Density-dependent quiescence in glioma invasion: instability in a simple reaction–diffusion model for the migration/proliferation dichotomy
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Helen M. Byrne | Vittorio Cristini | Haralambos Hatzikirou | John Lowengrub | Xiangrong Li | Arnaud Chauviere | Xiangrong Li | V. Cristini | J. Lowengrub | H. Byrne | A. Chauviere | H. Hatzikirou | K. Pham | Kara Pham
[1] M. Abercrombie,et al. The Croonian Lecture, 1978 - The crawling movement of metazoan cells , 1980, Proceedings of the Royal Society of London. Series B. Biological Sciences.
[2] T. Roberts,et al. Cell Density Modulates Protein-tyrosine Phosphorylation* , 1998, The Journal of Biological Chemistry.
[3] H. Frieboes,et al. Nonlinear modelling of cancer: bridging the gap between cells and tumours , 2010, Nonlinearity.
[4] N. Rashevsky,et al. Mathematical biology , 1961, Connecticut medicine.
[5] Pier Paolo Delsanto,et al. Insights from a novel tumor model: Indications for a quantitative link between tumor growth and invasion. , 2003, Medical hypotheses.
[6] A. Páldi,et al. Epigenetic gene expression noise and phenotypic diversification of clonal cell populations. , 2008, Differentiation; research in biological diversity.
[7] T. Hillen. Transport equations with resting phases , 2003, European Journal of Applied Mathematics.
[8] Jonathan A. Sherratt,et al. Oscillations and chaos behind predator–prey invasion: mathematical artifact or ecological reality? , 1997 .
[9] Leonard M. Sander,et al. A model for glioma growth , 2005, Complex..
[10] K. Schaller,et al. 'Go or grow': the key to the emergence of invasion in tumour progression? , 2012, Mathematical medicine and biology : a journal of the IMA.
[11] C. Schaller,et al. MATHEMATICAL MODELLING OF GLIOBLASTOMA TUMOUR DEVELOPMENT: A REVIEW , 2005 .
[12] K. P. Hadeler,et al. SPATIAL DYNAMICS OF THE DIFFUSIVE LOGISTIC EQUATION WITH A SEDENTARY COMPARTMENT , 2004 .
[13] P. Tracqui. From passive diffusion to active cellular migration in mathematical models of tumour invasion , 1995, Acta biotheoretica.
[14] J. Murray,et al. Virtual and real brain tumors: using mathematical modeling to quantify glioma growth and invasion , 2003, Journal of the Neurological Sciences.
[15] Thomas S Deisboeck,et al. Evolutionary game theory in an agent-based brain tumor model: exploring the 'Genotype-Phenotype' link. , 2006, Journal of theoretical biology.
[16] M. Westphal,et al. Cost of migration: invasion of malignant gliomas and implications for treatment. , 2003, Journal of clinical oncology : official journal of the American Society of Clinical Oncology.
[17] H. Byrne. Dissecting cancer through mathematics: from the cell to the animal model , 2010, Nature Reviews Cancer.
[18] Jonathan A. Sherratt,et al. Periodic travelling waves in cyclic predator–prey systems , 2001 .
[19] L. Sander,et al. Dynamics and pattern formation in invasive tumor growth. , 2005, Physical review letters.
[20] A. Iomin,et al. Migration and proliferation dichotomy in tumor-cell invasion. , 2006, Physical review letters.
[21] Michael Berens,et al. A mathematical model of glioblastoma tumor spheroid invasion in a three-dimensional in vitro experiment. , 2007, Biophysical journal.
[22] S. Leibler,et al. Phenotypic Diversity, Population Growth, and Information in Fluctuating Environments , 2005, Science.
[23] M. Owen,et al. Oscillatory dynamics in a model of vascular tumour growth - implications for chemotherapy , 2010, Biology Direct.
[24] Steven M. Wise,et al. Solving the regularized, strongly anisotropic Cahn-Hilliard equation by an adaptive nonlinear multigrid method , 2007, J. Comput. Phys..
[25] Mark A J Chaplain,et al. Mathematical modelling of the spatio-temporal response of cytotoxic T-lymphocytes to a solid tumour. , 2004, Mathematical medicine and biology : a journal of the IMA.
[26] Thomas S Deisboeck,et al. Simulating the impact of a molecular 'decision-process' on cellular phenotype and multicellular patterns in brain tumors. , 2004, Journal of theoretical biology.
[27] L. Preziosi,et al. A model of cell migration within the extracellular matrix based on a phenotypic switching mechanism. , 2010, Mathematical medicine and biology : a journal of the IMA.
[28] K. Schaller,et al. Identification of intrinsic in vitro cellular mechanisms for glioma invasion. , 2011, Journal of theoretical biology.
[29] G. Schmitz,et al. Biological Invasion of an Organism with Separate Mobile and Stationary States : Modeling and Analysis , 1996 .