The Neuroelectromagnetic Inverse Problem and the Zero Dipole Localization Error

A tomography of neural sources could be constructed from EEG/MEG recordings once the neuroelectromagnetic inverse problem (NIP) is solved. Unfortunately the NIP lacks a unique solution and therefore additional constraints are needed to achieve uniqueness. Researchers are then confronted with the dilemma of choosing one solution on the basis of the advantages publicized by their authors. This study aims to help researchers to better guide their choices by clarifying what is hidden behind inverse solutions oversold by their apparently optimal properties to localize single sources. Here, we introduce an inverse solution (ANA) attaining perfect localization of single sources to illustrate how spurious sources emerge and destroy the reconstruction of simultaneously active sources. Although ANA is probably the simplest and robust alternative for data generated by a single dominant source plus noise, the main contribution of this manuscript is to show that zero localization error of single sources is a trivial and largely uninformative property unable to predict the performance of an inverse solution in presence of simultaneously active sources. We recommend as the most logical strategy for solving the NIP the incorporation of sound additional a priori information about neural generators that supplements the information contained in the data

신경전자기 신호원의 고유특성을 고려한 신호원 복원 알고리즘

학위논문 (박사)-- 서울대학교 대학원 : 협동과정 계산과학전공, 2013. 2. 정현교.뇌전도 및 뇌자도를 이용한 신경전자기 신호원 영상법은 분포전류원 모델의 경우, 추가적인 정보와 제한조건이 주어져야만 유일한 신호원을 복원할 수 있는 역문제이다. 본 학위 논문에서는 뇌전도 및 뇌자도를 이용한 신호원 영상법의 정확도를 향상시키기 위한 새로운 방법을 제안한다. 뇌자도는 대뇌피질상에 존재하는 반지름 방향의 신호원에 둔감한 반면 뇌전도는 뇌자도에 비해 상대적으로 방향성에 큰 영향을 받지 않는 것으로 알려져 있다. 이러한 신호원 고유의 방향 특성은 현재까지 분포전류원 모델의 신호원 추정에 적용되지 않았다. 본 학위 논문에서는 뇌전도와 뇌자도를 동시 측정한 경우에 대해 신호원의 방향성을 고려해 대뇌피질 상에 존재하는 신호원을 복원하는 방법을 제안하였다. 기존의 뇌전도/뇌자도 신호원 영상법을 통해 복원된 신호원은 실제 신호원과 비교했을 때 한점에 집중되거나 넓은 영역에 퍼져 있다. 따라서 다양한 분포 형태를 가진 신호원의 경우 기존 복원법을 통해서는 신호원의 분포 형태를 추정하기 힘들다는 단점이 있었다. 본 학위 논문에서는 신호원의 최대값을 추정해 이러한 한계를 극복하여 신호원의 분포를 복원할 수 있는 새로운 신호원 영상법을 제안하였다. 제안된 방법들을 다양한 상황의 시뮬레이션을 통해 정확도를 평가했으며 간질환자의 데이터에 적용해 수술로 제거된 뇌부위와 뇌자도를 이용해 복원된 신호원의 위치와 분포영역을 비교하였다. 그 결과, 본 논문에서 제안한 방법들은 기존 방법에 비해 뇌자도 및 뇌전도의 국지화 정확도를 향상시켰 수 있었으며 앞으로 뇌영역 활성부위를 추정하는 의학 분야 및 역문제 연구에서 널리 사용될 것으로 기대된다.The functional imaging of neuroelectromagnetic sources of electroencephalographic (EEG) and magnetoencephalographic (MEG) based on distributed source models requires additional information and constraints on the source in order to overcome the ill-posedness and to obtain a plausible solution. In this dissertation, we present two methods to enhance accuracy of MEG and EEG source reconstruction. We propose a new cortical source imaging algorithm for integrating simultaneously recorded EEG and MEG, which takes into account the different sensitivity characteristics of the two modalities with respect to cortical source orientations. It is well known that MEG cannot reliably detect neuronal sources with radial orientation, whereas EEG is relatively less dependent on the source orientations than MEG. However, this intrinsic difference has not previously been taken into account in the integrative cortical source imaging using simultaneously recorded EEG and MEG data. On the other hands, most imaging algorithms explicitly favor either spatially more focal or diffuse current source patterns. Naturally, in a situation where both focal and extended sources are present or the source is arbitrary distributed, such reconstruction algorithms may yield inaccurate estimate. The other algorithm proposed in this dissertation improves accuracy of bio-electromagnetic source estimation regardless the extension of source distribution. The additional maximum amplitude constraint does successively enhance the localization accuracy in EEG/MEG source imaging. The proposed approaches are validated through numerical simulations and applied to practical epilepsy measurements and compared to the resection region. From the extensive analysis, it will be shown that the proposed approaches can enhance the source localization accuracy considerably, compared to the conventional approaches. Therefore the proposed methods in this dissertation are expected to be a promising approach on the research of inverse problem and many clinical applications of EEG and MEG.Abstracts 1 Contents 3 List of Tables 5 List of Figures 6 List of Symbols 8 1. Introduction 9 1.1 Motivation and Aim 9 1.2 Overview of Chapters 14 2. Basics of Functional Neuroimaging 16 2.1 Functional Neuroimaging 16 2.2 Measurment of EEG and MEG 19 2.2.1 EEG 19 2.2.2 MEG 22 2.3 Anatomy of Human Brain 24 2.4 Generation of Neuroelectromagnetic Fields 29 3. Forward and Inverse Problems 31 3.1 Neuroelectromagnetic Forward Problem 31 3.1.1 Quasi-Static Approximation 31 3.1.2 Analytic Formulation 32 3.1.3 Numerical Approach 35 3.1.4 Linearization of Forward Problem 38 3.2 Neuroelectromagnetic Inverse Problem 39 3.2.1 Distributed Source Model 39 3.2.2 L2 Norm Mminimization Approach 40 3.2.3 L1 Norm Minimization Approach 42 4. Preprocessing and Quantitative Evalution Metrics 43 4.1 Preprosessing 43 4.2 Techniques of Quantification of Distributed Source 46 5. Algorithm Considering Directional Characteristics 56 5.1 Proposed Algorithm 56 5.2 Numerical Experiment of Proposed Method 63 6. Algorithm Considering the Maximum Current Density 70 6.1 Proposed Algorithm 70 6.2 Numerical Experiment of Proposed Method 72 6.3 Application to Localization of Epileptic Zone 84 7. Conclsion 89 References 92 Appendix A. Derivation of L2 Norm Minimization Problem 100 Appendix B. Derivation of Directional Inverse Operators 105 Appendix C. Derivation of L1 Norm Minimization Problem 107 Abstract (in Korean) 110Docto

