癫痫脑电信号的非线性分析
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摘要
癫痫疾病严重威胁着人们的身体健康。癫痫脑电分析是研究癫痫的一个重要手段。当前，癫痫的脑电分析主要以病灶区单导联或双导联皮层脑电(Electrocorticogram, ECoG)作为脑电研究对象。本文研究的脑电数据包括两部分，一部分数据来自所设计的脑电采集实验，为临床采集的20导联头皮脑电(Electroencephalogram, EEG)数据；另一部分数据为网上数据库中提供的颅内皮层脑电数据。本文针对脑电数据进行了复杂性、同步性和多尺度等非线性分析，提取了线性分析方法无法提取的有效特征。
利用LZ复杂度和关联维数等复杂度分析方法，分析了癫痫脑电数据，提取了癫痫脑电的复杂度特征。分析表明，癫痫EEG的复杂度普遍低于健康EEG，癫痫发作阶段的ECoG的复杂度低于发作间隙ECoG的复杂度。脑电信号的复杂度特征可以作为癫痫疾病的诊断和预测特征。
利用排序递归图的分析方法对癫痫脑电进行了确定性的分析。分析表明，癫痫脑电的确定性特征与复杂度特征分析所得的结论一致。但确定性的计算速度更快，更适合分析短时高噪且高度非平稳脑电信号。从大脑是一个相互耦合和相互作用的复杂网络的观点出发，提出了利用排序互信息的方法研究不同导联之间的信息传输，对EEG进行多导联同步性分析。分析表明，癫痫患者的大脑不同区域之间的信息交流明显强于健康对象，即癫痫患者的大脑同步性明显增强。
利用小波分解和小波重构技术，得到不同节律(频带)的脑电信号。分析了小波熵、复杂度和确定性特征在不同节律下的变化规律。分析表明，这些特征在不同节律中的变化规律并不相同。通过单独分析子频带，可以提取潜藏在癫痫脑电信号中的更精确的信息。
提出了将基于无迹卡尔曼滤波(Unscented Kalman Filter, UKF)的神经网络作为癫痫脑电特征的分类器。UKF算法通过迭代运算可快速估计神经网络的权值，解决神经网络的训练问题。结果表明，该分类器的分类性能优于线性判别分析(Linear Discriminant Analysis, LDA)分类器。
本文利用非线性分析方法提取了癫痫脑电数据的多种特征，为癫痫的自动诊断和发作预测提供了理论依据。
Epilepsy disease seriously threatens the health of patients. Analysis of brainelectrical signal is an important approach for epilepsy study. At present, intracranialelectrocorticogram (ECoG) of single electrode or double electrodes in focal area is themain research data for epilepsy analysis. There are two pieces of data which is studiedin this thesis. One part of data was taken from the designed electroencephalogram(EEG) acquisition experiment. This part of data includes20electrodes of scalp EEGcollected clinical. The other part is the ECoG data provided on line. In this thesis,nonlinear analysis methods of complexity, synchronism and multi-scale are applied toEEG and ECoG. The effective features that can not be extracted by linear methods areobtained.
The complexity analysis of LZ complexity and correlation dimension of phasespace was used to analyze the epilepsy brain electrical data. The complexity feature ofbrain electrical signals was extracted. The results show that the complexity ofepilepsy EEG is lower than that of healthy EEG, and that complexity of ECoG duringa seizure (ictal ECoG) is lower than that of a seizure-free interval (interictal ECoG).The complexity can be used as features to auto-diagnose and predict epilepsy.
The method of order recurrence plot was used to analyze the determination ofepileptic brain electrical signals. The results show that the determination feature isconsistent with complexity feature analysis. Nevertheless, the computation speed ofdetermination is much faster. It is more appropriate for the brain electrical signals ofshort time, high noises, and high nonstationarity. Base on the point that brain is anintercoupling and interacting complex net work, permutation mutual information waspresented to study the information transmission of different electrodes.Multi-electrodes synchronism analysis is used to EEG data. The results show that theexchange of information of different brain regions of epilepsy patients is obviouslymore than that of healthy objects. That is the synchronism of epilepsy patients isobviously enhanced.
Different rhythms of brain electrical signals are obtained by waveletdecomposition and reconstruction techniqes. Feathures of wavelet entropy,complexity and determination were analyzed in different rhythms. The results showthe changing rules of these feathures in different rhythms are not identical. By independently analyzing subbands, more accurate information underlying the epilepsybrain electric signals can be extracted.
Neural network based on unscented Kalman filter(UKF) was used as an classifierof the features of epilepsy brain electric signals. The algorithm of UKF can estimatethe weights of neural network at a high rate of speed. So the problem the lower speedof net training is solved. The results show the classification performance of theclassifier is superior to linear discriminant analysis(LDA).
In this thesis, multiple features were extracted from epilepsy brain electric datataking advantage of nonlinear analysis methods. A theoretical basis is provided forauto-diagnosis of epilepsy and seizure prediction.
利用LZ复杂度和关联维数等复杂度分析方法，分析了癫痫脑电数据，提取了癫痫脑电的复杂度特征。分析表明，癫痫EEG的复杂度普遍低于健康EEG，癫痫发作阶段的ECoG的复杂度低于发作间隙ECoG的复杂度。脑电信号的复杂度特征可以作为癫痫疾病的诊断和预测特征。
利用排序递归图的分析方法对癫痫脑电进行了确定性的分析。分析表明，癫痫脑电的确定性特征与复杂度特征分析所得的结论一致。但确定性的计算速度更快，更适合分析短时高噪且高度非平稳脑电信号。从大脑是一个相互耦合和相互作用的复杂网络的观点出发，提出了利用排序互信息的方法研究不同导联之间的信息传输，对EEG进行多导联同步性分析。分析表明，癫痫患者的大脑不同区域之间的信息交流明显强于健康对象，即癫痫患者的大脑同步性明显增强。
利用小波分解和小波重构技术，得到不同节律(频带)的脑电信号。分析了小波熵、复杂度和确定性特征在不同节律下的变化规律。分析表明，这些特征在不同节律中的变化规律并不相同。通过单独分析子频带，可以提取潜藏在癫痫脑电信号中的更精确的信息。
提出了将基于无迹卡尔曼滤波(Unscented Kalman Filter, UKF)的神经网络作为癫痫脑电特征的分类器。UKF算法通过迭代运算可快速估计神经网络的权值，解决神经网络的训练问题。结果表明，该分类器的分类性能优于线性判别分析(Linear Discriminant Analysis, LDA)分类器。
本文利用非线性分析方法提取了癫痫脑电数据的多种特征，为癫痫的自动诊断和发作预测提供了理论依据。
Epilepsy disease seriously threatens the health of patients. Analysis of brainelectrical signal is an important approach for epilepsy study. At present, intracranialelectrocorticogram (ECoG) of single electrode or double electrodes in focal area is themain research data for epilepsy analysis. There are two pieces of data which is studiedin this thesis. One part of data was taken from the designed electroencephalogram(EEG) acquisition experiment. This part of data includes20electrodes of scalp EEGcollected clinical. The other part is the ECoG data provided on line. In this thesis,nonlinear analysis methods of complexity, synchronism and multi-scale are applied toEEG and ECoG. The effective features that can not be extracted by linear methods areobtained.
