Modeling of drug resistance: Comparison of two hypotheses for slowly proliferating tumors on the example of low‐grade gliomas

Acquired drug resistance (ADR) syndrome is one of the most important features associated with tumor treatment and it is therefore a topic of intensive studies. We present two simple mathematical models reflecting different mechanisms of ADR with some Darwinian effects included. These effects allow bi-directional flow between resistant and sensitive compartments, meaning that not only sensitive cells become resistant but also resistant cells may become sensitive again. Basing on this mathematical approach, we conclude that, for constant continuous treatment, if there is no flow back to the sensitive compartment, then once resistant cells appear, sensitive cells are eventually eliminated, independently of the mechanism of acquiring the resistance. However, with bi-directional flow, the situation is a little better as the sensitive cells are not completely eliminated, although they are still outcompeted by the resistant ones. Moreover, if the therapy is stopped, resistant cells become dominated by sensitive cells and the situation changes. We discuss these mechanisms for slowly proliferating tumors on the example of gliomas.