脑电非线性时间序列仿真研究
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摘要
人脑是复杂的非线性动力学系统，脑科学研究已成为21世纪最重要的研究热点之一。自上世纪20年代脑电(EEG)被发现以来，人类便开始利用脑电对大脑进行无创伤性研究，从而脑电在许多领域都起到了重要作用。在生物医学中，脑电被作为医疗诊断和疾病治疗的有效手段；在认知研究中，脑电作为研究人类思维起源的主要工具；在脑-机接口(BCI)中，脑电作为人机交互的主要媒介。为了能够更有效地将脑电运用于这些领域，高效正确的分析方法是必须的，此外，方法能否对脑电和脑电所刻画的系统做出合理且有意义的解释是在理论和实践中需要考虑的重要标准。传统的方法从频谱和统计学的角度研究脑电时间序列，能够对脑电的部分特征给出详细的解释，为脑电在这些领域中的有效应用作出了一定贡献。然而，这些方法无法对大脑的非线性动力学性质进行深入有效的理解。本文从非线性动力学和定性仿真的角度研究脑电，给出了相应的分析方法和实验结果。在本文中，作者从以下5个方面对脑电非线性时间序列进行仿真研究：
(1)在构建癫痫状态大脑的结构化模型的基础上，提出了一种从癫痫行为的定性仿真(QSIM)构建模糊推理系统(FIS)的方法，将QSIM模型中的量化空间和FIS的语言变量对应起来，并且在定性行为的仿真过程中建立有效的模糊规则库。
(2)脑电非线性动力学研究的基础需要重构系统的相空间模型。运用Takens的延迟坐标法重构系统相空间模型需要确定两个关键参数：嵌入延迟和嵌入维。本文对确定参数的两种方法进行优化和改进，分别给出了C-C方法和Cao方法的高效实现。
(3)基于重构的系统相空间模型，对刻画脑电复杂性、稳定性等非线性特征的不变量进行对比研究，对它们的非线性特征表达能力和计算性能进行详细比较，实验结果表明在区分大脑的不同生理状态的脑电分析应用中，排列熵(PE)和Hurst指数(HE)是两种最具实用价值的非线性不变量。
(4)在脑电非线性时间序列的重构相空间中，基于系统的非线性动力学特征，定义系统在相空间中的定性状态和定性行为的概念，提出对相空间轨迹进行定性建模的方法，并给出了提取定性状态的算法。在定性行为的刻画中，给出三种不同的表示方法，分别反映了系统定性行为的不同侧面。
(5)以脑电非线性时间序列的非线性特征和定性行为作为分类方法的输入，给出脑电分类和识别的集成分析方法。该集成方法在自适应训练阶段确定分类模型自身参数的同时，还能够自动选出最具代表性的脑电通道，有效的通道选择策略对于提高分类模型的时间性能和识别精度具有重要意义。在医疗诊断中，这种自学习方法还能够自动识别和判断病灶区域，在脑疾病诊断和治疗中具有突出的参考价值。在BCI应用中，自学习分类方法还能对特定的脑功能区域进行有效定位。
本文给出的方法都经过了实验验证，同时还进行了相关方法的对比分析和讨论。本文用到的脑电数据一部分来源于国内外的公共数据库，这些数据已经被许多文献所使用：另一部分来自安徽医科大学第一附属医院神经内科。本文给出的方法在这些数据集上的分析均能给出较满意的结果。
本文提出的方法并不局限于脑电时间序列的分析，可以通过适当的扩展应用到其他时间序列的非线性分析中。如定性状态和定性行为的研究方法可以应用到由一般非线性系统所输出的非线性时间序列的分析中。
本文的工作受到了国家自然科学基金项目“基于定性仿真方法的脑电波诊断模型研究”(69974038)、国家自然科学基金重点项目“复杂仿真系统的评估理论与方法”(60434010)、安徽省国际科技合作项目“一种新型麻醉深度监测信息技术”(06088023)以及安徽省科技计划项目“基于定性推理的复杂系统建模方法研究”的支持。
The research on the human brain, which is one of the most complex nonlinear dynamics systems, has become one of the hottest areas and will be full developed in the 21st century. After the discovery of electroencephalogram (EEG) in 1929 by Hans Berger, EEG has been utilized as a non-invasive method to study the brain and plays an important role in many areas. In biomedicine, EEG is an efficient tool to diagnose and treat some brain disorders, and in cognitive science, EEG is a key to open the door of the nature of human thought, and in Brain-Computer Interface (BCI), EEG is the medium of connecting human and computer. In order to effectively apply EEG into these areas, it is necessary to find more efficient and more accurate methods to deeply understand the behavior of the underlying system described by EEGs. Traditional methods, such as frequency-spectrum and statistics, can't correctly explain the nonlinear dynamical characteristics of human brain. This thesis proposed novel methods of studying EEG from the points of nonlinear dynamics and system simulation. In the thesis, there are following five aspects discussed for simulation research on EEG nonlinear time series.
