外电场作用下神经元动力学分析与同步控制
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摘要
精神疾病是危害人类健康的主要疾病之一,其主要原因体现在神经元及神经网络放电编码异常,如帕金森症(Parkinson's disease,PD)发病时主要表现为基底核放电同步异常。精神疾病的治疗通常有药物和物理疗法,在物理疗法中,以外部电刺激为手段的深度脑刺激(Deep Brain Stimulation,DBS)已经成为治疗这类疾病的基本医疗手段之一。DBS的基本原理是通过外部电刺激改变神经网络的状态,其机理尚不完全清楚。目前,DBS的治疗处于开环状态,其治疗效果和能量消耗、参数调整等方面仍不能令人满意。因此采用闭环控制DBS来提高其治疗效果、实现能效优化、参数自动整定是十分必要的。通过研究外部刺激下神经元及其网络的放电模式和特性以及神经元网络的同步控制,能够揭示DBS的作用原理,拓展DBS的控制方法,对于研究DBS的机制和提高DBS的治疗水平具有重要意义。
本文首先分析了神经元放电模式研究与DBS治疗疾病研究的现状,在此基础上建立了外电场作用下神经元放电的最小模型,研究了不同频率、不同幅值的外电场对神经元放电模式的影响,得到了外部刺激与放电模式之间的关系。其次,建立了外电场作用下神经元放电敏感性的简化模型,分析了不同频率、不同幅值的交变信号及噪声与神经元放电之间的关系,证明了神经元对幅值、频率及噪声的敏感特性。第三,分析了不同幅值与不同相位的高频扰动对神经元响应的影响─振动共振,得到一个高频扰动幅值的最优值,在该最优值下神经元对外部低频信号输入的响应最强;研究了化学突触与电突触耦合的神经元对外部低频信号的响应情况,发现当神经系统受到局部刺激时,化学突触对神经信息的传递比电突触更有效率。最后,针对开环DBS现状,将非线性控制理论应用到神经元网络同步和去同步控制,以实现闭环控制。为抑制干扰,提出自适应内模控制神经元网络混沌同步,使神经元达到期望的同步特性;提出利用人工神经网络逼近HH模型,利用H?抑制逼近误差和外部干扰的方法,实现了HH模型的同步控制;引入HH模型离子通道的随机噪声,利用模糊自适应控制实现了在随机噪声作用下HH模型的同步控制;提出采用自适应神经网络H?控制,实现了两个ML神经元模型的同步控制;用ML神经元模型网络模拟神经疾病的同步状态,采用本文提出的控制方法实现了该网络的去同步控制,模拟了DBS闭环控制,通过仿真证明了所提控制算法的有效性。
本文的研究成果可为DBS治疗精神疾病提供理论基础,并可望应用到临床DBS的闭环控制。
Mental disease is a kind of diseases harmful to human health seriously. It is showed that these diseases are caused mainly by the abnormal firing and encoding of neurons and neural network. For example, Parkinson’s Disease is corresponding to the abnormal synchronization of neurons in basal ganglia. These diseases are generally treated by medical therapies and physical therapies. Deep Brain Stimulation (DBS) has become a basic physical method and been widely applied. DBS would change the states of the neural network, but its mechanism remains uncertain. At present, DBS is modulated manually, and its therapy effects, energy efficiency and parameters adjustment are not satisfied. Therefore, it is necessary to utilize closed-loop control methods to optimize its power efficiency, tune its parameters and enhance its therapeutic outcome. To study firing patterns, features and synchronization control of neurons and neural network are helpful to reveal the principle and extend the ability of DBS, and have potential prospects in investigating the mechanism and the therapy effects of DBS.
Firstly, this thesis analyzes the progress of neuron model and its firing patterns, also the applications of DBS in the treatment of mental diseases. The minimum neuron firing model under external electrical field is established. The influences of different frequencies and amplitudes of the external electrical field on the firing patterns are studied based on this model, and the relationships between the external stimulus and firing patterns are obtained. The results show that the frequency and amplitude have significant effects on the firing patterns.
Secondly, a simplified model is established to analyze neural firing sensitivity under external electrical field, the relationships between the firing patterns and alternative signals with different frequencies, amplitudes and noises are analyzed, that shows that neurons are sensitive and certain adaptive to amplitudes, frequencies and noises.
Then, the influence of high frequency signals with different amplitudes and phases on neural dynamics is analyzed. It is found that there exists an optimal high-frequency amplitude that makes the neuron faithfully response to the external low frequency input. The responses of coupled neurons with chemical synapses and electrical synapses to the external low frequency input are also studied, which proves that the information transferred by chemical synapses is more efficient than electrical synapses when being stimulated locally.
