动作电位模式分类及神经元模型响应频率同步性研究
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摘要
随着植入式多电极阵列技术的逐步成熟,计算神经科学研究有了新的实验手段。如何从多电极阵列采集的神经电信号中,快速准确地检测出神经元动作电位(spike)的发生,并将其归属于非同源的神经元,是后续神经元或神经元网络编码研究的前提和基础。针对spike信号短时长、非线性和非平稳性,以及奇异谱熵可反映spike信号在奇异值分解下的复杂度与信息量,本文提出利用奇异谱熵算法提取spike特征,结合C均值聚类算法实现spike分类。针对非同源spike信号波形及幅值波动等方面存在的差异,以及排列组合熵特征可表征spike信号波形变化的复杂度与信息量,本文继而提出采用spike信号排列组合熵特征结合寻谷聚类算法实现spike分类。通过实验证明两种spike模式分类新方法均具有较佳的分类效果。又由于神经元模型响应与刺激对应关系的仿真研究,可为后期真实spike信号编码研究提供必要的理论基础,是神经编码研究的一种有效途径,所以本文以神经元电特性建模中被广泛应用的Hodgkin-Huxley(HH)神经元多输入单输出模型为例进行研究,发现在一定情形下该模型响应与刺激间存在着频率同步性;以双层HH网络模型为例的研究进一步发现,网络结构可使频率同步性得到一定的提升;进而说明频率编码方式可能是生物神经编码的一种可行方式。
本文主要工作和研究成果如下:
(1)本文提出了基于奇异谱熵进行非同源spike特征提取的新方法,以反映spike信号在奇异值分解下的复杂度与信息量;经过KS检验等步骤完成特征向量的选择;最后利用C均值聚类算法实现了非同源spike信号的快速准确分类。实验结果表明,奇异谱熵特征能表达和区分非同源spike的动态特性,可作为spike信号分类的有效依据。
(2)本文提出了基于排列组合熵的非同源spike特征提取新方法,以表征spike波形变化及幅值波动的复杂度与信息量,经特征向量选择后根据二维特征空间中特征点分布的特殊性,利用寻谷聚类法实现spike信号分类。研究表明,spike排列组合熵特征结合寻谷聚类法的spike分类新方法,能较好区分非同源spike信号的相互干扰,方法具有一定的有效性。
(3)本文将HH神经元模型推广为多输入单输出模型,使其更符合神经元多突触输入的情形;进而研究模型响应在独立多输入情况下的频率同步特性。以双输入为例的仿真结果表明,在特定刺激信号输入情形下,输出的spike序列能在频率上响应输入刺激信号;进而研究膜电容、刺激信号频率跨度等因素对模型频率同步性的影响。
(4)本文构建了HH神经元的双层网络模型,以便更真实模拟神经元之间的突触连接方式,并进一步研究网络结构对频率同步性的影响。双输入仿真结果表明,神经元网络结构能够有效加强系统频率同步性;且在强相关双变频刺激信号输入情况下,网络模型的频率同步性表现得尤为显著。研究结果将为后续神经频率编码的电生理实验开展提供必要的理论基础。
There are some new methods on computational neuroscience research with the implovement of implanted multi-electrode array. It is the base of neuron or network coding research that how to quickly and accuracily detect neural spikes and classify them to non-homologous neurons. Singular spectrum entropy (SSE) features, reflecting the complexities and informations of spikes under the singular value decomposition (SVD), are extracted and spike-sorting is achieved using c-means clustering method, on account of short-time, nonlinearity and nonstationarity of spikes. According to the differences of non-homologous spikes’waveforms and amplitude fluctuations, the spike- sorting method combining spikes’permutation entropy (PE) features with valley-seeking clustering is used to reflect the complexities and informations of spikes’waveform-variations. It is indicated that the perfect results of clustering are gained by these two new spike-sorting methods. The simulated research on the relation between neuron model response and impulse is an effective approach of neural coding, and it also can provide necessary theoretical basis. So the case of Hodgkin-Huxley (HH) model of multi-input and single-output, which is extensively used in neural characteristics modeling, is researched. The frequency synchronization between model response and impulse on special condition is considered. And the case of double-layer HH neural network model is indicated that the network structure can strengthen the frequency synchronization. The research also shows that frequency coding may be a viable mode of neural coding.
