Stochastic competitive release and adaptive chemotherapy

We develop a finite-cell model of tumor natural selection dynamics to investigate the stochastic fluctuations associated with multiple rounds of adaptive chemotherapy. The adaptive cycles are designed to avoid chemo-resistance in the tumor by managing the ecological mechanism of competitive release of a resistant sub-population. Our model is based on a three-component evolutionary game played among healthy (H), sensitive (S), and resistant (R) populations of N cells, with a chemotherapy control parameter, C ( t ), used to dynamically impose selection pressure on the sensitive sub-population to slow tumor growth but manage competitive release of the resistant population. The adaptive chemo-schedule is designed based on the deterministic ( N → ∞) adjusted replicator dynamical system, then implemented using the finite-cell stochastic frequency dependent Moran process model ( N = 10 K – 50 K ) to ascertain the size and variations of the stochastic fluctuations associated with the adaptive schedules. We quantify the stochastic fixation probability regions of the R and S populations in the HSR tri-linear phase plane as a function of the control parameter C ∈ [0, 1], showing that the size of the R region increases with increasing C . We then implement an adaptive time-dependent schedule C ( t ) for the stochastic model and quantify the variances (using principal component coordinates) associated with the evolutionary cycles for multiple rounds of adaptive therapy, showing they grow according to power-law scaling. The simplified low-dimensional model provides some insights on how well multiple rounds of adaptive therapies are likely to perform over a range of tumor sizes if the goal is to maintain a sustained balance among competing sub-populations of cells so as to avoid chemo-resistance via competitive release in a stochastic environment.