A general analytic derivation of the diffusion MR signal from a stochastic microscopic model
-
1
Weizmann Institute of Science, Department of Condensed Matter Physics, Israel
-
2
Harvard Medical School, Brigham and Women’s Hospital, United States
-
3
University of Tel Aviv, Department of Applied Mathematics, Israel
As new diffusion encoding schemes are emerging, it is important to provide general mathematical frameworks that predict the MR signal for any given encoding. The Bloch-Torrey equations are a common way to predict the signal. However these equations are based on certain homogeneity assumptions, which may not hold in cases of complex microstructure. Alternative approaches such as the random phase approach require ad-hoc diffusion propagators to predict the signal. A fundamental question important for any diffusion encoding scheme is 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 for any diffusion encoding. For example we can approximate the propagator in the short time limit and evaluate for which cases the often-used Gaussian propagator is valid. Using the expression for the propagator we can also derive the macroscopic MR signal through either the random phase approach or through a generalized version for the Bloch-Torrey equations. The advantage of deriving the MR signal from our microscopic model 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 spatially varying diffusion coefficient. Including this term may predicts better the MR signal in complex microstructures, such as those expected in most biological experiments.
Keywords:
Diffusion,
MRI,
dMRI,
multidimensional,
diffusion encoding
Conference:
New dimensions in diffusion encoding, Fjälkinge, Sweden, 11 Jan - 14 Jan, 2016.
Presentation Type:
Oral presentation
Topic:
New Dimensions in Diffusion Encoding
Citation:
Seroussi
I,
Pasternak
O and
Sochen
N
(2016). A general analytic derivation of the diffusion MR signal from a stochastic microscopic model.
Front. Phys.
Conference Abstract:
New dimensions in diffusion encoding.
doi: 10.3389/conf.FPHY.2016.01.00020
Copyright:
The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers.
They are made available through the Frontiers publishing platform as a service to conference organizers and presenters.
The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated.
Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed.
For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions.
Received:
07 Jul 2016;
Published Online:
07 Jul 2016.
*
Correspondence:
Prof. Nir Sochen, University of Tel Aviv, Department of Applied Mathematics, Tel Aviv, 6997801, Israel, sochen@post.tau.ac.il