脑电的复杂度分析
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摘要
脑电作为一种无损伤,高时间分辨率,直接反映神经元电活动的技术,在理论研究和临床应用上至今仍有重要意义。但是如何从脑电这种极度复杂的信号中提取有用信息一直是一个难题。复杂度提供了一种客观、定量的描述事物复杂程度的方法。用复杂度方法分析脑电活动的复杂程度,可以提供一些有关大脑工作特性的新知识,新认识。从上世纪八十年代起,这一方向的研究已成为交叉学科研究的一个新热点。本文就是在这个方向上就以下五个方面进行了新的探索。
一些传统的复杂度方法需要对所分析的时间序列进行粗粒化处理。通过对logistic mapping迭代序列和一些实际脑电序列的研究表明:过分的粗粒化有时会歪曲时间序列的性质,给出错误的结果。过去,我们实验室曾提出一种无须过分粗粒化的新复杂度算法——CO复杂度,但是缺乏严格的数学基础。现在我们对CO复杂度进行了改进,应用改进后的CO复杂度对正常人睁眼休息和闭眼休息状态下脑电的复杂度进行分析,并同时应用另一种被广泛采用的同样无须过分粗粒化的复杂度算法——近似熵复杂度进行比较。CO复杂度的结果与近似熵复杂度具有一致的趋势。并且相比于近似熵复杂度,它还具有计算量小的优势。
目前国际上对二维结构复杂度的研究还处于刚起步的阶段。我们把CO复杂度推广到二维的情形,为这个领域提供一种很有希望的新方法。通过构造一系列不同规则程度的图像对二维CO复杂度进行了研究,结果表明,二维CO复杂度确实能反映图像的不规则程度,可以作为一种“随机性复杂度”意义上的复杂度方法用于图像等二维结构的分析。我们又首次把二维CO复杂度应用到猫初级视皮层光学成像方位功能图的研究。这一研究显示了二维CO复杂度在生物数据分析领域的应用前景。
关于完全随机的事物是否复杂,目前还存在争议。我们对此提出自己的观点,认为“复杂”这个概念包含不同方面或不同层次的含义,并提出了一种新概念——高阶复杂度实现了这
Electroencephalogram (EEG) has very fine time resolution. It's a noninvasive approach and can directly reflect brain action. It's very important for both science research and clinical application by now. Complexity measures provide objective and quantificational descriptors for the complex extent of a time series. Scientists can get new knowledge or new understanding about brain natures from analyzing EEG signals with complexity measures. From 1980's, this field becomes an important interdisciplinary subject. In this paper we will expatiate on five problems of the subject.Some conventional complexity algorithms have coarse graining procedure when applied to real time series. Researches on logistic mapping series and some real EEG signals show that in some cases, over coarse graining may distort the dynamics of series analyzed and lead to spurious results. Our lab once presented a new complexity algorithm - CO complexity(陈芳,顾凡及, 徐京华等 ,1998), which needn't over coarse graining procedure. In this paper, we improved CO complexity and analyzed EEG signals recorded from normal subjects during rest with eyes closed (REC) and rest with eyes opened (REO) with CO complexity and approximate entropy (ApEn), a wide accepted complexity algorithm which needn't over coarse graining procedure either, for compare. The CO complexity value of EEG signals shows a similar trend as approximate entropy. Its low computation cost makes it prior to approximate entropy.We extended CO complexity to two-dimensional cases. Now in the field of 2-dimensional complexity there's not so many progress as in one-dimensional series. So 2-dimensional CO complexity may be an important new method of the field. A series of images with different random degrees were constructed and their 2-dimensional CO complexity values were calculated. The 2-dimensional CO complexity value increases when random degree becoming larger, which infers that 2-dimensional CO complexity is a suitable randomness finding complexity (Rapp PE and Schmah TI (1996), Rapp PE and Schmah TI (2000)) for analysis of 2D structures. For the first time, 2-dimensional CO complexity was applied to analyzing orientation maps in the primary visual cortex of cat revealed by optical imaging method. This research shows that 2-dimensional CO complexity will be good in biological data analysis.Now there's a debate of whether totally random systems are complex. We consider that there are different levels or orders of complexity; a different order is concerned with a different aspect of complexity. Higher order complexity, a new method to consider the different levels of complexity, was presented. From the research in some quasi-stationary time series it's revealed that the first order complexity is suggested to be a measure of randomness of the original time series, while the second order complexity is a measure of its degree of nonstationarity. The different order is concerned with different aspect of complexity. For the first time, we applied higher order complexity to analyzing EEG signals. On some channels, the 2nd order ApEn values of EEG signals recorded from 8 normal subjects when doing simple and complex mental arithmetic are significantly higher than those from subjects when resting with eyes closed.We present a method to consider the influence of analysis scale. We call the approach macroscopic complexity. The affection of different observation scales on logistic mapping series
一些传统的复杂度方法需要对所分析的时间序列进行粗粒化处理。通过对logistic mapping迭代序列和一些实际脑电序列的研究表明:过分的粗粒化有时会歪曲时间序列的性质,给出错误的结果。过去,我们实验室曾提出一种无须过分粗粒化的新复杂度算法——CO复杂度,但是缺乏严格的数学基础。现在我们对CO复杂度进行了改进,应用改进后的CO复杂度对正常人睁眼休息和闭眼休息状态下脑电的复杂度进行分析,并同时应用另一种被广泛采用的同样无须过分粗粒化的复杂度算法——近似熵复杂度进行比较。CO复杂度的结果与近似熵复杂度具有一致的趋势。并且相比于近似熵复杂度,它还具有计算量小的优势。
目前国际上对二维结构复杂度的研究还处于刚起步的阶段。我们把CO复杂度推广到二维的情形,为这个领域提供一种很有希望的新方法。通过构造一系列不同规则程度的图像对二维CO复杂度进行了研究,结果表明,二维CO复杂度确实能反映图像的不规则程度,可以作为一种“随机性复杂度”意义上的复杂度方法用于图像等二维结构的分析。我们又首次把二维CO复杂度应用到猫初级视皮层光学成像方位功能图的研究。这一研究显示了二维CO复杂度在生物数据分析领域的应用前景。
