RT Journal Article
T1 Evaluation of Classical Mathematical Models of Tumor Growth Using an On-Lattice Agent-Based Monte Carlo Model
A1 Ruiz-Arrebola, Samuel
A1 Guirado, Damian
A1 Villalobos, Mercedes
A1 Lallena, Antonio M.
K1 on-lattice agent-based models
K1 classical tumor growth models
K1 exponential
K1 Gompertz
K1 logistic
K1 Bertalanffy
K1 multicellular spheroids
K1 Monte Carlo
K1 Cancer
K1 Spheroids
K1 Radiotherapy
K1 Kinetics
K1 Cultures
K1 Biology
K1 Systems
AB 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 chi(2) distributions obtained in the fits. The Gompertz model provided the best fits to the whole growth curves, yielding an average value of the chi(2) 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.
PB Mdpi
YR 2021
FD 2021-06-01
LK http://hdl.handle.net/10668/19247
UL http://hdl.handle.net/10668/19247
LA en
DS RISalud
RD Apr 8, 2025