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

Applied Sciences

Antonio M. Lallena¹  Mercedes Villalobos¹  Samuel Ruiz-Arrebola²  Damián Guirado³ 

[1] Instituto de Investigación Biosanitaria (ibs.GRANADA), Universidad de Granada, E-18016 Granada, Spain;Servicio de Oncología Radioterápica, Hospital Universitario Marqués de Valdecilla, E-39008 Santander, Spain;Unidad de Radiofísica, Hospital Universitario Clínico San Cecilio, E-18016 Granada, Spain;

关键词: on-lattice agent-based models;    classical tumor growth models;    exponential;    Gompertz;    logistic;    Bertalanffy;   

DOI  :  10.3390/app11115241

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown