Autowaves in the Model of Infiltrative Tumour Growth with Migration-Proliferation Dichotomy
A.V. Kolobov; V.V. Gubernov; A.A. Polezhaev
Mathematical Modelling of Natural Phenomena (2011)
- Volume: 6, Issue: 7, page 27-38
- ISSN: 0973-5348
Access Full Article
top
Abstract
topHow to cite
topKolobov, A.V., Gubernov, V.V., and Polezhaev, A.A.. "Autowaves in the Model of Infiltrative Tumour Growth with Migration-Proliferation Dichotomy." Mathematical Modelling of Natural Phenomena 6.7 (2011): 27-38. <http://eudml.org/doc/222432>.
@article{Kolobov2011,
abstract = {A mathematical model of infiltrative tumour growth is investigated taking into account transitions between two possible states of malignant cells: proliferation and migration. These transitions are considered to depend on oxygen level in a threshold manner where high oxygen concentration allows cell proliferation, while concentration below a certain critical value induces cell migration. The infiltrative tumour spreading rate dependence on model parameters is obtained. It is shown that the tumour growth rate depends on the tissue oxygen level in a threshold manner.},
author = {Kolobov, A.V., Gubernov, V.V., Polezhaev, A.A.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {tumor growth; proliferation and migration dichotomy; oxygen},
language = {eng},
month = {6},
number = {7},
pages = {27-38},
publisher = {EDP Sciences},
title = {Autowaves in the Model of Infiltrative Tumour Growth with Migration-Proliferation Dichotomy},
url = {http://eudml.org/doc/222432},
volume = {6},
year = {2011},
}
TY - JOUR
AU - Kolobov, A.V.
AU - Gubernov, V.V.
AU - Polezhaev, A.A.
TI - Autowaves in the Model of Infiltrative Tumour Growth with Migration-Proliferation Dichotomy
JO - Mathematical Modelling of Natural Phenomena
DA - 2011/6//
PB - EDP Sciences
VL - 6
IS - 7
SP - 27
EP - 38
AB - A mathematical model of infiltrative tumour growth is investigated taking into account transitions between two possible states of malignant cells: proliferation and migration. These transitions are considered to depend on oxygen level in a threshold manner where high oxygen concentration allows cell proliferation, while concentration below a certain critical value induces cell migration. The infiltrative tumour spreading rate dependence on model parameters is obtained. It is shown that the tumour growth rate depends on the tissue oxygen level in a threshold manner.
LA - eng
KW - tumor growth; proliferation and migration dichotomy; oxygen
UR - http://eudml.org/doc/222432
ER -
References
top- A.C. Burton. Rate of growth of solid tumours as a problem of diffusion. Growth, 30 (1966), 157–176.
- 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.
- H.M. Byrne, M.A.J. Chaplain. Growth of necrotic tumours in the presence and absence of inhibitors. Math. Biosci., 135 (1996), 187–216.
- S.K. Chintala, J.R. Rao. Invasion of human glioma: role of extracellular matrix proteins. Frontiers in Bioscience, 1 (1996), 324–339.
- S. Fedotov, V. Mendez. Continuous-time random walks and traveling fronts. Phys. Rev. E, 66 (2002), 030102.
- S. Fedotov, A. Iomin. Migration and Proliferation Dichotomy in Tumor-Cell Invasion. Phys. Rev. Lett., 98 (2007), 118101.
- 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.
- H.P. Greenspan. On the growth and stability of cell cultures and solid tumors. J. Theor. Biol., 56 (1976), 229–242.
- 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.
- D. Hanahan, R.A. Weinberg. The hallmarks of cancer. Cell, 100 (2000), 57–70.
- A.L. Harris. Hypoxia – a key regulatory factor in tumour growth. Nat. Rev. Cancer, 2 (2002), 38–47.
- 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.
- A. Iomin. Toy model of fractional transport of cancer cells due to self-entrapping. Phys. Rev. E, 73 (2006), 061918.
- 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.
- A.K. Laird. Dynamics of tumor growth. Br. J. Cancer, 18 (1964), 490–502.
- 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.
- W. van Saarloos. Front propagation into unstable states. Physics Reports, 386 (2003), 29–222.
- J.A. Sherratt, M.A.J. Chaplain. A new mathematical model for avascular tumour growth. J. Math. Biol., 43 (2001), 291–312.
- K.R. Swansona, C. Bridge, J.D. Murray, E.C. AlvordJr. Virtual and real brain tumors: using mathematical modeling to quantify glioma growth and invasion. J. Neurolog. Sci., 216 (2003), 1–10.
- Y. Tao, M. Chen. An elliptic-hyperbolic free boundary problem modelling cancer therapy. Nonlinearity, 19 (2006), 419–440.
- 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.
- J.P. Ward, J.R. King. Mathematical modelling of avascular-tumour growth. IMA J. Math. Appl. Med. Biol., 14 (1997), 39–69.
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.