(1) A method of constructing fuzzy inference system (FIS) from QSIM model of epileptic behaviors is proposed. The relationship of quantity space of QSIM and the linguistic values of FIS are viewed as the basis of the conversion rules. The efficient fuzzy rules base is built according the proposed method.
(2) Reconstruction of phase space of underlying system is the basis of EEG research according to nonlinear dynamics. To reconstruct the phase space must determine the two parameters, embedding delay and embedding dimension. Two methods are proposed to improve the original ones. C-C method and Cao's algorithm are implemented in efficient ways.
(3) Based on the reconstructed phase space, some nonlinear dynamical invariants are compared according their nonlinear ability and computational performance. The results show that permutation entropy (PE) and Hurst exponent (HE) are the two most practical measures to characterize and distinguish difference psycho-physiological states of human brain.
(4) In the artificial phase space reconstructed from EEG nonlinear time series, the concepts of qualitative state and qualitative behavior based on nonlinear dynamical properties are presented. The algorithm of extracting qualitative states from the reconstructed phase space is proposed as well as the method of modeling the phase-space trajectory. Three methods of characterizing the qualitative behavior are also given to show different aspects of underlying system.
(5) The integration methods of EEG classification and identification are presented. The nonlinear properties and the qualitative behavior are fed as the input information of the classifier. The hybrid methods can not only determine their intrinsic parameters, but also select the most respective channels, which hold the critical distinguishable information. These efforts may help improve the accuracy and performance of the classifier. In medicine diagnose, these adaptive learning methods may help automatically identify the disease foci, and in BCI, they also help to find the location of specific brain function.
The methods proposed in the thesis are evaluated on several EEG data sets acquired from some common databases. These data sets have been studied by some research groups. The proposed methods may give satisfactory results on these data sets.
The proposed methods are not limited in EEG time series. They can be developed and extended for other questions. The method about qualitative state and qualitative behavior in reconstructed phase space may be used in the general nonlinear times series, which recorded from underlying nonlinear dynamical systems.
(1)在构建癫痫状态大脑的结构化模型的基础上，提出了一种从癫痫行为的定性仿真(QSIM)构建模糊推理系统(FIS)的方法，将QSIM模型中的量化空间和FIS的语言变量对应起来，并且在定性行为的仿真过程中建立有效的模糊规则库。
(2)脑电非线性动力学研究的基础需要重构系统的相空间模型。运用Takens的延迟坐标法重构系统相空间模型需要确定两个关键参数：嵌入延迟和嵌入维。本文对确定参数的两种方法进行优化和改进，分别给出了C-C方法和Cao方法的高效实现。
(3)基于重构的系统相空间模型，对刻画脑电复杂性、稳定性等非线性特征的不变量进行对比研究，对它们的非线性特征表达能力和计算性能进行详细比较，实验结果表明在区分大脑的不同生理状态的脑电分析应用中，排列熵(PE)和Hurst指数(HE)是两种最具实用价值的非线性不变量。
(4)在脑电非线性时间序列的重构相空间中，基于系统的非线性动力学特征，定义系统在相空间中的定性状态和定性行为的概念，提出对相空间轨迹进行定性建模的方法，并给出了提取定性状态的算法。在定性行为的刻画中，给出三种不同的表示方法，分别反映了系统定性行为的不同侧面。
(5)以脑电非线性时间序列的非线性特征和定性行为作为分类方法的输入，给出脑电分类和识别的集成分析方法。该集成方法在自适应训练阶段确定分类模型自身参数的同时，还能够自动选出最具代表性的脑电通道，有效的通道选择策略对于提高分类模型的时间性能和识别精度具有重要意义。在医疗诊断中，这种自学习方法还能够自动识别和判断病灶区域，在脑疾病诊断和治疗中具有突出的参考价值。在BCI应用中，自学习分类方法还能对特定的脑功能区域进行有效定位。
本文给出的方法都经过了实验验证，同时还进行了相关方法的对比分析和讨论。本文用到的脑电数据一部分来源于国内外的公共数据库，这些数据已经被许多文献所使用：另一部分来自安徽医科大学第一附属医院神经内科。本文给出的方法在这些数据集上的分析均能给出较满意的结果。
本文提出的方法并不局限于脑电时间序列的分析，可以通过适当的扩展应用到其他时间序列的非线性分析中。如定性状态和定性行为的研究方法可以应用到由一般非线性系统所输出的非线性时间序列的分析中。
本文的工作受到了国家自然科学基金项目“基于定性仿真方法的脑电波诊断模型研究”(69974038)、国家自然科学基金重点项目“复杂仿真系统的评估理论与方法”(60434010)、安徽省国际科技合作项目“一种新型麻醉深度监测信息技术”(06088023)以及安徽省科技计划项目“基于定性推理的复杂系统建模方法研究”的支持。
