NMDA受體被認為與認知學習有高度相關性，故NMDA受體失能常導致病理現象產生如規律性的慢波，且由於受到細胞膜外的鎂離子阻斷，離子通道的開啟與膜電位的變化密切相關，為NMDA受體主要的特性。故本研究於多群神經網路中加入NMDA受體，建構局部大腦皮質(layer IV~V)的神經網路模型，並模擬腦電圖波形以探討其可能病理機轉。然而腦電圖並非反映單一神經元的電生理活動，而是記錄神經群體電活動的總和，因此有必要整合平均場模型與NMDA受體模型，由於現今神經塊模型缺乏神經電生理的理論支持，而無法解釋生理實驗中各神經群體於網路架構之功能及生理意義。故本研究將延伸密度式神經塊模型，結合NMDA受體通道電導的完整動態行為，推導單群神經網路模型，並實現多群神經網路模擬。結果顯示不論動作電位頻率輸入為常數或隨機過程，突觸電導的平均場模型能定性且定量估測NMDA受體的統計量，在產生動作電位頻率輸出後，由於不滿足高斯分布假設，故平均膜電位的估測誤差較大，但平均動作電位頻率的估測依然準確，誤差最大僅為3~4 Hz。神經群體網路模擬關注的是平均動作電位頻率，其次為平均膜電位，故平均場模型的估測效能佳，並可運用於多群神經網路模擬。藉由調變NMDA受體電導，可觀察穩態下系統的動態由平衡點轉為極限軌跡，產生規律性的慢波，生理上普遍認為是病理症狀的表現，驗證本研究假設NMDA受體失能與突觸電導的變化相關。

NMDA receptors are believed to be highly related to cognitive learning, so dysfunction of NMDA receptors usually results in psychiatric diseases. The pathological phenomena in EEG signal such as regular slow waves were observed. Besides, the opening of NMDA channels is mediated by the postsynaptic voltage due to the block of magnesium ion. In this thesis, the dynamics of NMDA receptor were integrated into a multi-population neural network to build the model of local cerebral cortex(layer IV~V). The model was used to simulate EEG signal and explore its underlying pathological mechanism. However, EEG signal didn’t reflect electrical activity of a neuron but record the summed electrical activity of a neuronal population. It is necessary to derive the mean field model. Because neural mass model lacks physiological basis of a neuron, it can’t explain the function and physiological significance of each neuronal population. Hence, the density-based neural mass model(dNMM) was extended by considering the dynamic behavior of synaptic conductance of NMDA receptors. The single-population neural network was built and applied to the multi-population neural network. The results showed the dNMM could estimate the statistics(ensemble average and standard deviation) of NMDA receptors and firing rates of a neuronal population in response to time-varying or stochastic firing input. The dNMM was further applied to the multi-population neural network with NMDA receptors. The trajectory of the system states converged to an equilibrium point. As conductance of NMDA receptors increased, it was transformed into the limit cycle at steady state, generating low frequency waves at 6 Hz in EEG. The simulation proved the hypothesis that the regular slow waves in EEG may be due to dysfunction of NMDA receptors.

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