The complexity analysis of LZ complexity and correlation dimension of phasespace was used to analyze the epilepsy brain electrical data. The complexity feature ofbrain electrical signals was extracted. The results show that the complexity ofepilepsy EEG is lower than that of healthy EEG, and that complexity of ECoG duringa seizure (ictal ECoG) is lower than that of a seizure-free interval (interictal ECoG).The complexity can be used as features to auto-diagnose and predict epilepsy.
The method of order recurrence plot was used to analyze the determination ofepileptic brain electrical signals. The results show that the determination feature isconsistent with complexity feature analysis. Nevertheless, the computation speed ofdetermination is much faster. It is more appropriate for the brain electrical signals ofshort time, high noises, and high nonstationarity. Base on the point that brain is anintercoupling and interacting complex net work, permutation mutual information waspresented to study the information transmission of different electrodes.Multi-electrodes synchronism analysis is used to EEG data. The results show that theexchange of information of different brain regions of epilepsy patients is obviouslymore than that of healthy objects. That is the synchronism of epilepsy patients isobviously enhanced.
Different rhythms of brain electrical signals are obtained by waveletdecomposition and reconstruction techniqes. Feathures of wavelet entropy,complexity and determination were analyzed in different rhythms. The results showthe changing rules of these feathures in different rhythms are not identical. By independently analyzing subbands, more accurate information underlying the epilepsybrain electric signals can be extracted.
Neural network based on unscented Kalman filter(UKF) was used as an classifierof the features of epilepsy brain electric signals. The algorithm of UKF can estimatethe weights of neural network at a high rate of speed. So the problem the lower speedof net training is solved. The results show the classification performance of theclassifier is superior to linear discriminant analysis(LDA).
In this thesis, multiple features were extracted from epilepsy brain electric datataking advantage of nonlinear analysis methods. A theoretical basis is provided forauto-diagnosis of epilepsy and seizure prediction.
引文
[1] K. Lehnertz, B. Litt, The First International Collaborative Workshop onSeizure Prediction: summary and data description, Clinical Neurophysiology,2005,116(3):493-505.
[2] H.P. Zaveri, M.G. Frei, S. Arthurs, Seizure prediction: The FourthInternational Workshop, Epilepsy&Behavior,2010,19(1):1-3.
[3] S.S. Viglione, G. O. Walsh, Epileptic seizure prediction, Electroencephalogr.Clin. Neurophysiol.,1975,39:435-436.
[4] Z. Rogowski, I. Gath, E. Bental, On the prediction of epileptic seizures,BIOLOGICAL CYBERNETICS,1981,42(1):9-15.
[5] Y. Salant, I. Gath, O. Henriksen, Prediction of epileptic seizures from twochannel EEG, Medical and Biological Engineering and Computing,1998,36(5):549-556.
[6] I. Osorio, M.G. Frei, S.B. Wilkinson, Real-time automated detection andquantitative analysis of seizures and short-term prediction of clinical onset,Epilepsia,1998,39(6):615-627.
[7] H.H. Lange, J.P. Lieb, J. Engel Jr, Temporo-spatial patterns of preictal spikeactivity in human temporal lobe epilepsy, Electroencephalography andClinical Neurophysiology,1983,56(6):543-555.
[8] J. Gotman, M.G. Marciani, Electroencephalographic spiking activity, druglevels and seizure occurrence in epileptic patients, Annals of Neurology,1985,17(6):597-603.
[9] J. Gotman, D.J. Koffler. Interictal spiking increases after seizures but does notafter decrease in medication, Electroencephalography and ClinicalNeurophysiology,1989,72(1):7-15.
[10] A. Katz, D.A. Marks, G. McCarthy, et al., Does interictal spiking rate changeprior to seizures?, Electroencephalography and Clinical Neurophysiology,1991,79:153-156.
[11] B. Litt, R. Esteller, J. Echauz, et al., Epileptic seizures may begin hours inadvance of clinical onset: a report of five patients. Neuron,2001,30(1):51–64.
[12] S. Gigola, F. Ortiz, C.E. D’Attellis, et al., Prediction of epileptic seizuresusing accumulated energy in a multiresolution framework, Journal ofNeuroscience Methods,2004,138(1):107-111.
[13] L.D. Iasemidis, J.C. Sackellares, H.P. Zaveri, et al., Phase space topographyand the Lyapunov exponent of electrocorticograms in partial seizures, BrainTopography,1990,2(3):187-201.
[14] K. Lehnertz, C.E. Elger, Spatio-temporal dynamics of the primaryepileptogenic area in temporal lobe epilepsy characterized by neuronalcomplexity loss, Electroencephalography and Clinical Neurophysiology,1995,95(2):108-117.
[15] A. L. Benabid, P. Pollak, C. Gervason, et al., Long-term suppression of tremorby chronic stimulation of the ventral intermediate thalamic nucleus, THELANCET,1991,337(8738):403-406.
[16] V. Navarro, J. Martinerie, M.L.V. Quyen, et al. Seizure anticipation in humanneocortical partial epilepsy, Brain,2002,125(3):640-655.
