腦磁波訊號源估測與同調性造影

Abstract

腦磁圖儀非侵入地量測腦部活化源誘發出的磁場訊號。其能夠在高時間解析度的取樣下對腦部活化源做時空造影，利用此方式將可有助於人腦功能在臨床與基礎神經生理學方面的研究。在此論文之中，我們將提出新的空間濾波技術，其利用腦磁圖儀所量測的訊號記錄來估測腦中訊號源的顯著程度以及訊號源間的相關性。 利用磁圖儀所量測的紀錄來估算腦部活化源的問題稱之為逆估算問題。為了解此類的不適定問題，加入些假設與限制是需要的，例如等效電偶極的腦部訊號源模型、固定訊號源電偶極個數等假設以及結構性或是最小範數限制等。在眾多的訊號源逆估算方法中，光束構成法—一種空間濾波技術—在近十年來漸漸的引人注目。此訊號源逆估算法是藉由探測訊號源空間中一個接一個的體素，此時空間濾波器在每個位置會分別地被計算。此空間濾波器依據單位增益與最小變異量兩準則將可保留目標訊號源訊號並同時抑制其他訊號所造成的影響。然而，如何決定訊號源電偶極的方向會是個問題。在既有的文獻中主要提及三種方式，第一、此電偶極方向會垂直於該處大腦皮質表面，然而自動地且精確地重建出曲折的皮質表面是非常困難的；第二、利用搜尋的方式找出，但此方法是非常耗時的；第三、將訊號源電偶極拆解成三個互成正交的分量，但其有遺漏偵測的風險。 此論文中，我們開發了一個新空間濾波技術，稱之為最大對比光束構成法，用以對神經訊號源做統計量的造影。除了如同傳統的光束構成法一樣的採用單位增益與最小變異量準則，我們所提的方法還利用了最大對比（活化與休息狀態逆估算出的神經活化訊號變異量的比值）準則。藉由此最大對比準則，我們將可用閉形式解的方式解析地決定出訊號源電偶極方向，也就是說，對於某一位置而言，能夠有效率地得出其對應的空間濾波器。一旦藉由對腦磁圖儀所量測訊號濾波所估算出各個位置的訊號源，將可計算對應整個訊號源空間的F統計量以視覺化在活化狀態時於皮質區的訊號源相對應於休息狀態的顯著程度。 同調性訊號源造影是另一個在人腦功能研究上有趣的主題，其能有助於探索人腦相關功能區域間聯繫的機制。近來，在特殊頻帶下的同步震盪訊號被認為與神經網路間的溝通有著密切的關係。同調訊號源造影法利用光束構成法為基礎，對相對於一參考訊號擁有同調性的皮質區訊號源做造影。但其僅適用於同步頻帶具有穩恆的特性。在此，我們提出另一新技術—最大正規化相關光束構成法—利用最大正規化相關性的準則解析地且閉形式的決定訊號源方向以對同調訊號源造影。理論上，此方法是一般化的，也就是它能對在任一有定義自相關性與互相關性的定義域中互有相關性的訊號作造影。此論文中，我們在感興趣的Morlet小波域中計算腦磁波儀所量測訊號的自相關性以及其與參考訊號的互相關性，接著利用所提出的最大正規化相關光束構成法來對動態跨頻同調訊號源造影。 模擬、假體以及手指抬動的實驗被採用來驗證與評估所提方法的正確性與能力。根據模擬與假體實驗所得的分析結果，我們的方法的確，第一、能既有效率地並準確地決定出訊號源電偶極的方向；第二、能準確地分別定位出擁有顯著變異量與時頻同調性的訊號源。當應用在手指抬動的實驗分析時，我們可從F統計量圖明顯的指出在腦部感覺運動區在活化狀態相對於休息狀態有高度的對比。

Magnetoencephalography (MEG) non-invasively measures the electromagnetic signals induced by brain activities. It can provide spatiotemporal brain activation imaging with high temporal resolution to facilitate functional brain research in both clinical and basic neuroscience fields. In this thesis, we propose novel spatial filtering techniques for statistical mapping of neuronal sources as well as cortical oscillatory coupling by using the whole-head MEG recordings. The problem of estimating the activation sources in the brain from the MEG recordings is called the inverse problem. To solve this ill-posed problem, approximations such as equivalent current dipole for source modeling, assumptions such as a fixed number of dipoles during the task, and constraints such as anatomical constraint and minimum-norm constraint are required to limit the solution space. Among the various kinds of source estimation methods, beamforming technique, a kind of spatial filtering technique, has becoming more and more attractive during the past decade. By probing the source space in a voxel-by-voxel manner, a spatial filter is individually calculated for each position. This spatial filter can reconstruct the activation magnitude of the targeted source while suppressing the contribution from other sources by imposing the unit-gain constraint and by applying the minimum-variance criterion. However, the determination of dipole orientation can be problematic. There are three major kinds of methods proposed in the literature. First, the dipole orientation is aligned to be perpendicular to the cortical surface. Unfortunately, the surface reconstruction for the convoluted cortex is very difficult and the reconstruction deviation will decrease the accuracy of the orientation. Second, the dipole orientation is determined by (exhaustive) search, which is time-consuming. The third kinds of methods decompose the dipole into three orthogonal components, which may suffer the risk of miss-detection. In this work, we develop a novel spatial filtering technique, called the maximum contrast beamformer, for statistical mapping of neuronal sources. In addition to the unit-gain constraint and the minimum-variance criterion, as in the conventional beamformers, our method exploits a maximum-contrast criterion that can maximize the discrimination between the estimated neuronal activities in the active state and those in the control (or resting) state. The maximum-contrast criterion helps to analytically determine the dipole orientation in a closed-form manner and the spatial filter can be obtained very efficiently for each targeted position. Once the neuronal activity waveform is estimated in the source space by spatially filtering the MEG recordings, F-statistic map can be calculated to reveal cortical regions with significant difference of activities between the control and active states. Another interesting issue in functional brain studies is the coherent source mapping for probing the binding mechanism of connected functional assemblies. Recently, oscillatory synchronization in particular frequency bands has been shown to be closely related to the communication within a neural circuit. By using the beamforming-based algorithm, DICS (Dynamic Imaging of Coherence Source) method can map the cortical sources that are statistically coherent to a specified reference at a certain frequency band. The limitation of the DICS method is that the synchronization frequency band is considered to be stationary during the task. Here, we propose another new method, maximum-normalized-correlation beamformer, for the mapping of the cortical oscillatory coupling. Theoretically, this method is very general that can image the sources correlated in the domain where the autocorrelation and crosscorrelation can be defined. To demonstrate the capability of this method, we compute the autocorrelation and crosscorrelation for the MEG recordings in the Morlet wavelet domain and image the dynamic coherent sources across multiple frequency bands during the task. Moreover, the dipole orientation has a closed-form solution by applying the maximum-normalized-correlation criterion. Experiments with simulation, phantom, and real data are conducted to verify the correctness and to assess the capability of the proposed methods. According to the experiments with simulation and phantom data, our methods indeed can efficiently and accurately calculate the dipole orientation. Also, our methods correctly locate the sources with significant variance and significant time-frequency coherence. When applied to a finger-lifting study, F-statistic map computed from the estimated neuronal activities on the cortical surface clearly identify the sensorimotor area with high contrast.