Effect of impermeable boundaries on diffusion-attenuated MR signal

Area of Science:

• Biophysics
• Medical Imaging
• Diffusion MRI

Background:

• Nonlinear signal dependence on b-value in diffusion-weighted imaging (DWI) is often modeled as biexponential, implying distinct compartments.
• Biexponential models frequently yield unrealistic compartment sizes, limiting DWI's utility for cellular-level structural inference.
• Restricted diffusion due to confining boundaries is a hypothesized cause for observed nonlinear signal behavior.

Purpose of the Study:

• To analyze diffusion in confined spaces using a cumulant expansion of the diffusion-weighted signal.
• To evaluate the accuracy and stability of a Taylor expansion of the logarithm of the signal (lnS) in powers of the b-value (b).
• To compare the proposed model with the traditional biexponential model for inferring diffusion characteristics.

Main Methods:

• Analysis of diffusion in the presence of impermeable interfaces for short diffusion times.
• Application of the cumulant expansion to derive a Taylor series for lnS as a function of b.
• Investigation of the convergence properties of the cumulant expansion series.

Main Results:

• The cumulant expansion, truncated to a polynomial, accurately describes the signal for low b-values (error < 1%).
• The signal can be represented as lnS ≈ -A·bD + B·(bD)² for a significant range of b-values.
• Fitting parameters A and B, derived from molecular velocity correlations, is more stable than biexponential fitting.
• The cumulant expansion diverges for large b-values, where signal decay follows power laws (1/b, 1/b³/², 1/b²) in 1D, 2D, and 3D systems, respectively.

Conclusions:

• Restricted diffusion, modeled by cumulant expansion, provides a more robust explanation for nonlinear DWI signals than the biexponential model.
• The proposed model offers a stable method for extracting diffusion parameters at lower b-values, potentially improving cellular structure inference.
• Understanding signal behavior across different b-value regimes is crucial for accurate interpretation of diffusion MRI data.