Mathematical Biosciences and Engineering (MBE)

A therapy inactivating the tumor angiogenic factors
Pages: 185 - 198, Issue 1, February 2013

doi:10.3934/mbe.2013.10.185      Abstract        References        Full text (362.8K)           Related Articles

Cristian Morales-Rodrigo - Departamento de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, Calle Tar a s/n, 41012-Seville, Spain (email)

1 H. Amann, Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems, in "Function Spaces, Differential Operators and Nonlinear Analysis" (editors, H. J. Schmeisser and H. Triebel), Teubner, Stuttgart, Leipzig, (1993), 9-126.       
2 H. Amann and J. López-Gómez, A priori bounds and multiple solutions for superlinear indefinite elliptic problems, J. Differential Equations, 146 (1998), 336-374.       
3 A. R. A. Anderson and M. A. J. Chaplain, Continuous and Discrete Mathematical Models of Tumor-induced Angiogenesis, Bull. Math. Biol., 60 (1998), 857-899.
4 M. A. J. Chaplain and A. M. Stuart, A model mechanism for the chemotactic response of endothelial cells to tumour angiogenesis factor, IMA J. Math. Appl. Med. Biol., 10 (1993), 149-168.
5 M. A. J. Chaplain, Avascular growth, angiogenesis and vascular growth in solid tumours: the mathematical modelling of the stages of tumor development, Math. Comput. Modelling, 23 (1996), 47-87.
6 T. Cieślak and C. Morales-Rodrigo, Long-time behaviour of an angiogenesis model with flux at the tumor boundary, Preprint, arXiv:1202.4695.
7 M. Delgado, I. Gayte, C. Morales-Rodrigo and A. Suárez, An angiogenesis model with nonlinear chemotactic response and flux at the tumor boundary, Nonlinear Anal., 72 (2010), 330-347.       
8 M. Delgado, C. Morales-Rodrigo and A. Suárez, Anti-angiogenic therapy based on the binding receptors, Discrete Contin. Dyn. Syst. Ser A, 32 (2012), 3871-3894.
9 M. Delgado, C. Morales-Rodrigo, A. Suárez and J. I. Tello, On a parabolic-elliptic chemotactic model with coupled boundary conditions, Nonlinear Analysis RWA, 11 (2010), 3884-3902.       
10 M. Delgado and A. Suárez, Study of an elliptic system arising from angiogenesis with chemotaxis and flux at the boundary, J. Differential Equations, 244 (2008), 3119-3150.       
11 M. A. Fontelos, A. Friedman and B. Hu, Mathematical analysis of a model for the initiation of angiogenesis, SIAM J. Math. Anal., 33 (2002), 1330-1350.       
12 J. García-Melián, J. D. Rossi and J. Sabina, Existence and uniqueness of positive solutions to elliptic problems with sublinear mixed boundary conditions, Comm. Comtemporary Math., 11 (2009), 585-613.       
13 D. Henry, "Geometric Theory of Semilinear Parabolic Equations," Lecture Notes Math., 840, Springer 1981.       
14 H. A. Levine, B. D. Sleeman and M. Nilsen-Hamilton, Mathematical modeling of the onset of capillary formation initiating angiogenesis, J. Math. Biol., 42 (2001), 195-238.       
15 D. Manoussaki, A mechanochemical model of angiogenesis and vasculogenesis, ESAIM Math. Modelling Num. Anal., 37 (2003), 581-599.       
16 N. V. Mantzaris, S. Webb and H. G. Othmer, Mathematical modeling of tumor induced angiogenesis, J. Math. Biol., 49 (2004), 111-187.       
17 M. Owen, T. Alarcón, P. K. Maini and H. M. Byrne, Angiogenesis and vascular remodelling in normal and cancerous tissues, J. Math. Biol., 58 (2009), 689-721.       
18 R. M. Sutherland, Cell and environment interactions in tumor microregions: The multicell spheroid model, Science, 240 (1988), 177-184.
19 M. Winkler, Aggregation vs global diffusive behavior in the higher-dimensional Keller-Segel model, J. Differential Equations, 248 (2010), 2889-2905.       

Go to top