Xingfeng Li. Functional Magnetic Resonance Imaging Processing

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2 Xingfeng Li Functional Magnetic Resonance Imaging Processing

3 Functional Magnetic Resonance Imaging Processing

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5 Xingfeng Li Functional Magnetic Resonance Imaging Processing 123

6 Xingfeng Li Intelligent Systems Research Centre University of Ulster Londonderry UK ISBN ISBN (ebook) DOI / Springer Dordrecht Heidelberg New York London Library of Congress Control Number: Springer Science+Business Media Dordrecht 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (

7 To my mother Yufang Zhang and my father Yongkang Li

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9 Preface This book is about how to analyze perfusion-weighted imaging (PWI), functional MRI (fmri), diffusion-weighted imaging (DWI), and structural MRI (smri) data for investigating brain functions. Broadly speaking, there are two approaches to study brain function in vivo: one is bolus injection method and the other is noninvasive (no injections) method, e.g., blood-oxygen-level-dependent (BOLD) contrast method. For the tracer injection method, we will introduce dynamic susceptibility contrast imaging (DSC-MRI), which we focus on the Dirac delta function (impulse function) as an input for studying the brain blood flow system. The basic indicator theory is explained in details. Both linear and nonlinear regression methods are employed to smooth the DSC-MRI concentration time course. To solve the illposed problem for the residual function estimation, weighted damping method, i.e., Levenberg Marquardt (LM) algorithm is introduced to solve Toeplitz matrix regularization problem. Cerebral blood flow parameters are then estimated based on the indicator theory. BOLD-fMRI processing is the main part of this book; this includes both activation detection (segmentation view of the brain) and effective connectivity study (integration view of the brain). We begin with the first-level activation detection analysis, and we introduced the generalized linear model with autoregression model for error correction in activation detection. The threshold correction for the activation map using false discovery rate (FDR) and family-wise error (FWE) is introduced subsequently. Then mixed model is presented for the second-level analysis. To calculate the regression parameters, i.e., variance in the mixed effect model, Newton Raphson (NR), LM, and trust region methods are given in Chap. 3. In recent years, there has been increasing interest in studying effective connectivity using fmri method. Generally speaking, there are three methods to study effective connectivity from the viewpoint of system identification, i.e., black-box, gray-box, and white-box methods. Since the black-box method is model free and easy to apply, we concentrate on introducing this method. This includes model selection for first-level and robust regression for second-level effective connectivity analysis. We also apply this method for resting-state fmri study. vii

10 viii Preface The third part of this book is about processing diffusion-weighted imaging (DWI). The basic principle of MRI diffusion imaging is to study the motion of water molecules. The first concept is the apparent diffusion coefficient (ADC) which quantifies the magnitude of the water diffusion on one dimension. Because water diffusion is really 3D processing, diffusion tensor imaging (DTI) is introduced to describe this motion. Based on this information, we can infer the fiber directions in the human brain. But DTI method cannot resolve the problem of crossing fiber issue; to circumvent this limitation, high angle resolution diffusion imaging (HARDI) was proposed, and Q-ball imaging (QBI) and diffusion spectrum imaging (DSI) have been developed for studying diffusion orientation map. To estimate orientation distribution function (ODF) from QBI/DSI, regularization methods need to be adopted. We introduce the commonly used method, i.e., generalized cross validation (GCV) method for ODF regularization. Finally, smri data analysis method is presented. Instead of concentrating on smri image segmentation and registration, we present voxel-based morphometry (VBM) method and its application to Alzheimer s disease (AD) study. To begin with, we give the processing steps for VBM analysis based on cross-sectional study, and then we provided longitudinal VBM for smri data analysis. Furthermore, as an example, we apply this method to AD study to demonstrate how to use this method. Based on longitudinal VBM, we investigate the causality relationship between different brain regions at different stages of disease progression. I assume the reader has a certain background in computer programming, numerical analysis, statistics, and medical image analysis. This book can be used for graduate students who are interested in studying medical image analysis, particularly fmri image analysis. It can also be used as a reference book for radiologists, psychologists, neurologists, medical image physicists, computer scientists, and biomedical engineers for studying MRI image processing. I wish to thank Prof. Robert Hess and Prof. Kathy Mullen from McGill Vision Research, McGill University, Canada, for providing a huge amount of fmri data for this book. I appreciate Dr. Arun L. W. Bokde and Dr. Elizabeth Kehoe from Cognitive Systems group, Trinity College Dublin, Ireland, for collecting resting-state fmri and emotional facial experimental fmri data. I recognize Prof. Cyril Poupon from NeuroSpin, France, and Dr. Jennifer Campbell from Montreal Neurological Institute, McGill University, Canada, for providing the human and biological rat QBI datasets. I am obligated to Prof. Stefan Teipel and Dr. Maximilian Lerche from the University of Rostock in Germany to allow me to use their DSI data. Furthermore, I am especially grateful to Prof. Habib Benali and Dr. Arnaud Messe from functional imaging laboratory, INSERM/UPMC, Paris 6th University, France, for their help in developing the method for processing QBI. Finally, I acknowledge Prof. Thomas Martin McGinnity from University of Ulster, UK, for helping my work. Most of all, I am indebted to my wife, Feijun Wang, for her understanding, patience, and support for writing this book. Londonderry, UK Xingfeng Li

