Nonlinear active control of a cancerous tumour

  • Authors

    • Bhabani Shankar Dey
    • Manas Kumar Bera
    • Binoy Krishna Roy
    https://doi.org/10.14419/ijet.v7i2.21.11839

    Received date: April 21, 2018

    Accepted date: April 21, 2018

    Published date: April 20, 2018

  • Tumour, immune, active control, chemotherapy.
  • Abstract

    This paper deals with the control of a cancerous tumour growth. The model used is a Three-Dimensional Cancer Model (TDCM). The competition terms include tumour cells, healthy cells, and immune cells. Nature of the competition among the populations of tumour cells, healthy host cells, and immune cells results in a chaotic behaviour. In this paper, a nonlinear active control has been used to control the growth of a tumour. Effect of chemotherapy drug on the different cell populations has been studied. Our control objective is to control the tumour growth and minimize its population to a small value which can be considered as harmless.Along with the above objective, the normal cell population is also be maintained at a particular level. This work has been done completely inin-sillico environment. The simulation results are shown extensively to support the theoretical analysis and confirmed that the preliminary objectives of the paper are attained.

  • References

    1. De Pillis LG & Radunskaya AE, “A mathematical tumour model with immune resistance and drug therapy: an optimal control approach”, Theor. Med., Vol.3, No.2, (2001), pp.79–100.
    2. Norton L & Simon R, “Tumor size, sensitivity to therapy, and design of treatment schedules”, Cancer Treat. Rep., Vol.61, (1977), pp.1307–1317.
    3. Holford N & Sheiner L, “Pharmacokinetic and
    4. pharmaco-dynamicmodeling in vivo”, CRC Critical Reviews in Bioengineering, Vol.5, (1981), pp.273–322.
    5. Swan GW, “Role of optimal control theory in cancer chemotherapy”, Mathematical Biosciences, Vol.101, (1990), pp.237–284.
    6. Martin R.B, “Optimal control drug scheduling of cancer chemotherapy”, Automatica, Vol.28, (1992), pp.1113–1123.
    7. Neal T & Yoshida K, “Chemotherapy for tumors: an analysis of the dynamics and a study of quadratic and linear optimal controls”, Mathematical Biosciences, Vol.209, (2007), pp.292–315.
    8. Holford N & Sheiner L, “Pharmacokinetic and pharmaco-dynamicmodeling in vivo”, CRC Critical Reviews in Bioengineering, Vol.5, (1981), pp.273–322.
    9. Swierniak A & Duda Z, “Singularity of optimal control in some problems related to optimal chemotherapy”, Mathematical Computer Modelling, Vol.19, (1994), pp.255–262.
    10. Ledzewicz U, Maurer H & Schättler H, Bang–bang and singular controls in a mathematical model for combined anti-angiogenic and chemotherapy treatments, IEEE 48th Conference on Decision and Control, (2009).
    11. Mohammad S, “Control in Three Dimensional Cancer Model by State Space Exact Linearization Based on Lie Algebra”, MDPI, (2016)
    12. Liqun C &Yanzhu L, “Control of Lorenz chaos by the exact linearization”, Appl. Math. Mech., (1998), pp.67–73.
    13. Singh PP, Singh JP & Roy BK, “Synchronisation and anti-synchronisation of Lu and Bhalekar-Gejji chaotic systems using nonlinear active control”, Chaos, Solitons Fractals, Vol.69, (2014), pp.31–39.
    14. Slotine JJ & Li W, Applied Nonlinear Control, Prentice Hall Inc., Englewood cliffs, NJ, (1991).
    15. Moradi GR &Vossoughi H, “Optimal robust control of drug delivery in cancer chemotherapy:a comparison between three control approaches”, Computer Methods Programs Biomed., Vol.112, (2013), pp.69-83
    16. Moradi H, Sharifi M & Vossoughi G, “Adaptive robust control of cancer chemotherapy in presence of parametric uncertainties: A comparision between three hypotheses”, Computers in Biology and Medicine, Elsevier, Vol.56, No.1, (2014), pp.145-157.
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  • How to Cite

    Shankar Dey, B., Kumar Bera, M., & Krishna Roy, B. (2018). Nonlinear active control of a cancerous tumour. International Journal of Engineering and Technology, 7(2.21), 72-76. https://doi.org/10.14419/ijet.v7i2.21.11839