Finally, the nonlinear control theory is introduced for the synchronization and desynchronization control of neural network to realize the closed-loop control of DBS. The adaptive internal model control method is proposed to achieve chaotic synchronization of the neural network with expected performance. Next, the artificial neural network is adopted to approximate the HH model, and H? is hired to restrain the approximation error and external interference, thus the synchronization control of HH model is realized. Then, the synchronization control of HH model with random noise of ion channel is also achieved through fuzzy adaptive control algorithm. Furthermore the adaptive neural network H? control is proposed to realize synchronization control of ML neural network. The desynchronization of a synchronous neural network simulated by ML models is also realized using the proposed methods mentioned above, and the closed-loop DBS is simulated successfully. The simulation results prove the effectiveness of the proposed control algorithm.
This thesis’s results will provide theoretical foundation for DBS treating mental illness, and hopeful to be applied to clinical DBS closed-loop control.
本文首先分析了神经元放电模式研究与DBS治疗疾病研究的现状,在此基础上建立了外电场作用下神经元放电的最小模型,研究了不同频率、不同幅值的外电场对神经元放电模式的影响,得到了外部刺激与放电模式之间的关系。其次,建立了外电场作用下神经元放电敏感性的简化模型,分析了不同频率、不同幅值的交变信号及噪声与神经元放电之间的关系,证明了神经元对幅值、频率及噪声的敏感特性。第三,分析了不同幅值与不同相位的高频扰动对神经元响应的影响─振动共振,得到一个高频扰动幅值的最优值,在该最优值下神经元对外部低频信号输入的响应最强;研究了化学突触与电突触耦合的神经元对外部低频信号的响应情况,发现当神经系统受到局部刺激时,化学突触对神经信息的传递比电突触更有效率。最后,针对开环DBS现状,将非线性控制理论应用到神经元网络同步和去同步控制,以实现闭环控制。为抑制干扰,提出自适应内模控制神经元网络混沌同步,使神经元达到期望的同步特性;提出利用人工神经网络逼近HH模型,利用H?抑制逼近误差和外部干扰的方法,实现了HH模型的同步控制;引入HH模型离子通道的随机噪声,利用模糊自适应控制实现了在随机噪声作用下HH模型的同步控制;提出采用自适应神经网络H?控制,实现了两个ML神经元模型的同步控制;用ML神经元模型网络模拟神经疾病的同步状态,采用本文提出的控制方法实现了该网络的去同步控制,模拟了DBS闭环控制,通过仿真证明了所提控制算法的有效性。
本文的研究成果可为DBS治疗精神疾病提供理论基础,并可望应用到临床DBS的闭环控制。
Mental disease is a kind of diseases harmful to human health seriously. It is showed that these diseases are caused mainly by the abnormal firing and encoding of neurons and neural network. For example, Parkinson’s Disease is corresponding to the abnormal synchronization of neurons in basal ganglia. These diseases are generally treated by medical therapies and physical therapies. Deep Brain Stimulation (DBS) has become a basic physical method and been widely applied. DBS would change the states of the neural network, but its mechanism remains uncertain. At present, DBS is modulated manually, and its therapy effects, energy efficiency and parameters adjustment are not satisfied. Therefore, it is necessary to utilize closed-loop control methods to optimize its power efficiency, tune its parameters and enhance its therapeutic outcome. To study firing patterns, features and synchronization control of neurons and neural network are helpful to reveal the principle and extend the ability of DBS, and have potential prospects in investigating the mechanism and the therapy effects of DBS.
Firstly, this thesis analyzes the progress of neuron model and its firing patterns, also the applications of DBS in the treatment of mental diseases. The minimum neuron firing model under external electrical field is established. The influences of different frequencies and amplitudes of the external electrical field on the firing patterns are studied based on this model, and the relationships between the external stimulus and firing patterns are obtained. The results show that the frequency and amplitude have significant effects on the firing patterns.
Secondly, a simplified model is established to analyze neural firing sensitivity under external electrical field, the relationships between the firing patterns and alternative signals with different frequencies, amplitudes and noises are analyzed, that shows that neurons are sensitive and certain adaptive to amplitudes, frequencies and noises.
Then, the influence of high frequency signals with different amplitudes and phases on neural dynamics is analyzed. It is found that there exists an optimal high-frequency amplitude that makes the neuron faithfully response to the external low frequency input. The responses of coupled neurons with chemical synapses and electrical synapses to the external low frequency input are also studied, which proves that the information transferred by chemical synapses is more efficient than electrical synapses when being stimulated locally.
Finally, the nonlinear control theory is introduced for the synchronization and desynchronization control of neural network to realize the closed-loop control of DBS. The adaptive internal model control method is proposed to achieve chaotic synchronization of the neural network with expected performance. Next, the artificial neural network is adopted to approximate the HH model, and H? is hired to restrain the approximation error and external interference, thus the synchronization control of HH model is realized. Then, the synchronization control of HH model with random noise of ion channel is also achieved through fuzzy adaptive control algorithm. Furthermore the adaptive neural network H? control is proposed to realize synchronization control of ML neural network. The desynchronization of a synchronous neural network simulated by ML models is also realized using the proposed methods mentioned above, and the closed-loop DBS is simulated successfully. The simulation results prove the effectiveness of the proposed control algorithm.
This thesis’s results will provide theoretical foundation for DBS treating mental illness, and hopeful to be applied to clinical DBS closed-loop control.
引文
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