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

Simon D. Angus¹ ; Monika J. Piotrowska²

¹ Department of Economics Monash University Clayton 3800, Australia
² Department of Mathematics, Informatics and Mechanics University of Warsaw Banacha 2 02-097 Warszawa, Poland

Applicationes Mathematicae, Tome 37 (2010) no. 1, pp. 69-88

Résumé

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.

Détail

DOI : 10.4064/am37-1-5

Keywords: dimensional extension previously reported scaled dimensional cellular automaton model avascular multi cellular spheroid growth presented analysed emt cell line model outputs found compare favourably reported experimentally obtained vitro spheroids cell line necrosis unprogrammed central cell death observed delayed compared experimental furthermore found necrosis arises model due subcritical nutrient conditions due toxicity modelled production ions suggested authors indeed central conditions which followed facile manner setup never observed reach critical levels implications these results considered model approach underlying understanding tumour metabolism progression