Investigating tumor-host response dynamics in preclinical immunotherapy experiments using a stepwise mathematical modeling strategy.

Immunotherapies such as checkpoint blockade to PD1 and CTLA4 can have varied effects on individual tumors. To quantify the successes and failures of these therapeutics, we developed a stepwise mathematical modeling strategy and applied it to mouse models of colorectal and breast cancer that displayed a range of therapeutic responses. Using longitudinal tumor volume data, an exponential growth model was utilized to designate response groups for each tumor type. The exponential growth model was then extended to describe the dynamics of the quality of vasculature in the tumors via [18F] fluoromisonidazole (FMISO)-positron emission tomography (PET) data estimating tumor hypoxia over time. By calibrating the mathematical system to the PET data, several biological drivers of the observed deterioration of the vasculature were quantified. The mathematical model was then further expanded to explicitly include both the immune response and drug dosing, so that model simulations are able to systematically investigate biological hypotheses about immunotherapy failure and to generate experimentally testable predictions of immune response. The modeling results suggest elevated immune response fractions (> 30 %) in tumors unresponsive to immunotherapy is due to a functional immune response that wanes over time. This experimental-mathematical approach provides a means to evaluate dynamics of the system that could not have been explored using the data alone, including tumor aggressiveness, immune exhaustion, and immune cell functionality.