[17] M.L.V. Quyen, J. Martinerie, M. Baulac, et al., Anticipating epileptic seizurein real time by a nonlinear analysis of similarity between EEG recordings,NeuroReport,1999,10(10):2149-2155.
[18] M.L.V. Quyen, C. Adam, J. Martinerie, et al., Spatio-temporalcharacterizations of non-linear changes in intracranial activities prior to humantemporal lobe seizures, European Journal of Neuroscience,2000,12(6):2124-2134.
[19] M.L.V. Quyen, J. Martinerie, V. Navarro, et al., Anticipation of epilepticseizures from standard EEG recordings, THE LANCET,2001,357(9251):183-188.
[20] N. Thomasson, T.J. Hoeppner, C.L. Webber Jr., Recurrence quantification inepileptic EEGs, Physics Letters A,2001,279(1):94-101.
[21] J. P. Eckmann, S. O. Kamphorst, D. Ruelle, Recurrence Plots of DynamicalSystems, Europhysics Letters,1987,4(9):973-977.
[22] N. Marwan, A.Meinke, Extended recurrence plot analysis and its applicationto ERP data, International Journal of Bifurcation and Chaos “Cognition andComplex Brain Dynamics”,2004,14(2):1-5.
[23] V. Navarro, J. Martinerie, M.L.V. Quyen, et al. Seizure anticipation in humanneocortical partial epilepsy. Brain,2002,125(3):640-655.
[24] F. Mormann, K. Lehnertz, P. David,et al., Mean phase coherence as a measurefor phase synchronization and its application to the EEG of epilepsy patients,Physica D,2000,144(3):358-369.
[25] M.L.V. Quyen, J. Martinerie, V. Navarro, et al., Characterizing neurodynamicchanges before seizures, Journal of Clinical Neurophysiology,2001,18(3):191-208.
[26] M.L.V. Quyen, V. Navarro, J. Martinerie, et al., Towards a neurodynamicalunderstanding of ictogenesis, Epilepsia,2003,44(S12):30-43.
[27] S.J. Julier, J.K. Uhlmann, A consistent, debiased method for convertingbetween polar and Cartesian coordinate systems, UK PUBMED CENTRAL,1997,3086:110-121.
[28] C.E. Elger, K. Lehnertz, Seizure prediction by non-linear time series analysisof brain electrical activity, European Journal of Neuroscience,1998,10(2):786-789.
[29] K. Lehnertz, C.E. Elger. Can epileptic seizures be predicted? Evidence fromnonlinear time series analysis of brain electrical activity, Phys. Rev. Lett.1998,80(22):5019-5022.
[30] L.D. Iasemidis, P. Pardalos, J.C. Sackellares, et al., Quadratic binaryprogramming and dynamical system approach to determine the predictabilityof epileptic seizures. Journal of Combinatorial Optimization,2001,5(1):9-26.
[31] B. Litt, R. Esteller, J. Echauz, et al., Epileptic seizures may begin hours inadvance of clinical onset: a report of five patients, Neuron,2001,30(1):51-64.
[32] S. Gigola, F. Ortiz, C.E. D’Attellis, et al., Prediction of epileptic seizuresusing accumulated energy in a multiresolution framework. Journal ofNeuroscience Methods,2004,138(1):107-111.
[33] F. Mormann, T. Kreuz, R.G. Andrzejak, et al.,Epileptic seizures are precededby a decrease in synchronization. Epilepsy Research,2003,53(3):173-185.
[34] M. D’Alessandro, G. Vachtsevanos, R. Esteller, et al., A multi-feature andmulti-channel univariate selection process for seizure prediction. ClinicalNeurophysiology,2005,116(3):506-516.
[35] R. Esteller, J. Echauz, M. D’Alessandro, et al., Continuous energy variationduring the seizure cycle: towards an on-line accumulated energy. ClinNeurophysiol2005,116(3):517-526.
[36] M.A. Harrison, M.G. Frei, I. Osorio, Accumulated energy revisited. ClinicalNeurophysiology,2005,116(3):527-531.
[37] C.C. Jouny, P.J. Franaszczuk, G.K. Bergey, Signal complexity and synchronyof epileptic seizures: is there an identifiable preictal period? ClinicalNeurophysiology,2005,116(3):552-558.
[38] F. Mormann, T. Kreuz, C. Rieke, et al., On the predictability of epilepticseizures. Clinical Neurophysiology,2005,116(3):569-587.
[39] L.D. Iasemidis, D.S. Shiau, P.M. Pardalos, et al., Long-term prospectiveon-line real-time seizure prediction. Clinical Neurophysiology,2005,116(3):532–544.
[40] M.L.V. Quyen, J. Soss, V. Navarro, et al., Preictal state identification bysynchronization changes in long-term intracranial EEG recordings. ClinicalNeurophysiology,2005,116(3):559-568.
[41] L.D. Iasemidis, D.S. Shiau, W. Chaovalitwongse, et al., Adaptive epilepticseizure prediction system. IEEE Transactions on Biomedical Engineering,2003,50(5):616-627.
[42]欧阳高翔，癫痫脑电信号的非线性特征识别与分析：[博士学位论文]，燕山大学，2010.
[43]游宇，癫痫模型的中枢神经系统脱髓鞘改变及其对癫痫治疗意义的研究：[博士学位论文]，第四军医大学，2011
[44]赵龙莲，生物反馈中脑电信号分析及其在癫痫治疗中应用的研究：[博士学位论文]，清华大学，2009.
[45]汪春梅，癫痫脑电信号特征提取与自动检测方法研究：[博士学位论文]，华东理工大学，2011.
[46]谢丽娟，贺达仁，李小俚等，癫痫预测方法的分析与研究，医学与哲学，2006，27(1)：37-40.
[47]杜一鸣，王耘，黄光，癫痫预测面临问题的分析与展望，医学与哲学，2008，29(9)：59-61.
[48] F. Mormann, R.G. Andrzejak, C. E. Elger, et al., Seizure prediction: the longand winding road, Brain,2007,130(2):314-333.
[49] M. Valderrama, S. Nikolopoulos, C. Adam, et al. Patientspecific seizureprediction using a multi-feature and multi-modal EEG-ECG classification, XIIMediterranean Conference on Medical and Biological Engineering andComputing2010,2010,29:77-80.
