多維濾波器應用於腦病變源定位分析

Abstract

本論文之主要研究目的是發展一三維（3D）濾波器，並將其應用於腦殼表 面電位分佈的處理上。事實上，腦電位分佈的處理常受限於有限的錄製電 極數目（空間解析度）。經過我們與以往所被提出的數值方法，包括「 spherical spline method」和在腦電位分析上廣被利用的「四點最近法 」（4NN method）做一番比較之後發現，三維濾波器的表現確實足以與前 二者相匹敵。首先，我們討論了三維濾波器設計的基本理論與法則。本論 文中，應用「頻域轉換法」（frequency transformation method）所設 計的三維濾波器來重建腦電位的空間分佈，由此，我們觀察三維濾波器的 特性（頻寬）對腦電位分佈的影響。此外，為了更進一步瞭解傳統的數值 方法與此一方法的優缺點，我們提出一個以「電耦極模式法」（the current dipole model）為基礎的量化方法，針對不同方法的性能做比較 。最後，我們再利用此三種方法，針對實際錄製得的腦波信號（EEG signal）重建空間腦電位並予以比較。我們深信，「三維濾波器」不僅能 直接、有效地對多維頻道腦波訊號做作空間上的分析，它本身更兼具了物 理上的意義並且融合了多維濾波器的優點與潛力。 The purpose of this research is to develop the three-dimensional (3D) filtering technique to manipulate the distribution of the brain electrical potential on the scalp, based on a limited number of EEG ( electroencephalograph ) recording electrodes ( spatial resolution ). In comparison with the spherical spline and four-nearest-neighbor ( 4NN ) method which is widely used in EEG, the 3D filtering method is demonstrated to have competitive performance. First, the primary principles and algorithm to design three-dimensional filters are discussed.The 3D filters, designed by frequency transformation method, are then applied to reconstruction of brain potential mapping. We then investigate the effects of the 3D filter's characteristics ( mainly the bandwidth of the filter ) on constructed brain mapping. To further understand the advantages and drawbacks of conventional methods and our method, we propose a quantitative approach based on current dipole model to justify performance of different methods. Finally, we applied these methods to brain mapping construction from the recorded EEG signal. To our belief, this 3D filtering method, which explores the forte and potentiality of multi-dimensional filters, provides a straightforward, efficient, and physically meaningful approach to deal with multi-channel EEG signals.