Type Site of modelling Incorporated mechanisms Model validation and results Comments Reference Continuum Glioma Random motility with uniform diffusion; exponential proliferation N/A Prediction of basic behaviour of gliomas (e.g., tumour cell density is a function of
) Cruywagen et al. 1995 [14 ] Continuum Astrocytoma Random motility with uniform diffusion; logistic proliferation; cell loss due to chemotherapy 12 CT images of a patient/agreement between model parameters and experimental data The model is applicable for a specific course of treatment Tracqui et al. 1995 [12 ] Mechano-chemical Multisite Uniform diffusion; logistic proliferation; ECM-cell adhesion; haptotaxis N/A While important mechanisms in tumour invasion are considered, the behaviour of tumour at cellular level cannot be predicted Tracqui 1995 [16 ] Continuum Glioma Random motility with nonuniform diffusion; exponential proliferation Virtual MRI image/obtaining nonisotropic invasion pattern Rough prediction of the extent and concentration of local invasion. Applicable for tumours >1 (mm)3
Swanson et al. 2002, 2000 [2 , 17 ] Continuum Glioblastoma Nonuniform diffusion; exponential proliferation; mass effect MR images/capable to simulate complex tumour behaviour Migration and departure of cells not taken into account Clatz et al. 2005 [10 ] Continuum-Stochastic Multisite Random motility with uniform diffusion; haptotaxis; three-population tumour cells; heterogeneous ECM Model predictions consistent with clinical findings [18 ] Stochastic nature of the model allows to predict avascular invading tumour morphology by following individual cells with different phenotypes at each time and space step Anderson 2005 [19 ] Continuum Glioma Random motility with uniform diffusion; logistic proliferation; radially biased motility; shedding of invasive cell at tumour surface The model reproduces in vitro experiments data Assuming two-population tumour cells, proliferative (core) and invasive (periphery), and modelling invasive cells. Applicable for tumours <1 (mm)3 Stein et al. 2007 [20 ] Continuum Multisite Random motility with uniform diffusion; logistic proliferation; ECM-cell adhesion; haptotaxis, Cell-cell adhesion Comparison to simulation results of Anderson et al. [21 ] Simplifying assumptions: uniform diffusion and that haptotaxis is independent of ECM density; the simulation is 2D Gerisch and Chaplain 2008 [6 ] Continuum multisite Random motility with uniform diffusion; logistic proliferation; two-population tumour cells; oxygen concentration In vivo tumour growth observationAssumption: cells could either proliferate or migrate where transition between these two classes is environment-dependent; haptotaxis not considered Thalhauser et al. 2009 [22 ] Continuum-Stochastic Glioma Random motility with nonuniform diffusion; logistic proliferation; two-population tumour cells; haptotaxis The model predicts the tumour growth pattern of a clinical case Stochastic step of the model allows for introduction of patient-specific parameters (e.g., tumour location) Eikenberry et al. 2009 [8 ] Continuum Glioma Random motility with nonuniform diffusion; logistic proliferation; radiotherapy The biopsies of nine patients/the model reproduces RT response In contrast with imaging-based RT response, this model incorporates patient-specific tumour growth kinetics to quantify RT outcome Rockne et al. 2010 [23 ]