The work and research results are as follows in this paper:
(1) A new method of non-homologous spikes’features extraction based on SSE is presented in order to reflect the complexities and informations of spikes under SVD. After choosing feature vectors by KS test and other steps, c-means clustering method is used to classify the spikes of non-homologous neurons quickly and accuracily. It is indicated that the features based on SSE of spikes could distinguish the dynamic characteristics of spikes and be an effective basis of spike- sorting.
(2) In order to reflect the complexities and informations of spikes’waveform-variations and amplitude fluctuations, a new method of non-homologous spikes’features extraction based on PE is presented. After selecting feature vectors and according to the particularity of feature points’distribution in two-dimensional feature space, spike-sorting is achieved using valley-seeking clustering method. It is indicated that the new spike sorting method using spikes’PE features with valley-seeking clustering can perfectly distinguish the interference of non- homologous spikes.
(3) HH model of multi-input and single-output is proposed to accord with the condition of multi-synaptic-input mode, and then frequency synchronization of multi-input model response is researched. The result of two-input case shows that the frequency of spike-train could response the impulse on some condition. Then the frequency synchronization affected by membrane capacitance of model and frequency span of impulse and orher factors is researched.
(4) Double-layer HH neural network model is built to simulate synaptic connection mode, and the frequency synchronization affected by network structure is researched. It is indicated by two- input simulated case that the network structure can strengthen the frequency synchronization, and the synchronization is highly significant on condition that two strong-relative variable-frequency- impulses input. The simulated results provide a necessary theoretical basis for the neural electrophysiological experiments.
本文主要工作和研究成果如下:
(1)本文提出了基于奇异谱熵进行非同源spike特征提取的新方法,以反映spike信号在奇异值分解下的复杂度与信息量;经过KS检验等步骤完成特征向量的选择;最后利用C均值聚类算法实现了非同源spike信号的快速准确分类。实验结果表明,奇异谱熵特征能表达和区分非同源spike的动态特性,可作为spike信号分类的有效依据。
(2)本文提出了基于排列组合熵的非同源spike特征提取新方法,以表征spike波形变化及幅值波动的复杂度与信息量,经特征向量选择后根据二维特征空间中特征点分布的特殊性,利用寻谷聚类法实现spike信号分类。研究表明,spike排列组合熵特征结合寻谷聚类法的spike分类新方法,能较好区分非同源spike信号的相互干扰,方法具有一定的有效性。
(3)本文将HH神经元模型推广为多输入单输出模型,使其更符合神经元多突触输入的情形;进而研究模型响应在独立多输入情况下的频率同步特性。以双输入为例的仿真结果表明,在特定刺激信号输入情形下,输出的spike序列能在频率上响应输入刺激信号;进而研究膜电容、刺激信号频率跨度等因素对模型频率同步性的影响。
(4)本文构建了HH神经元的双层网络模型,以便更真实模拟神经元之间的突触连接方式,并进一步研究网络结构对频率同步性的影响。双输入仿真结果表明,神经元网络结构能够有效加强系统频率同步性;且在强相关双变频刺激信号输入情况下,网络模型的频率同步性表现得尤为显著。研究结果将为后续神经频率编码的电生理实验开展提供必要的理论基础。
There are some new methods on computational neuroscience research with the implovement of implanted multi-electrode array. It is the base of neuron or network coding research that how to quickly and accuracily detect neural spikes and classify them to non-homologous neurons. Singular spectrum entropy (SSE) features, reflecting the complexities and informations of spikes under the singular value decomposition (SVD), are extracted and spike-sorting is achieved using c-means clustering method, on account of short-time, nonlinearity and nonstationarity of spikes. According to the differences of non-homologous spikes’waveforms and amplitude fluctuations, the spike- sorting method combining spikes’permutation entropy (PE) features with valley-seeking clustering is used to reflect the complexities and informations of spikes’waveform-variations. It is indicated that the perfect results of clustering are gained by these two new spike-sorting methods. The simulated research on the relation between neuron model response and impulse is an effective approach of neural coding, and it also can provide necessary theoretical basis. So the case of Hodgkin-Huxley (HH) model of multi-input and single-output, which is extensively used in neural characteristics modeling, is researched. The frequency synchronization between model response and impulse on special condition is considered. And the case of double-layer HH neural network model is indicated that the network structure can strengthen the frequency synchronization. The research also shows that frequency coding may be a viable mode of neural coding.
The work and research results are as follows in this paper:
(1) A new method of non-homologous spikes’features extraction based on SSE is presented in order to reflect the complexities and informations of spikes under SVD. After choosing feature vectors by KS test and other steps, c-means clustering method is used to classify the spikes of non-homologous neurons quickly and accuracily. It is indicated that the features based on SSE of spikes could distinguish the dynamic characteristics of spikes and be an effective basis of spike- sorting.
