Beyond Directions: Symmetry-Aware Rotation Sets for Triaxial Diffusion Encoding by Geometric Filter Optimization

Area of Science:

• Diffusion Magnetic Resonance Imaging (dMRI)
• Signal Processing
• Computational Physics

Background:

• Accurate diffusion-weighted signals are crucial for understanding tissue microstructure in dMRI.
• Current methods for powder averaging of diffusion signals with arbitrary b-tensors face limitations in precision and accuracy.
• Understanding the inherent symmetries of diffusion signals is key to optimizing data acquisition.

Purpose of the Study:

• To enhance the accuracy of diffusion-weighted powder average signals for diffusion encoding with arbitrary b-tensors.
• To develop a method for generating optimal rotation sets for diffusion encoding gradient waveforms.

Main Methods:

• Identified an intrinsic dihedral (D2) symmetry of diffusion signals, defining their natural signal space.
• Developed Geometric Filter Optimization (GFO), a method to design sampling filters for maximal accuracy in powder averaging.
• Benchmarked GFO against spherical and electrostatic repulsion designs for accuracy and precision of powder averages and rotational invariants.

Main Results:

• GFO demonstrated significant improvements in precision and accuracy for powder averaging across various b-tensor configurations (axisymmetric, triaxial).
• Performance for higher-order rotational invariants showed nuanced trade-offs in bias and precision among GFO, electrostatic repulsion, and spherical designs.
• The method is computationally efficient and does not require enhanced gradient system performance.

Conclusions:

• The fundamental D2-symmetry of tensor-valued diffusion encoding constrains its rotational structure, guiding the design of optimal rotation sets.
• GFO provides an efficient strategy for optimizing orientations in powder averaging for axisymmetric and triaxial diffusion encoding.
• GFO can potentially shorten scan times in dMRI without compromising accuracy or requiring hardware upgrades.