The research on the human brain, which is one of the most complex nonlinear dynamics systems, has become one of the hottest areas and will be full developed in the 21st century. After the discovery of electroencephalogram (EEG) in 1929 by Hans Berger, EEG has been utilized as a non-invasive method to study the brain and plays an important role in many areas. In biomedicine, EEG is an efficient tool to diagnose and treat some brain disorders, and in cognitive science, EEG is a key to open the door of the nature of human thought, and in Brain-Computer Interface (BCI), EEG is the medium of connecting human and computer. In order to effectively apply EEG into these areas, it is necessary to find more efficient and more accurate methods to deeply understand the behavior of the underlying system described by EEGs. Traditional methods, such as frequency-spectrum and statistics, can't correctly explain the nonlinear dynamical characteristics of human brain. This thesis proposed novel methods of studying EEG from the points of nonlinear dynamics and system simulation. In the thesis, there are following five aspects discussed for simulation research on EEG nonlinear time series.
(1) A method of constructing fuzzy inference system (FIS) from QSIM model of epileptic behaviors is proposed. The relationship of quantity space of QSIM and the linguistic values of FIS are viewed as the basis of the conversion rules. The efficient fuzzy rules base is built according the proposed method.
(2) Reconstruction of phase space of underlying system is the basis of EEG research according to nonlinear dynamics. To reconstruct the phase space must determine the two parameters, embedding delay and embedding dimension. Two methods are proposed to improve the original ones. C-C method and Cao's algorithm are implemented in efficient ways.
(3) Based on the reconstructed phase space, some nonlinear dynamical invariants are compared according their nonlinear ability and computational performance. The results show that permutation entropy (PE) and Hurst exponent (HE) are the two most practical measures to characterize and distinguish difference psycho-physiological states of human brain.
(4) In the artificial phase space reconstructed from EEG nonlinear time series, the concepts of qualitative state and qualitative behavior based on nonlinear dynamical properties are presented. The algorithm of extracting qualitative states from the reconstructed phase space is proposed as well as the method of modeling the phase-space trajectory. Three methods of characterizing the qualitative behavior are also given to show different aspects of underlying system.
(5) The integration methods of EEG classification and identification are presented. The nonlinear properties and the qualitative behavior are fed as the input information of the classifier. The hybrid methods can not only determine their intrinsic parameters, but also select the most respective channels, which hold the critical distinguishable information. These efforts may help improve the accuracy and performance of the classifier. In medicine diagnose, these adaptive learning methods may help automatically identify the disease foci, and in BCI, they also help to find the location of specific brain function.
The methods proposed in the thesis are evaluated on several EEG data sets acquired from some common databases. These data sets have been studied by some research groups. The proposed methods may give satisfactory results on these data sets.
The proposed methods are not limited in EEG time series. They can be developed and extended for other questions. The method about qualitative state and qualitative behavior in reconstructed phase space may be used in the general nonlinear times series, which recorded from underlying nonlinear dynamical systems.
引文
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[1] H. Kantz, T. Schreiber. Nonlinear Time Series Analysis, 1st ed. Cambridge: Cambridge University Press, 1997.
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