White matter structure assessment from reduced HARDI data using low-rank polynomial approximations

Area of Science:

• Neuroimaging
• Diffusion MRI
• Computational Neuroscience

Background:

• Single-shell High Angular Resolution Diffusion Imaging (HARDI) offers advantages for assessing white matter fiber orientations.
• Direct fitting methods for HARDI can be unstable and initialization-dependent, especially with limited diffusion-weighted imaging (DWI) samples.
• Existing techniques often require more parameters and DW samples for accurate fiber orientation reconstruction.

Purpose of the Study:

• To present a novel, stable, and accurate direct fitting technique for single-shell HARDI.
• To enable reliable white matter fiber orientation assessment with a reduced number of gradient directions.
• To overcome the initialization-dependent instability of traditional direct fitting methods.

Main Methods:

• A novel direct fitting technique based on spherical deconvolution and symmetric tensor decomposition.
• Approximation of the fiber orientation distribution (fODF) using a sum of even-order linear forms related to rank-1 tensors.
• Optimization against DWI measurements using a robust iterative alternating numerical scheme based on the Levenberg-Marquardt technique.

Main Results:

• The proposed algorithm demonstrates stability and accuracy in assessing fiber orientations and volume fractions.
• Successful modeling of complex fiber structures was achieved using as few as 12 gradient directions.
• Validation was performed using both simulated and in vivo human brain diffusion-weighted imaging data.

Conclusions:

• The developed technique provides a stable and accurate direct fitting approach for single-shell HARDI.
• This method effectively models complex white matter architecture with a reduced number of diffusion-weighted imaging samples.
• The algorithm shows promise for efficient and reliable neuroimaging analysis, even in challenging low-angular-resolution scenarios.