Case Studies in Neural Data Analysis: A Guide for the Practicing Neuroscientist

386 Pages·2016·35.664 MB·English

by  Mark A. Kramer, Uri T. Eden

Case Studies in Neural Data Analysis
Computational Neuroscience
Terrence J. Sejnowski and Tomaso A. Poggio, editors
For a complete list of books in this series, see the back of the book and
http://mitpress.mit.edu/ComputationaLNeuroscience
Case Studies in Neural Data Analysis
A Guide for the Practicing Neuroscientist
Mark A. Kramer and
Uri T. Eden
The MIT Press
Cambridge, Massachusetts
London, England
© 2016 Massachusetts Institute of Technology
All rights reserved. No part of this book may be reproduced in any form or by any electronic or mechanical means
(including photocopying, recording, or information storage and retrieval) without permission in writing from the
publisher.
This book was set in Times Roman by diacriTech, Chennai.
Printed and bound in the United States of America.
Library of Congress Cataloging-in-Publication Data
Names: Kramer, Mark A., author. I Eden, Uri T., author.
Title: Case studies in neural data analysis : a guide for the practicing
neuroscientist I Mark A. Kramer and Uri T. Eden.
Description: Cambridge, MA : The MIT Press, 2016. I Series: Computational
neuroscience series I Includes bibliographical references and index.
Identifiers: LCCN 2016014656 I ISBN 9780262529372 (pbk.: alk. paper)
Subjects: LCSH: Neural analyzers. I Neuropsychological tests.
Classification: LCC QP357.5 .K69 2016 I DDC 616.8/0475-dc23 LC record available at
https://lccn.loc.gov /2016014656
10987654321
It is these boundary regions of science which offer the richest opportunities to the
qualified investigator. They are at the same time the most refractory to the accepted
techniques of mass attack and the division of labor.
-Norbert Wiener, Cybernetics
I am writing this book for students, dressmakers, secretaries, artists, lazy people, poets,
[people] of action, dreamers, scientists, and everyone else who has only an hour for lunch
or dinner but still wants thirty minutes of peace to enjoy a cup of coffee.
-Edouard de Pomiane, French Cooking in Ten Minutes

Contents
Preface xiii
1 Introductiont o MATLAB
Synopsis 1
1.1 Introduction 1
1.2 Starting MATLAB 1
1.3 MATLAB Is a Calculator 2
1.4 MATLAB Can Compute Complicated Quantities 2
1.5 Built-in Functions 2
1.6 Vectors 3
1.7 Manipulating Vectors with Scalars 3
1.8 Manipulating Vectors with Vectors 3
1.9 Defining Variables 4
1.10 Probing the Defined Variables 5
1.11 Summing Elements in a Vector 5
1.12 Clearing All Variables 6
1.13 Matrices 6
1.14 Indexing Matrices and Vectors 7
1.15 Finding Subsets of Elements in Matrices and Vectors 8
1.16 Plotting Data 9
1.17 Multiple Plots, One atop the Other 11
1.18 Random Numbers 11
1.19 Histograms 13
1.20 Repeating Commands 15
1.21 Defining a New Function: Them-file 16
1.22 Saving Your Work 19
1.23 Loading Data 19
1.24 Loading Additional Functionality 20
2 The Event-RelatedP otentialf rom a Scalp Electroencephalogram 21
Synopsis 21
2.1 Introduction 21
2.1.1 Background 21
2.1.2 Case Study Data 22
viii Contents
2.1.3 Goal 22
2.1.4 Tools 22
2.2 Data Analysis 23
2.2.1 Visual Inspection 23
2.2.2 Plotting the ERP 28
2.2.3 Confidence Intervals for the ERP (Method 1) 29
2.2.4 Comparing ERPs 32
2.2.5 Confidence Intervals for the ERP (Method 2) 34
2.2.6 A Bootstrap Test to Compare ERPs 39
Summary 42
Problems 42
Appendix: Standard Error of the Mean 45
3 Analysiso f RhythmicA ctivity in the Scalp Electroencephalogram 49
Synopsis 49
3.1 Introduction 49
3.1.1 Background 49
3.1.2 Case Study Data 49
3.1.3 Goal 50
3.1.4 Tools 50
3.2 Data Analysis 50
3.2.1 Visual Inspection 50
3.2.2 Mean, Variance, and Standard Deviation 53
3.2.3 Autocovariance 54
3.2.4 Power Spectral Density, or Spectrum 61
3.2.5 Reexamining the Spectrum-A Matter of Scale 75
3.2.6 The Spectrum Changing in Time-The Spectrogram 78
Summary 80
Problems 80
Appendix A: The Spectrum and Autocovariance 83
Appendix B: Aliasing 85
Appendix C: Numerical Scaling of the Spectrum 88
4 Analysiso f RhythmicA ctivity in an InvasiveE lectrocorticogram 93
Synopsis 93
4.1 Introduction 93
4.1.1 Background 93
4.1.2 Case Study Data 93
4.1.3 Goal 93
4.1.4 Tools 94
4.2 Data Analysis 94
4.2.1 Visual Inspection 94
4.2.2 Spectral Analysis: The Rectangular Taper and Zero Padding 95
4.2.3 Beyond the Rectangular Taper-the Hanning Taper 109
4.2.4 Beyond the Hanning Taper-The Multitaper Method 111
4.2.5 Confidence Intervals of the Spectrum 114
Contents ix
Summary 117
Problems 117
Appendix: Multiplication and Convolution in Different Domains 120
5 Analysiso f Coupled Rhythmsi n an InvasiveE ledrocorticogram 123
Synopsis 123
5.1 Introduction 123
5.1.1 Background 123
5.1.2 Case Study Data 123
5.1.3 Goal 124
5.1.4 Tools 124
5.2 Data Analysis 124
5.2.1 Visual Inspection 124
5.2.2 Autocovariance and Cross-covariance 126
5.2.3 Trial-Averaged Spectrum 133
5.2.4 Introduction to the Coherence 136
5.2.5 Visualizing the Phase Difference across Trials 143
5.2.6 Single-Trial Coherence 146
Summary 148
Problems 150
6 Applicationo f Filteringt o ScalpE lectroencephalogramD ata 155
Synopsis 155
6.1 Introduction 155
6.1.1 Background 155
6.1.2 Case Study Data 155
6.1.3 Goal 156
6.1.4 Tools 156
6.2 Data Analysis 156
6.2.1 Visual Inspection 156
6.2.2 Spectral Analysis 158
6.2.3 Evoked Response and Average Spectrum 159
6.2.4 Naive Filtering 161
6.2.5 More Sophisticated Filtering 177
6.2.6 What's Phase Got to Do with It? 184
6.2. 7 Analysis of the Filtered EEG Data 188
Summary 190
Problems 191
7 Investigationo f Cross-FrequencyC oupling in a Local Field Potential 195
Synopsis 195
7 .1 Introduction 195
7.1.1 Background 195
7.1.2 Case Study Data 195
7.1.3 Goal 196
7.1.4 Tools 196