Free Access
Math. Model. Nat. Phenom.
Volume 4, Number 3, 2009
Cancer modelling (Part 2)
Page(s) 134 - 155
Published online 05 June 2009
  1. B.P. Ayati, G.F. Webb, A.R.A Anderson. Computational methods and results for structured mutliscale methods of tumor invasion. Multiscale Model. Simul., 5 (2006), 1–20. [CrossRef] [MathSciNet] [Google Scholar]
  2. H.M. Byrne. The importance of intercellular adhesion in the development of carcinomas. I. MA J. Math. Appl. Med. Biol., 14 (1997), 305–323. [CrossRef] [Google Scholar]
  3. H.M. Byrne, M.A.J. Chaplain. Growth of nonnecrotic tumors in the presence and absence of inhibitors. Math. Biosci., 130 (1995), 130–151. [Google Scholar]
  4. H.M. Byrne, M.A.J. Chaplain. Modelling the role of cell-cell adhesion in the growth and development of carcinomas. Math. Comput. Modeling, 24 (1996), 1–17. [CrossRef] [Google Scholar]
  5. X. Chen, S. Cui, A. Friedman. A hyperbolic free boundary problem modeling tumor growth: Asymptotic behavior. Trans. Amer. Math. Soc., 357 (2005), 4771–4804. [CrossRef] [MathSciNet] [Google Scholar]
  6. X. Chen, A. Friedman. A free boundary problem for elliptic-hyperbolic system: An application to tumor growth. SIAM J. Math. Anal., 35 (2003), 974–986. [CrossRef] [MathSciNet] [Google Scholar]
  7. S. Cui, A. Friedman. A free boundary problem for a singular system of differential equations: An application to a model of tumor growth. Trans. Amer. Math. Soc., 355 (2003), 3537–3590. [CrossRef] [MathSciNet] [Google Scholar]
  8. S. Cui, A. Friedman. A hyperbolic free boundary problem modeling tumor growth. Interfaces Free Bound., 5 (2003) , 159–182. [Google Scholar]
  9. S.J.H. Franks, H.M. Byrne, J.P. King, J.C.E. Underwood, C.E. Lewis. Modelling the early growth of ductal carcinoma in situ of the breast. J. Math. Biology, 47 (2003), 424–452. [Google Scholar]
  10. S.J.H. Franks, H.M. Byrne, J.P. King, J.C.E. Underwood, C.E. Lewis. Modelling the growth of comedo ductal carcinoma in situ. Mathematical Medicine & Biology, 20 (2003), 277–308. [Google Scholar]
  11. S.J.H. Franks, H.M. Byrne, J.C.E. Underwood, C.E. Lewis. Biological inferences from a mathematical model of comedo ductal carcinoma in situ of the breast. J. Theoretical Biology, 232 (2005), 523–543. [Google Scholar]
  12. S.J.H. Franks, J.P. King. Interactions between a uniformly proliferating tumour and its surroundings: Uniform material properties. Mathematical Medicine & Biology, 20 (2003), 47–89. [Google Scholar]
  13. A. Friedman. Cancer models and their mathematical analysis. In: Tutorials in Mathematical Biosciences III. Lecture Notes in Mathematics, 1872, 223-246. Springer, Berlin, 2006. [Google Scholar]
  14. A. Friedman. A free boundary problem for a coupled system of elliptic, hyperbolic, and Stokes equations modeling tumor growth. Interfaces and Free Boundaries, 8 (2006), 247–261. [Google Scholar]
  15. A. Friedman. Mathematical analysis and challenges arising from models of tumor growth. Math. Models & Methods in Applied Sciences, 17 (2007), 1751–1772. [CrossRef] [Google Scholar]
  16. A. Friedman. A multiscale tumor model. Interfaces and Free Boundaries, 10 (2008), 245–262. [Google Scholar]
  17. A. Friedman, B. Hu. The role of oxygen in tissue maintenance: Mathematical modeling and qualitative analysis. Math. Mod. Meth. Appl. Sci., 18 (2008), 1–33. [CrossRef] [Google Scholar]
  18. A. Friedman, B. Hu, C-Y. Kao. Cell cycle control at the first restriction point and its effect on tissue growth. Submitted for publication. [Google Scholar]
  19. A. Friedman, F. Reitich. Quasi-static motion of a capillary drop, II: The three-dimensional case. J. Diff. Eqs., 186 (2002), 509–557. [CrossRef] [Google Scholar]
  20. Y. Jiang, J. Pjesivac-Grbovic, C. Cantrell, J.P. Freyer. A multiscale model for avascular tumor growth. Biophysical Journal, 89 (2005), 3884–3894. [Google Scholar]
  21. N. Komaraova. Stochastic modeling of loss- and gain-of-function mutation in cancer. Bull. Math. Biology, 17 (2007), 1647–1673. [Google Scholar]
  22. H.A. Levine, S.L. Pamuk, B.D. Sleeman, M. Nilsen-Hamilton. Mathematical modeling of capillary formation and development in tumor angiogenesis: penetration into the stroma. Bull. Math. Biology, 63 (2001), 801–863. [Google Scholar]
  23. G. Lolas. Mathematical modelling of proteolysis and cancer cell invasion of tissue. In: Tutorials in Mathematical Biosciences III, Lecture Notes in Mathematics, 1872, 77–130. Springer, Berlin, 2006. [Google Scholar]
  24. N. Mantzaris, S. Webb, H.G. Othmer. Mathematical modeling of tumor-induced angiogenesis. J. Math. Biol., 49 (2004), 87–111. [Google Scholar]
  25. M.A. Nowak, K. Sigmund. Evolutionary dynamics of biological games. Science, 303 (2004), 793–799. [CrossRef] [PubMed] [Google Scholar]
  26. G.J. Pettet, C.P. Please, M.J. Tindall, D.L.S. McElwain. The migration of cells in multicell tumor spheroids. Bull. Math. Biol., 63 (2001), 231–257. [CrossRef] [PubMed] [Google Scholar]
  27. R. Ribba, T. Colin, S. Schnell. A multiscale model of cancer, and its use in analyzing irradiation therapies. Theoretical Biology and Medical Modeling, 3 (2006), No. 7, 1–19. [Google Scholar]
  28. V.A. Solonnikov. On quasistationary approximation in the problem of a capillary drop. In: J. Escher & G. Simonett (Eds.), Progress in Nonlinear Differential Equations and Their Applications, 35, 643-671. Birkhäuser Verlag, Basel, 1999. [Google Scholar]
  29. M.M. Vainberg, V.A. Trenogin. Theory of branching solutions of non-linear equations. Nordhoff International Publishing, Leyden, 1974. [Google Scholar]

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