@article {1118851,
title = {Microscopic Interpretation and Generalization of the Bloch-Torrey Equation for Diffusion Magnetic Resonance},
journal = {J Magn Reson},
volume = {277},
year = {2017},
month = {2017 Apr},
pages = {95-103},
abstract = {In order to bridge microscopic molecular motion with macroscopic diffusion MR signal in complex structures, we propose a general stochastic model for molecular motion in a magnetic field. The Fokker-Planck equation of this model governs the probability density function describing the diffusion-magnetization propagator. From the propagator we derive a generalized version of the Bloch-Torrey equation and the relation to the random phase approach. This derivation does not require assumptions such as a spatially constant diffusion coefficient, or ad hoc selection of a propagator. In particular, the boundary conditions that implicitly incorporate the microstructure into the diffusion MR signal can now be included explicitly through a spatially varying diffusion coefficient. While our generalization is reduced to the conventional Bloch-Torrey equation for piecewise constant diffusion coefficients, it also predicts scenarios in which an additional term to the equation is required to fully describe the MR signal.},
issn = {1096-0856},
doi = {10.1016/j.jmr.2017.01.018},
author = {Seroussi, Inbar and Grebenkov, Denis S and Pasternak, Ofer and Sochen, Nir}
}