Math. Model. Nat. Phenom.
Volume 6, Number 7, 2011Mathematical modeling in biomedical applications
|Page(s)||27 - 38|
|Published online||15 June 2011|
- A.C. Burton. Rate of growth of solid tumours as a problem of diffusion. Growth, 30 (1966), 157–176. [PubMed] [Google Scholar]
- H. Bueno, G. Ercole, A. Zumpano. Asymptotic behaviour of quasi-stationary solutions of a nonlinear problem modelling the growth of tumours. Nonlinearity, 18 (2005), 1629–1642. [CrossRef] [MathSciNet] [Google Scholar]
- H.M. Byrne, M.A.J. Chaplain. Growth of necrotic tumours in the presence and absence of inhibitors. Math. Biosci., 135 (1996), 187–216. [CrossRef] [PubMed] [Google Scholar]
- S.K. Chintala, J.R. Rao. Invasion of human glioma: role of extracellular matrix proteins. Frontiers in Bioscience, 1 (1996), 324–339. [Google Scholar]
- S. Fedotov, V. Mendez. Continuous-time random walks and traveling fronts. Phys. Rev. E, 66 (2002), 030102. [Google Scholar]
- S. Fedotov, A. Iomin. Migration and Proliferation Dichotomy in Tumor-Cell Invasion. Phys. Rev. Lett., 98 (2007), 118101. [CrossRef] [PubMed] [Google Scholar]
- A. Giese, R. Bjerkvig, M.E. Berens, M. Westphal. Cost of migration: invasion of malignant gliomas and implications for treatment. J. Clinical Oncology, 21 (2003), 1624–1636. [Google Scholar]
- H.P. Greenspan. On the growth and stability of cell cultures and solid tumors. J. Theor. Biol., 56 (1976), 229–242. [Google Scholar]
- A. Gusev, A. Polezhaev. Modelling of a cell population evolution for the case existence of maximal possible total cell density. Kratkie soobscheniya po fizike FIAN, 11-12 (1997), 85–90. [Google Scholar]
- D. Hanahan, R.A. Weinberg. The hallmarks of cancer. Cell, 100 (2000), 57–70. [CrossRef] [PubMed] [Google Scholar]
- A.L. Harris. Hypoxia – a key regulatory factor in tumour growth. Nat. Rev. Cancer, 2 (2002), 38–47. [CrossRef] [PubMed] [Google Scholar]
- H. Hatzikirou, D. Basanta, M. Simon, K. Schaller, A. Deutsch. ’Go or Grow’: the key to the emergence of invasion in tumour progression? Math. Med. Biol., 7 (2010), 1–17. [Google Scholar]
- A. Iomin. Toy model of fractional transport of cancer cells due to self-entrapping. Phys. Rev. E, 73 (2006), 061918. [CrossRef] [Google Scholar]
- A.V. Kolobov, A.A. Polezhaev, G.I. Solyanyk. Stability of tumour shape in pre-angiogenic stage of growth depends on the migration capacity of cancer cells. Mathematical Modelling & Computing in Biology and Medicine (Ed. V. Capasso), 2003, 603–609. [Google Scholar]
- A.K. Laird. Dynamics of tumor growth. Br. J. Cancer, 18 (1964), 490–502. [Google Scholar]
- J.S. Lowengrub, H.B. Frieboes, F. Jin, Y-L. Chuang, X. Li, P. Macklin, S.M. Wise, V. Cristini. Nonlinear modelling of cancer: bridging the gap between cells and tumours. Nonlinearity, 23 (2010), 1–91. [Google Scholar]
- W. van Saarloos. Front propagation into unstable states. Physics Reports, 386 (2003), 29–222. [Google Scholar]
- J.A. Sherratt, M.A.J. Chaplain. A new mathematical model for avascular tumour growth. J. Math. Biol., 43 (2001), 291–312. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- K.R. Swansona, C. Bridge, J.D. Murray, E.C. Alvord Jr. Virtual and real brain tumors: using mathematical modeling to quantify glioma growth and invasion. J. Neurolog. Sci., 216 (2003), 1–10. [CrossRef] [Google Scholar]
- Y. Tao, M. Chen. An elliptic-hyperbolic free boundary problem modelling cancer therapy. Nonlinearity, 19 (2006), 419–440. [CrossRef] [MathSciNet] [Google Scholar]
- R.H. Thomlinson, L.H. Gray. The histological structure of some human lung cancers and the possible implications for radiotherapy. Br. J. Cancer, 9 (1955), 539–549. [CrossRef] [PubMed] [Google Scholar]
- J.P. Ward, J.R. King. Mathematical modelling of avascular-tumour growth. IMA J. Math. Appl. Med. Biol., 14 (1997), 39–69. [CrossRef] [PubMed] [Google Scholar]
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