Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2013, Article ID 519895, 10 pages
http://dx.doi.org/10.1155/2013/519895
Research Article

A Hybrid Cellular Automata Model of Multicellular Tumour Spheroid Growth in Hypoxic Microenvironment

1School of Biological Science and Medical Engineering, Southeast University, Nanjing 210096, China
2School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiaotong University, Shanghai 200240, China
3Department of Mechanics and Engineering Science, Fudan University, Shanghai 200433, China

Received 19 November 2012; Accepted 22 January 2013

Academic Editor: Martin Weiser

Copyright © 2013 Yan Cai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. G. Hamilton, “Multicellular spheroids as an in vitro tumor model,” Cancer Letters, vol. 131, no. 1, pp. 29–34, 1998. View at Publisher · View at Google Scholar · View at Scopus
  2. W. R. Inch, J. A. McCredie, and R. M. Sutherland, “Growth of nodular carcinomas in rodents compared with multi-cell spheroids in tissue culture,” Growth, Development and Aging, vol. 34, no. 3, pp. 271–282, 1970. View at Google Scholar · View at Scopus
  3. R. M. Sutherland, J. A. McCredie, and W. R. Inch, “Growth of multicell spheroids in tissue culture as a model of nodular carcinomas,” Journal of the National Cancer Institute, vol. 46, no. 1, pp. 113–120, 1971. View at Google Scholar · View at Scopus
  4. J. M. Kelm, N. E. Timmins, C. J. Brown, M. Fussenegger, and L. K. Nielsen, “Method for generation of homogeneous multicellular tumor spheroids applicable to a wide variety of cell types,” Biotechnology and Bioengineering, vol. 83, no. 2, pp. 173–180, 2003. View at Publisher · View at Google Scholar · View at Scopus
  5. D. Fukumura and R. K. Jain, “Tumor microvasculature and microenvironment: targets for anti-angiogenesis and normalization,” Microvascular Research, vol. 74, no. 2-3, pp. 72–84, 2007. View at Publisher · View at Google Scholar · View at Scopus
  6. D. Ribatti, B. Nico, E. Crivellato, and A. Vacca, “The structure of the vascular network of tumors,” Cancer Letters, vol. 248, no. 1, pp. 18–23, 2007. View at Publisher · View at Google Scholar · View at Scopus
  7. A. Krogh, The Anantomy and Physiology of Capillaries, Yale University Press, New York, NY, USA, 1922.
  8. G. Helmlinger, F. Yuan, M. Dellian, and R. K. Jain, “Interstitial pH and pO2 gradients in solid tumors in vivo: high-resolution measurements reveal a lack of correlation,” Nature Medicine, vol. 3, no. 2, pp. 177–182, 1997. View at Publisher · View at Google Scholar · View at Scopus
  9. A. L. Harris, “Hypoxia—a key regulatory factor in tumour growth,” Nature Reviews Cancer, vol. 2, no. 1, pp. 38–47, 2002. View at Publisher · View at Google Scholar · View at Scopus
  10. L. B. Gardner, Q. Li, M. S. Park, W. M. Flanagan, G. L. Semenza, and C. V. Dang, “Hypoxia inhibits G1/S transition through regulation of p27 expression,” Journal of Biological Chemistry, vol. 276, no. 11, pp. 7919–7926, 2001. View at Publisher · View at Google Scholar · View at Scopus
  11. T. Alarcón, H. M. Byrne, and P. K. Maini, “A mathematical model of the effects of hypoxia on the cell-cycle of normal and cancer cells,” Journal of Theoretical Biology, vol. 229, no. 3, pp. 395–411, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. J. J. Tyson and B. Novak, “Regulation of the eukaryotic cell cycle: molecular antagonism, hysteresis, and irreversible transitions,” Journal of Theoretical Biology, vol. 210, no. 2, pp. 249–263, 2001. View at Publisher · View at Google Scholar · View at Scopus
  13. T. Nederman, B. Norling, B. Glimelius, J. Carlsson, and U. Brunk, “Demonstration of an extracellular matrix in multicellular tumor spheroids,” Cancer Research, vol. 44, no. 7, pp. 3090–3097, 1984. View at Google Scholar · View at Scopus
  14. M. T. Santini, G. Rainaldi, and P. L. Indovina, “Apoptosis, cell adhesion and the extracellular matrix in the three-dimensional growth of multicellular tumor spheroids,” Critical Reviews in Oncology/Hematology, vol. 36, no. 2-3, pp. 75–87, 2000. View at Publisher · View at Google Scholar · View at Scopus
  15. S. M. Frisch and E. Ruoslahti, “Integrins and anoikis,” Current Opinion in Cell Biology, vol. 9, no. 5, pp. 701–706, 1997. View at Publisher · View at Google Scholar · View at Scopus
