Basic ingredients for mathematical modeling of tumor growth in vitro: Cooperative effects and search for space

• Published in: Journal of theoretical biology Vol. 337; pp. 24 - 29
• Main Authors: Costa, F.H.S., Campos, M., Aiéllo, O.E., da Silva, M.A.A.
• Format: Journal Article
• Language: English
• Published: England Elsevier Ltd 21.11.2013
• Subjects: Cell Aggregation; Cell Proliferation; developmental stages; Dynamical Monte Carlo; equations; evolution; growth models; HT29 Cells; Humans; in vitro studies; ingredients; Mathematical modeling; mathematical models; Models, Biological; neoplasms; Neoplasms - pathology; stochastic processes; Time Factors; Tumor growth; Tumor growth; Dynamical Monte Carlo; Mathematical modeling
• ISSN: 0022-5193; 1095-8541
• DOI: 10.1016/j.jtbi.2013.07.030

Based on the literature data from HT-29 cell monolayers, we develop a model for its growth, analogous to an epidemic model, mixing local and global interactions. First, we propose and solve a deterministic equation for the progress of these colonies. Thus, we add a stochastic (local) interaction and simulate the evolution of an Eden-like aggregate by using dynamical Monte Carlo methods. The growth curves of both deterministic and stochastic models are in excellent agreement with the experimental observations. The waiting times distributions, generated via our stochastic model, allowed us to analyze the role of mesoscopic events. We obtain log-normal distributions in the initial stages of the growth and Gaussians at long times. We interpret these outcomes in the light of cellular division events: in the early stages, the phenomena are dependent each other in a multiplicative geometric-based process, and they are independent at long times. We conclude that the main ingredients for a good minimalist model of tumor growth, at mesoscopic level, are intrinsic cooperative mechanisms and competitive search for space. •We show that a basic requirement to simulate successfully the tumor growing in vitro is to adopt a sigmoidal growth rate.•We use a different kind of dynamical Monte Carlo method, building the waiting times along the simulation.•We have obtained non-Poissonian distributions for these waiting times.