Document Detail

Generalized voronoi tessellation as a model of two-dimensional cell tissue dynamics.
MedLine Citation:
PMID:  20082148     Owner:  NLM     Status:  MEDLINE    
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 generators of the resulting model tissue. The interactions between cells are represented by adhesive and repelling force densities on the cell contact borders. In addition, protrusive locomotion forces are implemented along the cell boundaries at the tissue margin, and stochastic perturbations allow for non-deterministic motility effects. Simulations of the emerging system of stochastic differential equations for position and velocity of cell centers show the feasibility of this Voronoi method generating realistic cell shapes. In the limiting case of a single cell pair in brief contact, the dynamical nonlinear Ornstein-Uhlenbeck process is analytically investigated. In general, topologically distinct tissue conformations are observed, exhibiting stability on different time scales, and tissue coherence is quantified by suitable characteristics. Finally, an argument is derived pointing to a tradeoff in natural tissues between cell size heterogeneity and the extension of cellular lamellae.
Martin Bock; Amit Kumar Tyagi; Jan-Ulrich Kreft; Wolfgang Alt
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Publication Detail:
Type:  Journal Article; Research Support, Non-U.S. Gov't     Date:  2010-01-16
Journal Detail:
Title:  Bulletin of mathematical biology     Volume:  72     ISSN:  1522-9602     ISO Abbreviation:  Bull. Math. Biol.     Publication Date:  2010 Oct 
Date Detail:
Created Date:  2010-10-04     Completed Date:  2011-01-21     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  0401404     Medline TA:  Bull Math Biol     Country:  United States    
Other Details:
Languages:  eng     Pagination:  1696-731     Citation Subset:  IM    
IZMB, Theoretische Biologie, Universität Bonn, Bonn, Germany.
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MeSH Terms
Cell Adhesion / physiology*
Computer Simulation
Cytoskeleton / physiology*
Models, Biological*

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