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Agent-Based Model for Studying the Effects of Solid Stress and Nutrient Supply on Tumor Growth

Author

Listed:
  • Maxim Kuznetsov

    (Division of Theoretical Physics, P.N. Lebedev Physical Institute of the Russian Academy of Sciences, 53 Leninskiy Prospekt, 119991 Moscow, Russia
    Current address: Department of Computational and Quantitative Medicine, Division of Mathematical Oncology, City of Hope, Duarte, CA 91010, USA.)

  • Andrey Kolobov

    (Division of Theoretical Physics, P.N. Lebedev Physical Institute of the Russian Academy of Sciences, 53 Leninskiy Prospekt, 119991 Moscow, Russia)

Abstract

An off-lattice agent-based model of tumor growth is presented, which describes a tumor as a network of proliferating cells, whose dynamics depend on the stress generated by intercellular bonds. A numerical method is introduced that ensures the smooth dynamics of the cell network and allows for relative numerical cheapness while reproducing the effects typical of more complex approaches such as the elongation of cells toward low-pressure regions and their tendency to maximize the contact area. Simulations of free tumor growth, restricted only by the stress generated within the tumor, demonstrate the influence of the tissue hydraulic conductivity and strength of cell–cell interactions on tumor shape and growth rate. Simulations of compact tumor growth within normal tissue show that strong interaction between tumor cells is a major factor limiting tumor growth. Moreover, the effects of normal tissue size and strength of normal cell interactions on tumor growth are ambiguous and depend on the value of tissue hydraulic conductivity. Simulations of tumor growth in normal tissue with the account of nutrients yield different growth regimes, including growth without saturation for at least several years with the formation of large necrotic cores in cases of low tissue hydraulic conductivity and sufficiently high nutrient supply, which qualitatively correlates with known clinical data.

Suggested Citation

  • Maxim Kuznetsov & Andrey Kolobov, 2023. "Agent-Based Model for Studying the Effects of Solid Stress and Nutrient Supply on Tumor Growth," Mathematics, MDPI, vol. 11(8), pages 1-23, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1900-:d:1125627
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    References listed on IDEAS

    as
    1. Pascal Meier & Andrew Finch & Gerard Evan, 2000. "Apoptosis in development," Nature, Nature, vol. 407(6805), pages 796-801, October.
    2. Maxim Kuznetsov, 2020. "Mathematical Modeling Shows That the Response of a Solid Tumor to Antiangiogenic Therapy Depends on the Type of Growth," Mathematics, MDPI, vol. 8(5), pages 1-19, May.
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    Cited by:

    1. Maxim Kuznetsov & Andrey Kolobov, 2024. "Antiangiogenic Therapy Efficacy Can Be Tumor-Size Dependent, as Mathematical Modeling Suggests," Mathematics, MDPI, vol. 12(2), pages 1-15, January.

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