Mathematical Models of Tumor Growth and Therapy

Abstract

A number of mathematical models of cancer growth and treatment are presented. The most significant model presented is of the interactions between a growing tumor and the immune system. The equations and parameters of the model are based on experimental and clinical results from published studies. The model includes the primary cell populations involved in effector-T-cell-mediated tumor killing: regulatory T cells, helper T cells, and dendritic cells. A key feature is the inclusion of multiple mechanisms of immunosuppression through the main cytokines and growth factors mediating the interactions between the cell populations. Decreased access of effector cells to the tumor interior with increasing tumor size is accounted for.The model is applied to tumors of different growth rates and antigenicities to gauge the relative importance of the various immunosuppressive mechanisms in a tumor. The results suggest that there is an optimum antigenicity for maximal immune system effect. The immunosuppressive effects of further increases in antigenicity outweigh the increase in tumor cell control due to larger populations of tumor-killing effector T cells. The model is applied to situations involving cytoreductive treatment, specifically chemotherapy and a number of immunotherapies. The results how that for some types of tumors, the immune system is able to remove any tumor cells remaining after the therapy is finished. In other cases, the immune system acts to prolong remission periods. A number of immunotherapies are found to be ineffective at removing a tumor burden alone, but offer significant improvement on therapeutic outcome when used in combination with chemotherapy.Two simplified classes of cancer models are also presented. A model of cellular metabolism is formulated. The goal of the model is to understand the differences between normal cell and tumor cell metabolism. Several theories explaining the Crabtree Effect, hereby tumor cells reduce their aerobic respiration in the presence of glucose, have been put forth in the literature; the models test some of these theories, and examine their plausibility.A model of elastic tissue mechanics for a cylindrical tumor growing within a ductal membrane is used to determine the buildup of residual stress due to growth. These results can have possible implications for tumor growth rates and morphology.