應用於人腦腦磁圖分析之高空間解析度分散式神經電流源估計法

High spatial resolution distributed current source estimation using magnetoencephalography (MEG)

張偉棠(Wei-Tang Chang)

指導教授 ： 林發暄

國立臺灣大學/工學院/醫學工程學研究所/博士(2010年)

https://doi.org/10.6342/NTU.2010.00089

摘要

藉由超導量子干涉元件(SQUIDs)，腦磁儀(MEG)可以非侵入式地偵測到極微小的腦部磁場。要求出腦磁儀逆算問題(inverse problem)的解，相當於要藉由腦外的量測信號重建出腦內電流源的位置及方向。由於腦磁儀逆算問題本身的非良置特性(ill-posedness)，除非再外加條件限制，否則不會得到唯一解。這篇論文的主題就是藉由外加特殊的條件限制，提高電流源重建的準確性。論文包含兩部份：(1) 使用寬鬆方向限制之稀疏性電流源估計，以及(2) 使用壓縮性神經磁性造影之空間稀疏性來源叢集模型。
當神經電流源被假設為集中分佈於空間中時，其中一個電流源模型是最小電流源估計法(Minimum current estimate, MCE)，使估計之神經電流源在空間中會呈現集中分佈。最小電流源估計中所需要的電流源方向資訊是由使用了寬鬆方向限制的最小範數估計(Minimum norm estimate, MNE)來提供。在本論文的第一部份，我們提出的「使用寬鬆方向限制之最小L1範數估計」(l1 LOC)，可自動地將電流源方向資訊整合進成本函數中。使用l1LOC的結果表現出較小的空間散亂性及較高的定位準確度。本論文的第二部份為研究不需要假設電流來源是集中或分散式分佈的電流源估計方式。大部份逆算問題的解不是偏好空間上集中就是偏好空間上分散的來源型式。當集中與分散型的來源同時存在的時候，這些方法都有可能導致不正確的結果。為了克服這個問題，我們根據電流源的空間分佈是可壓縮(compressible)的假設，提出一個新的「壓縮性神經磁性造影」(ComprEssive Neuromagtic Tomography, CENT)技術。藉著結合原始域及轉換域的稀疏性，我們得到不但在區域空間上連續，並且在全域中各自分開的叢集。我們使用Laplacian及球面小波來做為壓縮條件中的轉換函數。針對模擬的集中型、分散型、和集中分散合併型的來源，CENT都表現出比最小L1範數或最小L2範數估計更好的定位準確度。不同的轉換有不同的優勢：藉著使用Laplacian矩陣，比較有機會壓制在腦溝對側的錯誤估計；藉著使用球面小波轉換，CENT能增加對相鄰但不相接的電流來源之辨識度。整體來說，CENT能適應性地估測電流源，對偵測由認知作業產生的神經活動來說是具有潛力的工具。

關鍵字

逆運算問題 ； 範數 ； 凸型最佳化 ； 皮質方向性 ； 腦磁圖 ； 腦電圖 ； 小波轉換

並列摘要

Magnetoencephalography (MEG) enables non-invasive detection of weak cerebral magnetic fields by utilizing super-conducting quantum interference devices (SQUIDs). Solving the MEG inverse problem requires reconstructing the strength, locations, and orientations of the underlying neuronal current sources based on the extracranial measurements. Due to the ill-posed nature of the MEG inverse problem, the neuronal current reconstruction is not unique unless additional constraints are imposed. The main theme of this thesis is to improve the accuracy of source reconstruction by imposing specific constraints. This thesis includes two parts: (i) sparse current source estimation using loose orientation constraint, and (ii) spatially sparse source cluster modeling by Compressive Neuromagnetic Tomography (CENT).
The assumption of a spatially focal distribution of underlying neuronal current sources can be incorporated into MEG source modeling. One method is the minimum-current estimate (MCE), which achieves spatially focal source estimates by imposing a minimum l1-norm constraint on the distribution of the current sources. The knowledge about the orientations of current sources in MCE can be first estimated by the minimum-norm estimate (MNE) with a loose orientation constraint (LOC). However, MCE is spatially unstable because the l1-norm minimization is sensitive to noise and any errors due to, for example, inaccurate source orientations estimated by MNE with the LOC. Inspired by the MCE minimizing the l1-norm of the source distribution, the first part of this thesis presents a minimum l1-norm estimation source modeling approach with loose orientation constraint l1LOC), which integrates the estimation of current source orientation, location, and strength into a cost function to jointly model the residual error and the -norm of the estimated sources. In simulations and MEG experiments, l1LOC can estimate sources with a smaller spatial extent and can achieve a higher localization accuracy.
In the second part of this thesis, we develop a distributed source modeling technique without the assumption on the spatial distribution of sources to be either focal or diffussive. Most inverse problem solvers explicitly favor either spatially focal or diffussive current source patterns. Naturally, in a situation where both focal and spatially extended sources are present, such reconstruction methods may yield inaccurate current estimates. To address this problem, we develop the ComprEssive Neuromagnetic Tomography (CENT) method based on the assumption that the current sources are “compressible”. By combining two complementary constraints of standard and transformed domain sparsity, we obtain source estimates not only locally smooth and regular but also forming globally separable clusters. We study the Laplacian matrix (CENTL) and spherical wavelets (CENTW) as alternatives for the transformation in the compression constraint. For simulated sources of focal, diffuse, or the combination of these two types, the CENT method shows better accuracy on estimating the source locations and spatial extents than the minimum l(1)-norm or minimum l(2)-norm constrained inverse solutions. Different transformations yield different benefits: By utilizing CENT with the Laplacian matrix it is possible to suppress activations extending across two opposite banks of a sulcus. With the spherical wavelet transform, CENT can improve the detection of two nearby yet not directly connected sources. Overall, the CENT method is demonstrated to be a promising tool for adaptive modeling of distributed neuronal currents associated with cognitive tasks.

並列關鍵字

inverse problem ； L1-norm ； convex optimization ； cortical orientation ； MEG ； EEG ； wavelet transform

參考文獻

Auranen, T., A. Nummenmaa, M. S. Hamalainen, I. P. Jaaskelainen, J. Lampinen, A. Vehtari and M. Sams (2005). "Bayesian analysis of the neuromagnetic inverse problem with l(p)-norm priors." Neuroimage 26(3): 870-84.

Baillet, S., J. J. Riera, G. Marin, J. F. Mangin, J. Aubert and L. Garnero (2001). "Evaluation of inverse methods and head models for EEG source localization using a human skull phantom." Phys Med Biol 46(1): 77-96.

Boyd, S. (2004). Convex Optimization, Cambridge University Press.

Bradshaw, L. A. and J. P. Wikswo, Jr. (2001). "Spatial filter approach for evaluation of the surface Laplacian of the electroencephalogram and magnetoencephalogram." Ann Biomed Eng 29(3): 202-13.

Buxton, R. B. (2002). Introduction to functional magnetic resonance imaging : principles and techniques. Cambridge, UK ; New York, Cambridge University Press.