Non-Markovian models for migration-proliferation dichotomy of cancer cells: Anomalous switching and spreading rate / Fedotov Sergei,Iomin Alexander,Ryashko Lev // PHYSICAL REVIEW E. - 2011. - V. 84, l. 6, 1.

ISSN/EISSN:

1539-3755 / нет данных

Type:

Article

Abstract:

Proliferation and migration dichotomy of the tumor cell invasion is examined within two non-Markovian models. We consider the tumor spheroid, which consists of the tumor core with a high density of cells and the outer invasive zone. We distinguish two different regions of the outer invasive zone and develop models for both zones. In model I we analyze the near-core-outer region, where biased migration away from the tumor spheroid core takes place. We suggest non-Markovian switching between the migrating and proliferating phenotypes of tumor cells. Nonlinear master equations for mean densities of cancer cells of both phenotypes are derived. In anomalous switching case we estimate the average size of the near-core-outer region that corresponds to sublinear growth < r(t)> similar to t(mu) for 0 < mu < 1. In model II we consider the outer zone, where the density of cancer cells is very low. We suggest an integrodifferential equation for the total density of cancer cells. For proliferation rate we use the classical logistic growth, while the migration of cells is subdiffusive. The exact formulas for the overall spreading rate of cancer cells are obtained by a hyperbolic scaling and Hamilton-Jacobi techniques.

Author keywords:

MATHEMATICAL-MODEL; FRONT PROPAGATION; INVASION; DIFFUSION; DYNAMICS; GROWTH; MULTISCALE; MECHANISMS; TUMORS

DOI:

10.1103/PhysRevE.84.061131

Web of Science ID:

ISI:000298669200002

Соавторы в МНС:

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Другие поля

Поле	Значение
Month	DEC 19
Publisher	AMER PHYSICAL SOC
Address	ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA
Language	English
Article-Number	061131
Keywords-Plus	MATHEMATICAL-MODEL; FRONT PROPAGATION; INVASION; DIFFUSION; DYNAMICS; GROWTH; MULTISCALE; MECHANISMS; TUMORS
Research-Areas	Physics
Web-of-Science-Categories	Physics, Fluids \& Plasmas; Physics, Mathematical
ResearcherID-Numbers	Fedotov, Sergei/H-5880-2012
Funding-Acknowledgement	Israel Science Foundation {[}GammaK N02-740-11-5172]
Funding-Text	This research was supported in part by the Israel Science Foundation and by Grant No. Gamma K N02-740-11-5172, ``Anomalous transport in biological and chemical systems.{''}
Number-of-Cited-References	55
Usage-Count-Last-180-days	1
Usage-Count-Since-2013	4
Journal-ISO	Phys. Rev. E
Doc-Delivery-Number	870KW