关于完全随机的事物是否复杂,目前还存在争议。我们对此提出自己的观点,认为“复杂”这个概念包含不同方面或不同层次的含义,并提出了一种新概念——高阶复杂度实现了这
Electroencephalogram (EEG) has very fine time resolution. It's a noninvasive approach and can directly reflect brain action. It's very important for both science research and clinical application by now. Complexity measures provide objective and quantificational descriptors for the complex extent of a time series. Scientists can get new knowledge or new understanding about brain natures from analyzing EEG signals with complexity measures. From 1980's, this field becomes an important interdisciplinary subject. In this paper we will expatiate on five problems of the subject.Some conventional complexity algorithms have coarse graining procedure when applied to real time series. Researches on logistic mapping series and some real EEG signals show that in some cases, over coarse graining may distort the dynamics of series analyzed and lead to spurious results. Our lab once presented a new complexity algorithm - CO complexity(陈芳,顾凡及, 徐京华等 ,1998), which needn't over coarse graining procedure. In this paper, we improved CO complexity and analyzed EEG signals recorded from normal subjects during rest with eyes closed (REC) and rest with eyes opened (REO) with CO complexity and approximate entropy (ApEn), a wide accepted complexity algorithm which needn't over coarse graining procedure either, for compare. The CO complexity value of EEG signals shows a similar trend as approximate entropy. Its low computation cost makes it prior to approximate entropy.We extended CO complexity to two-dimensional cases. Now in the field of 2-dimensional complexity there's not so many progress as in one-dimensional series. So 2-dimensional CO complexity may be an important new method of the field. A series of images with different random degrees were constructed and their 2-dimensional CO complexity values were calculated. The 2-dimensional CO complexity value increases when random degree becoming larger, which infers that 2-dimensional CO complexity is a suitable randomness finding complexity (Rapp PE and Schmah TI (1996), Rapp PE and Schmah TI (2000)) for analysis of 2D structures. For the first time, 2-dimensional CO complexity was applied to analyzing orientation maps in the primary visual cortex of cat revealed by optical imaging method. This research shows that 2-dimensional CO complexity will be good in biological data analysis.Now there's a debate of whether totally random systems are complex. We consider that there are different levels or orders of complexity; a different order is concerned with a different aspect of complexity. Higher order complexity, a new method to consider the different levels of complexity, was presented. From the research in some quasi-stationary time series it's revealed that the first order complexity is suggested to be a measure of randomness of the original time series, while the second order complexity is a measure of its degree of nonstationarity. The different order is concerned with different aspect of complexity. For the first time, we applied higher order complexity to analyzing EEG signals. On some channels, the 2nd order ApEn values of EEG signals recorded from 8 normal subjects when doing simple and complex mental arithmetic are significantly higher than those from subjects when resting with eyes closed.We present a method to consider the influence of analysis scale. We call the approach macroscopic complexity. The affection of different observation scales on logistic mapping series
引文
Aihara K et al. (1986). Structures of attractors in periodically forced neural oscillations, Phys. Lett., 7: 313-317
Aihara K, Matsumoto G & Ichiwaka M (1985). An alternating periodic-chaotic sequence observed in neural oscillators, Phys. Lett., 111: 251-255
Aihara K, Matsumoto G & Ikegaya Y(1984). Periodic and non-periodic responses of a periodically forced Hodgkin-Huxley oscillator, J. Theor. Biol., 109: 249-270
Aizawa K(1994). Representations without Rules, Connectionism and the Syntactic Argument, Synthese, 101: 465-492
Andrienko YA, Brilliantov NV & Kurths J(2000). Complexity of two-dimensional patterns, Eun. Phys. J. B, 15: 539-546
Babloyantz A, Salazar JM & Nicolis C (1985). Evidence of chaotic dynamics of brain activity during the sleep cycle, Physics Letters A, 111: 152-156
Barsar E (1992). B rain natural frequencies are cansal factor for resonances and induced rhythms, In: Basar E,Bullock TH(eds), Induced rhythms in the brain, pp. 425-467, Boston: Birkhauser
Bruhn J et al. (2000). Electroencephalogram approximate entropy correctly classifies the occurrence of burst suppression pattern as increasing anesthetic drug effect, Anesthesiology, 93: 981-985
