Concise derivation of oscillating-gradient-derived ADC.

Area of Science:

• Magnetic Resonance Imaging (MRI)
• Diffusion MRI
• Biophysical Measurements

Background:

• Apparent diffusion coefficient (ADC) analysis is crucial for understanding microstructural properties.
• Oscillating diffusion-sensitizing gradients offer advanced capabilities in diffusion MRI.
• Determining the surface-to-volume ratio (S/V) is a key goal in microstructural characterization.

Purpose of the Study:

• To derive an analytical expression for ADC with oscillating gradients.
• To investigate the feasibility of S/V determination using different gradient types and phases.
• To establish conditions under which S/V can be accurately measured.

Main Methods:

• Analysis of apparent diffusion coefficient (ADC) in the high-frequency regime.
• Derivation of analytical ADC expressions for arbitrary gradient oscillations (N) and initial phase (φ).
• Evaluation of S/V determination accuracy with cosine (φ=0) and sine (φ≠0) gradients.

Main Results:

• An analytical ADC expression is derived for N oscillations and initial phase φ.
• S/V can be determined using cosine gradients (φ=0) for any N.
• S/V determination with sine gradients (φ≠0) requires knowledge of the time-dependent diffusion coefficient D(t).

Conclusions:

• Cosine-type oscillating gradients enable robust S/V determination in diffusion MRI.
• Sine-type gradients necessitate estimating D(t), feasible in short-time or restricted diffusion regimes.
• This work provides a framework for advanced microstructural analysis using tailored diffusion gradients.