神经元放电模式同步的UKF-RBF-PID控制策略研究
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摘要
目的针对具有参数时变、强耦合以及非线性等复杂特性的神经系统,提出了一种神经元放电模式同步的UKF-RBF-PID控制策略。方法首先考虑到神经元膜上离子运动的随机性以及测量的干扰性,提出一种基于UKF(unscented Kalman filter)的神经元滤波方法,应用采样点集迭代过程实现更高的滤波估计精度;其次定义Jacobian阵表示计算值对激励变化的灵敏度信息,利用RBF(radial basis function)神经网络构建从神经元的在线辨识模型;最后设计了PID(proportion integration differentiation)控制器参数动态调整的规则,给出了参数调整的梯度下降法,经迭代实现从神经元和主神经元放电模式的同步。结果针对主从神经元脉冲发放状态的规则性差异情况,以及主从神经元模型参数不匹配的情形,分别进行了相应的仿真计算实验。主神经元为周期状态,从神经元为混沌状态,系统相位相关度0.9996,同步误差0.3907,主从神经元呈现较好的跟随状态;主从神经元均为初始状态不一致的周期类型,系统相位相关度0.9994,同步方差处于合理水平,主从神经元呈现较好的跟随状态;主、从神经元均为初始状态一致的周期类型,其中主神经元为标准参数,从神经元参数失配,系统相位相关度0.9996,有噪声干扰时,神经元间同步方差可接受。结论在噪声的干扰下,主从神经元实现了神经元间的同步,证明了本文提出方法的有效性,有望应用到深部脑刺激治疗方案中。
Objective Focusing the nervous system with complex characteristics such as time-varying parameters,strong coupling and nonlinearity,the UKF-RBF-PID control strategy for synchronizing neuron discharge patterns was proposed in this paper.Methods First,considering the randomness of ion motion on the neuron membrane and the measurement interference,a neuron filtering method based on unscented Kalman filter(UKF)was proposed.The sampling point set iterative process was applied to achieve higher filtering estimation accuracy.Then the Jacobian matrix was defined to represent the sensitivity information of the calculated value to the excitation change,and the online identification model was constructed from the neuron using the radial basis function(RBF)neural network.In the end,the rules of dynamic adjustment of proportion integration differentiation(PID)controller parameters were designed and the gradient descent method of parameter adjustment was given.So the synchronization of the discharge modes of the slave neuron and master neuron was iteratively realized.Results Targeting the regular difference of the spike issuing state of the master-slave neurons and the mismatch of the parameters of the master and slave neuron model,the corresponding simulation calculation experiments were carried out.When the main neuron was in a periodic state and the slave neuron was in a chaotic state,the phase correlation of the system was 0.9996,the synchronization error was 0.3907,and both neurons were in a good following state.When the main and slave neurons were in a period type with inconsistent initial state,the phase correlation of the system was 0.9994,the synchronization variance was at a reasonable level,and both neurons were in a good following state.When the main neuron with standard parameter,and the slave neurons with non-standard parameter,had consistent initial state in a period type,the phase correlation of the system was 0.9996.When there was noise disturbance,the synchronization variance between neurons was acceptable.Conclusion Under the interference of noise,master-slave neurons achieve synchronization between neurons,which proves the effectiveness of the proposed method and is expected to be applied to deep brain stimulation therapy.
Objective Focusing the nervous system with complex characteristics such as time-varying parameters,strong coupling and nonlinearity,the UKF-RBF-PID control strategy for synchronizing neuron discharge patterns was proposed in this paper.Methods First,considering the randomness of ion motion on the neuron membrane and the measurement interference,a neuron filtering method based on unscented Kalman filter(UKF)was proposed.The sampling point set iterative process was applied to achieve higher filtering estimation accuracy.Then the Jacobian matrix was defined to represent the sensitivity information of the calculated value to the excitation change,and the online identification model was constructed from the neuron using the radial basis function(RBF)neural network.In the end,the rules of dynamic adjustment of proportion integration differentiation(PID)controller parameters were designed and the gradient descent method of parameter adjustment was given.So the synchronization of the discharge modes of the slave neuron and master neuron was iteratively realized.Results Targeting the regular difference of the spike issuing state of the master-slave neurons and the mismatch of the parameters of the master and slave neuron model,the corresponding simulation calculation experiments were carried out.When the main neuron was in a periodic state and the slave neuron was in a chaotic state,the phase correlation of the system was 0.9996,the synchronization error was 0.3907,and both neurons were in a good following state.When the main and slave neurons were in a period type with inconsistent initial state,the phase correlation of the system was 0.9994,the synchronization variance was at a reasonable level,and both neurons were in a good following state.When the main neuron with standard parameter,and the slave neurons with non-standard parameter,had consistent initial state in a period type,the phase correlation of the system was 0.9996.When there was noise disturbance,the synchronization variance between neurons was acceptable.Conclusion Under the interference of noise,master-slave neurons achieve synchronization between neurons,which proves the effectiveness of the proposed method and is expected to be applied to deep brain stimulation therapy.
