Free Access
Issue
Math. Model. Nat. Phenom.
Volume 7, Number 1, 2012
Cancer modeling
Page(s) 105 - 135
DOI https://doi.org/10.1051/mmnp/20127106
Published online 25 January 2012
  1. C. Athale, Y. Mansury, T. Deisboeck. Simulating the impact of a molecular ‘decision-process’ on cellular phenotype and multicellular patterns in brain tumors. J. Theor. Biol., 233 (2005), 469–481. [CrossRef] [PubMed] [Google Scholar]
  2. J.P. Boon, D. Dab, R. Kapral, A. Lawniczak. Lattice gas automata for reactive systems. Phys. Rpts., 273 (1996), 55–147. [CrossRef] [MathSciNet] [Google Scholar]
  3. B.M. Caradoc-Davies. Vortex Dynamics in Bose-Einstein Condensates. Ph.D. dissertation, University of Otago, Dunedin, New Zealand (2000). [Google Scholar]
  4. B. Chopard, M. Droz. Cellular Automata Modeling of Physical Systems. Cambridge University Press (1998). [Google Scholar]
  5. A. Deutsch, S. Dormann. Cellular automaton modeling of biological pattern formation. Birkhäuser (2005). [Google Scholar]
  6. S. Fedotov, A. Iomin. Migration and Proliferation Dichotomy in Tumor-Cell Invasion. Phys. Rev. Let., 98 (2007), 118101–4. [CrossRef] [PubMed] [Google Scholar]
  7. C.W. Gardiner. Handbook of stochastic methods. Springer, Berlin (1990). [Google Scholar]
  8. A. Giese, M.A. Loo, N. Tran, D. Haskett, S.W. Coons, M.E. Berens. Dichotomy of astrocytoma migration and proliferation. Int. J. Cancer, 67 (1996), 275–282. [CrossRef] [PubMed] [Google Scholar]
  9. A. Giese, R. Bjerkvig, M.E. Berens, M. Westphal. Cost of Migration : Invasion of Malignant Gliomas and Implications for Treatment. J. Clin. Onc., 21 (8) (2003), 1624–1636. [CrossRef] [PubMed] [Google Scholar]
  10. J. Godlewski, M. Nowicki, A. Bronisz, G. Nuovo, J. Palatini, M. De Lay, J. Van Brocklyn, M. Ostrowski, E. A. Chiocca, S. E. Lawler. MicroRNA-451 regulates LKB1/AMPK signaling and allows adaptation to metabolic stress in glioma cells. Mol. Cell, 37 (2010), 620–32. [CrossRef] [PubMed] [Google Scholar]
  11. H.L.P. Harpold, E.C. Alvord Jr, K.R. Swanson. The evolution of mathematical modeling of glioma proliferation and invasion. J. Neuropathol. Exp. Neurol., 66 (1) (2007), 1–9. [CrossRef] [PubMed] [Google Scholar]
  12. H. Hatzikirou, D. Basanta, M. Simon, C. Schaller, A. Deutsch. ‘Go or Grow’ : the key to the emergence of invasion in tumor progression ? Mathematical Medicine and Biology (Published online July 2010), doi :10.1093/imammb/dqq01. [Google Scholar]
  13. H. Hatzikirou, L. Brusch, A. Deutsch. From cellular automaton rules to an effective macroscopic mean-field description. Acta Phys. Pol. B Proc., 3 (2010), 399–416. [Google Scholar]
  14. H. Hatzikirou, L. Brusch, C. Schaller, M. Simon, A. Deutsch. Prediction of traveling front behavior in a lattice-gas cellular automaton model for tumor invasion. Comput. Math. Appl., 59 (2010), 2326–2339. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  15. M.A. Lewis, G. Schmitz. Biological invasion of an organism with separate mobile and stationary states : Modeling and analysis. Forma, 11 (1996), 1–25. [MathSciNet] [Google Scholar]
  16. Y. Mansury, M. Diggory, T. Deisboeck. Evolutionary game theory in an agent-based brain tumor model : Exploring the ’Genotype-Phenotype’ link. J. Theor. Biol., 238 (2006), 146–156. [CrossRef] [PubMed] [Google Scholar]
  17. K. Pham, A. Chauviere, H. Hatzikirou, X. Li, H. M. Byrne, V. Cristini, J. Lowengrub. Density-dependent quiescence in glioma invasion : instability in a simple reaction-diffusion model for the migration/proliferation dichotomy. J. Biol. Dyn. (Published online June 2011), doi :10.1080/17513758.2011.590610. [Google Scholar]
  18. R.E. Baker, M.J. Simpson. Simulating invasion with cellular automata : connecting cell-scale and population-scale properties. Phys. Rev. E, 76 (2) (2007), 021918. [CrossRef] [Google Scholar]
  19. A.M. Stein, M. O. Nowicki, T. Demuth, M.E. Berens, S.E. Lawler, E.A. Chiocca, L.M. Sander. Estimating the cell density and invasive radius of 3d glioblastoma tumor spheroids grown in vitro. Appl. Optics, 46 (22) (2007), 5110–5118. [CrossRef] [Google Scholar]
  20. A.M. Stein, T. Demuth, D. Mobley, M. Berens, L.K. Sander. A mathematical model of glioblastoma tumor spheroid invasion in a three-dimensional in vitro experiment. Biophys. J., 92 (1) (2007), 356–365. [CrossRef] [PubMed] [Google Scholar]
  21. D. Stockholm, R. Benchaouir, J. Picot, P. Rameau, T.M.A. Neildez, G. Landini, C. Laplace-Builhe, A. Paldi. The origin of phenotypic heterogeneity in a clonal cell population in vitro. PLoS ONE, 4 (2007), 1–13. [Google Scholar]
  22. M. Tektonidis, H. Hatzikirou, A. Chauviere, M. Simmon, K. Schaller, A. Deutsch. Identification of intrinsic in vitro cellular mechanisms for glioma invasion. J. Theor. Biol., 287 (2011), 131–147. [CrossRef] [PubMed] [Google Scholar]
  23. C.H. Wang, J.K. Rockhill, M. Mrugala, D.L. Peacock, A. Lai, K. Jusenius, J.M. Wardlaw, T. Cloughesy, A.M. Spence, R. Rockne, et al. Prognostic significance of growth kinetics in newly diagnosed glioblastomas revealed by combining serial imaging with a novel biomathematical model. Cancer Res., 69 (23) (2009), 9133–9140. [CrossRef] [PubMed] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.