Generalized Voronoi Tessellation as a Model of Two-dimensional Cell Tissue Dynamics

@article{Bock2010GeneralizedVT,
  title={Generalized Voronoi Tessellation as a Model of Two-dimensional Cell Tissue Dynamics},
  author={Martin Bock and A. Tyagi and Jan-Ulrich Kreft and Wolfgang Alt},
  journal={Bulletin of Mathematical Biology},
  year={2010},
  volume={72},
  pages={1696-1731}
}
Voronoi tessellations have been used to model the geometric arrangement of cells in morphogenetic or cancerous tissues, however, so far only with flat hyper-surfaces as cell-cell contact borders. In order to reproduce the experimentally observed piecewise spherical boundary shapes, we develop a consistent theoretical framework of multiplicatively weighted distance functions, defining generalized finite Voronoi neighborhoods around cell bodies of varying radius, which serve as heterogeneous… 
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