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Geometrical Modeling of Cell Division and Cell Remodeling Based on Voronoi Tessellation Method

Liqiang Lin1, Xianqiao Wang2, Xiaowei Zeng1,3
Department of Mechanical Engineering, University of Texas, San Antonio, TX 78249.
College of Engineering and NanoSEC, University of Georgia, Athens, GA, 30602.
Corresponding Author. Email: xiaowei.zeng@utsa.edu

Computer Modeling in Engineering & Sciences 2014, 98(2), 203-220. https://doi.org/10.3970/cmes.2014.098.203

Abstract

The Voronoi tessellation is employed to describe cellular patterns and to simulate cell division and cell remodeling in epithelial tissue. First, Halton sequence is utilized to generate the random generators of Voronoi cell points. The centroidal Voronoi cell center is obtained by probabilistic Lloyd's method and polygonal structure of cell distribution is modeled. Based on the polygonal shape of cells, the instantaneous mechanism of cell division is applied to simulate the cell proliferation and remodeling. Four kinds of single-cell division algorithms are designed with the consideration of cleavage angle. From these simulations, we find that cell topological structure varies case by case, but the cell cycle time is almost the same. With respect to double-cell proliferation, the cycle time is shorter than single-cell division for the same number of replicated cells, but this doesn’t imply the direct linear relationship between cycle time and the total number of cell divisions. The current study provides a novel numerical tool for cell division simulation and may open a door for more realistic and more accurate modeling of the features of morphogenesis emerging from the complex interactions between geometric and biomechanical properties of epithelial tissues.

Keywords

Voronoi tessellation, Halton sequence, Lloyd's method, cell division, multi-cell proliferation, cell cycle.

Cite This Article

Lin, L., Wang, X., Zeng, X. (2014). Geometrical Modeling of Cell Division and Cell Remodeling Based on Voronoi Tessellation Method. CMES-Computer Modeling in Engineering & Sciences, 98(2), 203–220.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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