Summary

Water diffusion magnetic resonance imaging (DMRI) is a method which uses a combination of applied magnetic fields to measure, statistically, the diffusion of water molecules due to Brownian motion. Its spatial resolution is on the order of millimeters. An apparent diffusion coefficient (ADC) or diffusion tensor (DT) is computed for each voxel based on a model relating these quantities to signal attenuation. In the past three decades, DMRI has been successfully used to track brain white matter fibers and to detect acute brain ischemia. Diffusion functional MRI has also begun to gain momentum as an active area of research. The goal of this project is to go beyond the ADC or the DT to get more detailed information on tissue properties from the DMRI signal.

The cellular structure inside the human brain varies on the scale of micrometers, which is much smaller than the size of a voxel. There may be thousands of irregularly-shaped cells within a voxel, and they all contribute to the environment seen by water molecules whose displacement is measured by the MRI scanner. In the typical DMRI experiment, the time interval over which water diffusion is measured is in the range of 50-100 microseconds. Using the diffusion coefficient of 'free' water at 37 degrees Celsius, D = 3e-9 m2/s, we get an estimated diffusion distance of 15-25 micrometers. Clearly, in a DMRI experiment, water molecules encounter numerous times inhomogeneities in the cellular environment, such as cell membranes, fibers, and macromolecules.

We simulate the DMRI signal at the scale of a single voxel, while taking into account realistic cellular structure and the true shape and duration of the diffusion gradients. The accurate geometrical structure will be obtained by the automatic segmentation of electron micrograph images. The finite duration and ramp time of the gradient coils will be accurately reflected in the simulation. The numerical simulation will approached in two directions. One is based on the numerical solution of the Bloch-Torrey partial differential equation using Green's functions. The other is Monte Carlo simulation. The end result is a hybrid method incorporating both: the Green's function method will be used to speed up the Monte Carlo simulation in regimes where the results of the simulation satisfies the Bloch-Torrey equation and where the geometry can be modelled by simple objects such as smooth surfaces. The two approaches will be coupled in a unified numerical code where the coupling will occur across spatial regions and also in time.

The end goal of this project is the simulation of DMRI signal taking into account realistic 3D cellular structure, gradient sequence, while producing results which are reliably accurate, scalable, all in reasonable simulation time. This simulation tool will be valuable in understanding the tissue microstructure that gives rise to the DMRI signals and also aid in the design of new diffusion imaging protocols.