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Statistical and Computational Methods in Brain Image Analysis

By Moo K. Chung

CRC Press – 2013 – 400 pages

Series: Chapman & Hall/CRC Mathematical and Computational Imaging Sciences Series

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    978-1-43-983635-4
    July 23rd 2013

Description

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.

Contents

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

Author Bio

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.

Name: Statistical and Computational Methods in Brain Image Analysis (Hardback)CRC Press 
Description: By Moo K. Chung. 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...
Categories: Neuroscience, Biomedical Engineering, Statistics for the Biological Sciences