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Updated: Jun 4, 2026

Co-analysis of Brain Structure and Function using fMRI and Diffusion-weighted Imaging

Co-analysis of Brain Structure and Function using fMRI and Diffusion-weighted Imaging

Published on: November 8, 2012

A nonparametric Riemannian framework for processing high angular resolution diffusion images and its applications to

Alvina Goh¹, Christophe Lenglet, Paul M Thompson

¹Department of Mathematics, National University of Singapore, Singapore. agoh@nus.edu.sg

|February 5, 2011

Summary

This summary is machine-generated.

High angular resolution diffusion imaging (HARDI) enables detailed brain structure analysis. This study introduces a novel Riemannian framework for processing orientation probability density functions (PDFs) nonparametrically, improving HARDI data analysis.

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Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases

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Published on: July 28, 2013

Area of Science:

Neuroimaging
Diffusion MRI
Computational Anatomy

Background:

High angular resolution diffusion imaging (HARDI) is crucial for mapping complex tissue structures.
Existing methods for processing orientation probability density functions (PDFs) in HARDI are limited.
There is a need for advanced techniques for filtering, interpolation, and analysis of orientation PDF fields.

Purpose of the Study:

To present a novel Riemannian framework for processing orientation probability density functions (PDFs) in HARDI.
To enable nonparametric analysis of orientation PDFs without fixed parameterization.
To apply these methods to analyze brain asymmetries.

Main Methods:

Developed a Riemannian framework utilizing a nonparametric representation of orientation PDFs.
Leveraged the square-root re-parameterization to define orientation PDFs on a Riemannian manifold (Hilbert sphere).
Applied Riemannian gradient descent to solve optimization problems for PDF processing operations.

Main Results:

Demonstrated the framework's ability to perform filtering, interpolation, averaging, and principal geodesic analysis on orientation PDFs.
Validated the approach using synthetic, phantom, and real HARDI datasets.
Showcased the application in studying left/right brain asymmetries.

Conclusions:

The proposed Riemannian framework offers a robust and flexible approach for advanced HARDI data analysis.
Nonparametric processing on the Hilbert sphere provides a powerful tool for understanding complex tissue orientations.
This method enhances the study of neuroanatomical variations, such as brain asymmetries.