Computational and Applied Mathematics

, Volume 36, Issue 2, pp 991–1008 | Cite as

Optimal chemotherapy schedules from tumor entropy

  • Andrés A. Barrea
  • Matias E. Hernández
  • Rubén Spies


We propose a model for the dynamics of an heterogeneous tumor, which consists of sensitive and resistant cells. The model is analyzed and validated using a cellular automaton whose local rules are classic and widely accepted in Biology. We then extend the model to a tumor under therapy. We consider Shannon’s entropy for the tumor and analyze the problem of minimizing this entropy. From this minimization problem, we find viable therapies that maintain at low level the entropy of the tumor. These therapies could provide a valuable tool for designing protocols for disease control, maintaining a very low growth level, while the tumor remains composed mainly of sensitive cells.


Cancer Chemotheraphy Entropy Optimization 

Mathematics Subject Classification

97M60 Biology, Chemistry, Medicine 


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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2015

Authors and Affiliations

  • Andrés A. Barrea
    • 1
  • Matias E. Hernández
    • 1
  • Rubén Spies
    • 2
  1. 1.FaMAF(UNC)-CIEM (CONICET)CórdobaArgentina
  2. 2.FIQ(UNL)-IMAL (CONICET)Santa FeArgentina

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