Vol. 5, No. 3-4, 2017

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ISSN: 2325-3444 (e-only)
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Tumor growth modelling by cellular automata

Ruben Interian, Reinaldo Rodríguez-Ramos, Fernando Valdés-Ravelo, Ariel Ramírez-Torres, Celso C. Ribeiro and Aura Conci

Vol. 5 (2017), No. 3-4, 239–259
DOI: 10.2140/memocs.2017.5.239
Abstract

Tumor growth is a complex process that requires mathematical modeling approaches for studying real-life cancer behavior. The use of cellular automata (CA) to represent tumor growth in its avascular stage is explained in this work, and a stochastic CA describing tumor growth is obtained, based on a differential equations system in the range of continuum mechanics. The novelty of this research is the deduction of the neighborhood structure and rules for a probabilistic CA from these differential equations that describe the evolution of the tumor growth. In addition, the influence of the stresses on tumor growth is captured by the CA.

Keywords
tumor growth, stresses, stochastic rules, cellular automata
Mathematical Subject Classification 2010
Primary: 37B15, 68Q80, 74A10
Milestones
Received: 4 December 2016
Revised: 23 April 2017
Accepted: 6 June 2017
Published: 1 October 2017

Communicated by Francesco dell'Isola
Authors
Ruben Interian
Institute of Computing
Fluminense Federal University
Niterói
Brazil
Reinaldo Rodríguez-Ramos
Mathematics and Computer Science Faculty
Havana University, Havana
Cuba
Fernando Valdés-Ravelo
Molecular Immunology Center
Havana
Cuba
Ariel Ramírez-Torres
Institute for Research in Applied Mathematics and Systems
National Autonomous University of Mexico
Mexico City
Mexico
Celso C. Ribeiro
Institute of Computing
Fluminense Federal University
Niterói
Brazil
Aura Conci
Institute of Computing
Fluminense Federal University
Niterói
Brazil