引文
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[3] Kim JH,Jung AH,Jeong D,et al.Selectivity of neuromodulatory projections from the basal forebrain and locus ceruleus to primary sensory cortices[J].Journal of Neuroscience,2016,36(19):5314-5327.
[4] Fell J,FernNdez G,Klaver P,et al.Is synchronized neuronal gamma activity relevant for selective attention?[J].Brain Research Reviews,2003,42(3):265-272.
[5] Ray S,Niebur E,Hsiao SS,et al.High-frequency gamma activity(80-150 Hz)is increased in human cortex during selective attention[J].Clinical Neurophysiology,2008,119(1):116-133.
[6] Nunez PL,Srinivasan R.Scale and frequency chauvinism in brain dynamics:Too much emphasis on gamma band oscillations[J].Brain Structure and Function,2010,215(2):67-71.
[7] Yokoyama O,Nakayama Y,Hoshi E.Area-and bandspecific representations of hand movements by local field potentials in caudal cingulate motor area and supplementary motor area of monkeys[J].Journal of Neurophysiology,2016,115(3):1556-1576.
[8] Bacak BJ,Segaran J,Molkov YI.Modeling the effects of extracellular potassium on bursting properties in preBtzinger complex neurons[J].Journal of Computational Neuroscience,2016,40(2):1-15.
[9]朱俊玲,林宏,蒋大宗,等.相关积分检测癫痫发作前脑电的动力学变化[J].航天医学与医学工程,2004,17(4):248-250.Zhu JL,Lin H,Jiang DZ,et al.Detection of dynamic changes of pre-seizure scalp EEG with correlation integral[J].Space Medicine&Medical Engineering,2004,17(4):248-250.
[10] Baier G,Milton J.Dynamic diseases of the brain[M]//Dieter J,Ranu J.Encyclopedia of Computational Neuroscience.New York:Springer,2015:1051-1061.
[11] Morgan RJ,Soltesz I.Complexity untangled:Large-scale realistic computational models in epilepsy[J].Neuromethods,2009,40:163-182.
[12] Wang QY,Lu QS,Chen GR,et al.Chaos synchronization of coupled neurons with gap junctions[J].Physics Letters A,2006,356(1):17-25.
[13] Che YQ,Wang J,Chan WL,et al.Chaos synchronization of coupled neurons under electrical stimulation via robust adaptive fuzzy control[J].Nonlinear Dynamics,2010,61(4):847-857.
[14] Deng B,Wang J,Fei X.Synchronizing two coupled chaotic neurons in external electrical stimulation using backstepping control[J].Chaos Solitons&Fractals,2006,29(1):182-189.
[15] Mehdiabadi MR,Rouhani E,Mashhadi SK,et al.Adaptive fractional-order control for synchronizat-ion of two coupled neurons in the external electrical stimulation[J].Basic&Clinical Neuroscience,2014,5(2):144-155.
[16]梁仲刚,王勤,严洪.航天飞行中心电信号去噪方法研究[J].航天医学与医学工程,2006,19(5):354-357.Liang ZG,Wang Q,Yan H.Research on ECG denoising during spaceflight[J].Space Medicine&Medical Engineering,2006,19(5):354-357.
[17] Park J,Sandberg IW.Universal approximation using radial-basis-function networks[J].Neural Computation,2014,3(2):246-257.
[18] Singh A,Singh KK.Satellite image classification using genetic algorithm trained radial basis function neural network,application to the detection of flooded areas[J].Journal of Visual Communication&Image Representation,2017,42:173-182.
[19] Wang H,Yu Y,Wang S,et al.Bifurcation analysis of a two-dimensional simplified Hodgkin-Huxley model exposed to external electric fields[M]//Huang T,Zeng Z,Li C,et al.Neural Information Processing,Berlin Heidelberg:Springer,2012:288-295.
[20] Lankarany M,Zhu WP,Swamy MNS.Joint estimation of states and parameters of Hodgkin-Huxley neuronal model using Kalman filtering[J].Neurocomputing,2014,136(12):289-299.
[21] Zhou SS,Wang J,Che YQ,et al.Synchronization control of Hodgkin-Huxley neurons exposed to sinusoidal electric field[J].Chaos Solitons&Fractals,2009,40(4):1588-1598.
[22] Yi G,Wang J, Wei X, et al.Dynamic analysis of Hodgkin’s three classes of neurons exposed to extremely low-frequency sinusoidal induced electric field[J].Applied Mathematics&Computation,2014,231:100-110.