Monitoring noise-resonant effects in cancer growth influenced by external fluctuations and periodic treatment

TL;DR

This paper models tumor growth and immune response using stochastic differential equations, revealing how external noise and periodic treatment can enhance or hinder cancer extinction through resonance effects.

Contribution

It introduces a stochastic model of tumor-immune dynamics incorporating noise and periodic therapy, analyzing resonance phenomena to optimize treatment strategies.

Findings

Small noise can promote tumor extinction under certain conditions.

Resonant activation minimizes extinction time at specific treatment frequencies.

Noise can both aid and impede cancer treatment depending on system parameters.

Abstract

In the paper we investigate a mathematical model describing the growth of tumor in the presence of immune response of a host organism. The dynamics of tumor and immune cells is based on the generic Michaelis-Menten kinetics depicting interaction and competition between the tumor and the immune system. The appropriate phenomenological equation modeling cell-mediated immune surveillance against cancer is of the predator-prey form and exhibits bistability within a given choice of the immune response-related parameters. Under the influence of weak external fluctuations, the model may be analyzed in terms of a stochastic differential equation bearing the form of an overdamped Langevin-like dynamics in the external quasi-potential represented by a double well. We analyze properties of the system within the range of parameters for which the potential wells are of the same depth and when the additional perturbation, modeling a periodic treatment, is insufficient to overcome the barrier height and to cause cancer extinction. In this case the presence of a small amount of noise can positively enhance the treatment, driving the system to a state of tumor extinction. On the other hand, however, the same noise can give rise to return effects up to a stochastic resonance behavior. This observation provides a quantitative analysis of mechanisms responsible for optimization of periodic tumor therapy in the presence of spontaneous external noise. Studying the behavior of the extinction time as a function of the treatment frequency, we have also found the typical resonant activation effect: For a certain frequency of the treatment, there exists a minimum extinction time.