Conjugate Gradient Method Applied to Cortical Imaging in EEG/ERP

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Multimodal Integration: fMRI, MRI, EEG, MEG

This chapter provides a comprehensive survey of the motivations, assumptions and pitfalls associated with combining signals such as fMRI with EEG or MEG. Our initial focus in the chapter concerns mathematical approaches for solving the localization problem in EEG and MEG. Next we document the most recent and promising ways in which these signals can be combined with fMRI. Specically, we look at correlative analysis, decomposition techniques, equivalent dipole tting, distributed sources modeling, beamforming, and Bayesian methods. Due to difculties in assessing ground truth of a combined signal in any realistic experiment difculty further confounded by lack of accurate biophysical models of BOLD signal we are cautious to be optimistic about multimodal integration. Nonetheless, as we highlight and explore the technical and methodological difculties of fusing heterogeneous signals, it seems likely that correct fusion of multimodal data will allow previously inaccessible spatiotemporal structures to be visualized and formalized and thus eventually become a useful tool in brain imaging research

Improved EEG source localization with Bayesian uncertainty modelling of unknown skull conductivity

Electroencephalography (EEG) source imaging is an ill-posed inverse problem that requires accurate conductivity modelling of the head tissues, especially the skull. Unfortunately, the conductivity values are difficult to determine in vivo. In this paper, we show that the exact knowledge of the skull conductivity is not always necessary when the Bayesian approximation error (BAE) approach is exploited. In BAE, we first postulate a probability

Review on solving the inverse problem in EEG source analysis

In this primer, we give a review of the inverse problem for EEG source localization. This is intended for the researchers new in the field to get insight in the state-of-the-art techniques used to find approximate solutions of the brain sources giving rise to a scalp potential recording. Furthermore, a review of the performance results of the different techniques is provided to compare these different inverse solutions. The authors also include the results of a Monte-Carlo analysis which they performed to compare four non parametric algorithms and hence contribute to what is presently recorded in the literature. An extensive list of references to the work of other researchers is also provided