Advertisement

The European Physical Journal Special Topics

, Volume 222, Issue 8, pp 1875–1884 | Cite as

Fractional kinetics of glioma treatment by a radio-frequency electric field

  • A. Iomin
Regular Article

Abstract

A realistic model for estimation of the medical effect of brain cancer (glioma) treatment by a radio-frequency (RF) electric field is suggested. This low intensity, intermediate-frequency alternating electric field is known as the tumor-treating field (TTF). The model is based on a construction of 3D comb model for a description of the cancer cells dynamics, where the migration-proliferation dichotomy becomes naturally apparent, and the outer-invasive region of glioma cancer is considered as a fractal composite embedded in the 3D space. In the framework of this model, the interplay between the TTF and the migration-proliferation dichotomy of cancer cells is considered, and the efficiency of this TTF is estimated. It is shown that the efficiency of the medical treatment by the TTF depends essentially on the mass fractal dimension of the cancer in the outer-invasive region.

Keywords

Fractal Dimension European Physical Journal Special Topic Brain Cancer Fourier Inversion Fractal Composite 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D. Hanahan, R.A. Weinberg, Cell 100, 57 (2000)CrossRefGoogle Scholar
  2. 2.
    A. Giese, et al., Int. J. Cancer 67, 275 (1996)CrossRefGoogle Scholar
  3. 3.
    A. Giese, et al., J. Clin. Oncology 21, 1624 (2003)CrossRefGoogle Scholar
  4. 4.
    E. Khain, L.M. Sander, Phys. Rev. Lett. 96, 188103 (2006)ADSCrossRefGoogle Scholar
  5. 5.
    H. Hatzikirou, D. Basanta, M. Simon, K. Schaller, A. Deutsch, Math. Med. Biol. 7, 1 (2010)Google Scholar
  6. 6.
    A. Chauviere, L. Prziosi, H. Byrne, Math. Med. Biol. 27, 255 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    A.V. Kolobov, V.V. Gubernov, A.A. Polezhaev, Math. Model. Nat. Phenom. 6, 27 (2011)MathSciNetCrossRefGoogle Scholar
  8. 8.
    S. Fedotov, A. Iomin, L. Ryashko, Phys. Rev. E 84, 061131 (2011)ADSCrossRefGoogle Scholar
  9. 9.
    E.D. Kirson, et al., Cancer Res. 64, 3288 (2004)CrossRefGoogle Scholar
  10. 10.
    E.D. Kirson, et al., Proc. Nat. Acad. Sci. USA 104, 10152 (2007)ADSCrossRefGoogle Scholar
  11. 11.
    Y. Palti, Europ. Oncological Disease 1, 89 (2007)Google Scholar
  12. 12.
    H.A. Pohl, Dielectrophoresis (Cambridge University Press, Campbridge, 1978)Google Scholar
  13. 13.
    D.H. Geho, et al., Physiology, 20, 194 (2005)CrossRefGoogle Scholar
  14. 14.
    A. Iomin, Eur. Phys. J. E 35, 42 (2012)ADSCrossRefGoogle Scholar
  15. 15.
    E.W. Montroll, M.F. Shlesinger, in Studies in Statistical Mechanics, edited by J. Lebowitz, E.W. Montroll, Vol. 11 (North-Holland, Amsterdam, 1984)Google Scholar
  16. 16.
    R. Metzler, J. Klafter, Phys. Rep. 339, 1 (2000)MathSciNetADSCrossRefzbMATHGoogle Scholar
  17. 17.
    A. Iomin, Phys. Rev. E 73, 061918 (2006)ADSCrossRefGoogle Scholar
  18. 18.
