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

Author(s)

Costa, F. H. S. ^[1] ; Campos, M. ^[2] ; Aiello, O. E. ^[3] ; da Silva, M. A. A. ^[4]

Affiliation

^[1] Univ Sao Paulo, FFCLRP, Dept Fis, BR-14040901 Ribeirao Preto, SP - Brazil

^[2] Univ Estadual Paulista, IBILCE, Dept Quim & Ciencias Ambientais, BR-15054000 Sao Paulo - Brazil

^[3] UNIFEB, Dept Fis Med, BR-14783226 Sao Paulo - Brazil

^[4] Univ Sao Paulo, FCFRP, Dept Quim & Fis, BR-14040903 Ribeirao Preto, SP - Brazil

• Document type: Journal article
• Source: Journal of Theoretical Biology; v. 337, p. 24-29, NOV 21 2013.
• Web of Science Citations: 2

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. (C) 2013 Elsevier Ltd. All rights reserved. (AU)

• FAPESP's process: 12/03823-5 - On the mesoscopic mechanisms of tumor growth
• Grantee: Marco Antonio Alves da Silva
• Support Opportunities: Regular Research Grants