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Phase transitions in tumor growth: III vascular and metastasis behavior

Author

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  • Llanos-Pérez, J.A.
  • Betancourt-Mar, J.A.
  • Cocho, G.
  • Mansilla, R.
  • Nieto-Villar, José Manuel

Abstract

We propose a mechanism for avascular, vascular and metastasis tumor growth based on a chemical network model. Vascular growth and metastasis, appear as a hard phase transition type, as “first order”, through a supercritical Andronov–Hopf bifurcation, emergence of limit cycle and then through a cascade of bifurcations type saddle-foci Shilnikov’s bifurcation. Finally, the thermodynamics framework developed shows that the entropy production rate, as a Lyapunov function, indicates the directional character and stability of the dynamical behavior of tumor growth according to this model.

Suggested Citation

  • Llanos-Pérez, J.A. & Betancourt-Mar, J.A. & Cocho, G. & Mansilla, R. & Nieto-Villar, José Manuel, 2016. "Phase transitions in tumor growth: III vascular and metastasis behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 560-568.
    • Handle: RePEc:eee:phsmap:v:462:y:2016:i:c:p:560-568
    DOI: 10.1016/j.physa.2016.06.086
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    References listed on IDEAS

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    1. Castorina, Paolo & Zappalà, Dario, 2006. "Tumor Gompertzian growth by cellular energetic balance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(2), pages 473-480.
    2. Llanos-Pérez, J.A. & Betancourt-Mar, A. & De Miguel, M.P. & Izquierdo-Kulich, E. & Royuela-García, M. & Tejera, E. & Nieto-Villar, J.M., 2015. "Phase transitions in tumor growth: II prostate cancer cell lines," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 426(C), pages 88-92.
    3. El-Gohary, Awad, 2008. "Chaos and optimal control of cancer self-remission and tumor system steady states," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1305-1316.
    4. Hiroaki Kitano, 2003. "Cancer robustness: Tumour tactics," Nature, Nature, vol. 426(6963), pages 125-125, November.
    5. Anishchenko, V.S. & Vadivasova, T.E. & Okrokvertskhov, G.A. & Strelkova, G.I., 2003. "Correlation analysis of dynamical chaos," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 325(1), pages 199-212.
    6. Izquierdo-Kulich, E. & Rebelo, I. & Tejera, E. & Nieto-Villar, J.M., 2013. "Phase transition in tumor growth: I avascular development," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(24), pages 6616-6623.
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    Cited by:

    1. Guerra, A. & Rodriguez, D.J. & Montero, S. & Betancourt-Mar, J.A. & Martin, R.R. & Silva, E. & Bizzarri, M. & Cocho, G. & Mansilla, R. & Nieto-Villar, J.M., 2018. "Phase transitions in tumor growth VI: Epithelial–Mesenchymal transition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 208-215.
    2. Martin, R.R. & Montero, S. & Silva, E. & Bizzarri, M. & Cocho, G. & Mansilla, R. & Nieto-Villar, J.M., 2017. "Phase transitions in tumor growth: V what can be expected from cancer glycolytic oscillations?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 762-771.
    3. Betancourt-Mar, J.A. & Llanos-Pérez, J.A. & Cocho, G. & Mansilla, R. & Martin, R.R. & Montero, S. & Nieto-Villar, J.M., 2017. "Phase transitions in tumor growth: IV relationship between metabolic rate and fractal dimension of human tumor cells," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 344-351.

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