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Diffusion Analysis for Layered Brain Structures

Thursday, April 19, 2012
3:30PM – 5PM
POB 6.304

Karel Segeth

In the talk, we start with the biological motivation for modeling the diffusion in 2D and 3D brain structures. From physical principles, we derive the diffusion equation with the proper diffusion coefficient for several types of environment and formulate the corresponding initial and boundary conditions.

We approximate the complex inhomogeneous environment by a layered environment and add interface conditions to the problem. We assume that the problem is axially symmetric, and show and discuss numerical methods applicable to solving this problem.

In conclusion, we mention the problem of obtaining the physical coefficients in the diffusion equation (i.e. solving the inverse problem) and present some numerical results.

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