[50] L. Chisci, A. Mavino, G. Perferi, et al., Realtime epileptic seizure predictionusing AR models and support vector machines, IEEE Transactions onBiomedical Engineering,2010,57(5):1124-1132.
[51] S. Altunay, Z. Telatar, O. Erogul, Epileptic EEG detection using the linearprediction error energy, Expert Systems with Applications,2010,37(8):5661-5565.
[52] J. Dauwels, F. Vialatte, A. Cichocki, Diagnosis of Alzheimer’s disease fromeeg signals: where are we standing? Current Alzheimer Research,2010,7(6):487-505.
[53] H. Feldwisch-Drentrup, B. Schelter, M. Jachan, et al. Joining the benefits:combining epileptic seizure prediction methods. Epilepsia,2010,51(8):1598-1606.
[54] H. Feldwisch-Drentrup, A. Schulze-Bonhage, J. Timmer, et al., Statisticalvalidation of event predictors: a comparative study based on the field ofseizure prediction, Physical Review E,2011,83(6):066704.
[55] H. Feldwisch-Drentrup, M. Staniek, A. Schulze-Bonhage, et al. Identificationof preseizure states in epilepsy: a data-driven approach for multichannel EEGrecordings. Frontiers in COMPUTATIONAL NEUROSCIENCE,2011,5(32):1-9.
[56] B. He, Y. Dai, L. Astolfi, et al., eConnectome: a MATLAB toolbox formapping and imaging of brain functional connectivity. J Neurosci Methods2011,195(2):261-269.
[57] P. Mirowski. Comparing SVM and convolutional networks for epilepticseizure prediction from intracranial EEG. In: IEEE Workshop on MachineLearning for Signal Processing. MLSP2008,2008:244-249.
[58] P. Rajdev, M. Ward, J. Rickus, et al., Real-time seizure prediction from localfield potentials using an adaptive Wiener algorithm, Computers in Biology andMedicine,2010,40(1):97-108.
[59] B. Schelter, M. Winterhalder, H.F. Drentrup, et al. Seizure prediction: theimpact of long prediction horizons. Epilepsy Research,2007,73(2):213-217.
[60] D.E. Snyder, J. Echauz, D.B. Grimes, et al., The statistics of a practical seizurewarning system, Journal of Neural Engineering,2008,5(4):392-401.
[61] B. Swiderski, S. Osowski, A. Cichocki, et al., Single-class SVM and directedtransfer function approach to the localization of the region containing epilepticfocus. Neurocomputing,2009,72(7):1575-1583.
[62] I.T. Tokuda, J. Kurths, I.Z. Kiss, et al., Predicting phase synchronization ofnonphase-coherent chaos. Europhysics Letters,2008,83(5):50003.
[63] H.J. M ller, W.F. Gattaz, J.F.W. Deakin, European Archives of Psychiatry andClinical Neuroscience,1929,87(1):527-570.
[64] R.G. Andrzejak, K. Lehnertz, F. Mormann, et al. Indications of nonlineardeterministic and finite-dimensional structures in time series of brain electricalactivity: Dependence on recording region and brain state, PHYSICALREVIEW E,2001,64:061907.
[65] J. Ziv, A. Lempel, A universal algorithm for sequential data compression.IEEE Transactions on Information Theory,1977,23(3),337-343.
[66] J. Ziv, A. Lempel, Compression of individual sequences via variable-ratecoding. IEEE Transactions on Information Theory,1978,24(5),530-536.
[67] X.S. Zhang, R.J. Roy, E.W. Jensen, EEG complexity as a measure of depth ofanesthesia for patients, IEEE Transactions on Biomedical Engineering,2001,48(12):1424-1433.
[68]吴祥宝,徐京华,复杂性与脑功能,生物物理学报,1991,7(1):103-106.
[69] F. Takens, Detecting strange attractors in turbulence: Dynamical systems andturbulence. In Rand, D. A. and Young, L. S., editors, Lecture Notes inMathematics,1981. Vol.366. Springer-Verlag, Berlin.
[70] A.M. Fraser, H.L. Swinney, Independent coordinates for strange attractorsfrom mutual information, Physical Review A,1986,33(2):1134.
[71] W. Liebert, H. Schuster, Proper choice of the time delay for the analysis ofchaotic time series, Physics Letters A,1989,142(2-3):107-111.
[72] H.D.I. Abarbanel, M.B. Kennel, Local false nearest neighbors and dynamicaldimensions from observed chaotic data, Physical Review E,1993,47(5):3057.
[73] L. Cao, Practical method for determining the minimum embedding dimensionof a scalar time series, Physica D: Nonlinear Phenomena,1997,110(1):43-50.
[74]刘海峰，代正华，陈峰等，混沌动力系统小波变换模数的关联维数，物理学报，2002，51(6)：1186-1192.
[75] S. Borovkova, R. Burton, H. Dehling, Consistency of the Takens estimator forthe correlation dimension, The Annals of Applied Probability,1999,9(2):376-390.
[76] K. Natarajan, R. U. Acharya, F. Alias,et al., Nonlinear analysis of EEG signalsat different mental states, BioMedical Engineering OnLine,(2004),3(7):1-11.
[77]闫润强，语音信号动力学特性递归分析：[硕士学位论文]，上海交通大学，2006.
[78] J. P. Zbilut, A. Giuliani, C. L. Webber, Detecting deterministic signals inexceptionally noisy environments using cross-recurrence quantification,Physics Letters A,1998,246(1-2):122-128.
[79] N. Marwan, J. Kurths, Nonlinear analysis of bivariate data with crossrecurrence plots, Physics Letters A,2002,302(5-6):299-307.
[80] A. Groth, Visualization of coupling in time series by order recurrence plots,Physical Review E,2005,72(4):046220.
[81] O. Sosnovtseva, A. Balanov, T. Vadivasova, et al., Loss of lag synchronizationin coupled chaotic systems, Physical Review E,1999,60(6):6560.
[82] C. L. Webber Jr, J. Zbilut, Dynamical assessment of physiological systems andstates using recurrence plot strategies, Journal of Applied Physiology,1994,76(2):965-973.
