Effective medium theory of a diffusion-weighted signal

Area of Science:

• Biophysics
• Medical Imaging
• Materials Science

Background:

• Living tissues and heterogeneous media possess microstructural units (e.g., cells) with varying diffusion coefficients and NMR properties.
• These microstructural units are often smaller than imaging resolution limits (voxels) and comparable to diffusion lengths.
• Quantifying heterogeneity at scales finer than imaging resolution is crucial for understanding diffusion processes.

Purpose of the Study:

• To develop a general statistical approach for quantifying medium heterogeneity at scales finer than imaging resolution.
• To derive the diffusion-weighted signal based on spatial variations in local diffusivity.
• To investigate the contributions of correlation length and diffusivity variance to diffusion dynamics.

Main Methods:

• Statistical treatment of heterogeneous media using correlation functions of local parameters.
• Derivation of the diffusion-weighted signal in the lowest order of diffusivity variance.
• Monte Carlo simulations of diffusion in a 2D heterogeneous medium for validation.

Main Results:

• A general method to quantify sub-voxel heterogeneity in diffusion MRI.
• Explicit formulation of the diffusion-weighted signal considering spatial diffusivity variations.
• Demonstration of how correlation length and diffusivity variance influence time-dependent diffusion coefficient and kurtosis.

Conclusions:

• The developed statistical approach effectively quantifies sub-voxel heterogeneity in diffusion processes.
• Microstructural properties like correlation length and diffusivity variance significantly impact macroscopic diffusion measurements.
• This method provides a powerful tool for analyzing complex biological tissues and materials using diffusion imaging.