# Towards Sub-cellular Modeling with Delaunay Triangulation

Mathematical Modelling of Natural Phenomena (2010)

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

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topGrise, 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 -

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