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Phase transitions in tumor growth: IV relationship between metabolic rate and fractal dimension of human tumor cells

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  • Betancourt-Mar, J.A.
  • Llanos-Pérez, J.A.
  • Cocho, G.
  • Mansilla, R.
  • Martin, R.R.
  • Montero, S.
  • Nieto-Villar, J.M.

Abstract

By the use of thermodynamics formalism of irreversible processes, complex systems theory and systems biology, it is derived a relationship between the production of entropy per unit time, the fractal dimension and the tumor growth rate for human tumors cells. The thermodynamics framework developed demonstrates that, the dissipation function is a Landau potential and also the Lyapunov function of the dynamical behavior of tumor growth, which indicate the directional character, stability and robustness of the phenomenon. The entropy production rate may be used as a quantitative index of the metastatic potential of tumors. The current theoretical framework will hopefully provide a better understanding of cancer and contribute to improvements in cancer treatment.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:473:y:2017:i:c:p:344-351
    DOI: 10.1016/j.physa.2016.12.089
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    References listed on IDEAS

    as
    1. Lucia, Umberto, 2014. "Entropy generation and cell growth with comments for a thermodynamic anticancer approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 107-118.
    2. 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.
    3. 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.
    4. Lucia, Umberto, 2013. "Thermodynamics and cancer stationary states," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3648-3653.
    5. Lucia, Umberto & Ponzetto, Antonio & Deisboeck, Thomas S., 2015. "A thermodynamic approach to the ‘mitosis/apoptosis’ ratio in cancer," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 246-255.
    6. Lucia, Umberto & Ponzetto, Antonio & Deisboeck, Thomas S., 2016. "Investigating the impact of electromagnetic fields on human cells: A thermodynamic perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 42-48.
    7. Lucia, Umberto, 2014. "Transport processes in biological systems: Tumoral cells and human brain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 327-336.
    8. 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.

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