Evasion of tumours from the control of the immune system: consequences of brief encounters

In this work a mathematical model describing the growth of a solid tumour in the presence of an immune system response is presented. Specifically, attention is focused on the interactions between cytotoxic T-lymphocytes (CTLs) and tumour cells in a small, avascular multicellular tumour. At this stage of the disease the CTLs and the tumour cells are considered to be in a state of dynamic equilibrium or cancer dormancy. The precise biochemical and cellular mechanisms by which CTLs can control a cancer and keep it in a dormant state are still not completely understood from a biological and immunological point of view. The mathematical model focuses on the spatio-temporal dynamics of tumour cells, immune cells, chemokines and ``chemo-repellors'' in an immunogenic tumour. The CTLs and tumour cells are assumed to migrate and interact with each other in such a way that lymphocyte-tumour cell complexes are formed. These complexes result in either the death of the tumour cells (the normal situation) or the inactivation of the lymphocytes and consequently the survival of the tumour cells. In the latter case, we assume that each tumour cell which survives its ``brief encounter'' with the CTLs undergoes certain beneficial phenotypic changes. We explore the dynamics of the model under these assumptions and show that the process of immuno-evasion can arise as a consequence of these encounters. We also briefly discuss the evolutionary features of our model, by framing them in the recent quasi-Lamarckian theories.