Skip to main content
SpringerLink
Log in

The population dynamics of cancer incidence: The model of a second-order phase transition

  • Biophysics of Complex Systems
  • Published:
Biophysics Aims and scope Submit manuscript

Abstract

This paper considers an approach to the description of the age-specific and time-dependent dynamics of cancer incidence. This approach is based on a model that describes the age-specific dynamics of cancer as a phase transition of the second order and is widely used in the study of physical systems. The proposed model of cancer development as the second-order phase transitions is quite consistent with the data of medical statistics, is well described using only two free parameters, easily verified by the statistical data, and is interpreted well. The applicability of the model of second-order phase transitions to the description of the processes in the nonphysical systems is likely to be determined by the versatile nature of the processes that occur during the phase transitions.

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

Abbreviations

CFP:

cancer-free phase

CP:

cancer phase

References

  1. canSAR: https://cansar.icr.ac.uk/.

  2. SEER http://seer.cancer.gov/.

  3. GLOBOCAN: http://globocan.iarc.fr/Default.aspx.

  4. P. Armitage and R. Doll, Br. J. Cancer 8, 1 (1954).

    Article  Google Scholar 

  5. S. H. Moolgavkar, R. G. Stevens, and J. A. H. Lee, J. Natl. Cancer Inst. 62, 493 (1979).

    Google Scholar 

  6. S. H. Moolgavkar and D. J. Venzon, Math. Biosci. 47, 55 (1979).

    Article  MATH  Google Scholar 

  7. S. H. Moolgavkar and A. G. Knudson, J. Natl. Cancer Inst. 66, 1037 (1981).

    Google Scholar 

  8. R. Meza, J. Jeon, S. H. Moolgavkar, and E. G. Luebeck, Proc. Natl. Acad. Sci. U. S. A. 105, 16284 (2008).

    Article  ADS  Google Scholar 

  9. W. J. Ewens, Mathematical Population Genetics (Springer; New York, 2004).

    Book  MATH  Google Scholar 

  10. H. Schöllnberger, N. Beerenwinkel, R. Hoogenveen, and P. Vineis, Cancer Res. 70 (17), 6797 (2010).

    Article  Google Scholar 

  11. I. Akushevich, G. Veremeeva, and A. Yashin, in North Carolina Health Physics Society Spring 2007 Meeting (Charlotte, C, 2007), pp. 1–58.

    Google Scholar 

  12. A. Wienke, Frailty Models in Survival Analysis (Taylor and Francis, London, 2011).

    Google Scholar 

  13. V. G. Sukhovol’skii, L. M. Chailakhyan, Yu. Yu. Sharovskaya, and R. G. Khlebopros, in Homeostasis Reconstruction (Krasnoyarsk. Nauch. Tsentr Sib. Otd. Ross. Akad. Nauk, Krasnoyarsk, 1998), Vol.1, pp. 296–299 [in Russian].

    Google Scholar 

  14. V. A. Slepkov, V. G. Sukhovol’skii, and R. G. Khlebopros, Dokl. Biochem. Biophys. 411 (4), 342 (2006).

    Article  Google Scholar 

  15. V. A. Slepkov, V. G. Sukhovol’skii, R. G. Khlebopros, Dokl. Biochem. Biophys. 430 (4), 555 (2010).

    MATH  Google Scholar 

  16. L. D. Landau and E. M. Lifshitz, Statistical Physics, Vol. 5 of A Course of Theoretical Physics (Nauka, Moscow, 1964; Pergamon, New York, 1969).

    Google Scholar 

  17. Cancer Incidence in Four Member Countries (Cyprus, Egypt, Israel, and Jordan) of the Middle East Cancer Consortium (MECC) Compared with US SEER, Ed. by L. S. Freedman, B. K. Edwards, L.A.G. Ries, and J.L. Young, NIH Publ. no. 06-5873 (National Cancer Institute, Bethesda, 2006).

  18. L. D. Landau, Zh/Eksp. Teor. Fiz. 7 (1), 19 (1937).

    Google Scholar 

  19. State Report on the State and Conservation of the Environment in Kraznoyarsk Krai in the Year 2013 (Krasnoyarsk, 2014) [in Russian].

  20. V. M. Merabishvili, Biosfera 5 (1), 124 (2013).

    Google Scholar 

  21. S. A. Frank, Dynamics of Cancer: Incidence, Inheritance, and Evolution (Princeton Univ. Press, Princeton, NJ, 2007).

    Google Scholar 

  22. A. D. Bruce and R. A. Cowley, Structural Phase Transitions (Taylor and Francis, London, 1981; Mir. Moscow, 1984).

    Google Scholar 

  23. D. Hristova, Z. Zachariev, N. Mateva, and I. Grozdev, Neuroepidemiology 34, 76 (2010).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. International Scientific Center for Research on Extreme States of an Organism, Krasnoyarsk Scientific Center, Siberian Branch, Russian Academy of Sciences, Akademgorodok 50, Krasnoyarsk, 660036, Russia

    V. G. Soukhovolsky & R. G. Khlebopros

  2. Institute of Biophysics, Siberian Branch, Russian Academy of Sciences, Akademgorodok 50/50, Krasnoyarsk, 660036, Russia

    Yu. D. Ivanova & R. G. Khlebopros

  3. Hillel Yaffe Medical Center, Ha-Shalom str., Hadera, 38100, Israel

    K. Shulman

  4. Research Institute for Complex Problems of Hygiene and Occupational Diseases, ul. Kutuzova 23, Novokuznetsk, Kemerovo oblast, 654041, Russia

    V. F. Mazharov

  5. Voino-Yasenetsky Krasnoyarsk State Medical University, ul. Partizana Zheleznyaka 1, Krasnoyarsk, 660022, Russia

    V. F. Mazharov & I. V. Tarasova

  6. Siberian Federal University, Svobodniy prosp. 79, Krasnoyarsk, 660041, Russia

    V. G. Soukhovolsky, O. V. Tarasova & R. G. Khlebopros

Authors
  1. V. G. Soukhovolsky
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu. D. Ivanova
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. K. Shulman
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. V. F. Mazharov
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. I. V. Tarasova
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. O. V. Tarasova
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. R. G. Khlebopros
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. G. Soukhovolsky.

Additional information

Original Russian Text © V.G. Soukhovolsky, Yu.D. Ivanova, K. Shulman, V.F. Mazharov, I.V. Tarasova, O.V. Tarasova, R.G. Khlebopros, 2015, published in Biofizika, 2015, Vol. 60, No. 4, pp. 777–786.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Soukhovolsky, V.G., Ivanova, Y.D., Shulman, K. et al. The population dynamics of cancer incidence: The model of a second-order phase transition. BIOPHYSICS 60, 639–646 (2015). https://doi.org/10.1134/S0006350915040235

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0006350915040235

keywords

Search

Navigation