(2) In order to reflect the complexities and informations of spikes’waveform-variations and amplitude fluctuations, a new method of non-homologous spikes’features extraction based on PE is presented. After selecting feature vectors and according to the particularity of feature points’distribution in two-dimensional feature space, spike-sorting is achieved using valley-seeking clustering method. It is indicated that the new spike sorting method using spikes’PE features with valley-seeking clustering can perfectly distinguish the interference of non- homologous spikes.
(3) HH model of multi-input and single-output is proposed to accord with the condition of multi-synaptic-input mode, and then frequency synchronization of multi-input model response is researched. The result of two-input case shows that the frequency of spike-train could response the impulse on some condition. Then the frequency synchronization affected by membrane capacitance of model and frequency span of impulse and orher factors is researched.
(4) Double-layer HH neural network model is built to simulate synaptic connection mode, and the frequency synchronization affected by network structure is researched. It is indicated by two- input simulated case that the network structure can strengthen the frequency synchronization, and the synchronization is highly significant on condition that two strong-relative variable-frequency- impulses input. The simulated results provide a necessary theoretical basis for the neural electrophysiological experiments.
引文
[1] Chan H,Wu T,Lee S,et al.Classification of neuronal spikes over the reconstructed phase space[J].Journal of Neuroscience Methods,2008,168(1):203-211.
[2] Hirata Y,Aihara K.Representing spike trains using constant sampling intervals[J].Journal of Neuroscience Methods,2009,183(2):277-286.
[3] Ishitobi M,Nakasato N,Yamamoto,et al.Opercular to interhemispheric source distribution of benign rolandic spikes of childhood[J].NeuroImage,2005,25(2):417-423.
[4]范丽伟,唐焕文.一门新兴的交叉学科——神经信息学[J].自然杂志,2002,24(6):352-355.
[5] Vliet E,Stoppini L,Balestrino M,et al.Electrophysiological recording of re-aggregating brain cell cultures on multi-electrode arrays to detect acute neurotoxic effects[J].NeuroToxicology,2007,28(6):1136-1146.
[6] Hill A,Jones N,Williams C,et al.Development of multi-electrode array screening for anticonvulsants in acute rat brain slices[J].Brain Research,2006,1096(1):70-84.
[7] Steidl E,Neveu E,Bertrand D,et al.The adult rat hippocampal slice revisited with multi-electrode arrays[J].Journal of Neuroscience Methods,2010,185 (2):246-256.
[8] Segundo J.Some thoughts about neural coding and spike trains[J].Biosystems,2000,58(1-3):3-7.
[9] Miller E,Wilson M.All My Circuits:Using Multiple Electrodes to Understand Functioning Neural Networks[J].Neuron,2008,60(3):483-488.
[10] Song Mingzhou,Wang Hongbin.A spike sorting framework using nonparametric detection and incremental clustering[J].Neurocomputing,2006,69(10-12):1380-1384.
[11] Gruner C,Johnson D.Correlation and neural information coding fidelity and efficiency [J].Neurocomputing,1999,26-27:163-168.
[12] Tian Lingling,Li Donghai,Sun Xianfang.Nonlinear-estimator-based robust synchronization of Hodgkin-Huxley neurons[J].Neurocomputing,2008,72(1-3):186-196.
[13] Segundo J.A history of spike trains as Point Processes in neural coding[J].Journal of Physiology-Paris,2010,104(3-4):156-159.
[14]易晓斌,张海峰.HH神经元对信号编码的响应[J].青海大学学报,2006,24(5):86-88.
[15]陈良泉.Hodgkin-Huxley模型的分岔分析与控制[D].天津:天津大学,2006.
[16]丁伟东,袁景淇,梁培基.多电极锋电位信号检测与分类方法研究[J].仪器仪表学报,2006,27(12):1636-1640.
[17] Adamos D,Kosmidis E,Theophilidis G.Performance evaluation of PCA-based spike sorting algorithms[J].Computer Methods and Programs in Biomedicine,2008,91(3):232-244.
[18] Letelier J,Weber P.Spike sorting based on discrete wavelet transform coefficients[J].Journal of Neuroscience Methods,2000,101(2):93-106.
[19] Hulata E,Segev R,Eshel B.A method for spike sorting and detection based on wavelet packets and Shannon’s mutual information[J].Journal of Neuroscience Methods,2002,117(1):1-12.
