Statistical Analysis of fMRI Data, 2e
by Ashby
ISBN: 9780262042680 | Copyright 2019
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A guide to all aspects of experimental design and data analysis for fMRI experiments, completely revised and updated for the second edition.
Functional magnetic resonance imaging (fMRI), which allows researchers to observe neural activity in the human brain noninvasively, has revolutionized the scientific study of the mind. An fMRI experiment produces massive amounts of highly complex data for researchers to analyze. This book describes all aspects of experimental design and data analysis for fMRI experiments, covering every step—from preprocessing to advanced methods for assessing functional connectivity—as well as the most popular multivariate approaches. The goal is not to describe which buttons to push in the popular software packages but to help researchers understand the basic underlying logic, the assumptions, the strengths and weaknesses, and the appropriateness of each method.
The field of fMRI research has advanced dramatically in recent years, in both methodology and technology, and this second edition has been completely revised and updated. Six new chapters cover experimental design, functional connectivity analysis through the methods of psychophysiological interactions and beta-series regression, decoding using multi-voxel pattern analysis, dynamic causal modeling, and representational similarity analysis. Other chapters offer new material on recently discovered problems related to head movements, the multivariate GLM, meta-analysis, and other topics. All complex derivations now appear at the end of the relevant chapter to improve readability. A new appendix describes how to build a design matrix with effect coding for group analysis. As in the first edition, MATLAB code is provided with which readers can implement many of the methods described.
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Contents (pg. vii) | |
Preface to the Second Edition (pg. xiii) | |
Preface to the First Edition (pg. xv) | |
List of Acronyms (pg. xix) | |
1. Introduction (pg. 1) | |
1.1 What Is fMRI (pg. 4) | |
1.2 The Scanning Session (pg. 5) | |
1.3 Data Analysis (pg. 7) | |
1.4 Software Packages (pg. 8) | |
2. Data Formats (pg. 11) | |
2.1 Some Commonly Used Data Formats (pg. 12) | |
2.1.1 DICOM (pg. 12) | |
2.1.2 Analyze (pg. 13) | |
2.1.3 NIfTI (pg. 14) | |
2.1.4 MINC (pg. 14) | |
2.1.5 BIDS (pg. 14) | |
2.2 Converting from One Format to Another (pg. 15) | |
2.3 Reading fMRI Data into MATLAB (pg. 15) | |
3. Modeling the BOLD Response (pg. 17) | |
3.1 Linear Models of the BOLD Response (pg. 17) | |
3.2 Methods of Estimating the hrf (pg. 23) | |
3.2.1 Input an Impulse, and Observe the Response (pg. 23) | |
3.2.2 Open the Box; Study the Circuit (pg. 24) | |
3.2.3 Take a Guess (pg. 24) | |
3.2.4 Select a Flexible Mathematical Model of the hrf (pg. 26) | |
3.2.5 Deconvolution (pg. 35) | |
3.3 Nonlinear Models of the BOLD Response (pg. 38) | |
3.4 Conclusions (pg. 42) | |
4. Experimental Designs (pg. 45) | |
4.1 Organizing and Presenting Stimulus Events (pg. 45) | |
4.1.1 Block Designs (pg. 45) | |
4.1.2 Slow Event-Related Designs (pg. 49) | |
4.1.3 Rapid Event-Related Designs (pg. 50) | |
4.1.4 Free-Behavior Designs (pg. 51) | |
4.1.5 Resting-State fMRI (pg. 52) | |
4.2 Choosing the Right Experimental Conditions& (pg. 53) | |
4.2.1 The Method of Subtraction (pg. 53) | |
4.2.2 Conjunction Analysis Designs (pg. 55) | |
4.2.3 Factorial Designs and the Additive Factor Method& (pg. 57) | |
