Mathematical Model of the Biological Environment, Taking into Account the Active Interactions and Mutual Movements of its Constituent Cells

Publication type Article
Status Published
Journal nameIzvestiia Rossiiskoi akademii nauk. Mekhanika zhidkosti i gaza
EditionIssue 5


Publication date24.11.2018
Number of characters1175
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1. Armstrong N. J., Painter K. J., Sherratt J. A. A continuum approach to modelling cell–cell adhesion // J. Theor. Biol. 2006. V. 243. № 1. P. 98–113.

2. Domschke P., Trucu D., Gerisch A., Chaplain M. Mathematical modelling of cancer invasion: Implications of cell adhesion variability for tumour infiltrative growth patterns // J. Theor. Biol. 2014. V. 361. P. 41–60.

3. Gerisch A., Chaplain M. A.J. Mathematical modelling of cancer cell invasion of tissue: Local and nonlocal models and the effect of adhesion // J. Theor. Biol. 2008. V. 250. № 4. P. 684–704.

4. Painter K. J., Armstrong N. J., Sherratt J. A. The impact of adhesion on cellular invasion processes in cancer and development // J. Theor. Biol. 2010. V. 264. № 3. P. 1057–1067.

5. Preziosi L., Tosin A. Multiphase modeling of tumor growth and extracellular matrix interaction: Mathematical tools and applications // J. Math. Biol. 2009. V. 58. P. 625–656.

6. Arduino A., Preziosi L. A multiphase model of tumour segregation in situ by a heterogeneous extracellular matrix // Internat. J. Non-lin. Mech. 2015. V. 75. P. 22–30.

7. Giverso C, Scianna M, Grillo A. Growing avascular tumours as elasto-plastic bodies by the theory of evolving natural configurations // Mech. Res. Commun. 2015. V. 68. P. 31–39.

8. Jackson T. L., Byrne H. M. A mechanical model of tumor encapsulation and transcapsular spread // Math. Biosciences. 2002. V. 180. P. 307–328.

9. Byrne H., Preziosi L. Modelling solid tumour growth using the theory of mixtures // Math. Med. Biol. 2003. V. 20. P. 341–366.

10. Green J. E., Waters S. L., Shakesheff K. M., Byrne H. M. A mathematical model of liver cell aggregation in vitro // Bull. Math. Biol. 2009. V. 71. P. 906–930.

11. Lemon G., King J. R., Byrne H. M., Jensen O. E., Shakesheff K. M. Mathematical modelling of engineered tissue growth using a multiphase porous flow mixture theory // J. Math. Biol. 2006. V. 52. P. 571–594.

12. O’Dea R. D., Waters S. L., Byrne H. M. A multiphase model for tissue construct growth in a perfusion bioreactor // Math. Med. Biol. 2010. V. 27. № 2. P. 95–127.

13. Oster G. F., Murray J. D., Harris A. K. Mechanical aspects of mesenchymal morphogenesis // J. Embriol. Exp. Morph. 1983. V. 78. P. 83–125.

14. Dyson R. J., Green J. E.F., Whiteley J. P., Byrne H. M. An investigation of the influence of extracellular matrix anisotropy and cell–matrix interactions on tissue architecture // J. Math. Biol. 2016. V. 72. № 7. P. 1775–1809.

15. Davidson L. A., Joshi S. D., Kim H. Y., Dassow M., Zhang L., Zhou J. Emergent morphogenesis: elastic mechanics of a self-deforming tissue // J. Biomech. 2010. V. 43. № 1. P. 63–70.

16. Belousov L. V., Logvenkov S. A., Shtejn A. A. Matematicheskaya model' aktivnoj biologicheskoj sploshnoj sredy s uchetom deformatsij i pereupakovki kletok // Izv.RAN. MZhG. 2015. №№ 1. S. 3–14.

17. Logvenkov S. A., Shtejn A. A. Matematicheskaya model' prostranstvennoj samoorganizatsii v mekhanicheski aktivnoj kletochnoj srede // Biofizika. 2017. T. 6. № 2. S. 1123–1133.

18. Kizilova N. N., Logvenkov S. A., Shtejn A. A. Matematicheskoe modelirovanie transportno-rostovykh protsessov v mnogofaznykh biologicheskikh sploshnykh sredakh // Izv. RAN. MZhG. 2012. № 1. S. 3–13.

19. Tracqui P. Biophysical models of tumour growth // Rep. Prog. Phys. 2009. V. 72. № 5. P. 056701.

20. Vlahinic I., Jennings H. M., Andrade J. E., Thomas J. J. A novel and general form of effective stress in a partially saturated porous material: The influence of microstructure // Mech. Mater. 2011. V. 43. P. 25–35.

21. Nigmatulin R. I. Osnovy mekhaniki geterogennykh sred. M: Nauka, 1978. 336 s.

22. Drew D. A., Segel L. A. Averaged equations for two-phase flows // Stud. Appl. Math. 1971. V. 50. № 3. P. 205–231.

23. Samarskij A. A. Teoriya raznostnykh skhem // M.: Nauka, 1977. 656 s.

24. Samarskij A. A., Vabischevich P. N. Raznostnye skhemy dlya uravneniya perenosa // Dif. uravn. 1998. T. 34. № 12. S. 1675–1685.

25. Gerhart J. C. Mechanisms regulating pattern formation in the amphibian egg and early embryo // In: Biological Regulation and Development, Goldberger R. (ed), New York: Plenum Press, 1980. V. 2. P. 133–316.

26. White M. D., Zenker J., Bissiere S., Plachta N. How cells change shape and position in the early mammalian embryo // Curr. Opin. Cell Biol. 2017. V. 44. P. 7–13.

27. Fierro-Gonzalez J.C., White M. D., Silva1 J.C., Plachta N. Cadherin-dependent filopodia control preimplantation embryo compaction // Nat. Cell. Biol. 2013. V.15. № 12. P. 1424–1433.

28. Fleming T. P., Butler E., Collins J., Sheth B., Wild A. E. Cell polarity and mouse early development // Adv. Mol. and Cell Biol. 1998. V. 26. P. 67–94.

29. Gilbert S. F. Developmental Biology/ 6th Ed. Sunderland, Mass.: Sinauer Associates, 2000. 749 p.

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