Technical challenges, including significant ones associated with cell rearrangement, have hampered the development of three-dimensional finite element models for the mechanics of embryonic cells. These challenges have been overcome by a new formulation in which the contents of each cell, assumed to have a viscosity $\mu $, are modeled using a system of orthogonal dashpots. This approach overcomes a stiffening artifact that affects more traditional models, in which space-filling viscous elements are used to model the cytoplasm. Cells are assumed to be polyhedral in geometry, and each $n$-sided polygonal face is subdivided into $n$ triangles with a common node at the face center so that it needs not remain flat. A constant tension $\gamma $ is assumed to act along each cell-cell interface, and cell rearrangements occur through one of two complementary topological transformations. The formulation predicts mechanical interactions between pairs of similar or dissimilar cells that are consistent with experiments, two-dimensional simulations, contact angle theory, and intracellular pressure calculations. Simulations of the partial engulfment of one tissue type by another show that the formulation is able to model aggregates of several hundred cells without difficulty. Simulations carried out using this formulation suggest new experimental approaches for measuring cell surface tensions and interfacial tensions. The formulation holds promise as a tool for gaining insight into the mechanics of isolated or aggregated embryonic cells and for the design and interpretation of experiments that involve them.

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Department of Civil and Environmental Engineering,
Department of Civil and Environmental Engineering,

brodland@uwaterloo.ca

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October 2007

Technical Papers

# A Three-dimensional Finite Element Model for the Mechanics of Cell-Cell Interactions

Denis Viens,

Denis Viens

Department of Civil and Environmental Engineering,

University of Waterloo

, Waterloo, Ontario N2T 2N4, Canada
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G. Wayne Brodland

G. Wayne Brodland

Department of Civil and Environmental Engineering,

brodland@uwaterloo.ca
University of Waterloo

, Waterloo, Ontario N2T 2N4, Canada
Search for other works by this author on:

Denis Viens

University of Waterloo

, Waterloo, Ontario N2T 2N4, Canada
G. Wayne Brodland

University of Waterloo

, Waterloo, Ontario N2T 2N4, Canadabrodland@uwaterloo.ca

*J Biomech Eng*. Oct 2007, 129(5): 651-657 (7 pages)

**Published Online:**February 14, 2007

Article history

Received:

June 6, 2006

Revised:

February 14, 2007

Citation

Viens, D., and Brodland, G. W. (February 14, 2007). "A Three-dimensional Finite Element Model for the Mechanics of Cell-Cell Interactions." ASME. *J Biomech Eng*. October 2007; 129(5): 651–657. https://doi.org/10.1115/1.2768375

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