A mathematical modeling approach towards immunological control of minimal residual disease in CML patients

There is increasing evidence in patients with Chronic Myeloid Leukemia (CML) pointing to the role of the immune system in the sustained control of residual leukemic cells after cessation of treatment with tyrosine-kinase inhibitors. It has been speculated that, once the treatment decreases the leukemic burden below some threshold, the immune cells are capable to keep it at a residual level, or even to completely eliminate the leukemic clone. However, at the moment these mechanisms are poorly understood. Specifically, since the immune control appears to be effective only at a low level of leukemic cells, it is important to understand the interaction between two phenomena: (i) the stimulation of immune cells by the presence of leukemic cells and (ii) the elimination of these cells. We develop a mathematical framework describing CML progression and treatment in terms of ordinary differential equations. Within this model we make different assumptions about the mechanisms by which (i) immune cells are stimulated by leukemic cells and (ii) how leukemic cells are targeted by immune cells. The combination of the different assumptions leads to several structurally different models, which are characterized by the existence of different numbers of steady states. We compare our conceptual results with available data sets from CML patients after TKI cessation, thereby allowing us to speculate about the plausibility of the particular assumptions. Our results highlight the necessity to understand the mechanisms of immune control in leukemia therapy to employ this effect for optimal treatment results and to furthermore identify the clinically accessible measures that allow to derive better predictions about the outcome of treatment cessation.