Mathematical Modelling of Immuno-Oncology and Related Immunology

Immunotherapy offers new and promising treatments for many different types of cancer, but the problem of how to practically regulate the immune response in a way that allows it to fight cancer without overwhelming patients with potentially fatal inflammatory toxicity has yet to be solved. This partly results from lingering unanswered questions in immunology and partly results from the inevitable variability between one patient and the next. Here we look specifically at Chimeric Antigen Receptor (CAR)-T cell therapy, explore the mechanisms by which this living drug grows and changes inside the body, and explore how and why this process differs so dramatically between patients.

We develop two ordinary differential equation models -- one which unifies several currently conflicting theories on T cell differentiation pathways, and one which serves as a framework for a Simulated Randomized Clinical Trial (SRCT) to evaluate CAR-T cell therapy as a treatment for patients with leukemia. Our results provide a plausible mechanistic explanation for widely variable patient responses to CAR-T cell therapy seen clinically, and suggest possible ways to improve patient outcomes, even and especially when the patient population is highly heterogeneous. In particular, our results suggest that improvements in patient outcomes can be obtained by reintroducing key characteristics of the endogenous T-cell response that are lost with the dosing protocols currently being used in clinical trials. Our primary conclusion is that single or (homogeneously) split dose protocols should be replaced with protocols for achieving, during the initial stages of therapy, low serum concentrations of effector CAR-T cells, followed by higher serum concentrations of effector CAR-T cells as the tumor burden decreases, and finally substantial serum concentrations of memory CAR-T cells at the end of the treatment period.