Original paper| Volume 77, P194-203, September 2020

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An on-lattice agent-based Monte Carlo model simulating the growth kinetics of multicellular tumor spheroids

  • S. Ruiz-Arrebola
    Servicio de Oncología Radioterápica, Hospital Universitario Marqués de Valdecilla, E-39008 Santander, Spain
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  • A.M. Tornero-López
    Servicio de Radiofísica y Protección Radiológica, Hospital Universitario Dr. Negrín, E-35010 Gran Canaria, Spain
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  • D. Guirado
    Unidad de Radiofísica, Hospital Universitario San Cecilio, E-18016 Granada, Spain

    Instituto de Investigación Biosanitaria (ibs.GRANADA), Complejo Hospitalario Universitario de Granada/Universidad de Granada, E-18016 Granada, Spain
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  • M. Villalobos
    Instituto de Investigación Biosanitaria (ibs.GRANADA), Complejo Hospitalario Universitario de Granada/Universidad de Granada, E-18016 Granada, Spain

    Departamento de Radiología y Medicina Física, Universidad de Granada, E-18071 Granada, Spain

    Instituto de Biopatología y Medicina Regenerativa (IBIMER), Universidad de Granada, E-18071 Granada, Spain
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  • A.M. Lallena
    Corresponding author at: Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, E-18071 Granada, Spain.
    Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, E-18071 Granada, Spain

    Instituto de Investigación Biosanitaria (ibs.GRANADA), Complejo Hospitalario Universitario de Granada/Universidad de Granada, E-18016 Granada, Spain
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Published:September 01, 2020DOI:



      To develop an on-lattice agent-based model describing the growth of multicellular tumor spheroids using simple Monte Carlo tools.


      Cells are situated on the vertices of a cubic grid. Different cell states (proliferative, hypoxic or dead) and cell evolution rules, driven by 10 parameters, and the effects of the culture medium are included. About twenty spheroids of MCF-7 human breast cancer were cultivated and the experimental data were used for tuning the model parameters.


      Simulated spheroids showed adequate sizes of the necrotic nuclei and of the hypoxic and proliferative cell phases as a function of the growth time, mimicking the overall characteristics of the experimental spheroids. The relation between the radii of the necrotic nucleus and the whole spheroid obtained in the simulations was similar to the experimental one and the number of cells, as a function of the spheroid volume, was well reproduced. The statistical variability of the Monte Carlo model described the whole volume range observed for the experimental spheroids. Assuming that the model parameters vary within Gaussian distributions it was obtained a sample of spheroids that reproduced much better the experimental findings.


      The model developed allows describing the growth of in vitro multicellular spheroids and the experimental variability can be well reproduced. Its flexibility permits to vary both the agents involved and the rules that govern the spheroid growth. More general situations, such as, e. g., tumor vascularization, radiotherapy effects on solid tumors, or the validity of the tumor growth mathematical models can be studied.


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