[20] Bosnyakova D,Gabova A,Kuznetsova G,et al.Time-frequency analysis of spike-wave discharges using a modified wavelet transform[J].Journal of Neuroscience Methods,2006,154(1-2):80-88.
[21]übeyli E,?ahin G,Deniz,et al.Analysis of spike-wave discharges in rats using discrete wavelet transform[J].Computers in Biology and Medicine,2009,39(3):294-300.
[22] Zouridakis G,Tam D.Multi-unit spike discrimination using wavelet transforms[J].Computers in Biology and Medicine,1997,27(1):9-18.
[23]丁伟东.神经锋电位信号识别方法研究[D].上海:上海交通大学,2008.
[24] Herbst J,Gammeter S,Ferrero D,et al.Spike sorting with hidden Markov models[J].Journal of Neuroscience Methods,2008,174(1):126-134.
[25]丁勇,袁景淇.基于人工神经网络的低信噪比神经元峰电位分类[J].上海交通大学学报,2006,40(5):852-855.
[26] Aharon B,Adam S,Eran S.Spike sorting:Bayesian clustering of non-stationary data [J].Journal of Neuroscience Methods,2006,157(2):303-316.
[27] Frank W,Michael J.A nonparametric Bayesian alternative to spike sorting[J].Journal of Neuroscience Methods,2008,173(1):1-2.
[28]方正华.神经元集群编码与解码模型研究[D].安徽:合肥工业大学,2009.
[29]陈惟昌,王自强,陈志华,等.神经信息学的原理与展望[J].生物物理学报,2001,17(4):613-620.
[30]常文利.复杂网络上神经元系统对刺激的响应[D].甘肃:兰州大学,2007.
[31]傅晓婕.基于序空间的神经脉冲编码研究及应用[D].浙江:浙江工业大学,2009.
[32]吴朝晖,梁志明,李斌.一种植入式神经控制信号传输的数据编码方法[J].华南理工大学学报,2009,37(9):62-66.
[33] Burkitt A.An information-theoretic analysis of the coding of a periodic synaptic input by integrate-and-fire neurons[J].Neurocomputing,2002,44-46:69-74.
[34] Ucar A,Lonngren K,Bai E.Synchronization of the coupled FitzHugh-Nagumo systems [J].Chaos,Solitons & Fractals,2004,20(5):1085-1090.
[35] Izús G.,Sánchez A,Deza R.Noise-driven synchronization of a FitzHugh-Nagumo ring withphase-repulsive coupling : A perspective from the system’s nonequilibrium potential [J].Physica A:Statistical Mechanics and its Applications,2009,388(6):967-976.
[36] Liley D,Cadusch P,Dafilis M.A spatially continuous mean field theory of electrocortical activity[J].Computation in Neural Systems,2002,13(1):67-113.
[37] BazsóF,Zalányi L,Csárdi G.Channel noise in Hodgkin-Huxley model neurons[J].Physics Letters A,2003,311(1):13-20.
[38] Tuckwell H,Wan Y.Time to first spike in stochastic Hodgkin-Huxley systems[J].Physica A:Statistical Mechanics and its Applications,2005,351(2-4):427-438.
[39] Ginzburg S,Pustovoit M.Response of Hodgkin-Huxley stochastic bursting neuron to single-pulse stimulus[J].Physica A:Statistical Mechanics and its Applications,2006,369(2):354-368.
[40] Mishra D,Yadav A,Ray S,et al.Controlling synchronization of modified FitzHugh-Nagumo neurons under external electrical stimulation[J].NeuroQuantology,2006,4(1):50-67.
[41] Tuckwell H.Spike trains in a stochastic Hodgkin-Huxley system[J].Biosystems,2005,80(1):25-36.
[42] Casado J.Synchronization of two Hodgkin-Huxley neurons due to internal noise[J].Physics Letters A,2003,310(5-6):400-406.
[43] Wang Jiang,Che Yanqiu,Zhou Sisi,et al.Unidirectional synchronization of Hodgkin-Huxley neurons exposed to ELF electric field[J].Chaos,Solitons & Fractals,2009,39(3):1335-1345.
[44] Wei Xile,Wang Jiang,Deng Bin.Introducing internal model to robust output synchronization of FitzHugh-Nagumo neurons in external electrical stimulation[J].Communications in Nonlinear Science and Numerical Simulation,2009,14(7):3108-3119.
