Towards Sub-cellular Modeling with Delaunay Triangulation

G. Grise; M. Meyer-Hermann

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 5, Issue: 1, page 224-238
  • ISSN: 0973-5348

Abstract

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In this article a novel model framework to simulate cells and their internal structure is described. The model is agent-based and suitable to simulate single cells with a detailed internal structure as well as multi-cellular compounds. Cells are simulated as a set of many interacting particles, with neighborhood relations defined via a Delaunay triangulation. The interacting sub-particles of a cell can assume specific roles – i.e., membrane sub-particle, internal sub-particle, organelles, etc –, distinguished by specific interaction potentials and, eventually, also by the use of modified interaction criteria. For example, membrane sub-particles may interact only on a two-dimensional surface embedded on three-dimensional space, described via a restricted Delaunay triangulation. The model can be used not only to study cell shape and movement, but also has the potential to investigate the coupling between internal space-resolved movement of molecules and determined cell behaviors.

How to cite

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Grise, G., and Meyer-Hermann, M.. "Towards Sub-cellular Modeling with Delaunay Triangulation." Mathematical Modelling of Natural Phenomena 5.1 (2010): 224-238. <http://eudml.org/doc/197664>.

@article{Grise2010,
abstract = {In this article a novel model framework to simulate cells and their internal structure is described. The model is agent-based and suitable to simulate single cells with a detailed internal structure as well as multi-cellular compounds. Cells are simulated as a set of many interacting particles, with neighborhood relations defined via a Delaunay triangulation. The interacting sub-particles of a cell can assume specific roles – i.e., membrane sub-particle, internal sub-particle, organelles, etc –, distinguished by specific interaction potentials and, eventually, also by the use of modified interaction criteria. For example, membrane sub-particles may interact only on a two-dimensional surface embedded on three-dimensional space, described via a restricted Delaunay triangulation. The model can be used not only to study cell shape and movement, but also has the potential to investigate the coupling between internal space-resolved movement of molecules and determined cell behaviors.},
author = {Grise, G., Meyer-Hermann, M.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {cell shape; cell movement; sub-cellular model; delaunay triangulation; voronoi tessellation; surface reconstruction; Delaunay triangulation; Voronoi tessellation},
language = {eng},
month = {2},
number = {1},
pages = {224-238},
publisher = {EDP Sciences},
title = {Towards Sub-cellular Modeling with Delaunay Triangulation},
url = {http://eudml.org/doc/197664},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Grise, G.
AU - Meyer-Hermann, M.
TI - Towards Sub-cellular Modeling with Delaunay Triangulation
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/2//
PB - EDP Sciences
VL - 5
IS - 1
SP - 224
EP - 238
AB - In this article a novel model framework to simulate cells and their internal structure is described. The model is agent-based and suitable to simulate single cells with a detailed internal structure as well as multi-cellular compounds. Cells are simulated as a set of many interacting particles, with neighborhood relations defined via a Delaunay triangulation. The interacting sub-particles of a cell can assume specific roles – i.e., membrane sub-particle, internal sub-particle, organelles, etc –, distinguished by specific interaction potentials and, eventually, also by the use of modified interaction criteria. For example, membrane sub-particles may interact only on a two-dimensional surface embedded on three-dimensional space, described via a restricted Delaunay triangulation. The model can be used not only to study cell shape and movement, but also has the potential to investigate the coupling between internal space-resolved movement of molecules and determined cell behaviors.
LA - eng
KW - cell shape; cell movement; sub-cellular model; delaunay triangulation; voronoi tessellation; surface reconstruction; Delaunay triangulation; Voronoi tessellation
UR - http://eudml.org/doc/197664
ER -

References

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