New insights about time‐varying diffusivity and its estimation from diffusion MRI

Purpose Characterizing the relation between the applied gradient sequences and the measured diffusion MRI signal is important for estimating the time‐dependent diffusivity, which provides important information about the microscopic tissue structure. Theory and Methods In this article, we extend the classical theory of Stepišnik for measuring time‐dependent diffusivity under the Gaussian phase approximation. In particular, we derive three novel expressions which represent the diffusion MRI signal in terms of the mean‐squared displacement, the instantaneous diffusivity, and the velocity autocorrelation function. We present the explicit signal expressions for the case of single diffusion encoding and oscillating gradient spin‐echo sequences. Additionally, we also propose three different models to represent time‐varying diffusivity and test them using Monte‐Carlo simulations and in vivo human brain data. Results The time‐varying diffusivities are able to distinguish the synthetic structures in the Monte‐Carlo simulations. There is also strong statistical evidence about time‐varying diffusivity from the in vivo human data set. Conclusion The proposed theory provides new insights into our understanding of the time‐varying diffusivity using different gradient sequences. The proposed models for representing time‐varying diffusivity can be utilized to study time‐varying diffusivity using in vivo human brain diffusion MRI data. Magn Reson Med 78:763–774, 2017. © 2016 International Society for Magnetic Resonance in Medicine