Multi-Scale Aspects of Immune Responses to Solid Cancers: Mathematical and Computational Modelling Perspectives

Immunotherapy has now become a standard therapeutic approach against cancers (in addition and complementary to surgery, chemotherapy, radiotherapy, and targeted therapies). However, due to the complex interactions between immune cells and cancer cells, until now very few such immunotherapy approaches have led to significant results. Mathematical models of immune responses to cancer have been developed over the years to shed light on some of these complex immune–cancer interactions that usually take place across multiple spatial and temporal scales. The focus of this chapter is to briefly review some of these mathematical modelling approaches while emphasising the multi-scale aspect of the models. We do not aim to offer a comprehensive discussion of all mathematical models in the literature but rather to emphasise the different classes of continuum multi-scale models developed over the past decades (and in particular over the last few years) in the context of cancer–immune interactions. The review is build step by step: (i) first we discuss some biological aspects related to cell-level immune responses to cancers and then mention current immuno-therapeutic approaches targeting various molecules, (ii) next we present general mathematical equations for deterministic continuum models for cancer–immune interactions (where the multi-scale aspect is presented explicitly or implicitly), and for each of these different classes of mathematical models, we discuss in detail one particular model published in the past five years, and (iii) finally, we conclude by discussing some open problems related to available multi-scale data and model parametrisation.