Bruhn J, Ropcke H & Hoeft A(2000). Approximate entropy as an electroencephalographic measure of anesthetic drug effect during desflurane anesthesia, Anesthesiology, 92: 715-726
Chaitin GJ(1966). On the length of programs for computing finite binary sequences, J. Assoc. Comput. Machinery, 13: 547-569
Chen F, Xu J, Gu F, Yu X, Meng X, Qiu Z(2000). Dynamic process of information transmission complexity in human brains, Biol. Cybern., 83: 355-366
Crick F著(1994).汪云九等译(1999)惊人的假设,湖南科技出版社
Croft RJ & Barry RJ(2000). Removal of ocular artifact from the EEG: a review, Neurophysiol. Clin., 30:5-19
Dvorak I & Holden AV(1991). Mathematical Approaches to Brain Functioning Diagnostics, Manchester, UK: Manchester Univ. Press
Edelman GM & Tononi G(2000). A universe of Consciousness, New York: Basic Books
Elbert T et al. (1994). Chaos and physiology: deterministic chaos in excitable cell assemblies, Physiological Reviews, 74(1): 1-47
Elger CE, Widman G, Andrzejak R et al. (2000). Nonlinear EEG analysis and its potential role in epileptology, Epilepsia, 41: S34-S38
Feldman DP & Crutch JP(2002). Structural information in two-dimensional patterns: entropy convergence and excess entropy, Santa Fe Institute Working Paper, 02-12-065
Freeman WJ (1987a). Simulation of chaotic EEG patterns with a dynamic model of the olfactory system, Biol. Cybern., 56: 139-150
Freeman WJ(1987b). Techniques used in the search for the physiological basis for the EEG, In: Handbook of Electroencephalography and Clinical Neurophysiology, p. 583-664, Amsterdam: Elsevier
Freeman WJ (1988). Strange attractors that govern mammalian brain dynamics shown by trajectories of Electroencephalography (EEG). potentials, IEEE Trans. CAS, 35: 781-784
Freeman WJ (1991). The physiology of perception, Sci. Am., 264: 78-85
Freeman WJ (1992). Predictions on neocortical dynamics derived from studies in paleocotex, In: Basar E, Bullock TH(eds), Induced rhythms in the brain, pp. 183-199, Boston: Birkhauser
French CC & Beaumont JG (1984). A critical review of EEG coherence studies of hemisphere function, Intern. J. Psychophysiol., 1: 241-254
Friston KJ(1997). Imaging cognitive anatomy, Trends in Cognitive Science, 1: 21-27
Glass L & Mackey MC(1979). Pathological conditions resulting from instabilities in physiological control systems, In: Bifurcation Theory and Applications in Scientific Disciplines, p. 214-235, New York: NY Acad. Sci.
Goldberger A & West B (1987). Chaos in physiology, In: Chaos in Biological Systems, p. 1-5, New York: Plenum
Grassberger P & Procaccia I(1983). Measuring the strangeness of strange attractors, Physica D, 9: 189-208
Grassberger P(1986). Toward a quantitative theory of self-generated complexity, Intn. J. Theoret. Phys., 25: 907-938
Gu F, Meng X, Shen E et al. (2003). Can we measure consciousness with EEG complexities? International Journal of Bifurcation and Chaos, 13(3):733-742
Hagoort P, Brown CM & O sterhout L(1999). The neurocognition of syntatic processing, In C M Brown & P Hagoort: The neurocognition of language, Oxford: Oxford University Press
Haken H著(1995).郭治安,吕翎译(2000)大脑工作原理,上海科技教育出版社
Hodgkin A & Huxley AF(1952). A quantitative description of membrane current and application to conductin and excitation in nerve, L. Physiol. Lond., 117: 500-544
Holden AV(1976). Models of the Stochastic Activity of Neurons. Lecture Notes in Biomathematics, vol. 12, Heidelberg, Germany: Springer-Verlag
Horwitz B, Rumsey JM & Donohue BC(1998). Functional connectivity of the angular gyrus in normal reading and dyslexia, Proc. Natl. Acad. Sci. USA, 95: 8939-8944
Huang L et al. (2003). Prediction of response to incision using the mutual information of electroencephalograms during anaesthesia, Medical Engineering & Physics. 25: 321-327
Hubel DH & Wiesel TN (1962). Receptive fields, binocular interactions and functional architecture in the cat's visual cortex, J. Physiol., 160: 106-154
Iasemidis LD, Saekellares JC(1996). Chaos theory and epilepsy, Neuroscientist, 2: 118-126
Ivanitsky AM, Nikolaev AR & Ivanitsky GA (1999). Electroencephalography, In U.Windhorst, H. Johansson (eds): Modern techniques in neuroscience research, Chapter 35, Heidelberg, Germany: Springer-Verlag
Jausovec N & Jansovec K(2000), Correlations between BRP parameters and intelligence: a reconsideration, Biological Psychology, 50: 137-154
Jeong J, Kim SY & Han SH(1998). Non-linear dynamical analysis of the EEG in Alzheimer's disease with optimal embedding dimension, Electroencephalography and clinical Neurophysiology, 106: 220-228
Jung TP et al. (2000a). Removing electroencephalographic artifacts by blind source separation, Psychophysiology. 37: 163-178