4.2.4 Parametric Designs (pg. 59) | |
4.2.5 Repetition Suppression Designs (pg. 60) | |
4.3 Conclusions (pg. 61) | |
5. Preprocessing (pg. 63) | |
5.1 Slice-Timing Correction (pg. 64) | |
5.1.1 Slice-Timing Correction during Preprocessing (pg. 65) | |
5.1.2 Slice-Timing Correction during Task-Related Statistical Analysis (pg. 71) | |
5.2 Head Motion Correction (pg. 72) | |
5.2.1 Correcting for Motion-Induced Location Changes (pg. 73) | |
5.2.2 Motion-Induced Changes in the BOLD Response (pg. 80) | |
5.3 Coregistering the Functional and Structural Data (pg. 83) | |
5.4 Normalization (pg. 88) | |
5.4.1 Brain Atlases (pg. 88) | |
5.4.2 The Spatial Normalization Process (pg. 89) | |
5.5 Spatial Smoothing (pg. 92) | |
5.6 Temporal Filtering (pg. 97) | |
5.7 Other Preprocessing Steps (pg. 102) | |
5.7.1 Quality Assurance (pg. 102) | |
5.7.2 Distortion Correction (pg. 102) | |
5.7.3 Grand Mean Scaling (pg. 103) | |
5.8 Conclusions (pg. 104) | |
6. The General Linear Model (pg. 105) | |
6.1 The Correlation Approach (pg. 106) | |
6.2 Collinearity (pg. 111) | |
6.3 Accounting for Nuisance Effects (pg. 115) | |
6.4 The FBR Method (pg. 117) | |
6.5 Microlinearity versus Macrolinearity (pg. 122) | |
6.6 Block Designs (pg. 123) | |
6.7 A Graphical Convention for Displaying the Design Matrix (pg. 125) | |
6.8 An Introduction to the General Linear Model (pg. 126) | |
6.9 Parameter Estimation in the Correlation and FBR Models& (pg. 130) | |
6.10 Testing a Hypothesis by Constructing Statistical Parametric Maps (pg. 132) | |
6.10.1 Tests of One Linear Hypothesis (pg. 132) | |
6.10.2 Tests of Multiple Linear Hypotheses (pg. 139) | |
6.10.3 Testing a Nonlinear Hypothesis (pg. 140) | |
6.11 The Multivariate GLM (pg. 142) | |
6.12 Nonparametric Approaches to Hypothesis Testing (pg. 145) | |
6.12.1 Algorithm for Hypothesis Testing with a Permutation Test (pg. 145) | |
6.13 Percent Signal Change (pg. 146) | |
6.14 Comparing the Correlation and FBR Methods& (pg. 149) | |
6.15 Derivations of Propositions 6.1–6.3 (pg. 151) | |
6.15.1 Proposition 6.1 (pg. 151) | |
6.15.2 Proposition 6.2 (pg. 152) | |
6.15.3 Proposition 6.3 (pg. 153) | |
7. The Multiple Comparisons Problem (pg. 155) | |
7.1 The Sidak and Bonferroni Corrections (pg. 156) | |
7.2 Using Gaussian Random Fields (GRFs) to Make Single-Voxel Corrections (pg. 158) | |
7.3 Using GRFs to Correct at the Cluster Level& (pg. 166) | |
7.3.1 Cluster-Based Methods Using a Spatial Extent Criterion (pg. 170) | |
7.3.2 Cluster-Based Methods Using a Criterion That Depends on Cluster Height and Spatial Extent (pg. 171) | |
7.4 Permutation-Based Solutions to the Multiple Comparisons Problem (pg. 174) | |
7.4.1 Permutation-Based Algorithm for Finding the Threshold T That Leads to an Experiment-Wise Error Rate of αE When Decisions Are Made at the Single-Voxel Level (pg. 175) | |
7.4.2 Permutation-Based Algorithm for Finding the Threshold S on Cluster Size That Leads to an Experiment-Wise Error Rate of αE When Cluster-Based Decisions Are Made (pg. 175) | |
7.5 Comparing the Various Methods (pg. 176) | |
7.6 False Discovery Rate (pg. 178) | |
7.6.1 Benjamini and Hochberg (1995) Algorithm for Ensuring That FDR ≤ q (pg. 179) | |
7.7 Voodoo Correlations (pg. 182) | |
7.8 Conclusions (pg. 183) | |
7.9 Derivations (pg. 183) | |
7.9.1 Proposition 7.1 (pg. 183) | |
7.9.2 Proposition 7.2 (pg. 184) | |
7.9.3 Proposition 7.3 (pg. 185) | |
7.9.4 Proposition 7.4 (pg. 185) | |
7.9.5 Worsley et al. (1996) Algorithm for Computing Resel Counts (i.e., Rd) (pg. 186) | |
7.9.6 Why the FDR Algorithm Works (pg. 188) | |
