Mathematical modelling of heterogeneity in tumour-immune cell interactions

Tumours are highly heterogeneous entities. To understand cancer devel- opment from its initiation to metastases, research is needed to reveal the impact of heterogeneous populations of immune cells and tumour cells on outcomes. The presence of T cells of the adaptive immune response are correlated with favourable outcomes across a broad range of cancers. In this thesis we focus specifically on the T cell population and the impact of heterogeneity in both immune and tumour cells on model outcomes. To reveal the role played by the various aspects of heterogeneity in tumour- immune cell interactions, we develop a suite of mathematical models that explores in turn heterogeneity in: subpopulations of T cells; in different states of functionality of the same T cell (or states of exhaustion); and different subpopulations of tumour cells.
The models are formulated as ordinary differential equations. Each model is examined through a combination of numerical and analytical techniques. All three models exhibit three generic responses to immune cells: tumour elimination, equilibrium and escape (the three Es of immunoediting) [52]. The first model focuses on the behaviour of a tumour interacting with two subpopulations of T cells: helper and cytotoxic T cells. The likelihood of tumour elimination, equilibrium and escape is found to vary with both the rates of infiltration of cytotoxic and helper T cells. The results indi- cate that combined immunotherapies, where both rates of infiltration are increased comparably, may elicit the most favourable response outcomes.
The second model focuses on heterogeneity in the level of functionality of the cytotoxic T cells (exhaustion state). Tumour elimination, equilibrium and escape are found to depend on the rates of exhaustion of individual T cell functions, together with the ratio of the baseline T cell population (in the absence of a tumour) to the T cell population required to arrest tumour growth. The model suggests that the appropriate treatment is to block the ability of the tumour to dampen T cell proliferation.
The final model focuses on heterogeneity in both tumour and T cell populations. The tumour population is divided into an immune-resistant and an immune-sensitive subpopulation, and the T cell population is divided into a cytotoxic and an exhausted subpopulation. The likelihood of tumour elimination, equilibrium and escape are found to vary with the rate of infiltration of cytotoxic T cells, together with the growth rate of the tumour, the rate at which immune-sensitive tumour cells produce immune-resistant tumour cells, the rate of conversion of cytotoxic T cells to exhausted T cells and the exhausted T cell kill rate. The results suggest that boosting the infiltration of cytotoxic T cells would be most effective and that the necessary increase depends on the growth rate of the tumour.
This thesis uses a series of ODE models to comprehensively study how aspects of tumour-immune system heterogeneity impact tumour progres- sion. All three models show a close link between moderate immunosuppression and the presence of a dormant tumour state. The results suggest a number of potentially promising therapies depending on the degree of immunosuppression, tumour growth rate, and immune cell composition.

Advisor: Byrne, H
Waters, S
Roller, A