Jung TP et al. (2000b). Removal of eye activity artifacts from visual event-related potentials in normal and clinical subjects, Clin. Neurophysiol., 111: 1745-1758
Kai T & Tomita K (1979). Stroboscopic phase portrait of a forced nonlinear oscillator, Prog. Theor. Phys., 61: 54-73
Kaplan DT et al. (1991). Aging and the complexity of cardiovascular dynamics, Biophys. J., 59: 945-949
Kaspar F & Schuster HG (1987). Easily calculable measure for the complexity of spatiotemporal patterns, Physical Review A, 36(2): 842-848
Kauffrnan S (1995). At Home In The Universe. The Search for Laws of Self-Organization and Complexity, Great Britain: Viking Press
Koch C & Laurent G (1999). Complexity and the nervous system, Science, 284: 96-98
Kolmogorov AN(1959). Entropy per unit time as a metric invariant of automorphisms, Dokl. Akad. Nauk. SSSR, 124: 754
Kolmogorov AN(1965). Three approaches to the definition of the concept of quantity of information, Problems of Information Processing. 1: 3-11(Translated from the Russian Edition)
Le Van Quyen M, Martinerie J, Navarro V et al. (2001). Characterizing neurodynamic changes before seizures, J. Clin. Neurophysiol., 18: 191-208
Lehnertz K & Elger CE (1995). Spatio-temporal dynamics of the primary epileptogenic area in temporal lobe epilepsy characterized by neuronal complexity loss, Electroencephnlography and Clinical Neurophysiology, 95: 108-117
Lehnertz K & Elger CE(1998). Can epileptic seizures be predicted? Evidence from nonlinear time series analysis of brain electrical activity, Phys. Rev. Lett., 80: 5019-5022
Lehnertz K, Andrzejak RG, Arnhold J et al. (2001). Nonlinear EEG analysis in Epilepsy: Its possible use for interictal focus localization, seizure anticipation, and prevention, J. Clinical Neurophysiology, 18: 209-222
Lempel A & Ziv J (1986). Compression of two dimensional data, IEEE Transactions on Information Theory, 32: 2-8
Lempel A and Ziv J(1976). On complexity of finite sequences. IEEE Trans. Inform. Theor., 22: 75-88
Litt B & Echauz J(2002). Prediction of epileptic seizures, The Lancet Neurology, 1: 22-30
Livanov MN (1977). Spatial organization of cerebral processes, New York: Wiley and Sons
Lopes Da Silva FH (1991). Neural mechanisms underlying brain waves: from neural membranes to networks, Electroencephalogram Clin. Neurophysiol., 79: 81-93
Lopes da Silva FH et al. (1997). Alpha rhythms: noise, dynamics and models, International Journal of Psychophysiology, 26: 237-249
Lorenz E(1963). Deterministic nonperiodic flow, Journal of Atmospheric Sciences, 20: 130-141
Lyapunov AM Lectures on Theoretical Mechanics, 1885-1902, Charkov: Naukova Dumka
Madler C, Schwender D & Poeppel E(1991). Neuronal oscillators in auditory evoked potentials, Intern. J. Psychophysiol., 11: 55
Manuca R, Casdagli MC & Savit RS(1998). Nonstationarity in epileptic EEG and implications for neural dynamics, Mathematical Biosciences, 147: 1-22
Martinerie J, Adam C, Le Van Quyen M et al. (1998). Epileptic seizures can be anticipated by non-linear analysis, Nature Medicine, 4: 1173-1176
Matsumoto G et al. (1984). Periodic and nonperiodic responses of membrane potentials in squid giant axons during sinusoidal current stimulation, J. Theor. Neurobiol., 3: 1-14
May RM (1974). Biological populations with non-overlapping generations: stable cycles and chaos, Science, 186: 645-647
McCauley JL (1990). Introduction to multifractals in dynamical systems theory and fully developed fluid turbulence, Physics Reports, 189: 225-266
Miller R(1991). Cortico-hippocarapal interplay and the representation of contexts of the brain, Springer-Verlag
Mitzdorf U(1987). Properties of the evoked potential generators: current source-density analysis of evoked potential in cat cortex, Intern. J. Neurosci., 33: 33-59
Muthuswamy J & Thakor NV(1998). Spectral analysis methods for neurological signals, Journal of Neuroscience Methods, 83: 1-14
Osborne AR & Provenzale A (1989). A finite correlation dimension for stochastic systems with power-law spectra, Physica D, 35: 357-381
Pentose R著(1989).许明贤,吴忠超译(1994)皇帝新脑,湖南科技出版社
Pereda E et al. (1999). Interhemispheric differences in awake and sleep human EEG: a comparison between non-linear and spectral measures, Neurosci. Lett., 263: 37-40
Petsche H et al. (1992). Thinking with images or thinking with language: a pilot EEG probability mapping study, Intern. J. Psychophysiol., 12: 31-39
Pincus SM & Viscarello RR (1992). Approximate entropy: A regularity measure for fetal heart rate analysis, Obstet. Gynecol., 79: 249-255
Pincus SM(1991). Approximate entropy as a measure of system complexity, Proc. Natl. Acad. Sci. USA, 88: 2297-2301
Pincus SM (1995). Approximate entropy (ApEn). as a complexity measure, Chaos, 5:110-117
