title: Basic ingredients for mathematical modeling of tumor growth in vitro: cooperative effects and search for space.
abstract: 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.
authors: Departamento de Física, FFCLRP, Universidade de São Paulo, 14040-901 Ribeirão Preto, São Paulo, Brazil. Electronic address: fhsantanacosta@gmail.com.
authors: F H S
authors: FH
authors: Costa
authors: Departamento de Química e Ciências Ambientais, IBILCE, Universidade Estadual Paulista Júlio de Mesquita Filho, 15054-000 São José do Rio Preto, São Paulo, Brazil.
authors: M
authors: M
authors: Campos
authors: Departamento de Física Médica, UNIFEB, 14783-226 Barretos, São Paulo, Brazil.
authors: O E
authors: OE
authors: Aiéllo
authors: Departamento de Física e Química, FCFRP, Universidade de São Paulo, 14040-903 Ribeirão Preto, São Paulo, Brazil. Electronic address: maasilva@fcfrp.br.
authors: M A A
authors: MA
authors: da Silva
mesh_terms: D002449:Cell Aggregation; D049109:Cell Proliferation; D019073:HT29 Cells; D006801:Humans; D008954:Models, Biological; D009369:Neoplasms / Q000473:pathology*; D013997:Time Factors
keywords: Dynamical Monte Carlo; Mathematical modeling; Tumor growth