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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
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Abstract |
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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
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Mathematical Subject Classification 2010
Primary: 37B15, 68Q80, 74A10
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Milestones
Received: 4 December 2016
Revised: 23 April 2017
Accepted: 6 June 2017
Published: 1 October 2017
Communicated by Francesco dell'Isola
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Authors |
| Ruben Interian | |
| Institute of Computing Fluminense Federal University Niterói Brazil |
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| Reinaldo Rodríguez-Ramos | |
| Mathematics and Computer Science
Faculty Havana University, Havana Cuba |
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| Fernando Valdés-Ravelo | |
| Molecular Immunology Center Havana Cuba |
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| Ariel Ramírez-Torres | |
| Institute for Research in Applied
Mathematics and Systems National Autonomous University of Mexico Mexico City Mexico |
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| Celso C. Ribeiro | |
| Institute of Computing Fluminense Federal University Niterói Brazil |
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| Aura Conci | |
| Institute of Computing Fluminense Federal University Niterói Brazil |
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