臺灣博碩士論文加值系統

基於相位空間重建法的非線性相依性(Nonlinear Interdependence)分析，常被應用於分析大腦神經網路之間的動態連結特性。此方法主要包含腦電波時間序列的相空間軌跡重建與相似度指標(Similarity index)的量化。雖然相空間重建方法已被研究多年，但是針對不同系統的實驗參數之選定仍然是一個存在的問題。本論文以非線性動態系統的觀點，探究非線性相依性的方法論，並應用於禪定腦電波。首先，探究參數對於多通道腦電波在相空間重建過程的影響，並利用Cao方法與互資訊(Mutual Information)方法分別決定嵌入維度與延宕時間。
在選擇合適的參數範圍值之後，本論文進行禪定腦電波的非線性相依性案例研究。我們挑選出一些具有特殊節律的禪定腦電波訊號，分析每段腦波訊號在不同錄製電極通道之間的非線性相依性，並提出一個主被動優勢度指數(active-passive dominance index, IAPD)做為量化參數。分析結果指出，含有theta 與低頻alpha(8~10Hz)成分的腦電波會在前腦與中前腦區有主動性影響力較為主導的現象。這些初步的禪定腦電波研究結果，能針對大腦的神經網絡連結特性提供了一些新的見解。

Nonlinear-interdependence analysis based on phase space reconstruction may provide a feasible way to access brain dynamical interactions among regional neural networks. The analysis mainly involves the reconstruction of phase-space trajectory from EEG and the estimation of similarity index. The reconstruction of phase-space trajectory from time series has been studied for many years. Nevertheless, selection of appropriate implementation parameters is still an open question, particularly, for different dynamic systems. This study was aimed at the investigation of the systematic approach for determining implementation parameters adopted in the nonlinear interdependence analysis of the phase-space trajectory reconstructed from multichannel EEG signals. Embedding dimension was analyzed by Cao’s method and time delay was estimated by mutual information analysis.
With the reliably selected parameters, nonlinear interdependence analysis was applied to a number of screened EEG epochs collected from Chan-meditation practitioners. This thesis presents the results of some case studies on Chan-meditation practitioners based on the evaluation of EEG active-to-passive dominating characteristics. In conclusion, most theta and low-alpha EEG epochs with frontal or frontal-central focalization exhibit source dominating behaviors. This preliminary study may provide new insights into the neural-network interaction of Chan-meditation brain.

Content v
List of Figures vii
List of Tables ix

Chapter 1 Introduction 1
1-1 Background and Motivation 1
1-2 Introduction of Chan-Buddhist Meditation 5
1-3 Nonlinear Interdependence Analysis 7
1-4 Aims of This Study 9
1-5 Scope of thesis 9

Chapter 2 Methods and Theories 11
2-1 Introduction of EEG 11
2-2 Reconstruction of System Dynamics from observation 14
2-2-1 Estimation of Embedding Dimension 15
2-2-2 Estimation of Time Delay 17
2-3 Nonlinear Interdependence Measure 18
2-3-1 Definition and Estimation 19
2-3-2 Asymmetric property 22
2-4 Regional Nonlinear Interdependence Measure 23

Chapter 3 Experiment and Signal Analysis 26
3-1 Experiment Setup and Procedure 26
3-1-1 Experimental Group 26
3-1-2 Signal Acquisition 27
3-2 Signal Analysis 27
3-2-1 Outline of the scheme 28
3-2-2 Nonlinear Interdependence Analysis 29
3-2-3 Regional Nonlinear Interdependence 31

Chapter 4 Investigation of Implementation Parameters 33
4-1 Interdependence matrix and brain mapping of SI 33
4-2 Determination of time delay 37
4-2-1 Time delay analysis based on Lorenz model 37
4-2-2 Result of Mutual Information 39
4-2-3 Variations of S brain mapping for different τ 40
4-3 Analysis of embedding dimension 43
4-3-1 Result of Cao method 43
4-3-2 Variations of S brain mapping for different m 44
4-4 Determination of nearest neighbor K 46

Chapter 5 Results and Discussion 48
5-1 Active-to-passive dominating index (IAPD) 48
5-2 APD Interpretation for Chan-Meditation EEG 50

Chapter 6 Conclusion 58
6-1 Conclusion 58
6-2 Future Work 59

Reference 62
Appendix 68

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