8. Group Analyses (pg. 191) | |
8.1 Individual Differences (pg. 191) | |
8.2 Fixed versus Random Factors in the General Linear Model (pg. 194) | |
8.3 A Fixed-Effects Group Analysis (pg. 196) | |
8.4 A Random-Effects Group Analysis (pg. 201) | |
8.5 Comparing Fixed-Effects and Random-Effects Analyses (pg. 203) | |
8.6 Multiple-Factor Experiments (pg. 205) | |
8.7 Power Analysis (pg. 208) | |
8.8 Meta-Analysis (pg. 213) | |
8.9 Derivations (pg. 218) | |
8.9.1 Proposition 8.1 (pg. 218) | |
8.9.2 Proposition 8.2 (pg. 219) | |
9. Functional Connectivity Analysis via Psychophysiological Interactions and Beta-Series Regression (pg. 221) | |
9.1 The Method of Psychophysiological Interactions (PPI) (pg. 224) | |
9.1.1 Selecting a Seed (pg. 224) | |
9.1.2 PPI in Block Designs (pg. 225) | |
9.1.3 PPI in Rapid Event-Related Designs (pg. 231) | |
9.2 Beta-Series Regression (pg. 233) | |
9.3 Conclusions (pg. 241) | |
10. Functional Connectivity Analysis via Granger Causality (pg. 243) | |
10.1 Quantitative Measures of Causality (pg. 250) | |
10.2 Parameter Estimation (pg. 253) | |
10.3 Inference (pg. 257) | |
10.4 Conditional Granger Causality (pg. 258) | |
10.5 Theoretical Extensions (pg. 265) | |
10.6 Validity (pg. 266) | |
10.6.1 Is the Temporal Resolution of fMRI Good Enough for Granger Causality? (pg. 267) | |
10.6.2 Do Interregional Timing Differences in the hrf Invalidate Granger Causality? (pg. 267) | |
10.7 Software Packages (pg. 268) | |
10.8 Derivation of Proposition 10.1 (pg. 268) | |
11. Assessing Functional Connectivity via Coherence Analysis (pg. 269) | |
11.1 Autocorrelation and Cross-Correlation (pg. 269) | |
11.2 Power Spectrum and Cross-Power Spectrum (pg. 274) | |
11.3 Coherence (pg. 278) | |
11.3.1 Coherence in Rapid versus Slow Event-Related Designs (pg. 284) | |
11.3.2 An Empirical Application (pg. 288) | |
11.3.3 Hypothesis Testing (pg. 290) | |
11.4 Partial Coherence (pg. 290) | |
11.5 Using the Phase Spectrum to Determine Causality (pg. 293) | |
11.6 Conclusions (pg. 299) | |
11.7 Derivations (pg. 300) | |
11.7.1 Proposition 11.1 (pg. 300) | |
11.7.2 Proposition 11.2 (pg. 300) | |
12. Principal Component Analysis (pg. 303) | |
12.1 Principal Component Analysis (pg. 304) | |
12.2 PCA with fMRI Data (pg. 307) | |
12.3 Using PCA to Eliminate Noise (pg. 309) | |
12.3.1 Algorithm for Eliminating Noise from fMRI Data (pg. 311) | |
12.4 Singular-Value Decomposition (pg. 315) | |
12.5 Conclusions (pg. 318) | |
13. Independent Component Analysis (pg. 319) | |
13.1 The Cocktail-Party Problem (pg. 320) | |
13.2 Applying ICA to fMRI Data (pg. 320) | |
13.2.1 Spatial ICA (pg. 322) | |
13.2.2 Assessing Statistical Independence (pg. 324) | |
13.2.3 The Importance of Nonnormality in ICA (pg. 325) | |
13.2.4 Preparing Data for ICA (pg. 326) | |
13.3 ICA Algorithms (pg. 328) | |
13.3.1 Minimizing Mutual Information (pg. 328) | |
13.3.2 Methods That Maximize Nonnormality (pg. 330) | |
13.3.3 Maximum Likelihood Approaches (pg. 332) | |
13.3.4 Infomax (pg. 333) | |
13.4 Interpreting ICA Results (pg. 336) | |
13.4.1 Determining the Relative Importance of Each Component (pg. 336) | |
13.4.2 Assigning Meaning to Components (pg. 337) | |
13.5 The Noisy ICA Model (pg. 340) | |
13.6 Other Issues (pg. 345) | |
13.7 Group ICA (pg. 346) | |
13.8 Comparing ICA and GLM Approaches (pg. 347) | |
13.9 Conclusions (pg. 349) | |
13.10 Derivations (pg. 350) | |
13.10.1 Why Whitening Reduces the Number of Free Parameters in the ICA Model (pg. 350) | |
13.10.2 The Infomax Learning Algorithm (pg. 351) | |
