A new approach to time-dependent diffusion: Direct, time-domain measurement of the velocity autocorrelation function

Motivation: Time-dependent diffusion can reveal fine microstructural details, but its quantitative measurement is difficult. Oscillating gradient methods probe a limited range of frequencies, and the recovered spectrum is not straightforward to interpret. Goal(s): To measure time-dependent diffusion directly via the velocity autocorrelation function (VAF), i.e., half the second derivative of the mean-squared displacement (MSD). Approach: A double diffusion encoding method and analysis framework provides a semi-quantitative measurement of the VAF. The method is validated using simulations. Proof-of-concept data in ex vivo tissue are also presented. Results: The estimated VAF agrees with analytical and numerical ground truth. The VAF scaling in tissue indicates barrier-limited exchange. Impact: Time-dependent diffusion encapsulates diffusion microstructural MRI. The conventional oscillating gradient approach, however, is limited by slew rates and relaxation. We propose a new approach that is semi-quantitative and can access a wide range of times using a longitudinal storage period.