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

Ruiz-Arrebola, S.; Tornero-López, A.; Guirado, D.; Villalobos, Mercedes; Lallena, A. M.

doi:10.1016/j.ejmp.2020.07.026

Cited by 1 publication

(7 citation statements)

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“…The ABM also reproduces the linear relation experimentally found between the radius of the necrotic nucleus and that of the whole MTS: both the slope (b exp = 1.078 ± 0.096 and b sim = 1.006 ± 0.002) and the independent term (a exp = −151 ± 44 µm and a sim = −142.5 ± 1.6 µm) of the respective linear regressions coincide within the uncertainties (given with a coverage factor 2). Furthermore, the dependence of the number of hypoxic plus proliferative cells with the total volume of the MTS shows the same behavior as the experimental data [60], agreeing within uncertainties with them (see reference [53]).…”

Section: On-lattice Monte Carlo Agent-based Modelsupporting

confidence: 80%

“…In this way, only the variability linked to the Monte Carlo randomness of the different processes involved in the simulation has been taken into account. The variability observed in the MTS volumes measured in the experiment performed in [53] is within the statistical variability found in this sample #1 of simulated MTS. However, it has been realized that, in order to be fully described, some of the experimental details require an additional variability in the simulation.…”

Section: On-lattice Monte Carlo Agent-based Modelsupporting

confidence: 77%

“…In order to investigate their predictive capabilities, the classical mathematical models described in the previous section have been fitted to data obtained with an on-lattice ABM recently developed and tested [53], which has been used as a reference. In this ABM, cells are situated at the vertices of a cubic grid and are organized in layers forming regions characterized by one of the three possible states considered: proliferative (k = p), quiescent or hypoxic (k = h), or necrotic (k = n).…”

Section: On-lattice Monte Carlo Agent-based Modelmentioning

confidence: 99%

“…The values of the packing factors, f p = 0.9, f h = 1.0, and f n = 1.1 were selected according to experimental evidence [61]. Finally, d 0 = 6, κ = 0.8, were fine-tuned to reproduce the experimental results obtained in [53] for the MCF-7 line.…”

Section: On-lattice Monte Carlo Agent-based Modelmentioning

confidence: 99%

“…Recently, an on-lattice ABM of MTS growth that uses simple mathematical tools to describe the cell evolution has been developed [53]. The model includes Monte Carlo techniques to take into account the variability observed among the cells forming the spheroids and takes into account the basic features that characterize the MTS behavior when irradiated, allowing for addressing the capabilities of different therapeutic strategies for solid tumors.…”

Section: Introductionmentioning

confidence: 99%

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Evaluation of Classical Mathematical Models of Tumor Growth Using an On-Lattice Agent-Based Monte Carlo Model

et al. 2021

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Purpose:To analyze the capabilities of different classical mathematical models to describe the growth of multicellular spheroids simulated with an on-lattice agent-based Monte Carlo model that has already been validated. Methods: The exponential, Gompertz, logistic, potential, and Bertalanffy models have been fitted in different situations to volume data generated with a Monte Carlo agent-based model that simulates the spheroid growth. Two samples of pseudo-data, obtained by assuming different variability in the simulation parameters, were considered. The mathematical models were fitted to the whole growth curves and also to parts of them, thus permitting to analyze the predictive power (both prospective and retrospective) of the models. Results: The consideration of the data obtained with a larger variability of the simulation parameters increases the width of the χ2 distributions obtained in the fits. The Gompertz model provided the best fits to the whole growth curves, yielding an average value of the χ2 per degree of freedom of 3.2, an order of magnitude smaller than those found for the other models. Gompertz and Bertalanffy models gave a similar retrospective prediction capability. In what refers to prospective prediction power, the Gompertz model showed by far the best performance. Conclusions: The classical mathematical models that have been analyzed show poor prediction capabilities to reproduce the MTS growth data not used to fit them. Within these poor results, the Gompertz model proves to be the one that better describes the growth data simulated. The simulation of the growth of tumors or multicellular spheroids permits to have follow-up periods longer than in the usual experimental studies and with a much larger number of samples: this has permitted performing the type of analysis presented here.

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Section: On-lattice Monte Carlo Agent-based Modelsupporting

confidence: 80%

Section: On-lattice Monte Carlo Agent-based Modelsupporting

confidence: 77%

Section: On-lattice Monte Carlo Agent-based Modelmentioning

confidence: 99%

Section: On-lattice Monte Carlo Agent-based Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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