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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Carmeliet, P.: Angiogenesis in life, disease and medicine. Nature 438 (2005)
Carmeliet, P., Jain, R.K.: Angiogenesis in cancer and other disease. Nature 407 (2000)
Mantzaris, N.V., Webb, S., Othmer, H.G.: Mathematical modeling of tumour-induced angiogenesis. J. Math. Biol. (2004)
Coultas, L., Chawengsaksophak, K., Rossant, J.: Endothelial cells and VEGF in vascular development. Nature 438 December 15 (2005)
Ferrar, N., Kerbel, R.S.: Angiogenesis as a therapeutic target. Nature 438 (2005)
Tonini, T., Rossi, F., Claudio, P.P.: Molecular basis of angiogenesis and cancer. Oncogene 22, 6549–6556 (2003)
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)
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)
Stokes, C.L.: Lauffenburger: Analysis of the roles of microvessel endothelial cell random motility and chemotaxis in angiogenesis. J. Thoer. Biol. 152 (1991)
Alacorn, T., Byrne, H.M., Maini, P.K.: Towards whole-organ modeling of tumour growth. Progress in Biophysics & Molecular Biology 85, 451–472 (2004)
Alacorn, T., Byrne, H.M., Maini, P.K.: A multiple scale model for tumour growth. Multiscale Model. Simul. 3(2), 440–475 (2005)
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)
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)
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)
Chopard, B., Droz, M.: Cellular Automata Modeling of Physical Systems. Cambridge University Press, Cambridge (1998)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Topa, P. (2006). Towards a Two-Scale Cellular Automata Model of Tumour-Induced Angiogenesis. In: El Yacoubi, S., Chopard, B., Bandini, S. (eds) Cellular Automata. ACRI 2006. Lecture Notes in Computer Science, vol 4173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11861201_40
Download citation
DOI: https://doi.org/10.1007/11861201_40
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40929-8
Online ISBN: 978-3-540-40932-8
eBook Packages: Computer ScienceComputer Science (R0)