The brain rhythm is strongly associated with the brain function. Alzheimer's disease (AD) is characterized reflected by the brain rhythm switching from the alpha band (9–12 Hz) to the theta band (4–8 Hz), accompanied with the loss of brain function. However, extracting the implicating intrinsic characteristic variations of the brain network by utilizing the Electroencephalogram (EEG) information is challenging. Kaman observer, serving as an effective Bayesian technique, can provide a visualization service for probing the intrinsic characteristics underlying the pathological theta oscillations. This work first establishes an excitation-inhibitory neural network model and explores the role of the fraction of the inhibitory neurons and inhibitory synapses in the pathological theta oscillation. The results indicate that the reduced inhibitory neuronal proportion and attenuated inhibitory synaptic weight are the main neural bases of the frequency reduction of neural oscillation. Then, we further explore the intrinsic spiking characteristic by considering spike frequency adaptation (SFA) to the inhibitory neurons. The results show that the SFA reduces the firing rate of neurons, which facilitates the theta rhythm. The enhancement of SFA current by increasing the time constant of its gating variable can further decrease the theta frequency from 7 Hz to 4 Hz. Furthermore, for this high-dimensional nonlinear excitation-inhibitory neural network model, cubature Kalman filter (CKF) is employed to estimate the above potential variations from the EEG data. The observation results show that the attenuated trends of the inhibitory neuronal proportion and the decreased inhibitory SFA current result in the descending brain rhythm. Finally, the theoretical simulation is deduced by utilizing the mean field theory for simplifying high-dimensional model to verify the simulation results. The theoretical variations of inhibitory parameters and adaptation gating variable are consistent with the simulation results. In summary, we investigate the multi-origin factors related to inhibitory neuronal intrinsic characteristics from forward model simulation and inverse EEG estimation process. And we further verify the simulation and data-driven results by theoretical derivation. This work enhances the understanding of the systematic function of inhibitory intrinsic characteristics on pathological theta oscillation and provides an effective method to decode the dynamics underlying neural activities.

中文翻译：

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通过立方卡尔曼滤波器的组合数据和模型研究推断从神经元到网络的病理性 theta 振荡的多起源


大脑节律与大脑功能密切相关。阿尔茨海默病（AD）的特点是大脑节律从α波段（9-12赫兹）切换到θ波段（4-8赫兹），并伴有脑功能丧失。然而，利用脑电图（EEG）信息提取大脑网络的内在特征变化具有挑战性。卡曼观测器作为一种有效的贝叶斯技术，可以为探测病理性θ振荡的内在特征提供可视化服务。这项工作首先建立了兴奋抑制神经网络模型，并探讨了抑制性神经元和抑制​​性突触的比例在病理性θ振荡中的作用。结果表明，抑制性神经元比例减少和抑制性突触重量减弱是神经振荡频率降低的主要神经基础。然后，我们通过考虑抑制性神经元的尖峰频率适应（SFA）来进一步探索内在的尖峰特征。结果表明，SFA 降低了神经元的放电率，从而促进了 theta 节律。通过增加其门控变量的时间常数来增强 SFA 电流可以进一步将 theta 频率从 7 Hz 降低到 4 Hz。此外，对于这种高维非线性激励抑制神经网络模型，采用立方卡尔曼滤波器（CKF）来估计脑电图数据的上述潜在变化。观察结果表明，抑制性神经元比例的衰减趋势和抑制性SFA电流的降低导致脑节律下降。 最后利用平均场理论简化高维模型进行了理论仿真，验证了仿真结果。抑制参数和适应门控变量的理论变化与模拟结果一致。总之，我们从正向模型模拟和逆向脑电图估计过程中研究了与抑制性神经元内在特征相关的多源因素。我们通过理论推导进一步验证了模拟和数据驱动的结果。这项工作增强了对病理性θ振荡抑制内在特征的系统功能的理解，并提供了一种有效的方法来解码神经活动背后的动力学。