[45]孙倪.多电极阵列上培养神经元网络的锋电位信号处理[D].湖北:华中科技大学,2004.
[46]易晓斌.全局耦合HH神经元网络对动作电位输入的响应[D].甘肃:兰州大学,2005.
[47]耿丽硕.弱信号检测随机共振机制的网络模型及应用研究[D].浙江:杭州电子科技大学,2009.
[48] Quiroga Q,Nadasdy Z,Ben-Shaul Y.Unsupervised spike detection and sorting with wavelets and superparamagnetic clustering[J].Neural Computation,2004,16(8):1661-1687.
[49]郭强,田心.神经编码的信息熵表达研究进展[J].国际生物医学工程杂志,2006,29(6):330-333.
[50]陈芳.多电极阵列MEA在神经信息学与神经生理学研究中的应用[D].浙江:浙江大学,2007.
[51] Mtetwa N,Smith L.Smoothing and thresholding in neuronal spike detection[J].Neuro computing,2006,69(10-12):1366-1370.
[52] Fletcher M,Liang Bojian,Smith L,et al. Neural network based pattern matching and spikedetection tools and services-in the CARMEN neuroinformatics project[J].Neural Networks,2008,21(8):1076-1084.
[53] Chan H,Lin M,Wu T,et al.Detection of neuronal spikes using an adaptive threshold based on the max-min spread sorting method[J].Journal of Neuroscience Methods,2008,172(1):112-121.
[54] Takahashi S,Anzai Y,Sakurai Y.A new approach to spike sorting for multi-neuronal activities recorded with a tetrode-how ICA can be practical[J].Neuroscience Research,2003,46(3):265-272.
[55] Geng Xinling,Hu Guangshu,Tian Xin.Neural spike sorting using mathematical morphology, multiwavelets transform and hierarchical clustering[J].Neuro computing,2010,73(4-6):707-715.
[56] Horton P,Nicol A,Kendrick K,et al.Spike sorting based upon machine learning algorithms (SOMA)[J].Journal of Neuroscience Methods,2007,160(1):52-68.
[57] Deadwyler S,Hampson R.Ensemble activity and behavior:What’s the code[J].Science,1995,270:1316-1318.
[58] Ebner T,Chen G.Use of voltage-sensitive dyes and optical recordings in the central nervous system[J].Prog Neurobiol,1995,46:463-506.
[59]陈力超,顾蕴辉.神经元放电串中所含信息的编码理论和分析方法[J].生理科学进展,1999,30(2):101-106.
[60]焦贤发,王如彬.刺激下可变耦合神经振子群活动的非线性随机演化模型[J].控制与决策,2005,20(8):897-900.
[61]徐健学.基于非线性动力学概念神经编码[C].南京:第七届全国非线性动力学学术会议和第九届全国非线性振动学术会议论文集,2004:6-12.
[62] Torcini A,Luccioli S,Kreuz T.Coherent response of the Hodgkin-Huxley neuron in the high-input regime[J].Neurocomputing,2007,70(10-12):1943-1948.
[63] Schmid G,Goychuk I,Hanggi P.Channel noise and synchronization in excitable membranes [J].Physica A,2003,325:165-175.
[64] Wang Jiang,Si Wenjie,Che Yanqiu,et al.Spike trains in Hodgkin-Huxley model and ISIs of acupuncture manipulations[J].Chaos,Solitons & Fractals,2008,36(4):890-900.
[65] Che Yanqiu,Wang Jiang,Zhou Sisi,et al.Synchronization control of Hodgkin-Huxley neurons exposed to ELF electric field[J].Chaos,Solitons & Fractals,2009,40(4):1588-1598.
[66]吕晓莉,彭建华,刘延柱.延时FitzHugh-Nagumo神经网络的时空编码[J].上海交通学学报,2005,39(10):1664-1667.
[67] Meng Xin,Xu Jinghua,Gu Fanji.The singular spectrum of EEG from epileptic patients [J].Acta Biophysica Sinica,2001,17(1):86-90.
[68] Yao Baoheng,Yang Xiaju,Liu Yan,et al.The principle of optimum time lag choice based on singular value spectrum entropy[J].Journal of Shang Hai Jiao Tong University,2005,39(1):150-153.
[69] Li Xiaoli,Ouyang Gaoxian,Richards D.Predictability analysis of absence seizures with permutation entropy[J].Epilepsy Research,2007,77(1):70-74.
[70] Zhang Chaolin,Zhang Xuegong,Zhang M,et al.Neighbor number,valley seeking and clustering[J].Pattern Recognition Letters,2007,28(2):173-180.
