以自迴歸模型為基礎之禪坐腦電波隨時空變異之頻譜分析

Abstract

本論文主要利用單變數（univariate）與多變數（multivariate）之自迴歸模型（autoregressive model）來分析探討禪坐腦電波時間與空間之特性。在第一章的背景簡介之後，第二章提出了一個可程式化的方法Subband-AR EEG Viewer來進行腦電波的分析，該方法主要是追蹤禪坐中腦電波隨時間變化的頻譜特性，繼而可以提供禪坐腦電波的總覽。為了達到這樣的目的，禪坐腦電波首先會經由樹狀的濾波器組（filter banks）分解成子頻帶成份（subband components）。然後每個子頻帶成份再利用二階的自迴歸模型求出其主要頻率，利用求出來的主要頻率可以針對所欲解決的問題來設計演算法。根據Subband-AR EEG Viewer，我們發展了兩個特別用來研究禪坐中的視覺感知能力與禪坐腦電波時空特性的演算法。這些演算法在實際應用上不需要繁複決定參數的程序，並且因為採用了二階自迴歸模型而大大的降低了運算量。因此這個方法非常適合用來進行長時間的腦電波分析與即時處理。 在禪坐的視覺誘發電位（visual evoked potentials）研究中常會遇到一個問題就是無法得知可以作為參考的實際禪坐狀態來給予刺激，為了讓每一個視覺誘發電位取得時的大腦狀態盡量維持一致，我們選擇在前額alpha波出現時給予閃光刺激，這是因為前額alpha波被發現在禪坐的過程中會有顯著的增加，因此，我們根據第二章所述的Subband-AR EEG Viewer設計出一個即時的alpha波偵測器，如此一來，每一個視覺誘發電位便會是在類似的背景腦電波下所取得。然後我們再利用alpha波下之視覺誘發電位（alpha-dependent F-VEPs）來研究禪坐中大腦對於刺激的動態變化。根據實驗設計所得出的結果顯示出禪坐組與控制組有顯著的差異，與控制組在休息狀態下的比較下，禪坐組在禪坐中，特別是在Cz和Fz的視覺誘發電位P1-N2和N2-P2的振幅上有明顯的增加。因此，我們推測禪坐會導致主要視覺皮質層以及其相關區域對於閃光刺激產生較大振幅的反應。 另一個由Subband-AR EEG Viewer演繹過來的演算法為一個結合多重解析度（multi-resolution）技術與自迴歸模型的腦電波解讀器，它可以辨別出腦電波的低振幅波,delta, theta, chi, alpha和beta波，另外，對於常見的雜訊如基準線飄移（baseline drift）和肌電圖干擾（electromyograph interference）也可以被這個解讀器所偵測出來。這個解讀器擁有高效率的計算能力以及容易以硬體實現的特性，因此非常適合用來作為長時間的腦電波解讀以及即時的腦電波處理，它也可以對於大量的腦電波記錄提供一個快速的總覽。因此，禪坐腦電波階段性的變化就可經由不同灰階值表示不同的腦電波特徵所構成的圖表顯示出來。實驗結果顯示了禪坐組與控制組在時間與空間的腦電波節律特徵上有很大的不同，特別是禪坐中beta節律在大腦上的傳遞現象。 除了單變數的自迴歸模型外，在這論文的最後，我們也提出了殘餘共變異矩陣（residual covariance matrix），係根據多變數的自迴歸模型所發展出來的一個評估腦電波時空一致性的指標：LSTS（local spatiotemporal synchronization）指標。LSTS 指標針對大腦局部區域上相鄰腦電波頻道間一致性的程度進行估測。利用QR分解，LSTS 指標可以有效率的被計算出來。另外，我們也提供了自迴歸模型階數與相鄰頻道形態選擇的策略。根據初期的結果顯示腦電波頻道間一致性的降低（去一致性）會使得LSTS 指標的數值增加。為了評估這個指標的有效性，我們設計了一個由外部指示（externally-paced）的手指運動實驗，結果顯示在主要運動區所產生的去一致性成功的反應出較高數值的LSTS 指標。 因此，LSTS 指標或許可被用來研究如禪坐等尚未被完全了解的心智活動下大腦的動態變化。在我們的初步結果中，當禪坐中的低振幅波出現時，LSTS 指標顯示了整體腦電波一致性的增加，而這個現象被推測為與在深層禪坐中較不被環境刺激所影響的狀態有關。

