Mathematical Modeling of the Chemotherapy, Immunotherapy and Vaccine Therapy of Cancer

Harvey Mudd College, Claremont CA

Investigators

Abstract

The investigators bring together expertise in the areas of differential equations and numerics, differential geometry, and optimal control with the goal of developing mathematical modeling and analysis tools applied to the creation and testing of new combinations of chemo-immunotherapies for treating cancer. The investigators, together with their students, carry out work along three complementary paths. First, dynamical systems population models are created and analyzed to determine fundamental system behavior that helps guide the development of combination therapies. Second, differential geometry approaches allow for the analysis of idealized geometric forms approximating physical structures of spherical, cylindrical, elliptic, and harmonic spherical tumors, which can closely approximate certain in vivo tumor geometries. Third, optimal control theory is used to reveal paths to new optimal combination therapies with implementation of a variety of constraints to minimize tumor burden while keeping the patient's immune and normal cell populations above a healthy threshold. The results of these investigations have the potential to provide guidance in the structuring of improved patient-specific treatment protocols. The mathematical modeling of cancer growth and combination treatment strategies adds to our basic understanding of cancer response mechanisms in fundamental ways. The simulations, geometric visualization, and optimization the investigators undertake allow for an array of virtual experiments to be run that can be performed quickly with no risk to living persons, but that provide data that can significantly benefit medical decision making. The modeling of cancer growth and treatment requires skills from multiple disciplines. A major outcome of this project is the development of software for simulating and visualizing cancer growth and treatment pathways, involving chemotherapy and immunotherapy, which can result in the creation of new mathematically guided patient-specific combination treatment strategies. This work lies at the intersection of information technology and biotechnology, with mathematics at the core. The investigators have the ability to funnel discoveries for new treatment strategies suggested by the mathematics directly to collaborating clinical oncologists through the ongoing meetings of a California-based Mathematics of Medicine Study group. In turn, the physicians in this group can enhance the development of the mathematical models by sharing outcomes of ongoing clinical trials. The investigators directly involve undergraduates in the multiple facets of this cutting-edge endeavor through research assistantships, courses, and independent study. A unique aspect of this project is the collaboration of three women investigators who are attracting more women students to this area of research. The investigators as a team can serve as role models on the forefront of the fight against cancer, and in particular are in a good position to affect breast cancer studies, which are of special importance to women's health. The results from solving the challenging mathematical, computational and biological problems of this project are made publicly accessible through publications and web-based postings. This collaborative effort has the potential to help clinicians save lives and reduce the suffering of cancer patients.