Evaluation of Classical Mathematical Models of Tumor Growth Using an On-Lattice Agent-Based Monte Carlo Model
Metadatos
Mostrar el registro completo del ítemAutor
Ruíz Arrebola, Samuel; Guirado Llorente, Damián; Villalobos Torres, Mercedes; Lallena Rojo, Antonio MiguelEditorial
MDPI
Materia
On-lattice agent-based models Classical tumor growth models Exponential Gompertz Logistics Bertalanffy Multicellular spheroids Monte Carlo
Fecha
2021Referencia bibliográfica
Ruiz-Arrebola, S.; Guirado, D.; Villalobos, M.; Lallena A.M. Evaluation of Classical Mathematical Models of Tumor Growth Using an On-Lattice Agent-Based Monte Carlo Model. Appl. Sci. 2021, 11, 5241. https://doi.org/10.3390/app11115241
Patrocinador
Spanish Ministerio de Ciencia y Competitividad (FPA2015-67694-P, PID2019-104888GB-I00); European Regional Development Fund (ERDF); Junta de Andalucía (FQM0387, P18-RT-3237)Resumen
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
χ
2 distributions obtained in the fits. The Gompertz model provided the best fits to the whole growth
curves, yielding an average value of the χ
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.