Hyperspherical von Mises Fisher Mixture HvMF Modelling of High Angular Resolution Diffusion MRI 1st Edition by Abhir Bhalerao, Carl Fredrik Westin ISBN 9783540757573
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Authors:Abhir Bhalerao; Carl-Fredrik Westin , Tags:Medical Image Computing and Computer-Assisted Intervention – MICCAI 2007 , Author sort:Bhalerao, Abhir & Westin, Carl-Fredrik , Languages:Languages:eng , Comments:Comments:Medical Image Computing and Computer-Assisted Intervention – MICCAI 2007
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ISBN 10:
ISBN 13: 9783540757573
Author: Abhir Bhalerao, Carl Fredrik Westin
A mapping of unit vectors onto a 5D hypersphere is used to model and partition ODFs from HARDI data. This mapping has a number of useful and interesting properties and we make a link to interpretation of the second order spherical harmonic decompositions of HARDI data. The paper presents the working theory and experiments of using a von Mises-Fisher mixture model for directional samples. The MLE of the second moment of the HvMF pdf can also be related to fractional anisotropy. We perform error analysis of the estimation scheme in single and multi-fibre regions and then show how a penalised-likelihood model selection method can be employed to differentiate single and multiple fibre regions.
Hyperspherical von Mises Fisher Mixture HvMF Modelling of High Angular Resolution Diffusion MRI 1st Table of contents:
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Introduction
1.1 Motivation and Background
1.2 High Angular Resolution Diffusion Imaging (HARDI): Overview and Applications
1.3 The von Mises Fisher (vMF) Distribution and Its Role in Diffusion MRI
1.4 Hyperspherical von Mises Fisher Mixture (HvMF): Concept and Relevance
1.5 Key Contributions and Objectives of the Paper
1.6 Structure of the Paper -
Preliminaries
2.1 Diffusion Tensor Imaging (DTI) vs. HARDI
2.2 Mathematical Foundation of the von Mises Fisher Distribution
2.3 Hyperspherical Statistics and Its Application in Diffusion MRI
2.4 Overview of Mixture Models and Their Use in HARDI
2.5 Related Work in HARDI Modeling and Mixture Models -
Hyperspherical von Mises Fisher Mixture Model
3.1 Definition and Properties of the HvMF Model
3.2 Derivation of the HvMF Mixture Model for HARDI Data
3.3 Mixture of von Mises Fisher Distributions on the Sphere
3.4 Parameter Estimation for HvMF Mixture Models
3.5 Model Fitting and Optimization Techniques -
Application to High Angular Resolution Diffusion MRI
4.1 HARDI Data Representation and Preprocessing
4.2 Modeling Multiple Fiber Orientations with HvMF
4.3 Comparison with Traditional Diffusion Models (e.g., DTI, Q-ball Imaging)
4.4 Incorporating Multiple Fiber Directions in the Mixture Model
4.5 Impact on Fiber Tracking and White Matter Analysis -
Methodology
5.1 Data Acquisition and HARDI Imaging Protocol
5.2 Implementation of the HvMF Mixture Model in HARDI Analysis
5.3 Evaluation of Model Parameters and Convergence
5.4 Computational Considerations and Algorithms for Mixture Fitting
5.5 Model Validation and Robustness to Noise and Artifacts -
Experimental Results
6.1 Dataset Description and Experimental Setup
6.2 Quantitative Evaluation Metrics for Fiber Tracking and Orientation Estimation
6.3 Comparison of HvMF and Other Diffusion Models (e.g., CSD, NODDI)
6.4 Case Studies in White Matter Integrity and Fiber Bundle Analysis
6.5 Sensitivity Analysis and Robustness to Data Quality -
Applications and Implications
7.1 Clinical Applications of HvMF Modeling in HARDI
7.2 Applications in Neurological Disorders (e.g., Multiple Sclerosis, Alzheimer’s)
7.3 Improving Brain Mapping and White Matter Tractography
7.4 Potential for Longitudinal and Multi-Subject Studies -
Discussion
8.1 Insights from HvMF Mixture Modeling in HARDI
8.2 Limitations and Challenges in the Current Approach
8.3 Future Directions for HvMF Modeling in Diffusion MRI
8.4 Opportunities for Integration with Deep Learning and Advanced Imaging Techniques
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