Computational Modelling of Cancer Development and Growth: Modelling at Multiple Scales and Multiscale Modelling
@article{Szymanska2018ComputationalMO, title={Computational Modelling of Cancer Development and Growth: Modelling at Multiple Scales and Multiscale Modelling}, author={Zuzanna Szymanska and Maciej Cytowski and Elaine Irwin Mitchell and Cicely K. Macnamara and Mark A. J. Chaplain}, journal={Bulletin of Mathematical Biology}, year={2018}, volume={80}, pages={1366-1403} }
In this paper, we present two mathematical models related to different aspects and scales of cancer growth. The first model is a stochastic spatiotemporal model of both a synthetic gene regulatory network (the example of a three-gene repressilator is given) and an actual gene regulatory network, the NF-$$\upkappa $$κB pathway. The second model is a force-based individual-based model of the development of a solid avascular tumour with specific application to tumour cords, i.e. a mass of cancer…
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References
SHOWING 1-10 OF 125 REFERENCES
Multiscale modelling and nonlinear simulation of vascular tumour growth
- BiologyJournal of mathematical biology
- 2009
A new multiscale mathematical model for solid tumour growth is presented which couples an improved model of tumour invasion with a model of malignant tumour-induced angiogenesis and demonstrates the importance of the coupling between the development and remodeling of the vascular network, the blood flow through the network and the tumour progression.
Integrating Intracellular Dynamics Using CompuCell3D and Bionetsolver: Applications to Multiscale Modelling of Cancer Cell Growth and Invasion
- BiologyPloS one
- 2012
A multiscale, individual-based simulation environment that integrates CompuCell3D for lattice-based modelling on the cellular level and Bionetsolver for intracellular modelling and is applied to a model of cancer growth and invasion.
Mathematical modelling of dynamic adaptive tumour-induced angiogenesis: clinical implications and therapeutic targeting strategies.
- BiologyJournal of theoretical biology
- 2006
Simulating growth dynamics and radiation response of avascular tumour spheroids - model validation in the case of an EMT6/Ro multicellular spheroid
- MedicineComput. Methods Programs Biomed.
- 2004
A cellular automaton model for tumour growth in inhomogeneous environment.
- BiologyJournal of theoretical biology
- 2003
Spatio-temporal modelling of the Hes1 and p53-Mdm2 intracellular signalling pathways.
- BiologyJournal of theoretical biology
- 2011
Multi-scale modelling of the dynamics of cell colonies: insights into cell-adhesion forces and cancer invasion from in silico simulations
- BiologyJournal of The Royal Society Interface
- 2015
A multi-scale multi-compartment mathematical model is developed that accounts for the principal biophysical interactions and adhesion pathways not only at a cell–cell level but also at the level of cell colonies and suggests that adhesion/separation forces between cells may be lower in cell colonies than traditional isolated single-cell experiments infer.
Inferring Growth Control Mechanisms in Growing Multi-cellular Spheroids of NSCLC Cells from Spatial-Temporal Image Data
- BiologyPLoS Comput. Biol.
- 2016
The findings suggest that this iterative data integration together with intermediate model sensitivity analysis at each model development stage, provide a promising strategy to infer predictive yet minimal quantitative models of tumor growth, as prospectively of other tissue organization processes.
Multi-scale modelling of cancer cell intravasation: the role of cadherins in metastasis.
- BiologyPhysical biology
- 2009
This paper presents one of the first mathematical models considering the problem of cancer cell intravasation, using an individual force-based multi-scale approach which accounts for intra- and inter-cellular protein pathways and for the physical properties of the cells, and a modelling framework which Accounts for the biological shape of the vessel.
Spatio-temporal models of synthetic genetic oscillators.
- BiologyMathematical biosciences and engineering : MBE
- 2017
A model of the canonical GRN (the Hes1 protein) is presented and the effect of varying the spatial location of gene and protein production sites on the oscillations are shown and the approach is extended to examine spatio-temporal models of synthetic gene regulatory networks e.g. n-gene repressilators and activator-repressor systems.