[83] J. P. Zbilut, C. L. Webber Jr, Embeddings and delays as derived fromquantification of recurrence plots, Physics Letters A,1992,171(3-4):199-203.
[84] F. Lopes da Silva, A. Hoeks, H. Smits, et al., Model of brain rhythmic activity,Biological Cybernetics,1974,15(1):27-37.
[85] B. H. Jansen, G. Zouridakis, M. E. Brandt, A neurophysiologically-basedmathematical model of flash visual evoked potentials, Biological Cybernetics,1993,68(3):275-283.
[86] F. Wendling, J. Bellanger, F. Bartolomei, et al., Relevance of nonlinearlumped-parameter models in the analysis of depth-EEG epileptic signals,Biological Cybernetics,2000,83(4):367-378.
[87] C. Bandt, B. Pompe, Permutation entropy: A natural complexity measure fortime series, Physical Review Letters,2002,88(17):174102.
[88]边洪瑞，王江，韩春晓等，基于复杂度的针刺脑电信号特征提取，物理学报，2011，60(11)：118701.
[89]边洪瑞，针刺足三里对EEG影响的研究：[硕士学位论文]，天津大学，2011.
[90]李诺，针刺对脑功能影响的数据采集与分析：[硕士学位论文]，天津大学，2010.
[91] G. Pfurtscheller, A. Stancak, G. Edlinger, On the existence of different types ofcentral beta rhythms below30Hz, Electroencephalography and clinicalneurophysiology,1997,102(4):316-325.
[92] S. G. Mallat, A wavelet tour of signal processing, Academic Pr,1999.
[93] S. Blanco, R. Q. Quiroga, O. Rosso, et al., Time-frequency analysis ofelectroencephalogram series, Physical Review E,1995,51(3):2624.
[94] A. Shashua,“On the relationship between the support vector machine forclassification and sparsified fisher’s linear discriminant,” Neural ProcessingLetters,1999,9(2):129-139.
[95] D.E. Rumelhart, G.E. Hinton, R.J.Williams, Learning representations ofback-propagation errors, Nature,1986,323:533-536.
[96] R.E. Kalman. A new approach to linear filtering and prediction problems,Transactions of the ASME, Ser. D, Journal of Basic Engineering,1960,82:34-45.
[97] S.J. Julier, J.K. Uhlmann. A new extension of the Kalman filter to nonlinearsystems, Proceedings of AeroSense:11th Int Symposium Aerospace/DefenseSensing,Simulation and Controls.1997:54-65.
[98] G.V. Puskorius, L.A. Feldkamp, and L.I. Davis Jr., Dynamic neural networkmethods applied to on-vehicle idle speed control, Proceedings of the IEEE,1996,84:1407-1420.
[99] S.J. Julier, J.K. Uhlmann, and H. Durrant-Whyte. A new approach for filteringnonlinear systems, Proceedings of the American Control Conference,1995:1628-1632.
[100] E.A.Wan, R. van der Merwe. The unscented Kalman filter for nonlinearestimation, Proceedings of Symposium2000on Adaptive Systems for SignalProcessing, Communication and Control (AS-SPCC), IEEE,2000.
[101] E.W. Saad, D.V. Prokhorov, D.C.Wunsch III. Comparative study of stock trendprediction using time delay, recurrent and probabilistic neural networks,IEEE Transactions on Neural Networks,1998,9:1456C1470.
[102] K.C. Jim, C.L. Giles, B.G. Horne, An analysis of noise in recurrent neuralnetworks: convergence and generalization, IEEE Transactions on NeuralNetworks,1996,7:1424C1438.
[103] S. Singhal, L.Wu, Training multilayer perceptrons with the extended Kalmanfilter, Advances in Neural Information Processing Systems1,1989:133-140.
[104] S. Haykin. Kalman Filtering and Neural Networks[M]. New York: Wiley,Chap.7,2002.
[105] A. Sitz, U. Schwarz, J. Kurths, et al., Estimation of parameters and unobservedcomponents for nonlinear systems from noisy time series, Physical Review E,2002,66:016210.
[106] Bin Deng, Jiang Wang,and Yenqiu Che, A combined method to estimateparameters of neuron from a heavily noise-corrupted time series of activepotential, CHAOS,2009,19:015105.
[107] L. Zheng, J.E. O’Doherty, T.L. Hanson,et al. Unscented Kalman Filter forBrain-Machine Interfaces, PLoS one,2009,4(7)e6243:1-18.
[108] M. Clerc, J. Kennedy, The particle swarm-explosion, stability, andconvergence in a multidimensional complex space, IEEE Transactions onEvolutionary Computation,2002,6(1):58-73.
[2] H.P. Zaveri, M.G. Frei, S. Arthurs, Seizure prediction: The FourthInternational Workshop, Epilepsy&Behavior,2010,19(1):1-3.
[3] S.S. Viglione, G. O. Walsh, Epileptic seizure prediction, Electroencephalogr.Clin. Neurophysiol.,1975,39:435-436.
[4] Z. Rogowski, I. Gath, E. Bental, On the prediction of epileptic seizures,BIOLOGICAL CYBERNETICS,1981,42(1):9-15.
[5] Y. Salant, I. Gath, O. Henriksen, Prediction of epileptic seizures from twochannel EEG, Medical and Biological Engineering and Computing,1998,36(5):549-556.
[6] I. Osorio, M.G. Frei, S.B. Wilkinson, Real-time automated detection andquantitative analysis of seizures and short-term prediction of clinical onset,Epilepsia,1998,39(6):615-627.
[7] H.H. Lange, J.P. Lieb, J. Engel Jr, Temporo-spatial patterns of preictal spikeactivity in human temporal lobe epilepsy, Electroencephalography andClinical Neurophysiology,1983,56(6):543-555.
[8] J. Gotman, M.G. Marciani, Electroencephalographic spiking activity, druglevels and seizure occurrence in epileptic patients, Annals of Neurology,1985,17(6):597-603.
[9] J. Gotman, D.J. Koffler. Interictal spiking increases after seizures but does notafter decrease in medication, Electroencephalography and ClinicalNeurophysiology,1989,72(1):7-15.
