Particle Based Model of Tumor Progression Stimulated by the Process of Angiogenesis

  • Rafał Wcisło
  • Witold Dzwinel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5102)


We discuss a novel metaphor of tumor progression stimulated by the process of angiogenesis. The realistic 3-D dynamics of the entire system consisting of the tumor, tissue cells, blood vessels and blood flow can be reproduced by using interacting particles. The particles mimic the clusters of tumor cells. They interact with their closest neighbors via semi-harmonic forces simulating mechanical resistance of the cell walls and the external pressure. The particle dynamics is governed by both the Newtonian laws of motion and the rules of cell life-cycle. The particles replicate by a simple mechanism of division, similar to that of a single cell reproduction and die due to necrosis or apoptosis. We conclude that this concept can serve as a general framework for designing advanced multi-scale models of tumor dynamics. In respect to spatio-temporal scale, the interactions between particles can define e.g., cluster-to-cluster, cell-to-cell, red blood cells and fluid particles interactions, cytokines motion, etc. Consequently, they influence the macroscopic dynamics of the particle ensembles in various sub-scales ranging from diffusion of cytokines, blood flow up to growth of tumor and vascular network expansion.


tumor progression angiogenesis computer simulation particle model 


  1. 1.
    Folkman, J.: Tumor angiogenesis: Therapeutic implications. N. Engl. J. Med. 285, 1182–1186 (1971)Google Scholar
  2. 2.
    Ferrara, N., Chen, H., Davis Smyth, T., Gerber, H.P., Nguyen, T.N., Peers, D., Chisholm, V., Hillan, K.J., Schwall, R.H.: Vascular endothelial growth factor is essential for corpus luteum angiogenesis. Nat. Med. 4, 336–340 (1998)CrossRefGoogle Scholar
  3. 3.
    Mantzaris, N., Webb, S., Othmer, H.G.: Mathematical Modeling of Tumor-induced Angiogenesis. J. Math. Biol. 49(2), 1416–1432 (2004)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Bellomo, N., de Angelis, E., Preziosi, L.: Multiscale Modeling and Mathematical Problems Related to Tumor Evolution and Medical Therapy. J. Theor. Med. 5(2), 111–136 (2003)CrossRefzbMATHGoogle Scholar
  5. 5.
    Stéphanou, A., McDougall, S.R., Anderson, A.R.A., Chaplain, M.A.J., Sherratt, J.A.: Mathematical Modelling of Flow in 2D and 3D Vascular Networks: Applications to Anti-angiogenic and Chemotherapeutic Drug Strategies. J. Math. Comput. Model 41, 1137–1156 (2005)CrossRefzbMATHGoogle Scholar
  6. 6.
    Chaplain, M.A.J.: Mathematical modelling of angiogenesis. J. Neuro-Oncol. 50, 37–51 (2000)CrossRefGoogle Scholar
  7. 7.
    Luo, S., Nie, Y.: FEM-based simulation of tumor growth in medical image. In: Galloway Jr., R.L. (ed.) Medical Imaging 2004: Visualization, Image Guided Procedures, and Display. Proceedings of SPIE, vol. 5367, pp. 600–608 (2004)Google Scholar
  8. 8.
    Moreira, J., Deutsch, A.: Cellular Automaton Models of Tumor Development: A Critical Review. Adv. Complex Syst. 5/2(3), 247–269 (2002)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Fracchia, F.D., Prusinkiewicz, P., de Boer, M.J.M.: Animation of the development of multicellular structures. In: Magnenat-Thalmann, N., Thalmann, D. (eds.) Computer Animation 1990, pp. 3–18. Springer, Tokyo (1990)Google Scholar
  10. 10.
    Lappa, M.: A CFD level-set method for soft tissue growth: theory and fundamental equations. J. Biomech. 38(1), 185–190 (2005)Google Scholar
  11. 11.
    Hoekstra, A.G., Lorenz, E., Falcone, L.-C., Chopard, B.: Towards a Complex Automata Framework for Multi-scale Modeling: Formalism and the Scale Separation Map. In: Shi, Y., van Albada, G.D., Dongarra, J., Sloot, P.M.A. (eds.) ICCS 2007. LNCS, vol. 4487, pp. 1611–3349. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  12. 12.
    McDougall, S.R., Anderson, A.R.A., Chaplain, M.A.J., Sherratt, J.A.: Mathematical modelling of flow through vascular networks: Implications for tumour-induced angiogenesis and chemotherapy strategies. Bull. Math. Biol. 64, 673–702 (2002)CrossRefGoogle Scholar
  13. 13.
    Dzwinel, W., Alda, W., Yuen, D.A.: Cross-Scale Numerical Simulations Using Discrete-Particle Models. Molecular Simulation 22, 397–418 (1999)CrossRefGoogle Scholar
  14. 14.
    Dzwinel, W., Boryczko, K., Yuen, D.A.: A Discrete-Particle Model of Blood Dynamics in Capillary Vessels. J. Colloid Int Sci. 258(1), 163–173 (2003)CrossRefGoogle Scholar
  15. 15.
    Boryczko, K., Dzwinel, W., Yuen, D.A.: Modeling Heterogeneous Mesoscopic Fluids in Irregular Geometries using Shared Memory Systems. Molecular Simulation 31(1), 45–56 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Rafał Wcisło
    • 1
  • Witold Dzwinel
    • 1
  1. 1.Institute of Computer ScienceAGH University of Science and TechnologyKrakówPoland

Personalised recommendations