A unified treatment of the generation and analysis of brain-generated electromagnetic fields.
In Brain Signals, Risto Ilmoniemi and Jukka Sarvas present the basic physical and mathematical principles of magnetoencephalography (MEG) and electroencephalography (EEG), describing what kind of information is available in the neuroelectromagnetic field and how the measured MEG and EEG signals can be analyzed. Unlike most previous works on these topics, which have been collections of writings by different authors using different conventions, this book presents the material in a unified manner, providing the reader with a thorough understanding of basic principles and a firm basis for analyzing data generated by MEG and EEG.
The book first provides a brief introduction to brain states and the early history of EEG and MEG, describes the generation of electromagnetic fields by neuronal activity, and discusses the electromagnetic forward problem. The authors then turn to EEG and MEG analysis, offering a review of linear and matrix algebra and basic statistics needed for analysis of the data, and presenting several analysis methods: dipole fitting; the minimum norm estimate (MNE); beamforming; the multiple signal classification algorithm (MUSIC), including RAP-MUSIC with the RAP dilemma and TRAP-MUSIC, which removes the RAP dilemma; independent component analysis (ICA); and blind source separation (BSS) with joint diagonalization.
Author(s): Risto J. Ilmoniemi; Jukka Sarvas
Publisher: MIT Press
Year: 2019
Language: English
Pages: x+246
Contents
Preface
1. Introduction
1.1 The Brain
1.2 Brain States
1.3 Electrical States of the Brain
1.4 MEG and EEG Signals as Measures of Brain States
1.5 Historical and Technical Background of EEG
1.6 Historical and Technical Background of MEG
1.7 State of the Art and Future Prospects for MEG Technology
1.7.1 High-Tc SQUID Magnetometers
1.7.2 Optically Pumped Magnetometers
1.7.3 hyQUIDs
1.7.4 Hybrid MEG–MRI Systems
1.7.5 MEG Systems for Measuring Infants and Fetuses
1.7.6 Methods to Remove Unwanted Components in the Data
2. Genesis of MEG and EEG
2.1 Maxwell’s Equations
2.1.1 Impressed and Primary Currents
2.2 The Current Dipole and Lead Fields
2.3 Cellular Basis for Electromagnetic Fields
2.4 The Action Potential
2.5 Postsynaptic Potential (PSP)
2.6 Description of Synaptic Activity
3. Forward Problem
3.1 Conductor Models
3.2 The General Case
3.3 Fields in an Infinite Homogeneous Medium
3.4 Fields in an Inhomogeneous Medium
3.5 Computing the Lead Field
3.6 Spherical Model
3.7 Magnetic Field for the Spherical Model in Cartesian Coordinates
3.8 Magnetic Field for the Spherical Model in Spherical Coordinates
3.9 Triangle Construction and the Vector Potential of the Magnetic Field in the Spherical Model
3.10 Electric Potential V in a Layered Sphere and in a Homogeneous Sphere
3.11 Semi-Infinite Homogeneous Conductor
3.12 Appendix: Vector Potential Outside a Spherical Conductor Due to Current Dipole in the Conductor
3.13 Appendix: Series Expansion for Potential Due to Current Dipole in Multilayered Sphere
4. Review of Linear Algebra and Probability Theory for MEG and EEG Data Analysis
4.1 Notation and Terminology
4.2 Review of Linear Algebra for MEG and EEG
4.3 Review of Elementary Probability Theory
4.4 Solving Noisy Linear Equations
4.5 Solving Noisy Equations with Estimators
4.6 MNLS Solution and Tikhonov Regularization in Other Norms
5. Interpreting MEG and EEG Data
5.1 Approaches to the Interpretation of MEG and EEG Data
5.2 The Inverse Problem
5.3 The Solution Without A Priori Information
5.4 Signal Space and Signal-Space Projection (SSP)
5.5 The Solution If There Is A Priori Information
5.6 Measurement Data
5.7 Search for a Single Dipole Source
5.8 The EEG/MEG Inverse Problem and Its Solution by the MNE Method
5.8.1 Noise-Normalized MNE Methods
5.8.2 Minimum-Norm Estimates with Other Norms
6. Beamformers
6.1 Measurement Data Matrix for Beamformers
6.1.1 Signal-to-Noise Ratio (SNR)
6.2 Scalar Beamformer
6.3 Scalar Beamformer Filter Vector with Noiseless Data and Uncorrelated Time Courses
6.4 Filter Vector with Correlated Time Courses and Noiseless or Noisy Data
6.5 Linear Transform of the Data Equation
6.6 Search for Source Dipole Locations with the Output Power µ(p)
6.7 Improved Beamformer Localizers for Searching Source Dipoles
6.7.1 Regularizing Data and Noise Covariance Matrices
6.8 Finding Estimates for Time Courses
6.9 Scalar Beamformer with Optimal Orientations
6.10 Time-Dependent Orientations
6.11 Iterative Beamformers
6.12 Iterative RAP Beamformer with Fixed-Oriented Dipoles
6.13 Iterative RAP Beamformer with Freely-Oriented Dipoles
6.14 Out-Projecting and Null-Constraining
6.15 Iterative Multi-Source AI and PZ Beamformers with Fixed-Oriented Dipoles
6.16 Iterative MAI and MPZ Beamformers with Freely-Oriented Dipoles
6.17 Iterative MAI and PMZ Beamformers and Time-Dependent Orientations
6.18 Vector Beamformers
6.19 Summary on Beamformers
6.20 Appendix: Proof of Equation (6.27)
6.21 Appendix: Proofs of Equations (6.34) and (6.38)–(6.41)
6.22 Appendix: Approximations (6.36) and (6.37)
6.23 Appendix: Local Maxima of Localizers τ(p)
6.24 Appendix: Unbiasedness of Localizers τ(p)
7. MUSIC Algorithm for EEG and MEG
7.1 Measurement Data for MUSIC
7.2 MUSIC with Fixed-Oriented Source Dipoles
7.2.1 MUSIC with Freely-Oriented Source Dipoles
7.3 Whitening the Data Equation
7.4 RAP-MUSIC for Fixed-Oriented Dipoles
7.5 RAP-MUSIC for Freely-Oriented Dipoles
7.5.1 The RAP Dilemma
7.5.2 Truncated RAP-MUSIC (TRAP-MUSIC) for Fixed- and Freely-Oriented Dipoles
7.6 Double-Scanning (DS-) MUSIC
7.6.1 Recursive Double-Scanning MUSIC (RDS-MUSIC)
7.7 Summary on MUSIC Algorithm
8. Independent Component Analysis (ICA)
8.1 Measurement Data and the ICA Assumption
8.2 Preprocessing Data for ICA
8.3 FastICA for Finding One Weight Vector
8.4 FastICA for Finding All Weight Vectors (“Symmetric Mode")
8.4.1 Summary of the FastICA Algorithm
8.4.2 ICA with Nonstationary Multi-Trial Data
8.5 Appendix: Weight Vectors Are among the Roots of the Lagrange Equation
8.6 Appendix: Hessian H(w) of Function J(w)
8.7 Appendix: Local Maxima and Minima of J(w) for w=wk
9. Blind Source Separation by Joint Diagonalization
9.1 MUCA Algorithm
9.2 Two-Step Filtering for MUCA Algorithm
9.3 Appendix: FFdiag Algorithm
Bibliography
Index
