TY - JOUR

T1 - Microscopic interpretation and generalization of the Bloch-Torrey equation for diffusion magnetic resonance

AU - Seroussi, Inbar

AU - Grebenkov, Denis S.

AU - Pasternak, Ofer

AU - Sochen, Nir

N1 - Publisher Copyright:
© 2017 Elsevier Inc.

PY - 2017/4/1

Y1 - 2017/4/1

N2 - 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.

AB - 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.

KW - Bloch-Torrey equation

KW - Diffusion MR

KW - Inhomogeneous diffusion

KW - Random phase approach

KW - Stochastic model

UR - http://www.scopus.com/inward/record.url?scp=85013784600&partnerID=8YFLogxK

U2 - 10.1016/j.jmr.2017.01.018

DO - 10.1016/j.jmr.2017.01.018

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85013784600

SN - 1090-7807

VL - 277

SP - 95

EP - 103

JO - Journal of Magnetic Resonance

JF - Journal of Magnetic Resonance

ER -