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Abstract #0662

Microscopic Interpretation and Generalization of the Bloch-Torrey Equations for Diffusion MR

Inbar Seroussi1, Ofer Pasternak1,2, and Nir Sochen 1

1Tel-Aviv university, Tel Aviv, Israel, 2Psychiatry and Radiology, Harvard Medical School, Boston, MA, United States

How to bridge microscopic molecular motion with macroscopic diffusion MR signal? We suggest a simple stochastic microscopic model for molecular motion within a magnetic field. We derive the Fokker-Planck equation of this model, which is an analytic expression of the probability density function describing the magnetic diffusion propagator. This propagator is a crucial quantity and provides the link between the microscopic equations and the measured MR signal. Using the propagator we derive a generalized version for the macroscopic Bloch-Torrey equation. The advantage of this derivation is that it does not require assumptions such as constant diffusion coefficient, or ad-hoc selection of a propagator. In fact, we show that the generalized Bloch-Torrey equations have an additional term that was previously neglected and accounts for spatial varying diffusion coefficient. Including this term better predicts MR signal in complex microstructures, such as those expected in most biological experiments.

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