1st Edition

Statistical and Computational Methods in Brain Image Analysis

By Moo K. Chung Copyright 2014
    432 Pages 167 B/W Illustrations
    by CRC Press

    The massive amount of nonstandard high-dimensional brain imaging data being generated is often difficult to analyze using current techniques. This challenge in brain image analysis requires new computational approaches and solutions. But none of the research papers or books in the field describe the quantitative techniques with detailed illustrations of actual imaging data and computer codes. Using MATLAB® and case study data sets, Statistical and Computational Methods in Brain Image Analysis is the first book to explicitly explain how to perform statistical analysis on brain imaging data.

    The book focuses on methodological issues in analyzing structural brain imaging modalities such as MRI and DTI. Real imaging applications and examples elucidate the concepts and methods. In addition, most of the brain imaging data sets and MATLAB codes are available on the author’s website.

    By supplying the data and codes, this book enables researchers to start their statistical analyses immediately. Also suitable for graduate students, it provides an understanding of the various statistical and computational methodologies used in the field as well as important and technically challenging topics.

    Introduction to Brain and Medical Images
    Image Volume Data
    Surface Mesh Data
    Landmark Data
    Vector Data
    Tensor and Curve Data
    Brain Image Analysis Tools

    Bernoulli Models for Binary Images
    Sum of Bernoulli Distributions
    Inference on Proportion of Activation
    MATLAB Implementation

    General Linear Models
    General Linear Models
    Voxel-Based Morphometry
    Case Study: VBM in Corpus Callosum
    Testing Interactions

    Gaussian Kernel Smoothing
    Kernel Smoothing
    Gaussian Kernel Smoothing
    Numerical Implementation
    Case Study: Smoothing of DWI Stroke Lesions
    Effective FWHM
    Checking Gaussianness
    Effect of Gaussianness on Kernel Smoothing

    Random Fields Theory
    Random Fields
    Simulating Gaussian Fields
    Statistical Inference on Fields
    Expected Euler Characteristics

    Anisotropic Kernel Smoothing
    Anisotropic Gaussian Kernel Smoothing
    Probabilistic Connectivity in DTI
    Riemannian Metric Tensors
    Chapman-Kolmogorov Equation
    Cholesky Factorization of DTI
    Experimental Results
    Discussion

    Multivariate General Linear Models
    Multivariate Normal Distributions
    Deformation-Based Morphometry (DBM)
    Hotelling’s T2 Statistic
    Multivariate General Linear Models
    Case Study: Surface Deformation Analysis

    Cortical Surface Analysis
    Introduction
    Modeling Surface Deformation
    Surface Parameterization
    Surface-Based Morphological Measures
    Surface-Based Diffusion Smoothing
    Statistical Inference on the Cortical Surface
    Results
    Discussion

    Heat Kernel Smoothing on Surfaces
    Introduction
    Heat Kernel Smoothing
    Numerical Implementation
    Random Field Theory on Cortical Manifold
    Case Study: Cortical Thickness Analysis
    Discussion

    Cosine Series Representation of 3D Curves
    Introduction
    Parameterization of 3D Curves
    Numerical Implementation
    Modeling a Family of Curves
    Case Study: White Matter Fiber Tracts
    Discussion

    Weighted Spherical Harmonic Representation
    Introduction
    Spherical Coordinates
    Spherical Harmonics
    Weighted-SPHARM Package
    Surface Registration
    Encoding Surface Asymmetry
    Case Study: Cortical Asymmetry Analysis
    Discussion

    Multivariate Surface Shape Analysis
    Introduction
    Surface Parameterization
    Weighted Spherical Harmonic Representation
    Gibbs Phenomenon in SPHARM 
    Surface Normalization
    Image and Data Acquisition
    Results
    Discussion
    Numerical Implementation

    Laplace-Beltrami Eigenfunctions for Surface Data
    Introduction
    Heat Kernel Smoothing
    Generalized Eigenvalue Problem
    Numerical Implementation
    Experimental Results
    Case Study: Mandible Growth Modeling
    Conclusion

    Persistent Homology
    Introduction
    Rips Filtration
    Heat Kernel Smoothing of Functional Signal
    Min-max Diagram
    Case Study: Cortical Thickness Analysis
    Discussion

    Sparse Networks
    Introduction
    Massive Univariate Methods
    Why Are Sparse Models Needed?
    Persistent Structures for Sparse Correlations
    Persistent Structures for Sparse Likelihood
    Case Study: Application to Persistent Homology
    Sparse Partial Correlations
    Summary

    Sparse Shape Models
    Introduction
    Amygdala and Hippocampus Shape Models
    Data Set
    Sparse Shape Representation
    Case Study: Subcortical Structure Modeling
    Statistical Power
    Power under Multiple Comparisons
    Conclusion

    Modeling Structural Brain Networks
    Introduction
    DTI Acquisition and Preprocessing
    ε-Neighbor Construction
    Node Degrees
    Connected Components
    ε-Filtration
    Numerical Implementation
    Discussion

    Mixed Effects Models
    Introduction
    Mixed Effects Models

    Bibliography

    Index

    Biography

    Moo K. Chung, Ph.D. is an associate professor in the Department of Biostatistics and Medical Informatics at the University of Wisconsin-Madison. He is also affiliated with the Waisman Laboratory for Brain Imaging and Behavior. He has won the Vilas Associate Award for his applied topological research (persistent homology) to medical imaging and the Editor’s Award for best paper published in Journal of Speech, Language, and Hearing Research. Dr. Chung received a Ph.D. in statistics from McGill University. His main research area is computational neuroanatomy, concentrating on the methodological development required for quantifying and contrasting anatomical shape variations in both normal and clinical populations at the macroscopic level using various mathematical, statistical, and computational techniques.

    "The writing style is pleasing and the book has the important virtue of using a consistent mathematical notation and terminology throughout the book, unlike collections of chapters from various authors that are usually published on this kind of topic. One important and interesting aspect of this book is the use of MATLAB code to illustrate the theory that the author is developing. In addition, the data mentioned in the text are provided so that the reader can experiment and learn using the same examples as the ones described in the book. This provides an excellent supplement and will appeal to students starting in the field as well as researchers wanting to refresh their knowledge or learn more about some aspects of brain analysis. … a very good book to have in a lab, and it is a pleasure to recommend it."
    Australian & New Zealand Journal of Statistics, 56(4), 2014

    "… a great new reference text to the field of structural brain imaging. The presence of MATLAB code will make it easy for people to play around with the various data formats and more easily get involved in this exciting field. As a researcher already involved in neuroimaging data analysis, I have a feeling that this is a book I will return to often as a reference source, and I am happy to have it as part of my library."
    —Martin A. Lindquist, Journal of the American Statistical Association, September 2014, Vol. 109