Epilepsy is believed to be caused by a lack of balance between excitation and inhibitation in the brain. A promising strategy for the control of the disease is closed-loop brain stimulation. How to determine the stimulation control parameters for effective and safe treatment protocols remains, however, an unsolved question. To constrain the complex dynamics of the biological brain, we use a neural population model（NPM）. We propose that a proportional-derivative（PD） type closed-loop control can successfully suppress epileptiform activities. First, we determine the stability of root loci, which reveals that the dynamical mechanism underlying epilepsy in the NPM is the loss of homeostatic control caused by the lack of balance between excitation and inhibition. Then, we design a PD type closed-loop controller to stabilize the unstable NPM such that the homeostatic equilibriums are maintained; we show that epileptiform activities are successfully suppressed. A graphical approach is employed to determine the stabilizing region of the PD controller in the parameter space, providing a theoretical guideline for the selection of the PD control parameters. Furthermore, we establish the relationship between the control parameters and the model parameters in the form of stabilizing regions to help understand the mechanism of suppressing epileptiform activities in the NPM. Simulations show that the PD-type closed-loop control strategy can effectively suppress epileptiform activities in the NPM.
目的探讨大鼠在工作记忆过程中,前额叶皮层多通道局部场电位(local field potentials,LFPs)θ频段的功能性连接特性。方法记录成年雄性SD大鼠在Y迷宫工作记忆过程中16通道LFPs,应用短时傅里叶变换进行时频分析。选取与工作记忆相关的θ频段,应用同步似然分析计算工作记忆过程中前额叶皮层16通道同步似然矩阵值S、聚集系数C、特征路径长度L,并与静息状态下进行比对。结果时频分析显示LFPs能量密度分布集中于红外打标点前1s至打标点处的θ频段。大鼠工作记忆过程中LFPsθ频段同步似然值Sp=0.6593±0.0220,静息状态下Sp=0.5104±0.0516。当T=0.76时大鼠工作记忆过程和静息状态下功能性连接差异最明显,具有统计学意义。工作记忆过程LFPsθ频段聚集系数Cp=0.2206±0.0263,明显高于静息状态Cp=0.1065±0.0237(P<0.05)。工作记忆过程LFPsθ频段特征路径长度Lp=1.3110±0.1318,明显低于静息状态Lp=2.9329±0.2763(P<0.05)。结论大鼠在工作记忆过程中LFPs的特征频段是θ,而且工作记忆过程中LFPs的功能性连接强于静息状态。
