Seminar Event Detail

Differential Equations

Date:  Thursday, October 01, 2015
Location:  4088 East Hall (4:00 PM to 5:00 PM)

Title:  Numerical Simulation and Macroscopic Model Formulation for Diffusion Magnetic Resonance Imaging in the Brain

Abstract:   Diffusion Magnetic Resonance Imaging (dMRI) is an imaging modality that gives a measure of water diffusion in biological tissue. As water diffusion is strongly affected by the cellular environment, dMRI has become a widely used research and clinical tool for detecting and quantifying physiological and pathological conditions in-vivo, in particular in the brain.

In-vivo brain dMRI measures water diffusion (Brownian motion) during a diffusion time that is usually limited to between 10-40ms, and the dMRI signal is the average water proton magnetization over a voxel that is on the order of 8mm^3. Inside the voxel, there are many neurons, glial cells, and the extra-cellular space. Neurons have a solid cell body with attached axons and branching dendrites, while the extra-cellular space is very thin and geometrically complex. In addition, the cells are permeable to water, so water can move between the cells and the extra-cellular space. Due to such complex structure, the inverse problem of obtaining geometrical information on the brain tissue from the dMRI signal is a challenging and unsolved problem.

I will discuss two aspects of the modeling and simulation problem for brain dMRI. The first is the direct simulation of the dMRI signal from a prescribed cellular-level geometrical configuration defined in a voxel. The second is the formulation of macroscopic (voxel-level) models of the dMRI signal for the purpose of inverting for model parameters from the experimental signal. I will review the main existing approaches and describe current progress as well as future challenges. In particular, for direct simulation I will cover 1) the random walkers/Monte Carlo approach, and 2) the numerical solution of Bloch-Torrey partial differential equation (PDE). For the macroscopic modeling I will describe 1) the more heuristic approach that models cell components of the brain tissue by cylinders and spheres, and 2) the more mathematical approach that applies homogenization techniques to the Bloch-Torrey PDE.


Speaker:  Jing-Rebecca Li
Institution:  INRIA Saclay/Ecole Polytechnique

Event Organizer:   Robert Krasny   


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