Brain Source Localization Using EEG Signal Analysis

249 Pages·2018·15.08 MB·English

by  Munsif Ali Jatoi

Brain Source
Localization Using
EEG Signal Analysis

Brain Source
Localization Using
EEG Signal Analysis
Munsif Ali Jatoi and Nidal Kamel
MATLAB and Simulink are trademarks of the MathWorks, Inc. and are used with permission.
The MathWorks does not warrant the accuracy of the text or exercises in this book. This book’s
use or discussion of MATLAB and Simulink software or related products does not constitute
endorsement or sponsorship by the MathWorks of a particular pedagogical approach or particu-
lar use of the MATLAB and Simulink software.
CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 2018 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
No claim to original U.S. Government works
Printed on acid-free paper
International Standard Book Number-13: 978-1-4987-9934-8 (Hardback)
This book contains information obtained from authentic and highly regarded sources. Reason-
able efforts have been made to publish reliable data and information, but the author and pub-
lisher cannot assume responsibility for the validity of all materials or the consequences of their
use. The authors and publishers have attempted to trace the copyright holders of all material
reproduced in this publication and apologize to copyright holders if permission to publish in this
form has not been obtained. If any copyright material has not been acknowledged please write
and let us know so we may rectify in any future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, repro-
duced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now
known or hereafter invented, including photocopying, microfilming, and recording, or in any
information storage or retrieval system, without written permission from the publishers.
For permission to photocopy or use material electronically from this work, please access www.
copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc.
(CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organi-
zation that provides licenses and registration for a variety of users. For organizations that have
been granted a photocopy license by the CCC, a separate system of payment has been arranged.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks,
and are used only for identification and explanation without intent to infringe.
Library of Congress Cataloging-in-Publication Data
Names: Jatoi, Munsif Ali, author. | Kamel, Nidal, author.
Title: Brain source localization using EEG signal analysis / Munsif Ali Jatoi
and Nidal Kamel.
Description: Boca Raton : Taylor & Francis, 2018. | Includes bibliographical
references.
Identifiers: LCCN 2017031348 | ISBN 9781498799348 (hardback : alk. paper)
Subjects: | MESH: Electroencephalography | Brain Mapping | Brain
Diseases--diagnostic imaging | Brain--diagnostic imaging
Classification: LCC RC386.6.E43 | NLM WL 150 | DDC 616.8/047547--dc23
LC record available at https://lccn.loc.gov/2017031348
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com
Dedication
My grandparents: Mohammad Ali Jatoi, Sahib Khatoon
Jatoi, Muhib Ali Jatoi, and Meerzadi Jatoi
Parents: Hubdar Ali Jatoi and Ghulam Fatima Jatoi
And my lovely family: Lalrukh Munsif Ali, Kazim
Hussain Jatoi, and Imsaal Zehra Jatoi
With Love and Respect,
Munsif Ali Jatoi
To my beloved wife, Lama, and
adorable son, Adam
Nidal Kamel