Pritchard WS & Duke DW(1992). Measuring chaos in the brain: a tutorial review of nonlinear dynamical EEG analysis, Intern. J. Neuroscience, 67: 31-80
Putnam LE & Roth WT (1990). Effects of stimulus repetition, duration, and rise time on startle blink and automatically elicited P300, Psychophysiology, 27: 275-297
Rapp PE & Watanabe TAA (2002). Nonlinear signal classification, International J. Bifurcation and Chaos, 12(6): 1273-1293
Rapp PE (1993). Chaos in the neurosciences: cautionary tales from the frontier, Biologist, 40(2): 89-94
Rapp PE and Schmah TI (1996). Complexity measures in molecular psychiatry, Molecular Psychiatry, 1:408-416
Rapp PE and Schmah TI (2000). Dynamical analysis in clinical practice. In Lehnertz K, Arnhold J, Grassberger P and Elger CE(eds), Chaos in Brains? pp. 52-62, World Scientific, Singapore
Rowland V(1968). Cortical steady potential (direct current potential), in reinforcement and learning, Prog. Physiol. Psychol., 2: 1-77
Russ JC(1999). Fractal Surfaces, New York: Plenum
Salmelin R et al. (1996). Impaired visual word processing in dyslexia revealed with magnetoencephalography, Ann Neurol., 40(2): 157-162
Sal'nikova EM & Martyushev LM (2001). Determining the order parameter for the morphological analysis of two-dimensional Structures, Technical Physics Letters, 27(4): 301-304
Sate S, Sane M & Sawada Y (1987). Practical methods of measuring the generalized dimension and the largest Lyapunov exponent in high dimensional chaotic systems, Prog. Theor. Phys., 77: 1-5
Schiff SJ et al. (1994). Fast wavelet transformation of EEG, Electroencephalogram Clin. Neurophysiol.. 91: 442-455
Schreiber T (1999). Interdisciplinary application of nonlinear time series methods, Physics Reports, 308: 1-64
Serra R & Zanarini G(1990). Complex systems and cognitive processes, New York: VCH Publishers
Shaw FZ et al. (1999). Algorithmic complexity as an index of cortical function in awake and pentobarbital-anesthetized rates, J. of Neuroscience Methods, 93: 101: 110
Sheinwald D, Lempel A & Ziv J(1990). Two-dimensional encoding by finite-state encoders, Transactions on Communications, 38: 341-347
Skarda CA & Freeman WJ(1987). How brains make chaos in order to make sense of the world, Behav. Brain Sci., 10: 161-195
Skinner JE(1993). Neurocardiology: brain mechanisms underlying fatal cardiac arrhythmias, Neurol. Clin., 11: 325-351
Skinner JE, Pratt CM & Vybiral T(1993). Reduction in the correlation dimension of heartbeat intervals preceeds imminent ventricular fibrillation in human subjects, Am. Heart J., 125: 731-743
Sleight JW & Donovan J(1999). Comparison of bispectral index, 95% spectral edge frequency and approximate entropy of the EEG, with changes in heart rate variability during induction of general anaesthesia, Br. J. Anaesth., 82: 666-671
Steriade M et al. (1990). Report of IFCN Committee on basic mechanisms. Basic mechanisms of cortical rhythmic activity, Electroencephalogram Clin. Neurophysiol., 76: 481-508
Takens F(1980). Detecting strange attractors in turbulence, Lecture Notes in Mathematics, 898: 365-381
Tallon-Baudry C et al. (1996). Stimulus specificity of phase-locked and non-phase-locked 40 Hz visual responses in human, J. Neurosci., 16:4240-4249
Theiler J & Rapp PE(1996). Re-examination of the evidence for low-dimensional, nonlinear structure in the human electroencephalogram, Electroenceph. Clin. Neurophysiol., 98: 213-222
Tononi G & Edelman GM(1998). Consciousness and complexity, Science, 282: 1846-1851
Veils DN, Kalitzin S, Blanes W et al. (2000). Saturability index increase reliability of correlation dimension calculations for ictal state detection in intracranial EEG recordings, Epilepsia, 41: S205
Wackerbauer R, Witt A, Atmanspacher H, Kurths J, Scheingraber H(1994). A comparative classification of complexity measures, Chaos, Solitons and Fractals, 4: 133-173
Weiss S & Rappelsberger P(1996). EEG coherence within the 13-18Hz band as a correlate of a distinct lexical organization of concrete and abstract nouns in human, Neurosci. Lett., 209: 17-20
West BJ & Goldberger AL(1987). Physiology in fractal dimensions, American Scientist, 75:354-365
Xu J, Liu Z. Liu R, Yang Q(1997). Information transmission in human cerebral cortex, Physica D, 106:363-374
蔡志杰,顾凡及,沈恩华(2004).CO复杂度的数学基础,应用数学和力学,待发
陈芳,顾凡及,徐京华等(1998).一种新的人脑信息传输复杂性的研究,生物物理学报,14(3):508-512
顾凡及,宋如垓,王炯炯等(1994)不同状态下脑电图复杂性探索,生物物理学报,10(3):439-444
寿天德(1997).视觉信息处理的脑机制,P.214-222,上海科技教育出版社
谭郁玲主编(1999)临床脑电图与脑电地形图学,人民卫生出版社
童勤业,孔军,徐京华(1998)脑电复杂性分析的新方法,中国生物医学工程学报,17(3):222-225
吴祥宝 徐京华(1991)复杂性与脑功能,生物物理学报,7(1):103-106
徐京华,童勤业,刘仁(1996).大脑皮层信息传输和精神分裂症,生物物理学报,12(1):103-108
杨福生,洪波,唐庆玉(2000)独立分量分析及其在生物医学工程中的应用,国外医学生物医学工程分册,23(3):129-134
杨福生,廖旺才(1997).近似熵——一种适于短数据的复杂性度量,中国医疗器械杂志,21(5):283—286.