14. Decoding via Multivoxel Pattern Analysis (pg. 353) | |
14.1 General Overview of MVPA (pg. 353) | |
14.2 Determining the Search Region and the Curse of Dimensionality& (pg. 355) | |
14.3 Creating the Activity Vectors (pg. 360) | |
14.4 Preprocessing for MVPA (pg. 364) | |
14.5 Building a Classifier (pg. 366) | |
14.5.1 Fisher Linear Discriminant Analysis (pg. 370) | |
14.5.2 Support Vector Machines (pg. 371) | |
14.6 Validation (pg. 373) | |
14.7 Statistical Inference (pg. 376) | |
14.7.1 Individual-Subject Analysis (pg. 376) | |
14.7.2 Group-Level Inference (pg. 377) | |
14.8 Feature Selection (pg. 379) | |
14.9 MVPA Software (pg. 380) | |
14.10 Conclusions (pg. 381) | |
14.11 Description of the SVM Algorithm That Maximizes the Margin (pg. 382) | |
14.11.1 Linear SVMs (pg. 382) | |
14.11.2 Nonlinear SVMs (pg. 386) | |
15. Encoding Models (pg. 389) | |
15.1 Voxel-Based Encoding Models (pg. 390) | |
15.2 Inverting an Encoding Model to Produce a Decoding Scheme (pg. 397) | |
15.3 Model-Based fMRI (pg. 400) | |
15.4 Computational Cognitive Neuroscience (pg. 403) | |
15.5 Conclusions (pg. 405) | |
16. Dynamic Causal Modeling (pg. 407) | |
16.1 Linear Dynamical Models of Neural Activation (pg. 408) | |
16.2 Bilinear Dynamical Models of Neural Activation (pg. 412) | |
16.3 Generalizations of the Bilinear Model (pg. 419) | |
16.3.1 Quadratic DCM (pg. 419) | |
16.3.2 Two-State DCM (pg. 420) | |
16.3.3 Stochastic DCM (pg. 421) | |
16.4 The Hemodynamic Model (pg. 422) | |
16.5 Parameter Estimation (pg. 423) | |
16.6 Model Selection (pg. 429) | |
16.6.1 Model Selection by Minimizing BIC (pg. 438) | |
16.6.2 Model Selection by Maximizing Negative Free Energy (pg. 439) | |
16.7 Group Analysis (pg. 442) | |
16.7.1 Fixed-Effects DCM Analyses (pg. 442) | |
16.7.2 Random-Effects DCM Analyses (pg. 443) | |
16.8 Conclusions (pg. 445) | |
16.9 Derivation of Negative Free Energy (pg. 446) | |
17. Representational Similarity Analysis (pg. 453) | |
17.1 Extracting an RDM from the BOLD Data (pg. 455) | |
17.1.1 Selecting the ROI (pg. 455) | |
17.1.2 Estimating Activity Vectors (pg. 456) | |
17.1.3 Computing Dissimilarity between Activity Vectors (pg. 457) | |
17.2 Building a Geometric Model of the Similarity Structure (pg. 462) | |
17.3 Perceived Similarity in Humans (pg. 467) | |
17.4 Group-Level Inference with RSA (pg. 470) | |
17.5 Encoding and Decoding Using Representational Similarity (pg. 475) | |
17.6 RSA Software (pg. 477) | |
17.7 Conclusions (pg. 477) | |
Appendix A. Matrix Algebra (pg. 479) | |
A.1 Matrices and Their Basic Operations (pg. 479) | |
A.2 Rank (pg. 486) | |
A.3 Solving Linear Equations (pg. 488) | |
A.4 Eigenvalues and Eigenvectors (pg. 492) | |
A.4.1 Definitions (pg. 492) | |
A.4.2 Properties (pg. 495) | |
Appendix B. Multivariate Probability Distributions& (pg. 499) | |
B.1 Introduction (pg. 499) | |
B.2 Multivariate Normal Distributions (pg. 500) | |
Appendix C. Building a Design Matrix for Group Analysis (pg. 505) | |
C.1 Effect Coding (pg. 505) | |
C.2 Statistical Testing (pg. 509) | |
Notes (pg. 513) | |
Chapter 3 (pg. 513) | |
Chapter 4 (pg. 513) | |
Chapter 5 (pg. 513) | |
Chapter 6 (pg. 513) | |
Chapter 7 (pg. 515) | |
Chapter 8 (pg. 515) | |
Chapter 9 (pg. 515) | |
Chapter 10 (pg. 516) | |
Chapter 11 (pg. 516) | |
Chapter 12 (pg. 516) | |
Chapter 13 (pg. 517) | |
Chapter 14 (pg. 517) | |
Chapter 15 (pg. 518) | |
Chapter 16 (pg. 518) | |
Chapter 17 (pg. 518) | |
Appendix B (pg. 519) | |
References (pg. 521) | |
Index (pg. 539) |
F. Gregory Ashby
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