Restricted diffusion in susceptibility-induced magnetic fields

by D. S. Grebenkov

Email: denis.grebenkov@polytechnique.edu

In magnetic resonance imaging (MRI), inhomogeneous magnetic fields are
applied to "encode" stochastic trajectories of the nuclei. A linear
magnetic field gradient is the most usual encoding scheme, for
instance, in medical imaging of the lungs. However, the nuclei usually
diffuse in a bounded medium (e.g., cells or organs in biology, solid
matrices in material sciences). The difference in magnetic
susceptibility between the diffusing gas or liquid and its "container"
induces local magnetic fields that are superimposed with externally
applied linear gradients and may considerably bias the results of
measurement. On the other hand, the local fields can potentially be
used to enhance the image contrast. It is therefore important to
understand the influence of the susceptibility-induced magnetic fields
onto MRI measurements.

In this project, we consider model three-dimensional labyrinths
representing the lung structure. First, the spatial distribution of
the susceptibility-induced magnetic field will be calculated
numerically inside a given labyrinth. Second, restricted diffusion of
the nuclei in this field will be simulated by a Monte Carlo
technique. The numerical results can then be validated by a direct
comparison with experiments.