Modeling Immunotherapy of Cancer
(Lisette DePillis, Harvey Mudd College)

Mathematical models of tumor-immune interactions provide an analytical framework in which to address specific questions regarding tumor-immune dynamics.  We present a mathematical model that describes tumor-immune interactions, focusing on the role of NK and CD8+T cells in tumor surveillance, with the goal of understanding the dynamics of immune-mediated tumor rejection. The model describes tumor-immune cell interactions using a system of differential equations. The functions describing tumor-immune growth, response, and interaction rates, as well as associated parameters, are developed using a least squares method combined with a numerical differential equations solver. Parameter estimates and model validations used data from published mouse and human studies. Specifically, CD8+T-tumor and NK-tumor lysis data from chromium release assays as well as in-vivo tumor growth data were used. A parameter sensitivity analysis was performed on the model. The new functional forms developed show that there is a clear distinction between the dynamics of NK and CD8+T cells. Simulations of tumor growth using different levels of immune stimulating ligands, effector cells, and tumor challenge, are able to reproduce data from the published studies. A sensitivity analysis reveals that the parameter to which the model is most sensitive is patient-specific, and can be measured with a chromium release assay. The parameter sensitivity analysis suggests that the model can predict which patients may respond positively to treatment.  Further simulations suggest the importance of activating CD8+T-cells in cancer therapy. This is joint work with Prof. A.E. Radunskaya, Department of Mathematics, Pomona College, Claremont, CA, and Dr. C.L. Wiseman, Department of Immunotherapy, St. Vincent Medical Center, Los Angeles, CA.