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

Alessandro Fiasconaro, Bernardo Spagnolo, Ewa Gudowska-Nowak, Ochab-Marcinek, Alessandro Fiasconaro

Research output: Contribution to journalArticlepeer-review

72 Citations (Scopus)

Abstract

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 populations 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. © 2008 Springer.
Original languageEnglish
Pages (from-to)435-442
Number of pages8
JournalTHE EUROPEAN PHYSICAL JOURNAL. B, CONDENSED MATTER PHYSICS
Volume65
Publication statusPublished - 2008

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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