俞洪波(2000).用脑光学成像结合局部施药方法揭示的猫初级视皮层方位选择性形成机制,中国科学技术
Aihara K, Matsumoto G & Ichiwaka M (1985). An alternating periodic-chaotic sequence observed in neural oscillators, Phys. Lett., 111: 251-255
Aihara K, Matsumoto G & Ikegaya Y(1984). Periodic and non-periodic responses of a periodically forced Hodgkin-Huxley oscillator, J. Theor. Biol., 109: 249-270
Aizawa K(1994). Representations without Rules, Connectionism and the Syntactic Argument, Synthese, 101: 465-492
Andrienko YA, Brilliantov NV & Kurths J(2000). Complexity of two-dimensional patterns, Eun. Phys. J. B, 15: 539-546
Babloyantz A, Salazar JM & Nicolis C (1985). Evidence of chaotic dynamics of brain activity during the sleep cycle, Physics Letters A, 111: 152-156
Barsar E (1992). B rain natural frequencies are cansal factor for resonances and induced rhythms, In: Basar E,Bullock TH(eds), Induced rhythms in the brain, pp. 425-467, Boston: Birkhauser
Bruhn J et al. (2000). Electroencephalogram approximate entropy correctly classifies the occurrence of burst suppression pattern as increasing anesthetic drug effect, Anesthesiology, 93: 981-985
Bruhn J, Ropcke H & Hoeft A(2000). Approximate entropy as an electroencephalographic measure of anesthetic drug effect during desflurane anesthesia, Anesthesiology, 92: 715-726
Chaitin GJ(1966). On the length of programs for computing finite binary sequences, J. Assoc. Comput. Machinery, 13: 547-569
Chen F, Xu J, Gu F, Yu X, Meng X, Qiu Z(2000). Dynamic process of information transmission complexity in human brains, Biol. Cybern., 83: 355-366
Crick F著(1994).汪云九等译(1999)惊人的假设,湖南科技出版社
Croft RJ & Barry RJ(2000). Removal of ocular artifact from the EEG: a review, Neurophysiol. Clin., 30:5-19
Dvorak I & Holden AV(1991). Mathematical Approaches to Brain Functioning Diagnostics, Manchester, UK: Manchester Univ. Press
Edelman GM & Tononi G(2000). A universe of Consciousness, New York: Basic Books
Elbert T et al. (1994). Chaos and physiology: deterministic chaos in excitable cell assemblies, Physiological Reviews, 74(1): 1-47
Elger CE, Widman G, Andrzejak R et al. (2000). Nonlinear EEG analysis and its potential role in epileptology, Epilepsia, 41: S34-S38
Feldman DP & Crutch JP(2002). Structural information in two-dimensional patterns: entropy convergence and excess entropy, Santa Fe Institute Working Paper, 02-12-065
Freeman WJ (1987a). Simulation of chaotic EEG patterns with a dynamic model of the olfactory system, Biol. Cybern., 56: 139-150
Freeman WJ(1987b). Techniques used in the search for the physiological basis for the EEG, In: Handbook of Electroencephalography and Clinical Neurophysiology, p. 583-664, Amsterdam: Elsevier
Freeman WJ (1988). Strange attractors that govern mammalian brain dynamics shown by trajectories of Electroencephalography (EEG). potentials, IEEE Trans. CAS, 35: 781-784
Freeman WJ (1991). The physiology of perception, Sci. Am., 264: 78-85
Freeman WJ (1992). Predictions on neocortical dynamics derived from studies in paleocotex, In: Basar E, Bullock TH(eds), Induced rhythms in the brain, pp. 183-199, Boston: Birkhauser
French CC & Beaumont JG (1984). A critical review of EEG coherence studies of hemisphere function, Intern. J. Psychophysiol., 1: 241-254
Friston KJ(1997). Imaging cognitive anatomy, Trends in Cognitive Science, 1: 21-27
Glass L & Mackey MC(1979). Pathological conditions resulting from instabilities in physiological control systems, In: Bifurcation Theory and Applications in Scientific Disciplines, p. 214-235, New York: NY Acad. Sci.
Goldberger A & West B (1987). Chaos in physiology, In: Chaos in Biological Systems, p. 1-5, New York: Plenum
Grassberger P & Procaccia I(1983). Measuring the strangeness of strange attractors, Physica D, 9: 189-208
Grassberger P(1986). Toward a quantitative theory of self-generated complexity, Intn. J. Theoret. Phys., 25: 907-938
Gu F, Meng X, Shen E et al. (2003). Can we measure consciousness with EEG complexities? International Journal of Bifurcation and Chaos, 13(3):733-742
Hagoort P, Brown CM & O sterhout L(1999). The neurocognition of syntatic processing, In C M Brown & P Hagoort: The neurocognition of language, Oxford: Oxford University Press
Haken H著(1995).郭治安,吕翎译(2000)大脑工作原理,上海科技教育出版社
Hodgkin A & Huxley AF(1952). A quantitative description of membrane current and application to conductin and excitation in nerve, L. Physiol. Lond., 117: 500-544
Holden AV(1976). Models of the Stochastic Activity of Neurons. Lecture Notes in Biomathematics, vol. 12, Heidelberg, Germany: Springer-Verlag
Horwitz B, Rumsey JM & Donohue BC(1998). Functional connectivity of the angular gyrus in normal reading and dyslexia, Proc. Natl. Acad. Sci. USA, 95: 8939-8944
Huang L et al. (2003). Prediction of response to incision using the mutual information of electroencephalograms during anaesthesia, Medical Engineering & Physics. 25: 321-327
Hubel DH & Wiesel TN (1962). Receptive fields, binocular interactions and functional architecture in the cat's visual cortex, J. Physiol., 160: 106-154
Iasemidis LD, Saekellares JC(1996). Chaos theory and epilepsy, Neuroscientist, 2: 118-126
