HYDI-DSI revisited: Constrained non-parametric EAP imaging without q-space re-gridding

Area of Science:

• Neuroimaging
• Biophysics
• Medical Physics

Background:

• Hybrid Diffusion Imaging (HYDI) uses multi-shell q-space sampling for diffusion MRI beyond DTI and HARDI.
• Conventional HYDI-DSI involves q-space re-gridding and Discrete Fourier Transform (DFT) for Ensemble Average Propagator (EAP) estimation.
• This process is acquisition-dependent and limits the direct computation of certain diffusion metrics.

Purpose of the Study:

• To reformulate HYDI-DSI using a Fourier Transform encoding matrix to eliminate q-space re-gridding.
• To preserve the non-parametric nature of HYDI-DSI while improving EAP sampling.
• To enable analytical computation of diffusion descriptors and impose positivity constraints.

Main Methods:

• Developed an adaptive Fourier Transform encoding matrix for each voxel, tailored to DTI approximations.
• Estimated the EAP using a regularized Quadratic Programming (QP) problem with positivity constraints.
• Utilized the adaptive matrix for analytical computation of diffusion metrics, avoiding numerical approximations.

Main Results:

• The proposed method analytically computes diffusion descriptors like Return To Origin Probability (RTOP) and Mean Squared Displacement (MSD).
• Introduced and computed Return to Axis/Plane Probabilities (RTAP/RTPP), which are not available with conventional HYDI-DSI.
• Demonstrated improved accuracy, robustness, and computational efficiency, especially with standard q-space samplings.

Conclusions:

• The adaptive encoding matrix approach offers a more accurate and efficient non-parametric estimation of EAP in diffusion MRI.
• This method overcomes limitations of conventional HYDI-DSI by enabling analytical calculations and direct computation of directional diffusion metrics.
• The findings suggest significant benefits for diffusion MRI analysis, particularly when using non-dedicated acquisition protocols.