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



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.



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.



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.
Department of Psychiatry, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, USA.
Lipeng
L
Ning
Athinoula A Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Harvard Medical School, Boston, Massachusetts, USA.
Kawin
K
Setsompop
Department of Radiology, Brigham and Women's Hospital, Harvard Medical School, Boston, Massachusetts, USA.
Carl-Fredrik
CF
Westin
Department of Psychiatry, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, USA.
Yogesh
Y
Rathi
D001921:Brain / Q000000981:diagnostic imaging; D003198:Computer Simulation; D038524:Diffusion Magnetic Resonance Imaging / Q000379:methods*; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D015233:Models, Statistical
autocorrelation function; diffusion MRI; mean-squared displacement; oscillating gradient spin-echo; single-diffusion encoding; time-varying diffusivity