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Phase transition in tumor growth: I avascular development

Author

Listed:
  • Izquierdo-Kulich, E.
  • Rebelo, I.
  • Tejera, E.
  • Nieto-Villar, J.M.

Abstract

We propose a mechanism for avascular tumor growth based on a simple chemical network. This model presents a logistic behavior and shows a “second order” phase transition. We prove the fractal origin of the empirical logistics and Gompertz constant and its relation to mitosis and apoptosis rate. Finally, the thermodynamics framework developed demonstrates the entropy production rate as a Lyapunov function during avascular tumor growth.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:24:p:6616-6623
    DOI: 10.1016/j.physa.2013.08.010
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    References listed on IDEAS

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    1. R. Solé, 2003. "Phase transitions in unstable cancer cell populations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 35(1), pages 117-123, September.
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    Cited by:

    1. 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.
    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. Miranda, Luiza M.S. & Souza, Andre M.C., 2023. "Fractality in tumor growth at the avascular stage from a generalization of the logistic-Gompertz dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).
    4. 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.
    5. 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.

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