PI:    Professor L.G. de Pillis, Mathematics, HMC
Title: Analyzing Immunotherapy and Chemotherapy of Tumors through Mathematical Modeling
Date:  Summer 2003

Abstract:
We develop and analyze three distinct mathematical models of
tumor-immune system interactions that
describe how certain types of cancer treatment affect
both tumor and immune cell populations in the human body.  The first 
of these models is a population based model that is time-dependent,
and is represented by a system of ordinary differential equations.  
This ODE model allows us to observe creation and destruction 
trends in overall cell populations.
The second model includes both a spatial component and a probabilistic
component.  With this second model we simulate nutrient diffusion and the
effect of nutrient distribution on cell growth.  From this model,
a range of possible tumor structures can arise.
The third model incoprorates geometries that allow us to
investigate the macroscopic stages of tumor evolution.  We deal with
all models on a cellular level as well as on a macroscopic level in order
to encompass various degrees of interaction and form a broader
perspective.  The models are validated using experimental
data from published literature.  Simulations that include experimental
combination chemoimmunotherapies are run and analyzed.  Mathematical
analysis of the models is carried out.

This work was done in collaboration with

Professor W. Gu, Mathematics, HMC
William Chang, HMC 2004
Lindsay Crowl, HMC 2004
Eric Malm, HMC 2005
Lorraine Thomas, HMC 2005
Katherine Todd-Brown, HMC 2004
Michael Vrable, HMC 2004