Orientationally-averaged diffusion-attenuated magnetic resonance signal for locally-anisotropic diffusion

Area of Science:

• Magnetic Resonance Imaging (MRI)
• Diffusion Tensor Imaging (DTI)
• Solid-State Nuclear Magnetic Resonance (NMR) Spectroscopy

Background:

• Diffusion MRI signal analysis in heterogeneous media often relies on approximations of anisotropic Gaussian sub-domains.
• Macroscopic anisotropy effects can obscure underlying microstructural information.
• Existing models often simplify diffusion tensor characteristics or measurement configurations.

Purpose of the Study:

• To derive exact expressions for orientationally-averaged diffusion MRI signals in heterogeneous media.
• To account for general diffusion tensors with potentially three distinct eigenvalues.
• To extend applicability beyond axisymmetric diffusion and simplified measurement tensors.

Main Methods:

• Mathematical derivation of orientationally-averaged signals.
• Utilizing general gradient waveforms in the signal acquisition model.
• Averaging signal values from differently oriented experimental schemes to remove macroscopic anisotropy.

Main Results:

• Exact mathematical expressions for orientationally-averaged diffusion MRI signals are provided.
• The derived expressions accommodate general diffusion tensors, including those with three distinct eigenvalues.
• The results are shown to be equivalent to analyzing isotropically distributed micro-domains (powdered specimens).

Conclusions:

• The developed framework offers a more accurate representation of diffusion MRI signals in complex heterogeneous materials.
• This work extends previous findings by incorporating more general diffusion tensor properties.
• The findings are anticipated to benefit multidimensional diffusion MRI and solid-state NMR spectroscopy due to shared mathematical principles.