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