Multicellular Tumor Spheroid in an off-lattice Voronoi/Delaunay cell   model
  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 in 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 G_1 phase.   We test hypotheses on the functional dependence of the uptake rates and use the computer simulation to find suitable mechanisms for 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. 
Gernot Schaller and Michael Meyer-Hermann