Numerical Simulations of an Immune Response

Start: 02/23/2011 - 4:15pm
End  : 02/23/2011 - 5:00pm


Timothy Lucas (Pepperdine University)


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.

Roberts North 15, Claremont McKenna College

Claremont Graduate University | Claremont McKenna | Harvey Mudd | Pitzer | Pomona | Scripps
Proudly Serving Math Community at the Claremont Colleges Since 2007
Copyright © 2018 Claremont Center for the Mathematical Sciences