Diffusion in inhomogenous media
Date
2009-10-30
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Abstract
This project considers the diffusion of water molecules through a cellular medium
in which the cells are modeled by square compartments placed symmetrically in a
square domain. We assume the diffusion process is governed by the 2D diffusion
equations and the solution is provided by implementing the Crank-Nicolson
scheme. These results are verified and illustrated to agree well with the finite
element method using the Comsol Multiphysics package. The model is used to
compute the values of the apparent diffusion coefficient, (ADC) which is a
measure that is derived from diffusion weighted MRI data and can be used to
identify, e.g., regions of ischemia in the brain. With our model, it is possible to
examine how the value of the apparent diffusion coefficient is affected whenever
the extracellular space is varied. We observe that the average distance that the
water molecules travel in a definite time is highly dependent on the geometrical
properties of the cellular media.
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Keywords
Crank-Nicolson scheme, Water molecule diffusion, Comsol Multiphysics, Apparent Diffusion Coefficient (ADC), Ischemia