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Fractality in tumor growth at the avascular stage from a generalization of the logistic-Gompertz dynamics

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  • Miranda, Luiza M.S.
  • Souza, Andre M.C.

Abstract

The dynamics between healthy and malignant cells at the avascular stage of growth is described by a set of chemical reactions representing the populations of both types of cells. We obtain a generalization of the logistic-Gompertz dynamics and study the consequences in terms of the properties of tumor growth associated with the Warburg effect, mitosis and nutrient and space apoptosis. As a result of the stochastic nature of this process, a fractal morphology is observed in this region. Our results agree with experimental results for growth of tumor cell colonies.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:618:y:2023:i:c:s0378437123002194
    DOI: 10.1016/j.physa.2023.128664
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    References listed on IDEAS

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    1. Reis, E.A. & Santos, L.B.L. & Pinho, S.T.R., 2009. "A cellular automata model for avascular solid tumor growth under the effect of therapy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(7), pages 1303-1314.
    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. Sweta Sinha & Paramjeet Singh, 2022. "Mathematical modeling and simulation of mechano-chemical effect on two-phase avascular tumor," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 33(05), pages 1-22, May.
    4. 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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