[10] A. Katz, D.A. Marks, G. McCarthy, et al., Does interictal spiking rate changeprior to seizures?, Electroencephalography and Clinical Neurophysiology,1991,79:153-156.
[11] B. Litt, R. Esteller, J. Echauz, et al., Epileptic seizures may begin hours inadvance of clinical onset: a report of five patients. Neuron,2001,30(1):51–64.
[12] S. Gigola, F. Ortiz, C.E. D’Attellis, et al., Prediction of epileptic seizuresusing accumulated energy in a multiresolution framework, Journal ofNeuroscience Methods,2004,138(1):107-111.
[13] L.D. Iasemidis, J.C. Sackellares, H.P. Zaveri, et al., Phase space topographyand the Lyapunov exponent of electrocorticograms in partial seizures, BrainTopography,1990,2(3):187-201.
[14] K. Lehnertz, C.E. Elger, Spatio-temporal dynamics of the primaryepileptogenic area in temporal lobe epilepsy characterized by neuronalcomplexity loss, Electroencephalography and Clinical Neurophysiology,1995,95(2):108-117.
[15] A. L. Benabid, P. Pollak, C. Gervason, et al., Long-term suppression of tremorby chronic stimulation of the ventral intermediate thalamic nucleus, THELANCET,1991,337(8738):403-406.
[16] V. Navarro, J. Martinerie, M.L.V. Quyen, et al. Seizure anticipation in humanneocortical partial epilepsy, Brain,2002,125(3):640-655.
[17] M.L.V. Quyen, J. Martinerie, M. Baulac, et al., Anticipating epileptic seizurein real time by a nonlinear analysis of similarity between EEG recordings,NeuroReport,1999,10(10):2149-2155.
[18] M.L.V. Quyen, C. Adam, J. Martinerie, et al., Spatio-temporalcharacterizations of non-linear changes in intracranial activities prior to humantemporal lobe seizures, European Journal of Neuroscience,2000,12(6):2124-2134.
[19] M.L.V. Quyen, J. Martinerie, V. Navarro, et al., Anticipation of epilepticseizures from standard EEG recordings, THE LANCET,2001,357(9251):183-188.
[20] N. Thomasson, T.J. Hoeppner, C.L. Webber Jr., Recurrence quantification inepileptic EEGs, Physics Letters A,2001,279(1):94-101.
[21] J. P. Eckmann, S. O. Kamphorst, D. Ruelle, Recurrence Plots of DynamicalSystems, Europhysics Letters,1987,4(9):973-977.
[22] N. Marwan, A.Meinke, Extended recurrence plot analysis and its applicationto ERP data, International Journal of Bifurcation and Chaos “Cognition andComplex Brain Dynamics”,2004,14(2):1-5.
[23] V. Navarro, J. Martinerie, M.L.V. Quyen, et al. Seizure anticipation in humanneocortical partial epilepsy. Brain,2002,125(3):640-655.
[24] F. Mormann, K. Lehnertz, P. David,et al., Mean phase coherence as a measurefor phase synchronization and its application to the EEG of epilepsy patients,Physica D,2000,144(3):358-369.
[25] M.L.V. Quyen, J. Martinerie, V. Navarro, et al., Characterizing neurodynamicchanges before seizures, Journal of Clinical Neurophysiology,2001,18(3):191-208.
[26] M.L.V. Quyen, V. Navarro, J. Martinerie, et al., Towards a neurodynamicalunderstanding of ictogenesis, Epilepsia,2003,44(S12):30-43.
[27] S.J. Julier, J.K. Uhlmann, A consistent, debiased method for convertingbetween polar and Cartesian coordinate systems, UK PUBMED CENTRAL,1997,3086:110-121.
[28] C.E. Elger, K. Lehnertz, Seizure prediction by non-linear time series analysisof brain electrical activity, European Journal of Neuroscience,1998,10(2):786-789.
[29] K. Lehnertz, C.E. Elger. Can epileptic seizures be predicted? Evidence fromnonlinear time series analysis of brain electrical activity, Phys. Rev. Lett.1998,80(22):5019-5022.
[30] L.D. Iasemidis, P. Pardalos, J.C. Sackellares, et al., Quadratic binaryprogramming and dynamical system approach to determine the predictabilityof epileptic seizures. Journal of Combinatorial Optimization,2001,5(1):9-26.
[31] B. Litt, R. Esteller, J. Echauz, et al., Epileptic seizures may begin hours inadvance of clinical onset: a report of five patients, Neuron,2001,30(1):51-64.
[32] S. Gigola, F. Ortiz, C.E. D’Attellis, et al., Prediction of epileptic seizuresusing accumulated energy in a multiresolution framework. Journal ofNeuroscience Methods,2004,138(1):107-111.
[33] F. Mormann, T. Kreuz, R.G. Andrzejak, et al.,Epileptic seizures are precededby a decrease in synchronization. Epilepsy Research,2003,53(3):173-185.
[34] M. D’Alessandro, G. Vachtsevanos, R. Esteller, et al., A multi-feature andmulti-channel univariate selection process for seizure prediction. ClinicalNeurophysiology,2005,116(3):506-516.
[35] R. Esteller, J. Echauz, M. D’Alessandro, et al., Continuous energy variationduring the seizure cycle: towards an on-line accumulated energy. ClinNeurophysiol2005,116(3):517-526.
[36] M.A. Harrison, M.G. Frei, I. Osorio, Accumulated energy revisited. ClinicalNeurophysiology,2005,116(3):527-531.
[37] C.C. Jouny, P.J. Franaszczuk, G.K. Bergey, Signal complexity and synchronyof epileptic seizures: is there an identifiable preictal period? ClinicalNeurophysiology,2005,116(3):552-558.
[38] F. Mormann, T. Kreuz, C. Rieke, et al., On the predictability of epilepticseizures. Clinical Neurophysiology,2005,116(3):569-587.
[39] L.D. Iasemidis, D.S. Shiau, P.M. Pardalos, et al., Long-term prospectiveon-line real-time seizure prediction. Clinical Neurophysiology,2005,116(3):532–544.