[71] Cao Yinhe,Tung Wenwen,Gao J,et al.Detecting dynamical changes in time series using the permutation entropy[J].Physical Review E,2004,70(4):046217.
[72] Bandt C,Pompe B.Permutation entropy-a complexity measure for time series[J].Physical Review Letters,2002,88(17):174102.
[73] Krumin M,Shoham S.Generation of Spike Trains with Controlled Auto-and Cross- Correlation Functions[J].Neural Computation,2009,21(6):1642-1664.
[74]韩晓鹏,刘军,童勤业.双层Hodgkin-Huxley神经元网络中的随机共振[J].生物物理学报,2004,20(5):408-412.
[2] Hirata Y,Aihara K.Representing spike trains using constant sampling intervals[J].Journal of Neuroscience Methods,2009,183(2):277-286.
[3] Ishitobi M,Nakasato N,Yamamoto,et al.Opercular to interhemispheric source distribution of benign rolandic spikes of childhood[J].NeuroImage,2005,25(2):417-423.
[4]范丽伟,唐焕文.一门新兴的交叉学科——神经信息学[J].自然杂志,2002,24(6):352-355.
[5] Vliet E,Stoppini L,Balestrino M,et al.Electrophysiological recording of re-aggregating brain cell cultures on multi-electrode arrays to detect acute neurotoxic effects[J].NeuroToxicology,2007,28(6):1136-1146.
[6] Hill A,Jones N,Williams C,et al.Development of multi-electrode array screening for anticonvulsants in acute rat brain slices[J].Brain Research,2006,1096(1):70-84.
[7] Steidl E,Neveu E,Bertrand D,et al.The adult rat hippocampal slice revisited with multi-electrode arrays[J].Journal of Neuroscience Methods,2010,185 (2):246-256.
[8] Segundo J.Some thoughts about neural coding and spike trains[J].Biosystems,2000,58(1-3):3-7.
[9] Miller E,Wilson M.All My Circuits:Using Multiple Electrodes to Understand Functioning Neural Networks[J].Neuron,2008,60(3):483-488.
[10] Song Mingzhou,Wang Hongbin.A spike sorting framework using nonparametric detection and incremental clustering[J].Neurocomputing,2006,69(10-12):1380-1384.
[11] Gruner C,Johnson D.Correlation and neural information coding fidelity and efficiency [J].Neurocomputing,1999,26-27:163-168.
[12] Tian Lingling,Li Donghai,Sun Xianfang.Nonlinear-estimator-based robust synchronization of Hodgkin-Huxley neurons[J].Neurocomputing,2008,72(1-3):186-196.
[13] Segundo J.A history of spike trains as Point Processes in neural coding[J].Journal of Physiology-Paris,2010,104(3-4):156-159.
[14]易晓斌,张海峰.HH神经元对信号编码的响应[J].青海大学学报,2006,24(5):86-88.
[15]陈良泉.Hodgkin-Huxley模型的分岔分析与控制[D].天津:天津大学,2006.
[16]丁伟东,袁景淇,梁培基.多电极锋电位信号检测与分类方法研究[J].仪器仪表学报,2006,27(12):1636-1640.
[17] Adamos D,Kosmidis E,Theophilidis G.Performance evaluation of PCA-based spike sorting algorithms[J].Computer Methods and Programs in Biomedicine,2008,91(3):232-244.
[18] Letelier J,Weber P.Spike sorting based on discrete wavelet transform coefficients[J].Journal of Neuroscience Methods,2000,101(2):93-106.
[19] Hulata E,Segev R,Eshel B.A method for spike sorting and detection based on wavelet packets and Shannon’s mutual information[J].Journal of Neuroscience Methods,2002,117(1):1-12.
[20] Bosnyakova D,Gabova A,Kuznetsova G,et al.Time-frequency analysis of spike-wave discharges using a modified wavelet transform[J].Journal of Neuroscience Methods,2006,154(1-2):80-88.
[21]übeyli E,?ahin G,Deniz,et al.Analysis of spike-wave discharges in rats using discrete wavelet transform[J].Computers in Biology and Medicine,2009,39(3):294-300.
[22] Zouridakis G,Tam D.Multi-unit spike discrimination using wavelet transforms[J].Computers in Biology and Medicine,1997,27(1):9-18.
[23]丁伟东.神经锋电位信号识别方法研究[D].上海:上海交通大学,2008.
