Statistical and Computational Methods in Brain Image Analysis

 Content: 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  epsilon-Neighbor Construction  Node Degrees  Connected Components  epsilon-Filtration  Numerical Implementation Discussion  Mixed Effects Models  Introduction  Mixed Effects Models  Bibliography Index
 Abstract:             "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."