[40] M.L.V. Quyen, J. Soss, V. Navarro, et al., Preictal state identification bysynchronization changes in long-term intracranial EEG recordings. ClinicalNeurophysiology,2005,116(3):559-568.
[41] L.D. Iasemidis, D.S. Shiau, W. Chaovalitwongse, et al., Adaptive epilepticseizure prediction system. IEEE Transactions on Biomedical Engineering,2003,50(5):616-627.
[42]欧阳高翔，癫痫脑电信号的非线性特征识别与分析：[博士学位论文]，燕山大学，2010.
[43]游宇，癫痫模型的中枢神经系统脱髓鞘改变及其对癫痫治疗意义的研究：[博士学位论文]，第四军医大学，2011
[44]赵龙莲，生物反馈中脑电信号分析及其在癫痫治疗中应用的研究：[博士学位论文]，清华大学，2009.
[45]汪春梅，癫痫脑电信号特征提取与自动检测方法研究：[博士学位论文]，华东理工大学，2011.
[46]谢丽娟，贺达仁，李小俚等，癫痫预测方法的分析与研究，医学与哲学，2006，27(1)：37-40.
[47]杜一鸣，王耘，黄光，癫痫预测面临问题的分析与展望，医学与哲学，2008，29(9)：59-61.
[48] F. Mormann, R.G. Andrzejak, C. E. Elger, et al., Seizure prediction: the longand winding road, Brain,2007,130(2):314-333.
[49] M. Valderrama, S. Nikolopoulos, C. Adam, et al. Patientspecific seizureprediction using a multi-feature and multi-modal EEG-ECG classification, XIIMediterranean Conference on Medical and Biological Engineering andComputing2010,2010,29:77-80.
[50] L. Chisci, A. Mavino, G. Perferi, et al., Realtime epileptic seizure predictionusing AR models and support vector machines, IEEE Transactions onBiomedical Engineering,2010,57(5):1124-1132.
[51] S. Altunay, Z. Telatar, O. Erogul, Epileptic EEG detection using the linearprediction error energy, Expert Systems with Applications,2010,37(8):5661-5565.
[52] J. Dauwels, F. Vialatte, A. Cichocki, Diagnosis of Alzheimer’s disease fromeeg signals: where are we standing? Current Alzheimer Research,2010,7(6):487-505.
[53] H. Feldwisch-Drentrup, B. Schelter, M. Jachan, et al. Joining the benefits:combining epileptic seizure prediction methods. Epilepsia,2010,51(8):1598-1606.
[54] H. Feldwisch-Drentrup, A. Schulze-Bonhage, J. Timmer, et al., Statisticalvalidation of event predictors: a comparative study based on the field ofseizure prediction, Physical Review E,2011,83(6):066704.
[55] H. Feldwisch-Drentrup, M. Staniek, A. Schulze-Bonhage, et al. Identificationof preseizure states in epilepsy: a data-driven approach for multichannel EEGrecordings. Frontiers in COMPUTATIONAL NEUROSCIENCE,2011,5(32):1-9.
[56] B. He, Y. Dai, L. Astolfi, et al., eConnectome: a MATLAB toolbox formapping and imaging of brain functional connectivity. J Neurosci Methods2011,195(2):261-269.
[57] P. Mirowski. Comparing SVM and convolutional networks for epilepticseizure prediction from intracranial EEG. In: IEEE Workshop on MachineLearning for Signal Processing. MLSP2008,2008:244-249.
[58] P. Rajdev, M. Ward, J. Rickus, et al., Real-time seizure prediction from localfield potentials using an adaptive Wiener algorithm, Computers in Biology andMedicine,2010,40(1):97-108.
[59] B. Schelter, M. Winterhalder, H.F. Drentrup, et al. Seizure prediction: theimpact of long prediction horizons. Epilepsy Research,2007,73(2):213-217.
[60] D.E. Snyder, J. Echauz, D.B. Grimes, et al., The statistics of a practical seizurewarning system, Journal of Neural Engineering,2008,5(4):392-401.
[61] B. Swiderski, S. Osowski, A. Cichocki, et al., Single-class SVM and directedtransfer function approach to the localization of the region containing epilepticfocus. Neurocomputing,2009,72(7):1575-1583.
[62] I.T. Tokuda, J. Kurths, I.Z. Kiss, et al., Predicting phase synchronization ofnonphase-coherent chaos. Europhysics Letters,2008,83(5):50003.
[63] H.J. M ller, W.F. Gattaz, J.F.W. Deakin, European Archives of Psychiatry andClinical Neuroscience,1929,87(1):527-570.
[64] R.G. Andrzejak, K. Lehnertz, F. Mormann, et al. Indications of nonlineardeterministic and finite-dimensional structures in time series of brain electricalactivity: Dependence on recording region and brain state, PHYSICALREVIEW E,2001,64:061907.
[65] J. Ziv, A. Lempel, A universal algorithm for sequential data compression.IEEE Transactions on Information Theory,1977,23(3),337-343.
[66] J. Ziv, A. Lempel, Compression of individual sequences via variable-ratecoding. IEEE Transactions on Information Theory,1978,24(5),530-536.
[67] X.S. Zhang, R.J. Roy, E.W. Jensen, EEG complexity as a measure of depth ofanesthesia for patients, IEEE Transactions on Biomedical Engineering,2001,48(12):1424-1433.
[68]吴祥宝,徐京华,复杂性与脑功能,生物物理学报,1991,7(1):103-106.
[69] F. Takens, Detecting strange attractors in turbulence: Dynamical systems andturbulence. In Rand, D. A. and Young, L. S., editors, Lecture Notes inMathematics,1981. Vol.366. Springer-Verlag, Berlin.
[70] A.M. Fraser, H.L. Swinney, Independent coordinates for strange attractorsfrom mutual information, Physical Review A,1986,33(2):1134.
[71] W. Liebert, H. Schuster, Proper choice of the time delay for the analysis ofchaotic time series, Physics Letters A,1989,142(2-3):107-111.
[72] H.D.I. Abarbanel, M.B. Kennel, Local false nearest neighbors and dynamicaldimensions from observed chaotic data, Physical Review E,1993,47(5):3057.
[73] L. Cao, Practical method for determining the minimum embedding dimensionof a scalar time series, Physica D: Nonlinear Phenomena,1997,110(1):43-50.
