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Towards a Two-Scale Cellular Automata Model of Tumour-Induced Angiogenesis

  • Paweł Topa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4173)

Abstract

This paper presents a new framework for modelling tumour-induced angiogenesis. Classical Cellular Automata approach is employed to model cellular and intracellular processes that occur in cancer tissue and neighbourhood. Vascular system is modelled by using Graph of Cellular Automata, which combines graph theory with Cellular Automata paradigm. A new model is proposed as a starting point for further investigations on multiscale model covering wide range of spatio-temporal scales including blood flow processes. The basis of the model with the algorithms are presented. Preliminary results with short discussion are also included.

Keywords

Cellular Automaton Vascular Network Transportation Network Capillary Vessel Vessel Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Carmeliet, P.: Angiogenesis in life, disease and medicine. Nature 438 (2005)Google Scholar
  2. 2.
    Carmeliet, P., Jain, R.K.: Angiogenesis in cancer and other disease. Nature 407 (2000)Google Scholar
  3. 3.
    Mantzaris, N.V., Webb, S., Othmer, H.G.: Mathematical modeling of tumour-induced angiogenesis. J. Math. Biol. (2004)Google Scholar
  4. 4.
    Coultas, L., Chawengsaksophak, K., Rossant, J.: Endothelial cells and VEGF in vascular development. Nature 438 December 15 (2005)Google Scholar
  5. 5.
    Ferrar, N., Kerbel, R.S.: Angiogenesis as a therapeutic target. Nature 438 (2005)Google Scholar
  6. 6.
    Tonini, T., Rossi, F., Claudio, P.P.: Molecular basis of angiogenesis and cancer. Oncogene 22, 6549–6556 (2003)CrossRefGoogle Scholar
  7. 7.
    Anderson, A.R.A., Chaplain, M.A.J.: Continuous and discrete mathematical models of tumour-induced angiogenesis. Bull. of Math. Biol. 60, 857–900 (1998)MATHCrossRefGoogle Scholar
  8. 8.
    Plank, M.J., Sleeman, B.D., Jones, P.F.: A mathematical model of tumour growth, regulated by vascular endothelial growth factor and the angiopoietins. J. of Theor. Biology 229, 435–454 (2004)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Stokes, C.L.: Lauffenburger: Analysis of the roles of microvessel endothelial cell random motility and chemotaxis in angiogenesis. J. Thoer. Biol. 152 (1991)Google Scholar
  10. 10.
    Alacorn, T., Byrne, H.M., Maini, P.K.: Towards whole-organ modeling of tumour growth. Progress in Biophysics & Molecular Biology 85, 451–472 (2004)CrossRefGoogle Scholar
  11. 11.
    Alacorn, T., Byrne, H.M., Maini, P.K.: A multiple scale model for tumour growth. Multiscale Model. Simul. 3(2), 440–475 (2005)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Topa, P., Dzwinel, W.: Consuming Environment with Transportation Network Modelled Using Graph of Cellular Automata. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds.) PPAM 2004. LNCS, vol. 3019, pp. 513–520. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  13. 13.
    Topa, P., Dzwinel, W., Yuen, D.: A multiscale cellular automata model for simulating complex transport systems. Int. J. Mod. Phys. C (accepted for publication) (2006)Google Scholar
  14. 14.
    Topa, P., Paszkowski, M.: Anastomosing transportation networks. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds.) PPAM 2001. LNCS, vol. 2328, pp. 904–911. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  15. 15.
    Chopard, B., Droz, M.: Cellular Automata Modeling of Physical Systems. Cambridge University Press, Cambridge (1998)MATHCrossRefGoogle Scholar
  16. 16.
    Dzwinel, W., Boryczko, K., Yuen, D.: A discrete-particle model of blood dynamics in capillary vessels. J. Colloid Int. Sci. 258/1, 163–173 (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Paweł Topa
    • 1
  1. 1.AGH University of Science and TechnologyKrakówPoland

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