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.
