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Microscopic Interpretation and Generalization of the Bloch-Torrey Equation for Diffusion Magnetic Resonance

1Department of Applied Mathematics, School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel. Electronic address:
2Laboratoire de Physique de la Matière Condensée, CNRS - Ecole Polytechnique, University Paris-Saclay, France.
3Departments of Psychiatry and Radiology, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, USA.
Publication Date:
J Magn Reson
Volume Number:
J Magn Reson. 2017 Apr;277:95-103.
PubMed ID:
Bloch-Torrey equation, Diffusion MR, Inhomogeneous diffusion, Random phase approach, Stochastic model
Appears in Collections:
R01 MH102377/MH/NIMH NIH HHS/United States
R01 MH074794/MH/NIMH NIH HHS/United States
R01 MH108574/MH/NIMH NIH HHS/United States
R01 AG042512/AG/NIA NIH HHS/United States
P41 EB015902/EB/NIBIB NIH HHS/United States
Generated Citation:
Seroussi I., Grebenkov D.S., Pasternak O., Sochen N. Microscopic Interpretation and Generalization of the Bloch-Torrey Equation for Diffusion Magnetic Resonance. J Magn Reson. 2017 Apr;277:95-103. PMID: 28242566. PMCID: PMC5486415.
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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.