Multicellular tumor spheroid in an off-lattice Voronoi-Delaunay cell model
- 27 May 2005
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 71 (5), 051910
- https://doi.org/10.1103/physreve.71.051910
Abstract
We study multicellular tumor spheroids by introducing a new three-dimensional agent-based Voronoi-Delaunay hybrid model. In this model, the cell shape varies from spherical in thin solution to convex polyhedral in dense tissues. The next neighbors of the cells are provided by a weighted Delaunay triangulation with on average linear computational complexity. The cellular interactions include direct elastic forces and cell-cell as well as cell-matrix adhesion. The spatiotemporal distribution of two nutrients—oxygen and glucose—is described by reaction-diffusion equations. Viable cells consume the nutrients, which are converted into biomass by increasing the cell size during the phase. We test hypotheses on the functional dependence of the uptake rates and use computer simulations to find suitable mechanisms for the induction of necrosis. This is done by comparing the outcome with experimental growth curves, where the best fit leads to an unexpected ratio of oxygen and glucose uptake rates. The model relies on physical quantities and can easily be generalized towards tissues involving different cell types. In addition, it provides many features that can be directly compared with the experiment.
Keywords
Other Versions
This publication has 46 references indexed in Scilit:
- How cellular movement determines the collective force generated by the Dictyostelium discoideum slugJournal of Theoretical Biology, 2004
- Kinetic and dynamic Delaunay tetrahedralizations in three dimensionsComputer Physics Communications, 2004
- A three-dimensional vertex dynamics cell model of space-filling polyhedra simulating cell behavior in a cell aggregateJournal of Theoretical Biology, 2004
- Intercellular Adhesion and Cancer Invasion: A Discrete Simulation Using the Extended Potts ModelJournal of Theoretical Biology, 2002
- Mechanics of Motor Proteins and the CytoskeletonApplied Mechanics Reviews, 2002
- An Insight into Cell Elasticity and Load-Bearing Ability. Measurement and TheoryPlant Physiology, 2001
- BacSim, a simulator for individual-based modelling of bacterial colony growthMicrobiology, 1998
- Monte Carlo approach to tissue-cell populationsPhysical Review E, 1995
- Description of cellular patterns by Dirichlet domains: The two-dimensional caseJournal of Theoretical Biology, 1978
- Ueber die Berührung fester elastischer Körper.Journal für die reine und angewandte Mathematik (Crelles Journal), 1882