[74]刘海峰，代正华，陈峰等，混沌动力系统小波变换模数的关联维数，物理学报，2002，51(6)：1186-1192.
[75] S. Borovkova, R. Burton, H. Dehling, Consistency of the Takens estimator forthe correlation dimension, The Annals of Applied Probability,1999,9(2):376-390.
[76] K. Natarajan, R. U. Acharya, F. Alias,et al., Nonlinear analysis of EEG signalsat different mental states, BioMedical Engineering OnLine,(2004),3(7):1-11.
[77]闫润强，语音信号动力学特性递归分析：[硕士学位论文]，上海交通大学，2006.
[78] J. P. Zbilut, A. Giuliani, C. L. Webber, Detecting deterministic signals inexceptionally noisy environments using cross-recurrence quantification,Physics Letters A,1998,246(1-2):122-128.
[79] N. Marwan, J. Kurths, Nonlinear analysis of bivariate data with crossrecurrence plots, Physics Letters A,2002,302(5-6):299-307.
[80] A. Groth, Visualization of coupling in time series by order recurrence plots,Physical Review E,2005,72(4):046220.
[81] O. Sosnovtseva, A. Balanov, T. Vadivasova, et al., Loss of lag synchronizationin coupled chaotic systems, Physical Review E,1999,60(6):6560.
[82] C. L. Webber Jr, J. Zbilut, Dynamical assessment of physiological systems andstates using recurrence plot strategies, Journal of Applied Physiology,1994,76(2):965-973.
[83] J. P. Zbilut, C. L. Webber Jr, Embeddings and delays as derived fromquantification of recurrence plots, Physics Letters A,1992,171(3-4):199-203.
[84] F. Lopes da Silva, A. Hoeks, H. Smits, et al., Model of brain rhythmic activity,Biological Cybernetics,1974,15(1):27-37.
[85] B. H. Jansen, G. Zouridakis, M. E. Brandt, A neurophysiologically-basedmathematical model of flash visual evoked potentials, Biological Cybernetics,1993,68(3):275-283.
[86] F. Wendling, J. Bellanger, F. Bartolomei, et al., Relevance of nonlinearlumped-parameter models in the analysis of depth-EEG epileptic signals,Biological Cybernetics,2000,83(4):367-378.
[87] C. Bandt, B. Pompe, Permutation entropy: A natural complexity measure fortime series, Physical Review Letters,2002,88(17):174102.
[88]边洪瑞，王江，韩春晓等，基于复杂度的针刺脑电信号特征提取，物理学报，2011，60(11)：118701.
[89]边洪瑞，针刺足三里对EEG影响的研究：[硕士学位论文]，天津大学，2011.
[90]李诺，针刺对脑功能影响的数据采集与分析：[硕士学位论文]，天津大学，2010.
[91] G. Pfurtscheller, A. Stancak, G. Edlinger, On the existence of different types ofcentral beta rhythms below30Hz, Electroencephalography and clinicalneurophysiology,1997,102(4):316-325.
[92] S. G. Mallat, A wavelet tour of signal processing, Academic Pr,1999.
[93] S. Blanco, R. Q. Quiroga, O. Rosso, et al., Time-frequency analysis ofelectroencephalogram series, Physical Review E,1995,51(3):2624.
[94] A. Shashua,“On the relationship between the support vector machine forclassification and sparsified fisher’s linear discriminant,” Neural ProcessingLetters,1999,9(2):129-139.
[95] D.E. Rumelhart, G.E. Hinton, R.J.Williams, Learning representations ofback-propagation errors, Nature,1986,323:533-536.
[96] R.E. Kalman. A new approach to linear filtering and prediction problems,Transactions of the ASME, Ser. D, Journal of Basic Engineering,1960,82:34-45.
[97] S.J. Julier, J.K. Uhlmann. A new extension of the Kalman filter to nonlinearsystems, Proceedings of AeroSense:11th Int Symposium Aerospace/DefenseSensing,Simulation and Controls.1997:54-65.
[98] G.V. Puskorius, L.A. Feldkamp, and L.I. Davis Jr., Dynamic neural networkmethods applied to on-vehicle idle speed control, Proceedings of the IEEE,1996,84:1407-1420.
[99] S.J. Julier, J.K. Uhlmann, and H. Durrant-Whyte. A new approach for filteringnonlinear systems, Proceedings of the American Control Conference,1995:1628-1632.
[100] E.A.Wan, R. van der Merwe. The unscented Kalman filter for nonlinearestimation, Proceedings of Symposium2000on Adaptive Systems for SignalProcessing, Communication and Control (AS-SPCC), IEEE,2000.
[101] E.W. Saad, D.V. Prokhorov, D.C.Wunsch III. Comparative study of stock trendprediction using time delay, recurrent and probabilistic neural networks,IEEE Transactions on Neural Networks,1998,9:1456C1470.
[102] K.C. Jim, C.L. Giles, B.G. Horne, An analysis of noise in recurrent neuralnetworks: convergence and generalization, IEEE Transactions on NeuralNetworks,1996,7:1424C1438.
[103] S. Singhal, L.Wu, Training multilayer perceptrons with the extended Kalmanfilter, Advances in Neural Information Processing Systems1,1989:133-140.
[104] S. Haykin. Kalman Filtering and Neural Networks[M]. New York: Wiley,Chap.7,2002.
[105] A. Sitz, U. Schwarz, J. Kurths, et al., Estimation of parameters and unobservedcomponents for nonlinear systems from noisy time series, Physical Review E,2002,66:016210.
[106] Bin Deng, Jiang Wang,and Yenqiu Che, A combined method to estimateparameters of neuron from a heavily noise-corrupted time series of activepotential, CHAOS,2009,19:015105.
[107] L. Zheng, J.E. O’Doherty, T.L. Hanson,et al. Unscented Kalman Filter forBrain-Machine Interfaces, PLoS one,2009,4(7)e6243:1-18.
[108] M. Clerc, J. Kennedy, The particle swarm-explosion, stability, andconvergence in a multidimensional complex space, IEEE Transactions onEvolutionary Computation,2002,6(1):58-73.