The onset of necrosis in a 3D cellular automaton model of EMT6 multi-cellular spheroids

Tom 37 / 2010

Simon D. Angus, Monika J. Piotrowska Applicationes Mathematicae 37 (2010), 69-88 MSC: 92C37, 92-08. DOI: 10.4064/am37-1-5


A 3-dimensional (3D) extension to a previously reported scaled 2-dimensional Cellular Automaton (CA) model of avascular multi-cellular spheroid growth is presented and analysed for the EMT6/Ro cell line. The model outputs are found to compare favourably with reported experimentally obtained data for in vitro spheroids of the same cell line. Necrosis (unprogrammed central cell death) is observed to be delayed when compared with the experimental data. Furthermore, it is found that necrosis arises in the model due to subcritical nutrient conditions and not due to toxicity (modelled as the production of H$^+$ ions) as suggested by some authors. Indeed, central pH conditions, which can be followed in a facile manner in the CA setup, are never observed to reach critical levels. Implications of these results are considered both for the CA model approach and the underlying understanding of tumour metabolism and progression.


  • Simon D. AngusDepartment of Economics
    Monash University
    Clayton 3800, Australia
  • Monika J. PiotrowskaDepartment of Mathematics,
    Informatics and Mechanics
    University of Warsaw
    Banacha 2
    02-097 Warszawa, Poland

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