We have developed a hybrid off-lattice cell-based version of Anderson et al. model [1]. We consider the hybridization on two levels: discrete space for molecules such as matrix-degradative enzymes (MDEs), nutrient or oxygen, and extracellular matrix (ECM) material, and continuous space for an individual cell. An important advantage of the off-lattice implementation is that there is no assumption made about whether the cells movements are in the diffusive regime (mean squared displacement ~ t) or the ballistic regime (mean squared displacement ~ t^2). According to the experimental results [2], the diffusive regime (in which the cell motion can be described by a random motility coefficient) takes a considerable time to develop (over 100 minutes for the mammalian cancer cells studied). We are going to present simulation results in terms of tumor shape and size which is strongly influenced by initial micro-environment.

References

1. Anderson, A.R.A.: A hybrid mathematical model of solid tumour invasion: the importance of cell adhesion. Math. Med. Biol. 22, 163-186 (2005).

2) Potdar, A. A., J. Lu, J. Jeon, A. M. Weaver, and P. T. Cummings: Bimodal Analysis of Mammary Epithelial Cell Migration in Two Dimensions, Annals of Biomedical Engineering, submitted (2007)