%0 Journal Article
%J J Magn Reson
%D 2017
%T Microscopic Interpretation and Generalization of the Bloch-Torrey Equation for Diffusion Magnetic Resonance
%A Seroussi, Inbar
%A Grebenkov, Denis S
%A Pasternak, Ofer
%A Sochen, Nir
%X 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.
%B J Magn Reson
%V 277
%P 95-103
%8 2017 Apr
%G eng
%1 http://www.ncbi.nlm.nih.gov/pubmed/28242566?dopt=Abstract
%R 10.1016/j.jmr.2017.01.018