Free Access
Issue |
Math. Model. Nat. Phenom.
Volume 15, 2020
Cancer modelling
|
|
---|---|---|
Article Number | 22 | |
Number of page(s) | 29 | |
DOI | https://doi.org/10.1051/mmnp/2019039 | |
Published online | 18 March 2020 |
- D. Ambrosi and L. Preziosi, Cell adhesion mechanisms and stress relaxation in the mechanics of tumours. Biomech. Model. Mechanobiol. 8 (2009) 397–413. [CrossRef] [PubMed] [Google Scholar]
- R.P. Araujo and D.L.S. McElwain, A mixture theory for the genesis of residual stresses in growing tissues I: a general formulation. SIAM J. Appl. Math. 65 (2005) 1261–1284. [Google Scholar]
- R.P. Araujo and D.L.S. McElwain, A mixture theory for the genesis of residual stresses in growing tissues II: solutions to the biphasic equations for a multicell spheroid. SIAM J. Appl. Math. 66 (2005) 447–467. [Google Scholar]
- J.A. Bertout, S.A. Patel and M.C. Simon, The impact of O2 availability on human cancer. Nat. Rev. Cancer 8 (2008) 967–975. [Google Scholar]
- C.J. Breward, H.M. Byrne and C.E. Lewis, The role of cell–cell interactions in a two-phase model for a vascular tumour growth. J. Math. Biol. 45 (2002) 125–152. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- J.M. Brown and A.J. Giaccia, The unique physiology of solid tumors: opportunities (and problems) for cancer therapy. Cancer Res. 58 (1998) 1408–1416. [Google Scholar]
- H. Byrne and M. Chaplain, Necrosis and apoptosis: distinct cell loss mechanisms in a mathematical model of avascular tumour growth. J. Theor. Med. 1 (1998) 223–235. [CrossRef] [Google Scholar]
- H.M. Byrne, J.R. King, D.L.S. McElwain and L. Preziosi, A two-phase model of solid tumour growth. Appl. Math. Lett. 16 (2003) 567–573. [Google Scholar]
- P. Carmeliet and R.K. Jain, Angiogenesis in cancer and other diseases. Nature 407 (2000) 249–257. [Google Scholar]
- E.J. Crampin, E.A. Gaffney and P.K. Maini, Reaction and diffusion on growing domains: scenarios for robust pattern formation. Bull. Math. Biol. 61 (1999) 1093–1120. [Google Scholar]
- M.J. Dorie, R.F. Kallman, D.F. Rapacchietta, D. Van Antwerp and Y.R. Huang, Migration and internalization of cells and polystyrenemicrospheres in tumor cell spheroids. Exp. Cell Res. 141 (1982) 201–209. [PubMed] [Google Scholar]
- D. Eriksson and T. Stigbrand, Radiation-induced cell death mechanisms. Tumor Biol. 31 (2010) 363–372. [CrossRef] [Google Scholar]
- J. Folkman, Self-regulation of growth in three dimensions. J. Exp. Med. 138 (1973) 745–753. [CrossRef] [PubMed] [Google Scholar]
- H. Greenspan, Models for the growth of a solid tumor by diffusion. Stud. Appl. Math. L1 (1972) 317–340. [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]
- D.R. Grimes, C. Kelly, K. Bloch and M. Partridge, A method for estimating the oxygen consumption rate in multicellular tumour spheroids. J. Roy. Soc. Interface 11 (2014) 20131124. [CrossRef] [Google Scholar]
- D. Hanahan and R.A. Weinberg, The hallmarks of cancer. Cell 100 (2000) 57–70. [CrossRef] [PubMed] [Google Scholar]
- D. Hanahan and R.A. Weinberg, Hallmarks of cancer: the next generation. Cell 144 (2011) 646–674. [CrossRef] [PubMed] [Google Scholar]
- F. Hirschhaeuser, H. Menne, C. Dittfeld, J. West, W. Mueller-Klieser and L.A. Kunz-Schughart, Multicellular tumor spheroids: an underestimated tool is catching up again. J. Biotechnol. 148 (2010) 3–15. [Google Scholar]
- M.E. Hubbard and H.M. Byrne, Multiphase modelling of vascular tumour growth in two spatial dimensions. J. Theor. Biol. 316 (2013) 70–89. [CrossRef] [PubMed] [Google Scholar]
- K.A. Landman and C.P. Please, Tumour dynamics and necrosis: surface tension and stability. IMA J. Math. Appl. Med. Biol. 18 (2001) 131–158. [Google Scholar]
- G. Lemon and J.R. King, Travelling-wave behaviour in a multiphase model of a population of cells in an artificial scaffold. J. Math. Biol. 55 (2007) 449–480. [Google Scholar]
- G. Lemon, J.R. King, H.M. Byrne, O.E. Jensen and K.M. Shakesheff, Mathematical modelling of engineered tissue growth using a multiphase porous flow mixture theory. J. Math. Biol. 52 (2006) 571–594. [CrossRef] [PubMed] [Google Scholar]
- R.J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations. Society for Industrial and Applied Mathematics (2007). [CrossRef] [Google Scholar]
- T.D. Lewin, P.K. Maini, E.G. Moros, H. Enderling and H.M. Byrne, The evolution of tumour composition during fractionated radiotherapy: implications for outcome. Bull. Math. Biol. 80 (2018) 1207–1235. [Google Scholar]
- M. Massoudi, Boundary conditions in mixture theory and in CFD applications of higher order models. Comput. Math. Appl. 53 (2007) 156–167. [Google Scholar]
- R.D. O’Dea, M.R. Nelson, A.J. El Haj, S.L. Waters and H.M. Byrne, A multiscale analysis of nutrient transport and biological tissue growth in vitro. Math. Med. Biol. 32 (2015) 345–366. [Google Scholar]
- H. Okada and T.W. Mak, Pathways of apoptotic and non-apoptotic death in tumour cells. Nat. Rev. Cancer 4 (2004) 592–603. [Google Scholar]
- L. Preziosi and A. Tosin, Multiphase modelling of tumour growth and extracellular matrix interaction: mathematical tools and applications. J. Math. Biol. 58 (2009) 625–656. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- S. Prokopiou, E.G. Moros, J. Poleszczuk, J. Caudell, J.F. Torres-Roca, K. Latifi, J.K. Lee, R. Myerson, L.B. Harrison and H. Enderling, A proliferation saturation index to predict radiation response and personalize radiotherapy fractionation. Radiat. Oncol. 10 (2015) 159. [CrossRef] [PubMed] [Google Scholar]
- S. Proskuryakov and V. Gabai, Mechanisms of tumor cell necrosis. Curr. Pharm. Des. 16 (2010) 56–68. [CrossRef] [PubMed] [Google Scholar]
- L. Tao and K.R. Rajagopal, On Boundary Conditions In Mixture Theory (1995) 130–149. [Google Scholar]
- J.P. Ward and J.R. King, Mathematical modelling of avascular-tumour growth. IMA J. Math. Appl. Med. Biol. 14 (1997) 39–69. [Google Scholar]
- J.P. Ward and J.R. King, Mathematical modelling of avascular-tumour growth. II: Modelling growth saturation. IMA J. Math. Appl. Med. Biol. 16 (1999) 171–211. [Google Scholar]
- L.-B. Weiswald, D. Bellet and V. Dangles-Marie, Spherical cancer models in tumor biology. Neoplasia 17 (2015) 1–15. [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.