[24] Herbst J,Gammeter S,Ferrero D,et al.Spike sorting with hidden Markov models[J].Journal of Neuroscience Methods,2008,174(1):126-134.
[25]丁勇,袁景淇.基于人工神经网络的低信噪比神经元峰电位分类[J].上海交通大学学报,2006,40(5):852-855.
[26] Aharon B,Adam S,Eran S.Spike sorting:Bayesian clustering of non-stationary data [J].Journal of Neuroscience Methods,2006,157(2):303-316.
[27] Frank W,Michael J.A nonparametric Bayesian alternative to spike sorting[J].Journal of Neuroscience Methods,2008,173(1):1-2.
[28]方正华.神经元集群编码与解码模型研究[D].安徽:合肥工业大学,2009.
[29]陈惟昌,王自强,陈志华,等.神经信息学的原理与展望[J].生物物理学报,2001,17(4):613-620.
[30]常文利.复杂网络上神经元系统对刺激的响应[D].甘肃:兰州大学,2007.
[31]傅晓婕.基于序空间的神经脉冲编码研究及应用[D].浙江:浙江工业大学,2009.
[32]吴朝晖,梁志明,李斌.一种植入式神经控制信号传输的数据编码方法[J].华南理工大学学报,2009,37(9):62-66.
[33] Burkitt A.An information-theoretic analysis of the coding of a periodic synaptic input by integrate-and-fire neurons[J].Neurocomputing,2002,44-46:69-74.
[34] Ucar A,Lonngren K,Bai E.Synchronization of the coupled FitzHugh-Nagumo systems [J].Chaos,Solitons & Fractals,2004,20(5):1085-1090.
[35] Izús G.,Sánchez A,Deza R.Noise-driven synchronization of a FitzHugh-Nagumo ring withphase-repulsive coupling : A perspective from the system’s nonequilibrium potential [J].Physica A:Statistical Mechanics and its Applications,2009,388(6):967-976.
[36] Liley D,Cadusch P,Dafilis M.A spatially continuous mean field theory of electrocortical activity[J].Computation in Neural Systems,2002,13(1):67-113.
[37] BazsóF,Zalányi L,Csárdi G.Channel noise in Hodgkin-Huxley model neurons[J].Physics Letters A,2003,311(1):13-20.
[38] Tuckwell H,Wan Y.Time to first spike in stochastic Hodgkin-Huxley systems[J].Physica A:Statistical Mechanics and its Applications,2005,351(2-4):427-438.
[39] Ginzburg S,Pustovoit M.Response of Hodgkin-Huxley stochastic bursting neuron to single-pulse stimulus[J].Physica A:Statistical Mechanics and its Applications,2006,369(2):354-368.
[40] Mishra D,Yadav A,Ray S,et al.Controlling synchronization of modified FitzHugh-Nagumo neurons under external electrical stimulation[J].NeuroQuantology,2006,4(1):50-67.
[41] Tuckwell H.Spike trains in a stochastic Hodgkin-Huxley system[J].Biosystems,2005,80(1):25-36.
[42] Casado J.Synchronization of two Hodgkin-Huxley neurons due to internal noise[J].Physics Letters A,2003,310(5-6):400-406.
[43] Wang Jiang,Che Yanqiu,Zhou Sisi,et al.Unidirectional synchronization of Hodgkin-Huxley neurons exposed to ELF electric field[J].Chaos,Solitons & Fractals,2009,39(3):1335-1345.
[44] Wei Xile,Wang Jiang,Deng Bin.Introducing internal model to robust output synchronization of FitzHugh-Nagumo neurons in external electrical stimulation[J].Communications in Nonlinear Science and Numerical Simulation,2009,14(7):3108-3119.
[45]孙倪.多电极阵列上培养神经元网络的锋电位信号处理[D].湖北:华中科技大学,2004.
[46]易晓斌.全局耦合HH神经元网络对动作电位输入的响应[D].甘肃:兰州大学,2005.
[47]耿丽硕.弱信号检测随机共振机制的网络模型及应用研究[D].浙江:杭州电子科技大学,2009.
[48] Quiroga Q,Nadasdy Z,Ben-Shaul Y.Unsupervised spike detection and sorting with wavelets and superparamagnetic clustering[J].Neural Computation,2004,16(8):1661-1687.
[49]郭强,田心.神经编码的信息熵表达研究进展[J].国际生物医学工程杂志,2006,29(6):330-333.
