Abstract: Mathematical modeling of cancer growth and treatment

Mathematical models for cancer treatment have potential application to optimizing therapy, and can lead to a better understanding of how anti-cancer treatments work. In the last decade, the use of immunotherapies and targeted therapies has greatly increased, while more traditional therapies such as chemotherapy and radiation remain widely used clinically. This presentation will cover two specific areas relating to modeling anti-cancer therapy: (a) developing models for cellular response to drugs and drug combinations, and (b) modeling the killing of cancer cells by CD8+ cytolytic T cells, which are believed to be the primary immune cells involved in anti-cancer responses. Cellular response to drugs has been described by several mathematical formulations that in many cases do not describe experimental results well. Our peak damage and additive damage model formulations, which perform better, will be discussed, as will the elusive concept of “synergy,” transient drug resistance, and the challenge of modeling multiple exposures. On the topic of cytolytic T cells, which are quite relevant to current cancer therapy, a particular mathematical form designed to describe T cell killing of target cells by contact kill has been used in the vast majority of mathematical modeling studies of tumor-immune interactions. However, we show that an alternative model describes data far better. The exact biological interpretation is difficult to specify with certainty, but it suggests that most kill is via a diffusible factor rather than direct contact. Overall, these models are expected to have application to optimizing therapy and and can help guide the development of new therapies.