Ivanitsky AM, Nikolaev AR & Ivanitsky GA (1999). Electroencephalography, In U.Windhorst, H. Johansson (eds): Modern techniques in neuroscience research, Chapter 35, Heidelberg, Germany: Springer-Verlag
Jausovec N & Jansovec K(2000), Correlations between BRP parameters and intelligence: a reconsideration, Biological Psychology, 50: 137-154
Jeong J, Kim SY & Han SH(1998). Non-linear dynamical analysis of the EEG in Alzheimer's disease with optimal embedding dimension, Electroencephalography and clinical Neurophysiology, 106: 220-228
Jung TP et al. (2000a). Removing electroencephalographic artifacts by blind source separation, Psychophysiology. 37: 163-178
Jung TP et al. (2000b). Removal of eye activity artifacts from visual event-related potentials in normal and clinical subjects, Clin. Neurophysiol., 111: 1745-1758
Kai T & Tomita K (1979). Stroboscopic phase portrait of a forced nonlinear oscillator, Prog. Theor. Phys., 61: 54-73
Kaplan DT et al. (1991). Aging and the complexity of cardiovascular dynamics, Biophys. J., 59: 945-949
Kaspar F & Schuster HG (1987). Easily calculable measure for the complexity of spatiotemporal patterns, Physical Review A, 36(2): 842-848
Kauffrnan S (1995). At Home In The Universe. The Search for Laws of Self-Organization and Complexity, Great Britain: Viking Press
Koch C & Laurent G (1999). Complexity and the nervous system, Science, 284: 96-98
Kolmogorov AN(1959). Entropy per unit time as a metric invariant of automorphisms, Dokl. Akad. Nauk. SSSR, 124: 754
Kolmogorov AN(1965). Three approaches to the definition of the concept of quantity of information, Problems of Information Processing. 1: 3-11(Translated from the Russian Edition)
Le Van Quyen M, Martinerie J, Navarro V et al. (2001). Characterizing neurodynamic changes before seizures, J. Clin. Neurophysiol., 18: 191-208
Lehnertz K & Elger CE (1995). Spatio-temporal dynamics of the primary epileptogenic area in temporal lobe epilepsy characterized by neuronal complexity loss, Electroencephnlography and Clinical Neurophysiology, 95: 108-117
Lehnertz K & Elger CE(1998). Can epileptic seizures be predicted? Evidence from nonlinear time series analysis of brain electrical activity, Phys. Rev. Lett., 80: 5019-5022
Lehnertz K, Andrzejak RG, Arnhold J et al. (2001). Nonlinear EEG analysis in Epilepsy: Its possible use for interictal focus localization, seizure anticipation, and prevention, J. Clinical Neurophysiology, 18: 209-222
Lempel A & Ziv J (1986). Compression of two dimensional data, IEEE Transactions on Information Theory, 32: 2-8
Lempel A and Ziv J(1976). On complexity of finite sequences. IEEE Trans. Inform. Theor., 22: 75-88
Litt B & Echauz J(2002). Prediction of epileptic seizures, The Lancet Neurology, 1: 22-30
Livanov MN (1977). Spatial organization of cerebral processes, New York: Wiley and Sons
Lopes Da Silva FH (1991). Neural mechanisms underlying brain waves: from neural membranes to networks, Electroencephalogram Clin. Neurophysiol., 79: 81-93
Lopes da Silva FH et al. (1997). Alpha rhythms: noise, dynamics and models, International Journal of Psychophysiology, 26: 237-249
Lorenz E(1963). Deterministic nonperiodic flow, Journal of Atmospheric Sciences, 20: 130-141
Lyapunov AM Lectures on Theoretical Mechanics, 1885-1902, Charkov: Naukova Dumka
Madler C, Schwender D & Poeppel E(1991). Neuronal oscillators in auditory evoked potentials, Intern. J. Psychophysiol., 11: 55
Manuca R, Casdagli MC & Savit RS(1998). Nonstationarity in epileptic EEG and implications for neural dynamics, Mathematical Biosciences, 147: 1-22
Martinerie J, Adam C, Le Van Quyen M et al. (1998). Epileptic seizures can be anticipated by non-linear analysis, Nature Medicine, 4: 1173-1176
Matsumoto G et al. (1984). Periodic and nonperiodic responses of membrane potentials in squid giant axons during sinusoidal current stimulation, J. Theor. Neurobiol., 3: 1-14
May RM (1974). Biological populations with non-overlapping generations: stable cycles and chaos, Science, 186: 645-647
McCauley JL (1990). Introduction to multifractals in dynamical systems theory and fully developed fluid turbulence, Physics Reports, 189: 225-266
Miller R(1991). Cortico-hippocarapal interplay and the representation of contexts of the brain, Springer-Verlag
Mitzdorf U(1987). Properties of the evoked potential generators: current source-density analysis of evoked potential in cat cortex, Intern. J. Neurosci., 33: 33-59
Muthuswamy J & Thakor NV(1998). Spectral analysis methods for neurological signals, Journal of Neuroscience Methods, 83: 1-14
Osborne AR & Provenzale A (1989). A finite correlation dimension for stochastic systems with power-law spectra, Physica D, 35: 357-381
Pentose R著(1989).许明贤,吴忠超译(1994)皇帝新脑,湖南科技出版社
Pereda E et al. (1999). Interhemispheric differences in awake and sleep human EEG: a comparison between non-linear and spectral measures, Neurosci. Lett., 263: 37-40
Petsche H et al. (1992). Thinking with images or thinking with language: a pilot EEG probability mapping study, Intern. J. Psychophysiol., 12: 31-39