[50]陈芳.多电极阵列MEA在神经信息学与神经生理学研究中的应用[D].浙江:浙江大学,2007.
[51] Mtetwa N,Smith L.Smoothing and thresholding in neuronal spike detection[J].Neuro computing,2006,69(10-12):1366-1370.
[52] Fletcher M,Liang Bojian,Smith L,et al. Neural network based pattern matching and spikedetection tools and services-in the CARMEN neuroinformatics project[J].Neural Networks,2008,21(8):1076-1084.
[53] Chan H,Lin M,Wu T,et al.Detection of neuronal spikes using an adaptive threshold based on the max-min spread sorting method[J].Journal of Neuroscience Methods,2008,172(1):112-121.
[54] Takahashi S,Anzai Y,Sakurai Y.A new approach to spike sorting for multi-neuronal activities recorded with a tetrode-how ICA can be practical[J].Neuroscience Research,2003,46(3):265-272.
[55] Geng Xinling,Hu Guangshu,Tian Xin.Neural spike sorting using mathematical morphology, multiwavelets transform and hierarchical clustering[J].Neuro computing,2010,73(4-6):707-715.
[56] Horton P,Nicol A,Kendrick K,et al.Spike sorting based upon machine learning algorithms (SOMA)[J].Journal of Neuroscience Methods,2007,160(1):52-68.
[57] Deadwyler S,Hampson R.Ensemble activity and behavior:What’s the code[J].Science,1995,270:1316-1318.
[58] Ebner T,Chen G.Use of voltage-sensitive dyes and optical recordings in the central nervous system[J].Prog Neurobiol,1995,46:463-506.
[59]陈力超,顾蕴辉.神经元放电串中所含信息的编码理论和分析方法[J].生理科学进展,1999,30(2):101-106.
[60]焦贤发,王如彬.刺激下可变耦合神经振子群活动的非线性随机演化模型[J].控制与决策,2005,20(8):897-900.
[61]徐健学.基于非线性动力学概念神经编码[C].南京:第七届全国非线性动力学学术会议和第九届全国非线性振动学术会议论文集,2004:6-12.
[62] Torcini A,Luccioli S,Kreuz T.Coherent response of the Hodgkin-Huxley neuron in the high-input regime[J].Neurocomputing,2007,70(10-12):1943-1948.
[63] Schmid G,Goychuk I,Hanggi P.Channel noise and synchronization in excitable membranes [J].Physica A,2003,325:165-175.
[64] Wang Jiang,Si Wenjie,Che Yanqiu,et al.Spike trains in Hodgkin-Huxley model and ISIs of acupuncture manipulations[J].Chaos,Solitons & Fractals,2008,36(4):890-900.
[65] Che Yanqiu,Wang Jiang,Zhou Sisi,et al.Synchronization control of Hodgkin-Huxley neurons exposed to ELF electric field[J].Chaos,Solitons & Fractals,2009,40(4):1588-1598.
[66]吕晓莉,彭建华,刘延柱.延时FitzHugh-Nagumo神经网络的时空编码[J].上海交通学学报,2005,39(10):1664-1667.
[67] Meng Xin,Xu Jinghua,Gu Fanji.The singular spectrum of EEG from epileptic patients [J].Acta Biophysica Sinica,2001,17(1):86-90.
[68] Yao Baoheng,Yang Xiaju,Liu Yan,et al.The principle of optimum time lag choice based on singular value spectrum entropy[J].Journal of Shang Hai Jiao Tong University,2005,39(1):150-153.
[69] Li Xiaoli,Ouyang Gaoxian,Richards D.Predictability analysis of absence seizures with permutation entropy[J].Epilepsy Research,2007,77(1):70-74.
[70] Zhang Chaolin,Zhang Xuegong,Zhang M,et al.Neighbor number,valley seeking and clustering[J].Pattern Recognition Letters,2007,28(2):173-180.
[71] Cao Yinhe,Tung Wenwen,Gao J,et al.Detecting dynamical changes in time series using the permutation entropy[J].Physical Review E,2004,70(4):046217.
[72] Bandt C,Pompe B.Permutation entropy-a complexity measure for time series[J].Physical Review Letters,2002,88(17):174102.
[73] Krumin M,Shoham S.Generation of Spike Trains with Controlled Auto-and Cross- Correlation Functions[J].Neural Computation,2009,21(6):1642-1664.
[74]韩晓鹏,刘军,童勤业.双层Hodgkin-Huxley神经元网络中的随机共振[J].生物物理学报,2004,20(5):408-412.