ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Semenova N. И., Tuchin V. V. Impact of osmotic pressure on cancer cells in a three-dimensional cellular lattice and cell spheroid. Izvestiya VUZ. Applied Nonlinear Dynamics, 2021, vol. 29, iss. 4, pp. 559-570. DOI: 10.18500/0869-6632-2021-29-4-559-570

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
PDF icon semenova.pdf
(downloads: 732)
Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
530.182, 616.5-006
DOI: 
10.18500/0869-6632-2021-29-4-559-570

Impact of osmotic pressure on cancer cells in a three-dimensional cellular lattice and cell spheroid

Autors: 
Semenova Nadezhda Игоревна, Saratov State University
Tuchin Valerij Viktorovich, Saratov State University
Abstract: 

The purpose of this work is to study the peculiarities of external influence, namely osmotic pressure, on cancer cells. Methods. For this purpose, spatially distributed systems describing the dynamics of a three-dimensional cell lattice, a cell spheroid, and a cell surface have been considered. The studied models are based on the basic principles of hydrodynamics, and their numerical simulation has been performed using a modified Euler method. Results. The paper proposes three-dimensional models to study the dynamics of cancer cells in the epidermal layer of the skin; the models include the possibility of adding additional pressure and changing it with a single parameter. It is shown that it is possible to achieve a slowdown of cancer cell growth in all considered models at certain values of osmotic pressure.

Key words: 
cancer cells
cellular lattice
cell spheroid
self-organizing
osmotic pressure
logistic growth
Acknowledgments: 
This study is supported by the grant of RF Government No. 14.Z50.31.0044
Reference: 
  1. Murray JD. Mathematical Biology. Berlin, Heidelberg: Springer-Verlag; 1993. 770 p. DOI: 10.1007/978-3-662-08542-4.
  2. Prigogine I, Nicolis G. Self-Organisation in Nonequilibrium Systems: Towards A Dynamics of Complexity. In: Hazewinkel M, Jurkovich R, Paelinck JHP, editors. Bifurcation Analysis. Dordrecht: Springer; 1985. P. 3–12. DOI: 10.1007/978-94-009-6239-2_1.
  3. Turing AM. The chemical basis of morphogenesis. Phil. Trans. R. Soc. Lond. B. 1952;237(641): 37–72. DOI: 10.1098/rstb.1952.0012.
  4. Maini PK. Hierarchical models for spatial pattern formation in biology. Journal of Biological Systems. 1995;3(4):987–997. DOI: 10.1142/S0218339095000885.
  5. Murray JD, Cook J, Tyson R, Lubkin SR. Spatial pattern formation in biology: I. Dermal wound healing. II. Bacterial patterns. Journal of the Franklin Institute. 1998;335(2):303–332. DOI: 10.1016/S0016-0032(97)00034-3.
  6. Scarabotti P, Govezensky T, Bolcatto P, Barrio RA. Universal model for the skin colouration patterns of neotropical catfishes of the genus Pseudoplatystoma. Sci. Rep. 2020;10(1):12445. DOI: 10.1038/s41598-020-68700-0.
  7. Clarke MA, Fisher J. Executable cancer models: successes and challenges. Nat. Rev. Cancer. 2020;20(6):343–354. DOI: 10.1038/s41568-020-0258-x.
  8. Karolak A, Markov DA, McCawley LJ, Rejniak KA. Towards personalized computational oncology: from spatial models of tumour spheroids, to organoids, to tissues. J. R. Soc. Interface. 2018;15(138):20170703. DOI: 10.1098/rsif.2017.0703.
  9. Metzcar J, Wang Y, Heiland R, Macklin P. A review of cell-based computational modeling in cancer biology. JCO Clinical Cancer Informatics. 2019;3(3):1–13. DOI: 10.1200/CCI.18.00069.
  10. Voutouri C, Stylianopoulos T. Evolution of osmotic pressure in solid tumors. J. Biomech. 2014;47(14):3441–3447. DOI: 10.1016/j.jbiomech.2014.09.019.
  11. Cheng G, Tse J, Jain RK, Munn LL. Micro-environmental mechanical stress controls tumor spheroid size and morphology by suppressing proliferation and inducing apoptosis in cancer cells. PLoS ONE. 2009;4(2):e4632. DOI: 10.1371/journal.pone.0004632.
  12. Tse JM, Cheng G, Tyrrell JA, Wilcox-Adelman SA, Boucher Y, Jain RK, Munn LL. Mechanical compression drives cancer cells toward invasive phenotype. Proceedings of the National Academy of Sciences of the United States of America. 2012;109(3):911–916. DOI: 10.1073/pnas.1118910109.
  13. La Porta CAM, Ghilardi A, Pasini M, Laurson L, Alava MJ, Zapperi S, Ben Amar M. Osmotic stress affects functional properties of human melanoma cell lines. Eur. Phys. J. Plus. 2015;130(4):64. DOI: 10.1140/epjp/i2015-15064-x.
  14. Macklin P, Edgerton ME. Discrete cell modelling. In: Cristini V, Lowengrub J, editors. Multiscale Modeling of Cancer: An Integrated Experimental and Mathematical Modeling Approach. Cambridge: Cambridge University Press; 2010. P. 88–122. DOI: 10.1017/CBO9780511781452.007.
  15. Giatili SG, Stamatakos GS. A detailed numerical treatment of the boundary conditions imposed by the skull on a diffusion–reaction model of glioma tumor growth. Clinical validation aspects. Applied Mathematics and Computation. 2012;218(17):8779–8799. DOI:10.1016/j.amc.2012.02.036.
  16. Hoshino T, Liu MW, Wu KA, Chen HY, Tsuruyama T, Komura S. Pattern formation of skin cancers: Effects of cancer proliferation and hydrodynamic interactions. Phys. Rev. E. 2019;99(3):032416. DOI: 10.1103/PhysRevE.99.032416.
  17. Montel F, Delarue M, Elgeti J, Vignjevic D, Cappello G, Prost J. Isotropic stress reduces cell proliferation in tumor spheroids. New J. Phys. 2012;14(5):055008. DOI: 10.1088/1367-2630/14/5/055008.
  18. Villani TS, Gardner G, Johnson M, Crider N. 3D High Content Imaging of Optically-Cleared Spheroids for Cancer Drug Screening. New Jersey, US: Visikol; 2017.
  19. Grist SM, Nasseri SS, Poon T, Roskelley C, Cheung KC. On-chip clearing of arrays of 3-D cell cultures and micro-tissues. Biomicrofluidics. 2016;10(4):044107. DOI: 10.1063/1.4959031.
  20. Jain RK. Transport of molecules in the tumor interstitium: a review. Cancer Research. 1987;47(12): 3039–3051.
  21. Doi M. Soft Matter Physics. Oxford: Oxford University Press; 2013. 272 p. DOI: 10.1093/acprof:oso/9780199652952.001.0001.
  22. Chatelain C, Balois T, Ciarletta P, Ben Amar M. Emergence of microstructural patterns in skin cancer: a phase separation analysis in a binary mixture. New J. Phys. 2011;13(11):115013. DOI: 10.1088/1367-2630/13/11/115013.
Received: 
27.05.2021
Accepted: 
28.06.2021
Published: 
30.07.2021
  • 2640 reads