Pincus SM & Viscarello RR (1992). Approximate entropy: A regularity measure for fetal heart rate analysis, Obstet. Gynecol., 79: 249-255
Pincus SM(1991). Approximate entropy as a measure of system complexity, Proc. Natl. Acad. Sci. USA, 88: 2297-2301
Pincus SM (1995). Approximate entropy (ApEn). as a complexity measure, Chaos, 5:110-117
Pritchard WS & Duke DW(1992). Measuring chaos in the brain: a tutorial review of nonlinear dynamical EEG analysis, Intern. J. Neuroscience, 67: 31-80
Putnam LE & Roth WT (1990). Effects of stimulus repetition, duration, and rise time on startle blink and automatically elicited P300, Psychophysiology, 27: 275-297
Rapp PE & Watanabe TAA (2002). Nonlinear signal classification, International J. Bifurcation and Chaos, 12(6): 1273-1293
Rapp PE (1993). Chaos in the neurosciences: cautionary tales from the frontier, Biologist, 40(2): 89-94
Rapp PE and Schmah TI (1996). Complexity measures in molecular psychiatry, Molecular Psychiatry, 1:408-416
Rapp PE and Schmah TI (2000). Dynamical analysis in clinical practice. In Lehnertz K, Arnhold J, Grassberger P and Elger CE(eds), Chaos in Brains? pp. 52-62, World Scientific, Singapore
Rowland V(1968). Cortical steady potential (direct current potential), in reinforcement and learning, Prog. Physiol. Psychol., 2: 1-77
Russ JC(1999). Fractal Surfaces, New York: Plenum
Salmelin R et al. (1996). Impaired visual word processing in dyslexia revealed with magnetoencephalography, Ann Neurol., 40(2): 157-162
Sal'nikova EM & Martyushev LM (2001). Determining the order parameter for the morphological analysis of two-dimensional Structures, Technical Physics Letters, 27(4): 301-304
Sate S, Sane M & Sawada Y (1987). Practical methods of measuring the generalized dimension and the largest Lyapunov exponent in high dimensional chaotic systems, Prog. Theor. Phys., 77: 1-5
Schiff SJ et al. (1994). Fast wavelet transformation of EEG, Electroencephalogram Clin. Neurophysiol.. 91: 442-455
Schreiber T (1999). Interdisciplinary application of nonlinear time series methods, Physics Reports, 308: 1-64
Serra R & Zanarini G(1990). Complex systems and cognitive processes, New York: VCH Publishers
Shaw FZ et al. (1999). Algorithmic complexity as an index of cortical function in awake and pentobarbital-anesthetized rates, J. of Neuroscience Methods, 93: 101: 110
Sheinwald D, Lempel A & Ziv J(1990). Two-dimensional encoding by finite-state encoders, Transactions on Communications, 38: 341-347
Skarda CA & Freeman WJ(1987). How brains make chaos in order to make sense of the world, Behav. Brain Sci., 10: 161-195
Skinner JE(1993). Neurocardiology: brain mechanisms underlying fatal cardiac arrhythmias, Neurol. Clin., 11: 325-351
Skinner JE, Pratt CM & Vybiral T(1993). Reduction in the correlation dimension of heartbeat intervals preceeds imminent ventricular fibrillation in human subjects, Am. Heart J., 125: 731-743
Sleight JW & Donovan J(1999). Comparison of bispectral index, 95% spectral edge frequency and approximate entropy of the EEG, with changes in heart rate variability during induction of general anaesthesia, Br. J. Anaesth., 82: 666-671
Steriade M et al. (1990). Report of IFCN Committee on basic mechanisms. Basic mechanisms of cortical rhythmic activity, Electroencephalogram Clin. Neurophysiol., 76: 481-508
Takens F(1980). Detecting strange attractors in turbulence, Lecture Notes in Mathematics, 898: 365-381
Tallon-Baudry C et al. (1996). Stimulus specificity of phase-locked and non-phase-locked 40 Hz visual responses in human, J. Neurosci., 16:4240-4249
Theiler J & Rapp PE(1996). Re-examination of the evidence for low-dimensional, nonlinear structure in the human electroencephalogram, Electroenceph. Clin. Neurophysiol., 98: 213-222
Tononi G & Edelman GM(1998). Consciousness and complexity, Science, 282: 1846-1851
Veils DN, Kalitzin S, Blanes W et al. (2000). Saturability index increase reliability of correlation dimension calculations for ictal state detection in intracranial EEG recordings, Epilepsia, 41: S205
Wackerbauer R, Witt A, Atmanspacher H, Kurths J, Scheingraber H(1994). A comparative classification of complexity measures, Chaos, Solitons and Fractals, 4: 133-173
Weiss S & Rappelsberger P(1996). EEG coherence within the 13-18Hz band as a correlate of a distinct lexical organization of concrete and abstract nouns in human, Neurosci. Lett., 209: 17-20
West BJ & Goldberger AL(1987). Physiology in fractal dimensions, American Scientist, 75:354-365
Xu J, Liu Z. Liu R, Yang Q(1997). Information transmission in human cerebral cortex, Physica D, 106:363-374
蔡志杰,顾凡及,沈恩华(2004).CO复杂度的数学基础,应用数学和力学,待发
陈芳,顾凡及,徐京华等(1998).一种新的人脑信息传输复杂性的研究,生物物理学报,14(3):508-512
顾凡及,宋如垓,王炯炯等(1994)不同状态下脑电图复杂性探索,生物物理学报,10(3):439-444
寿天德(1997).视觉信息处理的脑机制,P.214-222,上海科技教育出版社
谭郁玲主编(1999)临床脑电图与脑电地形图学,人民卫生出版社
童勤业,孔军,徐京华(1998)脑电复杂性分析的新方法,中国生物医学工程学报,17(3):222-225
吴祥宝 徐京华(1991)复杂性与脑功能,生物物理学报,7(1):103-106
徐京华,童勤业,刘仁(1996).大脑皮层信息传输和精神分裂症,生物物理学报,12(1):103-108
杨福生,洪波,唐庆玉(2000)独立分量分析及其在生物医学工程中的应用,国外医学生物医学工程分册,23(3):129-134
杨福生,廖旺才(1997).近似熵——一种适于短数据的复杂性度量,中国医疗器械杂志,21(5):283—286.
俞洪波(2000).用脑光学成像结合局部施药方法揭示的猫初级视皮层方位选择性形成机制,中国科学技术