    G.H. Weiss, S. Havlin, Physica A 134, 474 (1986)ADSCrossRefGoogle Scholar
  19. 19.
    E. Baskin, A. Iomin, Phys. Rev. Lett. 93, 120603 (2004)ADSCrossRefGoogle Scholar
  20. 20.
    V.E. Arkhincheev, E.M. Baskin, Sov. Phys. JETP 73, 161 (1991)Google Scholar
  21. 21.
    A. Iomin, E. Baskin, Phys. Rev. E 71, 061101 (2005)ADSCrossRefGoogle Scholar
  22. 22.
    S. Fedotov, A.O. Ivanov, A.Y. Zubarev, Non-homogeneous random walks and subdiffusive transport of cells [ arXiv:1209.2851] [cond-mat.stat-mech]
  23. 23.
    E. Baskin, A. Iomin, Chaos, Solitons Fractals 44, 335, (2011)MathSciNetADSCrossRefzbMATHGoogle Scholar
  24. 24.
    A. Iomin, Phys. Rev. E 83, 052106 (2011)MathSciNetADSCrossRefGoogle Scholar
  25. 25.
    J.R. Liang, X.T. Wang, W.Y. Qiu, Chaos, Solitons Fractals 16, 107 (2003)MathSciNetADSCrossRefzbMATHGoogle Scholar
  26. 26.
    K.B. Oldham, J. Spanier, The Fractional Calculus (Academic Press, New York, 1974)Google Scholar
  27. 27.
    I. Podlubny, Fractional Differential Equations (Academic Press, San Diego, 1999)Google Scholar
  28. 28.
    B.J. West, M. Bologna, P. Grigolini, Physics of Fractal Operators (Springer, New York, 2002)Google Scholar
  29. 29.
    S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives (Gordon and Breach, New York, 1993)Google Scholar
  30. 30.
    I.M. Sokolov, J. Klafter, A. Blumen, Phys. Today 55, 48 (2002)CrossRefGoogle Scholar
  31. 31.
    M.V. Berry, I.C. Percival, Optica Acta 33, 577 (1986)ADSCrossRefGoogle Scholar
  32. 32.
    D. ben-Avraam, S. Havlin, Diffusion and Reactions in Fractals and Disodered Systems (University Press, Cambridge, 2000)Google Scholar
  33. 33.
    R.R. Nigmatulin, Theor. Math. Phys. 90, 245 (1992)CrossRefGoogle Scholar
  34. 34.
    A. Le Mehaute, R.R. Nigmatullin, L. Nivanen, Fleches du Temps et Geometric Fractale (Hermes, Paris, 1998), Chap. 5Google Scholar
  35. 35.
    H. Bateman, A. Erdélyi, Higher Transcendental functions, Vol. 3 (Mc Graw-Hill, New York, 1955)Google Scholar
  36. 36.
    G. Zumofen, J. Klafter, A. Blumen, Chem. Phys. 146, 433 (1990)CrossRefADSGoogle Scholar
  37. 37.
    G. Zumofen, J. Klafter, Phys. Rev. E 51, 1818 (1995)ADSCrossRefGoogle Scholar
  38. 38.
    A.P. Prudnikov, Yu.A. Brychkov, O.I. Marichev, Integrals and series, Special Functions (Gordon and Breach, New York, 1986)Google Scholar
  39. 39.
    L. Jerby, L. Wolf, C. Denkert, G.Y. Stein, M. Hilvo, M. Oresic, T. Geiger, E. Ruppin, Cancer Res. doi:  10.1158/00085472.CAN-12-2215
  40. 40.
    J.H.P. Schulz, E. Barkai, R. Metzler, Phys. Rev. Lett. 110, 020602 (2013)ADSCrossRefGoogle Scholar
  41. 41.
    E. Barkai, Phys. Rev. Lett. 90, 104101 (2003)ADSCrossRefGoogle Scholar
  42. 42.
    D.R. Cox, H.D. Miller, The Theory of Stochastic Processes (Methuen & CO LTD, London, 1970)Google Scholar

Copyright information

© EDP Sciences and Springer 2013

Authors and Affiliations

  • A. Iomin
    • 1
  1. 1.Department of PhysicsTechnionHaifaIsrael

Personalised recommendations