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TECHNICAL PAPERS

Cell-Level Finite Element Studies of Viscous Cells in Planar Aggregates

[+] Author and Article Information
Helen H. Chen, G. Wayne Brodland

Department of Civil Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1 Canada

J Biomech Eng 122(4), 394-401 (Mar 20, 2000) (8 pages) doi:10.1115/1.1286563 History: Received March 10, 1998; Revised March 20, 2000
Copyright © 2000 by ASME
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Figures

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(a) Part of an epithelial sheet. Large gaps are shown between the cells so that the desmosomes and cell adhesion molecules (CAMs) that bridge between them can be shown. Intracellular structures that are shown include microfilaments that form a mat at the apical end of the cells, circumferential microfilament bundles (CMBs) and intermediate filaments (IFs). Deformation of individual cells due to forces generated by these structures is regulated by the viscosity of the cytoplasm and its associated structures that fill each cell. (b) Finite element model of a single cell (shown shaded). Perimeter nodes (n1 to nm) are shown as unfilled circles while the auxiliary node (n0) is shown solid black. Boundaries between triangular subelements (e1 to em) are indicated with dashed lines. The total contractile edge force along a boundary between cells is FC while that along a patch edge is FC/2 (see text for explanation).
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How cells rearrange. (a) When Cells A and C move away from each other, the length of the side between them becomes shorter until eventually it becomes less than a specified minimum side length M. (b) Cells in a real sheet would instantaneously pass through a configuration where a quadruple junction existed, although cells in the simulation do not explicitly pass through this state (see text). (c) A new edge is then formed between cells B and D. In the simulations, the new side is assigned an initial length greater than M, typically 1.1M, to circumvent possible topological instability.
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Elongation of a sheet of cells (Q=24). (a) Initial configuration. (b) The patch has been elongated to twice its original width. (c) The patch has been stretched to four times its original width. All parts of the figure are shown at the same scale. For the sake of clarity, element numbers are not shown on part (c) of the figure.
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(a) Dimensionless true stress S and intracellular pressure P versus stretch ratio λ for the cell patch shown in Fig. 3. The stretch ratios corresponding to the patches shown in Fig. 3 are indicated along the top of the figure. (b) Cell shape ratio κ and number of neighbor changes NNC versus stretch ratio λ.
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The effect of the parameter Q on stress, S. Values of κ corresponding to λ=3 are also shown.

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