This dissertation reports the study on EEG (electroencephalograph) spatiotemporal characteristics under Zen meditation. Univariate and multivariate AR models were applied. Following the background introduction, Chapter 2 presents a computerized scheme Subband-AR EEG Viewer that provides a comprehensive view of the meditation EEG record. The scheme was mainly designed to trace the varying spectral characteristics in meditation EEG. To accomplish this task, a meditation EEG signal was first decomposed into subband components by tree-structured filter banks. The second-order autoregressive model was then applied to each subband component to estimate its root frequency. Based on the estimated root frequencies and sound logic, specific criterion can be deduced for a particular problem-domain application. Two algorithms were developed to investigate the visual perception under meditation and to explore the spatiotemporal characteristics of EEG rhythms. These algorithms do not require exhausting work at determining appropriate parameters in implementation. Further, due to the second-order autoregressive model adopted, the computation load is greatly reduced. This approach is practically favorable to long-term EEG monitoring and real-time processing. In the study of evoked response potential during Zen meditation, one issue encountered was the inaccessibility to the actual meditation level or stage as a reference. By modifying Subband-AR EEG Viewer, an alternative strategy was proposed for dealing with this problem. To secure a consistent condition of the brain dynamics when applying stimulation, a scheme of recording flash visual evoked potentials (F-VEPs) was designed, with main idea of applying flash stimuli during a constant background EEG (electroencephalograph)–frontal alpha-rhythm dominating activity. This particular activity was found increasing during Zen meditation. Thus the flash-light stimulus was to be applied upon emergence of the frontal alpha-rhythm. The alpha-dependent F-VEPs were then employed to inspect the effect of Zen meditation on brain dynamics. Based on the experimental protocol proposed, considerable differences between experimental and control groups were obtained. Our results showed that amplitudes of P1-N2 and N2-P2 on Cz and Fz increased significantly during meditation, contrary to the F-VEPs of control group at rest. We thus suggest that Zen meditation results in acute response on primary visual cortex and the associated parts. Another algorithm deduced from Subband-AR EEG Viewer was a unique interpreter that combined a multi-resolution scheme with autoregressive modeling to identify the EEG patterns including the flat wave, delta, theta, chi, alpha, and beta activities. In addition, such artifacts as the baseline drift and EMG (electromyograph) interference were identifiable in the scheme. With the merits of high computational efficiency and easy hardware realization, the method proposed is feasible for long-term EEG monitoring and online EEG processing. It also allows a quick overview of an enormous amount of EEG data and the meditation scenario can be illustrated by a running gray-scale chart with each gray tone coding a particular EEG rhythmic pattern. Moreover, results of applying the proposed scheme to an experimental group (Zen meditation practitioners) and a control group (normal, healthy subjects) revealed significant distinction in spatiotemporal characteristics of EEG rhythmic patterns, especially the spatial propagation of the beta rhythm during meditation sessions. Besides univariate AR model, this dissertation finally presented our study on a parameter called the local spatiotemporal synchronization index (LSTS index), mainly based on residual covariance matrix of a multivariate autoregressive (mAR) model. Analysis of The LSTS index measures the degree of synchronization among neighboring channels of a local brain area. By using the QR factorization, the index can be efficiently calculated. A strategy for determining the AR model order and the array of neighboring channels was also proposed. According to preliminary results, a reduction of synchronization (or, significant desynchronization) of evaluated brain areas was quantified by a relatively high index. An externally-paced finger-movement experiment was designed to evaluate the proposed method. The LSTS index estimated successfully reflected the spatiotemporal desynchronization in the primary motor area. Accordingly, the LSTS measurement could be considered as a potential approach for investigating the spatiotemporal synchronization of unknown brain dynamics under particular mental process, such as the Zen meditation. In the preliminary findings, the LSTS index of meditation EEG revealed an increasing global synchrony for the extremely low power EEG activities (to be called the ‘flat’ waves), that had been hypothesized as a detached state of sensory perception during deep meditation.