控制。

背景与目的

癫痫是一种神经网络的动态疾病，大脑中的癫痫活动应在尽可能短的时间内以最小的控制信号迅速抑制。因此，通过光遗传学方法使用固定时间积分超扭曲滑模控制器的闭环反馈控制用于抑制 Pinsky-Rinzel (PR) 模型中的癫痫发作，作为海马 CA3 区域的动态模型，其中发生癫痫发作。控制信号通过 ChR2 通道模型使用光遗传学方法以光子的形式应用于 PR 模型。本研究旨在确定控制器对参数变化和扰动的鲁棒性，以减少控制时间，在固定时间内接近正常期望状态的零跟踪误差，最后，

方法

为了将控制信号应用于光遗传学方法中的Pinsky-Rinzel模型，首先将光遗传学方法中由通道视紫红质2（ChR2）作为光敏蛋白模型产生的离子电流的动态模型应用于PR模型. 然后，针对该系统设计了一个固定时间积分超扭滑模控制器，它是PR和ChR2模型的结合。

结果

应用所提出的控制器后，仿真结果表明控制信号为-0.7 mV，正常期望状态的跟踪误差可以在1.5毫秒内达到零，解决了奇异性和颤振问题。

结论

控制信号的减少与研究的目标有关，并将所提出的控制器与经典的滑模控制器进行比较。因此，这种方法可以为大脑产生安全的控制输入。此外，两种类型的滑模控制器都对参数变化和外部干扰具有鲁棒性。因此，它们优于非鲁棒和简单的控制器。最后，基于结果验证了固定时间积分超扭滑模控制器在癫痫控制中的有效性。