11 Contents 1 MRI Perfusion-Weighted Imaging Analysis Perfusion Imaging Indicator Dilution Theory for DSC-MRI MTT and CBV Calculation DSC-MRI Time Series Analysis Gamma-Variate Fitting Linear Regression Method for Gamma-Variate Fitting Nonlinear Regression Method for Gamma-Variate Fitting Baseline Elimination for Gamma-Variate Fitting Linear Method and Nonlinear Method for Gamma-Variate Fitting AIF Selection Robust Method for AIF Determination Deconvolution Calculation and Residual Function Estimation SVD Method for Deconvolution L2 Norm Regularization for PWI Study Piecewise Linear Method for Ridge Regression Parameter Estimation CBF, MTT, CBV, Arrival Time, and T-max Maps Dispersion Effects in DSC-MRI Local Density Random Walk for Concentration Time Course Convolution Method to Study Disperse Effect Summary of the PWI Algorithm References First-Level fmri Data Analysis for Activation Detection fmri Experimental Design Block Design Random ER Design Phase-Encoded Design ix

12 x Contents 2.2 fmri Data Preprocessing fmri Data Motion Correction fmri Time Series Normalization Activation Detection: Model-Free and Model-Based Methods Model-Free Method: Two Sample t-test for Activation Detection Correlation Analysis Method Models for Hemodynamic Response Function and Drift HRF Models for Activation Detection Drift Models for Activation Detection General Linear Model (GLM) for Activation Detection Generalized Linear Model (GLM) for Activation Detection Ordinary Least Square for Parameter Estimation in GLM FOS to Solve the Inverse Problem Weighted Least Squares Estimation AR(1) Model AR(q) Model Hypothesis Test and Threshold Correction Hypothesis Testing for the Activation Detection Bonferroni and FDR/FWE Threshold Correction Number of Independent Tests Permutation/Random Test Summary of Algorithm for First-Level fmri Data Analysis References Second-Level fmri Data Analysis Using Mixed Model Mixed Model for fmri Data Analysis Fixed and Random Effects in fmri Analysis Generalized Linear Mixed Model for fmri Study Mixed Model and Its Numerical Estimations Numerical Analysis for Mixed-Effect Models Two-Stage Model for the Second-Level fmri Analysis Maximum-Likelihood Method for Variance Estimation Different Runs Combination Group Comparison in the Mixed Model Iterative Trust Region Method for ML Estimation Levenberg Marquardt (LM) Algorithm LM Algorithm Implementation T and Likelihood (LR) Tests for the Mixed Model Modified EM Algorithm for Group Average One Simulation Example for the Numerical Processing Simulation to Combine 2 Runs Combination of 100 Runs... 92

