A Cancer Dynamics Model for an Intermittent Treatment Involving Reduction of Tumor Size and Rise of Growth Rate

  • Virginia Giorno
  • Serena SpinaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9520)


We propose a model of tumor dynamics based on the Gompertz deterministic law influenced by jumps that occur at equidistant time instants. This model consents to study the effect of a therapeutic program that provides intermittent suppression of cancer cells. In this context a jump represents an application of the therapy that shifts the cancer mass to a fixed level and it produces a deleterious effect on the organism by increasing the growth rate of the cancer cells. The objective of the present study is to provide an efficient criterion to choose the instants in which to apply the therapy by maximizing the time in which the cancer mass is under a fixed control threshold.


Therapeutic Application Efficient Criterion Therapeutic Program Intermittent Treatment Control Threshold 
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  1. 1.
    Giorno, V., Spina, S.: A stochastic gompertz model with jumps for an intermittent treatment in cancer growth. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds.) EUROCAST. LNCS, vol. 8111, pp. 61–68. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  2. 2.
    Hirata, Y., Bruchovsky, N., Aihara, K.: Development of a mathematical model that predicts the outcome of hormone therapy for prostate cancer. J. Theor. Biol. 264, 517–527 (2010)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Migita, T., Narita, T., Nomura, K.: Activation and therapeutic implications in non-small cell lung cancer. Cancer Res. 268, 8547–8554 (2008)CrossRefGoogle Scholar
  4. 4.
    Parfitt, A.M., Fyhrie, D.P.: Gompertzian growth curves in parathyroid tumors: further evidence for the set-point hypothesis. Cell Prolif. 30, 341–349 (1997)CrossRefGoogle Scholar
  5. 5.
    Spina, S., Giorno, V., Román-Román, P., Torres-Ruiz, F.: A stochastic model of cancer growth subject to an intermittent treatment with combined effects: reduction of tumor size and rise of growth rate. Bull. Math. Biol. 76, 2711–2736 (2014). doi: 10.1007/s11538-014-0026-8 MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Tanaka, G., Hirata, Y., Goldenberg, S.L., Bruchovsky, N., Aihara, K.: Mathematical modelling of prostate cancer growth and its application to hormone therapy. Phil. Trans. R. Soc. A 368, 5029–5044 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Wang, J., Tucker, L.A., Stavropoulos, J.: Correlation of tumor growth suppression and methionine aminopetidase-2 activity blockade using an orally active inhibitor, Global pharmaceutical Research and Development, Abbott Laboratories. Edit by Brian W. Matthews, University of Oregon; Eugene, OR (2007)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Dipartimento di Studi e Ricerche Aziendali (Management and Information Technology)Università di SalernoFiscianoItaly
  2. 2.Dipartimento di MatematicaUniversità di SalernoFiscianoItaly

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