Apparent intravoxel fibre population dispersion (FPD) using spherical harmonics

Area of Science:

• Neuroimaging
• Diffusion MRI
• Computational Neuroscience

Background:

• High Angular Resolution Diffusion Imaging (HARDI) methods typically model neuronal fibre networks by extracting local orientations.
• Existing methods often rely on heuristic approaches for fibre orientation extraction.
• There is a need for methods that characterize the complexity of fibre populations within a single voxel.

Purpose of the Study:

• To introduce and validate a novel method for computing apparent intravoxel Fibre Population Dispersion (FPD).
• To statistically analyze fibre population partitioning within voxels without prior assumptions on the number or size of fibre populations.
• To develop and apply quaternion-based metrics for extracting FPD features.

Main Methods:

• Developed an analytical formulation of the diffusion signal autocorrelation function in the spherical harmonics basis.
• Computed apparent intravoxel Fibre Population Dispersion (FPD).
• Extracted FPD features using quaternion-based metrics on rotation groups.

Main Results:

• Demonstrated the effectiveness of FPD in analyzing the partitioning of distinct fibre populations within voxels.
• Showcased FPD's ability to identify regions with crossing tracts in simulated data and physical phantoms.
• Highlighted FPD's advantage over standard anisotropy measures in revealing complex fibre architectures.

Conclusions:

• Fibre Population Dispersion (FPD) offers a robust statistical analysis of intravoxel fibre organization.
• The proposed method effectively characterizes fibre partitioning, particularly in regions with crossing tracts.
• FPD provides a valuable new metric for HARDI analysis, complementing existing anisotropy measures.