In Silico Modelling of Tumour Margin Diffusion and Infiltration: Review of Current Status

Table 2

Summaries of stochastic models of tumour growth and invasion.

Type	Site of modelling	Incorporated mechanisms	Model validation and results	Comments	Reference
Monte Carlo (cellular automaton model)	Brain	3D tessellation lattice grid, three-population tumour, nutrition gradient, clonal competition, intercellular mechanical stress	N/A	Since active motility is not taken into account, the tumour invasion cannot be investigated	Kansal et al. 2000 [24]
Monte Carlo	multisite	Different phases of cell cycle, three-population tumour cells, shrinkage of tumour due to radiotherapy, cubic grid	Application of the model to small cell lung cancer/qualitative correspondence to in vitro experiments	The microscopic extension cannot be predicted since each grid element is almost 1 mm^3 accommodating 10^6 cells	Stamatakos 2001 [25]
Monte Carlo	Multisite	Different phases of cell cycle, three-population tumour cells, shrinkage of tumour due to radiotherapy, cubic grid, hypoxia	Application of the model to two GBM cases/qualitative correspondence to clinical observations	The possibility to optimize radiotherapy fractionation regimens, unable to depict microscopic spread	Antipas et al. 2004 [26]
Monte Carlo	Multisite	Different phases of cell cycle, three-population tumour cells, shrinkage of tumour due to radiotherapy, cubic grid, hypoxia, neo-angiogenesis	Parametric validation against two different categories of GBM/qualitative correspondence to experiments	Generally, the discrete nature of these models allows for inclusion of other parameters	Stamatakos et al. 2006 [27]
Markov model	Head and Neck	Lymphatic drainage pathway, T-stage, tumour location	Comparison to two surgical data/over prediction of metastasis	Quantitative prediction of microscopic spread was found to be feasible	Benson et al. 2006 [3]
Monte Carlo (individual-based model)	Multisite	Three-population tumour, 2D grid, nutrition and oxygen concentration, different phases of cell cycle	Comparison to the study of Anderson [19] and also experimental results [28, 29]/good agreement	Haptotaxis is not taken into account thus tumour invasion is not depicted	Gerlee and Anderson 2007 [30]
Monte Carlo (individual-based model)	Multisite	Three-population tumour, 2D grid, nutrition and oxygen concentration, different phases of cell cycle, haptotaxis	Comparison to the study of Anderson [19] and also experiment results/good agreement	The influence of evolution of tumour cell phenotype in response to microenvironment on tumour development and progression is an important conclusion to be used in the study of microscopic extension	Gerlee and Anderson 2009 [9]