Journal of Applied Mathematics
Volume 2013 (2013), Article ID 519895, 10 pages
Research Article

A Hybrid Cellular Automata Model of Multicellular Tumour Spheroid Growth in Hypoxic Microenvironment

1School of Biological Science and Medical Engineering, Southeast University, Nanjing 210096, China
2School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiaotong University, Shanghai 200240, China
3Department of Mechanics and Engineering Science, Fudan University, Shanghai 200433, China

Received 19 November 2012; Accepted 22 January 2013

Academic Editor: Martin Weiser

Copyright © 2013 Yan Cai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A three-dimensional hybrid cellular automata (CA) model is developed to study the dynamic process of multicellular tumour spheroid (MTS) growth by introducing hypoxia as an important microenvironment factor which influences cell migration and cell phenotype expression. The model enables us to examine the effects of different hypoxic environments on the growth history of the MTS and to study the dynamic interactions between MTS growth and chemical environments. The results include the spatial distribution of different phenotypes of tumour cells and associated oxygen concentration distributions under hypoxic conditions. The discussion of the model system responses to the varied hypoxic conditions reveals that the improvement of the resistance of tumour cells to a hypoxic environment may be important in the tumour normalization therapy.