13 Contents xi 3.4 Expectation Trust Region Algorithm for Second-Level fmri Data Analysis Average Runs Within Subject Comparing fmri Response Within Subject Compare Group of Subjects Numerical Implementation Details Further Numerical Improvement: BFGS Method Potential Applications and Further Development Degree of Freedom (DF) Estimation Estimation of DF for T Distribution ML Estimation of Mixture of t Distributions for Mixed Model Hessian Matrix Calculation for Trust Region Algorithm Trust Region and Expectation Trust Region Algorithms for df Estimation Future Directions for fmri Data Analysis Second-Level fmri Data Processing Algorithm Summary References fmri Effective Connectivity Study Nonlinear System Identification Method for fmri Effective Connectivity Analysis Current Methods for fmri Effective Connectivity Analysis Nonlinear System Identification Theory Granger Causality (GC) Tests Directionality Indices Network Structure and Regional Time Series Extraction Examples to Apply NSIM to Study Effective Connectivity Model Selection for Effective Connectivity Study Nonlinear Model for fmri Effective Connectivity Study Model Selection for NSIM in Effective Connectivity Study AIC and AICc Criteria for Model Selection MLARS Algorithm for Model Selection Nonlinear Interaction Terms for the Effective Connectivity Analysis Advantages and Disadvantages of NSIM Robust Method for Second-Level Analysis Robust Regression and Breakdown Point Least-Trimmed Squares for Second-Level Effective Connectivity Analysis Effective Connectivity for Resting-State fmri Data Resting-State fmri Example of Applying NSIM to RSN from rfmri Limitations for fmri Effective Connectivity in This Study

14 xii Contents 4.6 Summary of the Algorithm for fmri Effective Connectivity Study References Diffusion-Weighted Imaging Analysis Basic Principle of Diffusion MRI and DTI Data Analysis Physical Background of MRI Diffusion Equation Apparent Diffusion Coefficient (ADC) Map and DTI Calculation Invariant Indices for DTI Analysis High-Order DTI Data Analysis Fiber Tracking Color Encoding Method to Represent Fiber Fiber Tracking and 3D Representation High Angular Resolution Diffusion Imaging (HARDI) Analysis Q-Ball Imaging (QBI) ODF Representation ODF Reconstruction Theory Spherical Harmonics (SH) Transformation Least Squares Method with Constraints Testing the Algorithm on Rat Data Adaptive Q-Ball Imaging Regularization Generalized Cross-Validation (GCV) Algorithm for Regularization Regularization or Not Regularization? GFA and ODF Maps from Rat Data GCV Method for Human QBI ODF Regularization Diffusion Spectrum Imaging Difference Between QBI and DSI Acquisition DSI Image Analysis DSI GFA Map Using Fixed œ and GCV Regularization Method ODF Map for DSI Using Fixed œ Method and GCV Method Summary and Future Directions Summary of DTI, QBI, and DSI Image Analysis Methods References Voxel-Based Morphometry and Its Application to Alzheimer s Disease Study Background for Voxel-Based Morphometry Analysis MR Image Segmentation MR Image Registration Statistical Methods for VBM Analysis Enhanced VBM Histogram Match Application to AD Study

15 Contents xiii 6.3 Longitudinal VBM and Its Application to AD Study Longitudinal VBM Preprocessing Steps Results of Longitudinal VBM for AD Study Effective Connectivity for Longitudinal Data Analysis AR Model Within Subjects for Effective Connectivity Study An Example from Longitudinal AD Structural MRI Advantage and Disadvantages of This Study Other Types of smri Data Analysis AD Classification Structural Covariance Summary of (Longitudinal) VBM Analysis Methods References Appendices A. Maximum Likelihood Estimation B. NR Method for Second-Level Analysis C. PWI Dataset Collection D. Emotional Face fmri Data (Event-Related (ER) Design) E. Phase-Encoded Design Spatial Frequency Data F. Standard Block Design for Lateral Geniculate Nucleus (LGN) Study G. Phase-Encoded Retinotopic Mapping Dataset H. Resting-State fmri Data I. DTI and MRI Dataset J. Biological Rat Spinal Cord HARDI Data K. QBI Synthetic Dataset (Multi-tensor Model) L. HARDI and Low-Angle QBI Data M. DSI Data Collection N. OASIS Cross-Sectional Data O. OASIS Longitudinal Data Question Answers and Hints References Index