Contents
Preface .................................................................................................................xi
Authors ...........................................................................................................xvii
List of symbols .................................................................................................xix
List of abbreviations .......................................................................................xxi
Chapter 1 Introduction ..................................................................................1
1.1 Background ..............................................................................................3
1.1.1 Human brain anatomy and neurophysiology .......................3
1.1.2 Modern neuroimaging techniques for brain disorders .......9
1.1.3 Economic burden due to brain disorders .............................10
1.1.4 Potential applications of brain source localization .............12
Summary ...........................................................................................................12
References ..........................................................................................................13
Chapter 2 Neuroimaging techniques for brain analysis .....................17
Introduction ......................................................................................................17
2.1 fMRI, EEG, MEG for brain applications .............................................17
2.1.1 EEG: An introduction ..............................................................20
2.1.1.1 EEG rhythms ...........................................................23
2.1.1.2 Signal preprocessing ..............................................25
2.1.1.3 Applications of EEG ...............................................27
2.1.2 EEG source analysis ................................................................28
2.1.2.1 Forward and inverse problems .............................29
2.1.3 Inverse solutions for EEG source localization .....................31
2.1.4 Potential applications of EEG source localization ..............32
Summary ...........................................................................................................33
References ..........................................................................................................33
Chapter 3 EEG forward problem I: Mathematical background .........37
Introduction ......................................................................................................37
3.1 Maxwell’s equations in EEG inverse problems .................................37
3.2 Quasi-static approximation for head modeling ................................40
vii
viii Contents
3.3 Potential derivation for the forward problem ...................................41
3.3.1 Boundary conditions ...............................................................42
3.4 Dipole approximation and conductivity estimation ........................44
Summary ...........................................................................................................45
References ..........................................................................................................46
Chapter 4 EEG forward problem II: Head modeling approaches ......49
Introduction ......................................................................................................49
4.1 Analytical methods versus numerical methods for head
modeling .................................................................................................50
4.1.1 Analytical head modeling ......................................................50
4.1.2 Numerical head models ..........................................................51
4.2 Finite difference method ......................................................................52
4.3 Finite element method ..........................................................................53
4.4 Boundary element methods .................................................................55
Summary ...........................................................................................................59
References ..........................................................................................................60
Chapter 5 EEG inverse problem I: Classical techniques......................63
Introduction ......................................................................................................63
5.1 Minimum norm estimation..................................................................66
5.2 Low-resolution brain electromagnetic tomography .........................68
5.3 Standardized LORETA .........................................................................70
5.4 Exact LORETA ........................................................................................72
5.5 Focal underdetermined system solution ............................................73
Summary ...........................................................................................................75
References ..........................................................................................................75
Chapter 6 EEG inverse problem II: Hybrid techniques .......................79
Introduction ......................................................................................................79
6.1 Hybrid WMN .........................................................................................79
6.2 Weighted minimum norm–LORETA..................................................80
6.3 Recursive sLORETA-FOCUSS ..............................................................82
6.4 Shrinking LORETA-FOCUSS ...............................................................84
6.5 Standardized shrinking LORETA-FOCUSS ......................................86
Summary ...........................................................................................................87
References ..........................................................................................................88
Chapter 7 EEG inverse problem III: Subspace-based techniques .....91
Introduction ......................................................................................................91
7.1 Fundamentals of matrix subspaces .....................................................93
7.1.1 Vector subspace ........................................................................93
7.1.2 Linear independence and span of vectors ...........................94
7.1.3 Maximal set and basis of subspace .......................................94
Contents ix
7.1.4 The four fundamental subspaces of A∈rm×n .....................94
7.1.5 Orthogonal and orthonormal vectors ..................................96
7.1.6 Singular value decomposition ...............................................97
7.1.7 Orthogonal projections and SVD ..........................................97
7.1.8 Oriented energy and the fundamental subspaces ..............98
7.1.9 The symmetric eigenvalue problem......................................99
7.2 The EEG forward problem .................................................................100
7.3 The inverse problem ............................................................................102
7.3.1 The MUSIC algorithm ...........................................................103
7.3.2 Recursively applied and projected-multiple signal
classification ...........................................................................107
7.3.3 FINES subspace algorithm ...................................................108
Summary ..........................................................................................................110
References .........................................................................................................110
Chapter 8 EEG inverse problem IV: Bayesian techniques .................113
Introduction .....................................................................................................113
8.1 Generalized Bayesian framework ......................................................113
8.2 Selection of prior covariance matrices ...............................................118
8.3 Multiple sparse priors ..........................................................................119
8.4 Derivation of free energy ....................................................................121
8.4.1 Accuracy and complexity .....................................................125
8.5 Optimization of the cost function .....................................................126
8.5.1 Automatic relevance determination ...................................128
8.5.2 GS algorithm ..........................................................................130
8.6 Flowchart for implementation of MSP .............................................132
8.7 Variations in MSP ................................................................................132
Summary .........................................................................................................134
References ........................................................................................................134
Chapter 9 EEG inverse problem V: Results and comparison ............137
Introduction ....................................................................................................137
9.1 Synthetic EEG data ..............................................................................137
9.1.1 Protocol for synthetic data generation ................................137
9.2 Real-time EEG data..............................................................................139
9.2.1 Flowchart for real-time EEG data ........................................144
9.3 Real-time EEG data results .................................................................144
9.3.1 Subject #01: Results ................................................................145
9.3.2 Subject #01: Results for MSP, MNE, LORETA,
beamformer, and modified MSP .........................................145
9.4 Detailed discussion of the results from real-time EEG data ..........161
9.5 Results for synthetic data ....................................................................176
9.5.1 Localization error ...................................................................176
9.5.2 Synthetic data results for SNR = 5 dB .................................176