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

Inbar Seroussi*, Denis S. Grebenkov, Ofer Pasternak, Nir Sochen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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.

Original languageEnglish
Pages (from-to)95-103
Number of pages9
JournalJournal of Magnetic Resonance
StatePublished - 1 Apr 2017


FundersFunder number
National Institutes of HealthR01MH074794, R01MH108574, 2P41EB015902, R01MH102377
National Institute on AgingR01AG042512
Stiftelsen för Strategisk ForskningAM13-0090


    • Bloch-Torrey equation
    • Diffusion MR
    • Inhomogeneous diffusion
    • Random phase approach
    • Stochastic model


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