Measuring the velocity autocorrelation function using diffusion NMR

Molecular self-diffusion in the presence of barriers results in time-dependent displacements that are controlled by barrier characteristics, such as thickness, arrangement, and permeability, which manifests itself in the form of the ensemble-average velocity autocorrelation function (VAF). We describe a direct method to measure the VAF based on a combination of diffusion-weighted nuclear magnetic resonance (NMR) measurements in which two time-shifted diffusion encodings are separated by a longitudinal storage period. The VAF estimated from simulated data is shown to agree with the known expression for impermeable parallel planes. Simulations of diffusion in periodically spaced, permeable planes and connected, box-shaped pores are also presented. We find that scaling of the VAF faster than t-1/2 is indicative of barrier permeation or exchange between domains and that this can be captured by the proposed method. As an experimental proof-of-concept, we present data from an ex vivo neonatal mouse spinal cord studied using a permanent magnet NMR MOUSE system. We report a transition from t-1/2 to t-3/2 scaling at t ≈ 10 ms, consistent perhaps with transmembrane water exchange. Compared to other NMR-based approaches, this method can potentially access several orders of magnitude in time (ms - s), revealing a wealth of VAF behaviors with one experimental paradigm.