Combining cellular automata and lattice Boltzmann method to model multiscale avascular tumor growth coupled with nutrient diffusion and immune competition

Davide Alemani, Francesco Pappalardo, Marzio Pennisi, Santo Motta, Vladimir Brusic

Research output: Contribution to journalArticle

40 Citations (Scopus)

Abstract

In the last decades the Lattice Boltzmann method (LB) has been successfully used to simulate a variety of processes. The LB model describes the microscopic processes occurring at the cellular level and the macroscopic processes occurring at the continuum level with a unique function, the probability distribution function. Recently, it has been tried to couple deterministic approaches with probabilistic cellular automata (probabilistic CA) methods with the aim to model temporal evolution of tumor growths and three dimensional spatial evolution, obtaining hybrid methodologies. Despite the good results attained by CA-PDE methods, there is one important issue which has not been completely solved: the intrinsic stochastic nature of the interactions at the interface between cellular (microscopic) and continuum (macroscopic) level. CA methods are able to cope with the stochastic phenomena because of their probabilistic nature, while PDE methods are fully deterministic. Even if the coupling is mathematically correct, there could be important statistical effects that could be missed by the PDE approach. For such a reason, to be able to develop and manage a model that takes into account all these three level of complexity (cellular, molecular and continuum), we believe that PDE should be replaced with a statistic and stochastic model based on the numerical discretization of the Boltzmann equation: The Lattice Boltzmann (LB) method. In this work we introduce a new hybrid method to simulate tumor growth and immune system, by applying Cellular Automata Lattice Boltzmann (CA-LB) approach.

Original languageEnglish
Pages (from-to)55-68
Number of pages14
JournalJournal of Immunological Methods
Volume376
Issue number1-2
DOIs
Publication statusPublished - Feb 28 2012

Keywords

  • Cellular automata
  • Computational models
  • Dosage optimization
  • Hybrid models
  • Immune system
  • Lattice Boltzmann

ASJC Scopus subject areas

  • Immunology and Allergy
  • Immunology

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