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Competing species system as a qualitative model of radiation therapy

Author

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  • Wendykier, Jacek
  • Bieniasiewicz, Marcin
  • Lipowski, Adam
  • Pawlak, Andrzej

Abstract

To examine complex features of tumor dynamics we analyze a competing-species lattice model that takes into account the competition for nutrients or space as well as interaction with therapeutic factors such as drugs or radiation. Our model might be interpreted as a certain prey–predator system having three trophic layers: (i) the basal species that might be interpreted as nutrients; (ii) normal and tumor cells that consume nutrients, and (iii) therapeutic factors that might kill either nutrient, normal or tumor cells. Using a wide spectrum of parameters we examined survival of our species and tried to identify the corresponding dynamical regimes. It was found that the radiotherapy influences mainly the limit of starvation i.e. the value of an update probability where the tumor cells go extinct as a result of insufficient nutrient supply and competition with normal cells. The other limiting value of this probability, corresponding to the coexistence of the normal and tumor cells in abundance of nutrients, is almost not affected by radiotherapy. We have also found the coexistence of all species on the phase diagrams.

Suggested Citation

  • Wendykier, Jacek & Bieniasiewicz, Marcin & Lipowski, Adam & Pawlak, Andrzej, 2016. "Competing species system as a qualitative model of radiation therapy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 454(C), pages 81-93.
    • Handle: RePEc:eee:phsmap:v:454:y:2016:i:c:p:81-93
    DOI: 10.1016/j.physa.2016.01.089
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    References listed on IDEAS

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    1. Lipowski, Adam & Lipowska, Dorota, 2012. "Roulette-wheel selection via stochastic acceptance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(6), pages 2193-2196.
    2. Joana Moreira & Andreas Deutsch, 2002. "Cellular Automaton Models Of Tumor Development: A Critical Review," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 5(02n03), pages 247-267.
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