Influence of random malignant cell motility on growing tumor front stability

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List of references:

  1. M. A. Brockmann, U. Ulbricht, K. Gruner, R. Fillbrandt, M. Westphal, K. Lamszus. Glioblastoma and cerebral microvascular endothelial cell migration in response to tumor-associated growth factors // Neurosurgery. — 2003. — V. 52, no. 6. — P. 1391–1399. — DOI: 10.1227/01.NEU.0000064806.87785.AB.
  2. L. A. Truman, C. A. Ogden, S. E. Howie, C. D. Gregory. Macrophage chemotaxis to apoptotic Burkitt's lymphoma cells in vitro: role of CD14 and CD36 // Immunobiology. — 2004. — V. 209, no. 1–2. — P. 21–30. — DOI: 10.1016/j.imbio.2004.02.001.
  3. L. G. Quinones, I. Garcia-Castro. Characterization of human melanoma cell lines according to their migratory properties in vitro // In Vitro Cell Dev Biol Anim. — 2004. — V. 40, no. 1–2. — P. 35–42. — DOI: 10.1290/1543-706X(2004)40<35:COHMCL>2.0.CO;2.
  4. C. S. Patlak. Random walk with persistence and external bias // Bull. of Math. Biophys. — 1953. — V. 15. — P. 311–338. — DOI: 10.1007/BF02476407. — MathSciNet: MR0081586.
  5. E. F. Keller, L. A. Segel. Initiation of slide mold aggregation viewed as an instability // J. Theor. Biol. — 1970. — V. 26. — P. 399–415. — DOI: 10.1016/0022-5193(70)90092-5.
  6. S. Dormann, A. Deutsch. Modeling of self-organized avascular tumor growth with a hybrid cellular automaton // In Silico Biol. — 2002. — V. 2, no. 3. — P. 393–406.
  7. J. M. Stewart, P. Broadbridge, J. M. Goard. Symmetry Analysis and Numerical Modelling of Invasion by Malignant Tumour Tissue // Nonlinear Dynamics. — 2002. — V. 28. — P. 175–193. — DOI: 10.1023/A:1015009016590. — MathSciNet: MR1903274.
  8. 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. — 1997. — no. 11–12. — P. 85–90.
  9. A. V. Kolobov, A. A. Polezhaev, G. I. Solyanik. 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. — Bologna: Progetto Leonardo, 2003. — P. 603–609. — Ed. V. Capasso. — MathSciNet: MR2093305.

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