Journal of Molecular Modeling

, 15:1517 | Cite as

A 3-D model of tumor progression based on complex automata driven by particle dynamics

  • Rafał Wcisło
  • Witold Dzwinel
  • David A. Yuen
  • Arkadiusz Z. Dudek
Original Paper


The dynamics of a growing tumor involving mechanical remodeling of healthy tissue and vasculature is neglected in most of the existing tumor models. This is due to the lack of efficient computational framework allowing for simulation of mechanical interactions. Meanwhile, just these interactions trigger critical changes in tumor growth dynamics and are responsible for its volumetric and directional progression. We describe here a novel 3-D model of tumor growth, which combines particle dynamics with cellular automata concept. The particles represent both tissue cells and fragments of the vascular network. They interact with their closest neighbors via semi-harmonic central forces simulating mechanical resistance of the cell walls. The particle dynamics is governed by both the Newtonian laws of motion and the cellular automata rules. These rules can represent cell life-cycle and other biological interactions involving smaller spatio-temporal scales. We show that our complex automata, particle based model can reproduce realistic 3-D dynamics of the entire system consisting of the tumor, normal tissue cells, blood vessels and blood flow. It can explain phenomena such as the inward cell motion in avascular tumor, stabilization of tumor growth by the external pressure, tumor vascularization due to the process of angiogenesis, trapping of healthy cells by invading tumor, and influence of external (boundary) conditions on the direction of tumor progression. We conclude that the particle model can serve as a general framework for designing advanced multiscale models of tumor dynamics and it is very competitive to the modeling approaches presented before.


Angiogenesis Complex automata Computer simulation Discrete particle model Tumor progression 



This research is financed by the Polish Ministry of Education and Science, Project No.3 T11F 010 30, internal AGH Institute of Computer Science grant and Vlab project of National Science Foundation. The exemplar movies from simulations can be downloaded from∼wcislo/Angiogeneza/index.html.


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Rafał Wcisło
    • 1
  • Witold Dzwinel
    • 1
  • David A. Yuen
    • 2
  • Arkadiusz Z. Dudek
    • 3
  1. 1.Institute of Computer ScienceAGH University of Science and TechnologyKrakowPoland
  2. 2.Minnesota Supercomputing InstituteUniversity of MinnesotaMinneapolisUSA
  3. 3.Division of Hematology, Oncology, and Transplantation, Department of MedicineUniversity of Minnesota Medical SchoolMinneapolisUSA

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