  16. F. Hirschhaeuser, H. Menne, C. Dittfeld, J. West, W. Mueller-Klieser, and L. A. Kunz-Schughart, “Multicellular tumor spheroids: an underestimated tool is catching up again,” Journal of Biotechnology, vol. 148, no. 1, pp. 3–15, 2010. View at Publisher · View at Google Scholar · View at Scopus
  17. P. P. Delsanto, C. Guiot, P. G. Degiorgis, C. A. Condat, Y. Mansury, and T. S. Deisboeck, “Growth model for multicellular tumor spheroids,” Applied Physics Letters, vol. 85, no. 18, pp. 4225–4227, 2004. View at Publisher · View at Google Scholar · View at Scopus
  18. G. Schaller and M. Meyer-Hermann, “Continuum versus discrete model: a comparison for multicellular tumour spheroids,” Philosophical Transactions of the Royal Society A, vol. 364, no. 1843, pp. 1443–1464, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. C. A. Condat and S. A. Menchón, “Ontogenetic growth of multicellular tumor spheroids,” Physica A, vol. 371, no. 1, pp. 76–79, 2006. View at Publisher · View at Google Scholar · View at Scopus
  20. B. Brutovsky, D. Horvath, and V. Lisy, “Inverse geometric approach for the simulation of close-to-circular growth. The case of multicellular tumor spheroids,” Physica A, vol. 387, no. 4, pp. 839–850, 2008. View at Publisher · View at Google Scholar · View at Scopus
  21. G. J. Pettet, C. P. Please, M. J. Tindall C.P., and D. L. S. McElwain, “The migration of cells in multicell tumor spheroids,” Bulletin of Mathematical Biology, vol. 63, no. 2, pp. 231–257, 2001. View at Publisher · View at Google Scholar · View at Scopus
  22. M. Aubert, M. Badoual, S. Féreol, C. Christov, and B. Grammaticos, “A cellular automaton model for the migration of glioma cells,” Physical Biology, vol. 3, no. 2, pp. 93–100, 2006. View at Publisher · View at Google Scholar · View at Scopus
  23. Y. Mansury and T. S. Deisboeck, “Simulating 'structure-function' patterns of malignant brain tumors,” Physica A, vol. 331, no. 1-2, pp. 219–232, 2004. View at Publisher · View at Google Scholar · View at Scopus
  24. Y. Jiang, J. Pjesivac-Grbovic, C. Cantrell, and J. P. Freyer, “A multiscale model for avascular tumor growth,” Biophysical Journal, vol. 89, no. 6, pp. 3884–3894, 2005. View at Publisher · View at Google Scholar · View at Scopus
  25. A. R. A. Anderson, “A hybrid mathematical model of solid tumour invasion: the importance of cell adhesion,” Mathematical Medicine and Biology, vol. 22, no. 2, pp. 163–186, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  26. J. von Neumann, Theory of Self-Reproducing Automata, University of Illinois Press, 1966.
  27. Y. Cai, S. Xu, J. Wu, and Q. Long, “Coupled modelling of tumour angiogenesis, tumour growth and blood perfusion,” Journal of Theoretical Biology, vol. 279, no. 1, pp. 90–101, 2011. View at Publisher · View at Google Scholar · View at Scopus
  28. T. Roose, S. J. Chapman, and P. K. Maini, “Mathematical models of avascular tumor growth,” SIAM Review, vol. 49, no. 2, pp. 179–208, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  29. J. P. Freyer and R. M. Sutherland, “Regulation of growth saturation and development of necrosis in EMT6/Ro multicellular spheroids by the glucose and oxygen supply,” Cancer Research, vol. 46, no. 7, pp. 3504–3512, 1986. View at Google Scholar · View at Scopus
  30. J. P. Freyer and R. M. Sutherland, “Proliferative and clonogenic heterogeneity of cells from EMT6/Ro multicellular spheroids induced by the glucose and oxygen supply,” Cancer Research, vol. 46, no. 7, pp. 3513–3520, 1986. View at Google Scholar · View at Scopus
  31. J. P. Freyer, “Role of necrosis in regulating the growth saturation of multicellular spheroids,” Cancer Research, vol. 48, no. 9, pp. 2432–2439, 1988. View at Google Scholar · View at Scopus
  32. Y. Cai, K. Gulnar, H. Zhang, J. Cao, S. Xu, and Q. Long, “Numerical simulation of tumor-induced angiogenesis influenced by the extra-cellular matrix mechanical environment,” Acta Mechanica Sinica/Lixue Xuebao, vol. 25, no. 6, pp. 889–895, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  33. Y. Cai, J. Wu, S. X. Xu et al., “Numerical simulation of inhibiting effects on solid tumour cells in anti-angiogenic therapy: application of coupled mathematical model of angiogenesis with tumour growth,” Applied Mathematics and Mechanics, vol. 32, no. 10, pp. 1287–1296, 2011. View at Publisher · View at Google Scholar
  34. S. A. Menchón and C. A. Condat, “Quiescent cells: a natural way to resist chemotherapy,” Physica A, vol. 390, no. 20, pp. 3354–3361, 2011. View at Publisher · View at Google Scholar · View at Scopus