Skip to main content
SpringerLink
Log in

Instability of the Null Steady State: The Fundamental Problem of Inhibiting Malignant Cell Growth

  • BIOPHYSICAL CHEMISTRY
  • Published:
Russian Journal of Physical Chemistry A Aims and scope Submit manuscript

Abstract

Mathematical modeling of the process of inhibiting malignant growth by common chemotherapeutic agents and biological therapeutics is used to investigate the effect kinetic parameters of the model have on the outcome of treatment. It is shown that the ultimate suppression of growth, i.e., the formation of a stable steady-state with no cancer cells, cannot be attained if only the means of classical chemotherapy are used.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.

Similar content being viewed by others

REFERENCES

  1. N. M. Emanuel, Kinetics of Experimental Tumour Processes (Nauka, Moscow, 1977; Elsevier, Amsterdam, 1982).

  2. N. M. Emanuel’ and A. S. Evseenko, Clinical Oncology: A Quantitative Approach (Meditsina, Moscow, 1970; Israel Program Sci. Transl., Jerusalem, 1974).

  3. N. M. Emanuel’, L. P. Dronova, N. P. Konovalova, et al., Dokl. Akad. Nauk 152, 481 (1964).

    Google Scholar 

  4. N. M. Emanuel’, in Proceedings of the 2nd Symposium on Chemistry of Antitumor Substances, Moscow, May 12–13, 1965 (Meditsina, Moscow, 1967), p. 5 [in Russian].

  5. H. Abbasnejad, J. Artif. Intell. Electr. Eng. 4 (14), 19 (2015).

    Google Scholar 

  6. A. Ghaffari and N. Nasserifar, Iran. J. Electr. Electron. Eng. 5, 151 (2009).

    Google Scholar 

  7. A. El-alami laaroussi, M. El hia, M. Rachik, et al., Appl. Math. Sci. 8, 929 (2014).

  8. S. D. Varfolomeev and A. B. Lukovenkov, Russ. J. Phys. Chem. A 84, 1315 (2010).

    Article  CAS  Google Scholar 

  9. S. D. Varfolomeev, A. B. Lukovenkov, and N. A. Semenova, in Physical Chemistry of Bioprocesses, Ed. by S. D. Varfolomeev (URSS, Moscow, 2013), p. 13 [in Russian].

    Google Scholar 

  10. A. M. Lyapunov, General Problem of the Stability of Motion (Merkurii-Press, Moscow, 2000; CRC, Boca Raton, FL, 1992).

  11. I. G. Aramanovich, G. L. Lunts, and L. E. El’sgol’ts, Functions of a Complex Variable. Operational Calculus. The Theory of Stability (Nauka, Moscow, 1968) [in Russian].

    Google Scholar 

  12. L. E. Elsgolts, Differential Equations and the Calculus of Variations (Nauka, Moscow, 1969; Mir, Moscow, 1970).

  13. S. D. Varfolomeev and K. G. Gurevich, Biokinetics (Grand, Moscow, 1999) [in Russian].

    Google Scholar 

  14. V. V. Pleshkan, I. V. Alekseenko, M. V. Zinov’eva, et al., Acta Natur. 3 (2), 14 (2011).

    Google Scholar 

  15. I. V. Alekseenko, E. P. Kopantsev, T. V. Vinogradova, and E. D. Sverdlov, Dokl. Biochem. Biophys. 439, 174 (2011).

    Article  CAS  PubMed  Google Scholar 

  16. I. V. Alekseenko, M. V. Zinovieva, V. V. Pleshkan, and E. D. Sverdlov, Biopolym. Cells 28, 3 (2012).

    Article  CAS  Google Scholar 

Download references

ACKNOWLEDGMENTS

The authors are grateful to Academician E.D. Sverdlov for suggesting this research topic and his helpful comments.

Author information

Authors and Affiliations

  1. Emanuel Institute of Biochemical Physics, Russian Academy of Sciences, 119334, Moscow, Russia

    S. D. Varfolomeev & A. V. Lukovenkov

Authors
  1. S. D. Varfolomeev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. V. Lukovenkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. V. Lukovenkov.

Additional information

Translated by L. Brovko

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Varfolomeev, S.D., Lukovenkov, A.V. Instability of the Null Steady State: The Fundamental Problem of Inhibiting Malignant Cell Growth. Russ. J. Phys. Chem. 92, 1423–1428 (2018). https://doi.org/10.1134/S0036024418070300

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0036024418070300

Keywords:

Search

Navigation