Skip to main content
SpringerLink
Log in

A toy model of fractal glioma development under RF electric field treatment

  • Regular Article
  • Published:
The European Physical Journal E Aims and scope Submit manuscript

Abstract

A toy model for glioma treatment by a radio frequency electric field is suggested. This low-intensity, intermediate-frequency alternating electric field is known as the tumor-treating field (TTF). In the framework of this model the efficiency of this TTF is estimated, and the interplay between the TTF and the migration-proliferation dichotomy of cancer cells is considered. The model is based on a modification of a comb model for cancer cells, where the migration-proliferation dichotomy becomes naturally apparent. Considering glioma cancer as a fractal dielectric composite of cancer cells and normal tissue cells, a new effective mechanism of glioma treatment is suggested in the form of a giant enhancement of the TTF. This leads to the irreversible electroporation that may be an effective non-invasive method of treating brain cancer.

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

Similar content being viewed by others

References

  1. E.D. Kirson et al., Cancer Res. 64, 3288 (2004).

    Article  Google Scholar 

  2. E.D. Kirson et al., Proc. Natl. Acad. Sci. U.S.A. 104, 10152 (2007).

    Article  ADS  Google Scholar 

  3. Y. Palti, Europ. Oncol. Dis. 1, 89 (2007).

    Google Scholar 

  4. H.A. Pohl, Dielectrophoresis (Cambridge University Press, Cambridge, 1978).

  5. D.H. Geho et al., Physiology 20, 194 (2005).

    Article  Google Scholar 

  6. A. Giese et al., Int. J. Cancer 67, 275 (1996).

    Article  Google Scholar 

  7. A. Giese et al., J. Clin. Oncol. 21, 1624 (2003).

    Article  Google Scholar 

  8. E. Khain, L.M. Sander, Phys. Rev. Lett. 96, 188103 (2006).

    Article  ADS  Google Scholar 

  9. H. Hatzikirou, D. Basanta, M. Simon, K. Schaller, A. Deutsch, Math. Med. Biol. 7, 1 (2010).

    Google Scholar 

  10. A. Chauviere, L. Prziosi, H. Byrne, Math. Med. Biol. 27, 255 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  11. A.V. Kolobov, V.V. Gubernov, A.A. Polezhaev, Math. Model. Nat. Phenom. 6, 27 (2011).

    Article  MathSciNet  Google Scholar 

  12. S. Fedotov, A. Iomin, L. Ryashko, Phys. Rev. E 84, 061131 (2011).

    Article  ADS  Google Scholar 

  13. Yu. Polevaya, I. Ermolina, M. Schlesinger, B.-Z. Ginzburg, Yu. Feldman, Biochim. Biophys. Acta 1419, 257 (1999).

    Article  Google Scholar 

  14. U.A. Khan et al., IEEE Trans. Microwave Theor. Tech. 55, 2887 (2007).

    Article  ADS  Google Scholar 

  15. E.W. Montroll, M.F. Shlesinger, in Studies in Statistical Mechanics, edited by J. Lebowitz, E.W. Montroll, Vol. 11 (Noth-Holland, Amsterdam, 1984).

  16. R. Metzler, J. Klafter, Phys. Rep. 339, 1 (2000).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. A. Iomin, Phys. Rev. E 73, 061918 (2006).

    Article  ADS  Google Scholar 

  18. E. Baskin, A. Iomin, Chaos, Solitons Fractals 44, 335 (2011).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. A. Iomin, Phys. Rev. E 83, 052106 (2011).

    Article  MathSciNet  ADS  Google Scholar 

  20. J.R. Liang, X.T. Wang, W.Y. Qiu, Chaos, Solitons Fractals 16, 107 (2003).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. I. Podlubny, Fractional Differential Equations (Academic Press, San Diego, 1999).

  22. K.B. Oldham, J. Spanier, The Fractional Calculus (Academic Press, New York, 1974).

  23. B.J. West, M. Bologna, P. Grigolini, Physics of Fractal Operators (Springer, New York, 2002).

  24. S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives (Gordon and Breach, New York, 1993).

  25. I.M. Sokolov, J. Klafter, A. Blumen, Phys. Today 55, 48 (2002).

    Article  Google Scholar 

  26. H. Bateman, A. Erdélyi, Higher Transcendental Functions, Vol. 3 (Mc Graw-Hill, New York, 1955).

  27. M.V. Berry, I.C. Percival, Opt. Acta 33, 577 (1986).

    Article  ADS  Google Scholar 

  28. D. ben-Avraam, S. Havlin, Diffusion and Reactions in Fractals and Disodered Systems (Cambridge University Press, Cambridge, 2000).

  29. E. Baskin, A. Iomin, EPL 96, 54001 (2011).

    Article  ADS  Google Scholar 

  30. L.D. Landau, E.M. Lifshitz, L.P. Pitaevskii, Electrodynamics of Continuous Media (Butterworth-Heinenmann Ltd, Oxford, 1995).

  31. C.F. Bohren, D.R. Huffman, Absorbtion and Scattering of Light by Small Particles (John Wyley & Sons Inc, New York, 1983).

  32. B. Rubinsky, G. Onik, P. Mikus, Technol. Cancer Res. Treat. 6, 37 (2007).

    Google Scholar 

  33. A.K. Sarychev, V.M. Shalaev, Electrodynamics of Metamaterials (World Scientic, Singapore, 2007).

  34. M.I. Stockman, Phys. Today 64, 39 (2011).

    Article  Google Scholar 

  35. S. Fedotov, A. Iomin, Phys. Rev. Lett. 98, 118101 (2007).

    Article  ADS  Google Scholar 

  36. S. Fedotov, A. Iomin, Phys. Rev. E 77, 031911 (2008).

    Article  MathSciNet  ADS  Google Scholar 

  37. G.H. Weiss, S. Havlin, Physica A 134, 474 (1986).

    Article  ADS  Google Scholar 

  38. E. Baskin, A. Iomin, Phys. Rev. Lett. 93, 120603 (2004).

    Article  ADS  Google Scholar 

  39. V.E. Arkhincheev, E.M. Baskin, Sov. Phys. JETP 73, 161 (1991).

    Google Scholar 

  40. A. Iomin, E. Baskin, Phys. Rev. E 71, 061101 (2005).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Technion, 32000, Haifa, Israel

    A. Iomin

Authors
  1. A. Iomin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Iomin.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Iomin, A. A toy model of fractal glioma development under RF electric field treatment. Eur. Phys. J. E 35, 42 (2012). https://doi.org/10.1140/epje/i2012-12042-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epje/i2012-12042-9

Keywords

Search

Navigation