__Claremont Graduate University__ | __Claremont McKenna__ | __Harvey Mudd__ | __Pitzer__ | __Pomona__ | __Scripps__

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When

Start: 02/23/2011 - 4:15pm

End : 02/23/2011 - 5:00pm

End : 02/23/2011 - 5:00pm

Category

Colloquium

Speaker

Timothy Lucas (Pepperdine University)

Abstract

When immune cells detect foreign molecules, they secrete soluble factors that attract

other immune cells to the site of the infection. I will present a model by Kepler that focuses

on the motion of individual cells which is stochastic, but biased toward the gradient of the

soluble factors. The soluble factors are modeled by a system of reaction-diffusion equations

with sources that are centered on the cells. We can solve this system numerically using a

first order splitting for the reaction- diffusion-stochastic system. This allows us to make

use of known first order schemes for solving the diffusion, the reaction and the stochastic

differential equations separately. In this case, the three-dimensional domain is discretized

using finite elements and the diffusion is solved using a backward Euler scheme combined

with multigrid. The reaction is solved using a simple semi-implicit first order scheme. The

Langevin process for the immune cells can be simulated exactly. This work is part of a

larger project funded by the National Institute for Health to create simulation software

that will aid immunologists in the study of adjuvants for vaccines.

Where

Roberts North 15, Claremont McKenna College