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Article

Viscoelastic Properties of Single Attached Cells Under Compression

[+] Author and Article Information
Emiel A.G. Peeters1

 Eindhoven University of Technology, Department of Biomedical Engineering, P.O. Box 513, 5600 MB Eindhoven, The Netherlandse.a.g.peeters@tue.nl

Cees W.J. Oomens, Carlijn V.C. Bouten, Frank P.T. Baaijens

 Eindhoven University of Technology, Department of Biomedical Engineering, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

Dan L. Bader

 Queen Mary, University of London, IRC in Biomedical Materials and Medical Engineering Division, E1 4NS, London, United Kingdom

1

Corresponding author. Address for correspondence: Eindhoven University of Technology, Department of Biomedical Engineering, P.O. Box 513, Building W-hoog 4.123, 5600 MB Eindhoven, The Netherlands

J Biomech Eng 127(2), 237-243 (Sep 14, 2004) (7 pages) doi:10.1115/1.1865198 History: Received March 22, 2004; Revised September 14, 2004

The viscoelastic properties of single, attached C2C12 myoblasts were measured using a recently developed cell loading device. The device allows global compression of an attached cell, while simultaneously measuring the associated forces. The viscoelastic properties were examined by performing a series of dynamic experiments over two frequency decades (0.110Hz) and at a range of axial strains (1040%). Confocal laser scanning microscopy was used to visualize the cell during these experiments. To analyze the experimentally obtained force-deformation curves, a nonlinear viscoelastic model was developed. The nonlinear viscoelastic model was able to describe the complete series of dynamic experiments using only a single set of parameters, yielding an elastic modulus of 2120±900Pa for the elastic spring, an elastic modulus of 1960±1350 for the nonlinear spring, and a relaxation time constant of 0.3±0.12s. To our knowledge, it is the first time that the global viscoelastic properties of attached cells have been quantified over such a wide range of strains. Furthermore, the experiments were performed under optimal environmental conditions and the results are, therefore, believed to reflect the viscoelastic mechanical behavior of cells, such as would be present in vivo.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic representation (a) and actual realization (b) of the single cell loading device. The inset shows a close-up of the glass indenter.

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Figure 2

(a) Geometric representation of the undeformed cell with height H and area at the base Ab and (b) Nonlinear viscoelastic model used to describe the dynamic experiments with spring constants k1, k2(ϵz) and relaxation time τr

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Figure 3

Force (solid curves) and indentation depth (dashed curves) as a function of time before (a) and after (b) filtering obtained from a dynamic experiment

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Figure 4

Force as a function of time obtained from three dynamic experiments performed on one cell. In each dynamic experiment the cell was subjected to ten cycles with an amplitude and offset of 0.5μm at 1Hz. For each experiment, the forces of the previous eight cycles were averaged. The error bars represent the standard deviation of each experiment.

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Figure 5

Force as a function of axial strain (solid curves) obtained from dynamic experiments on one cell at different applied frequencies (a) 101, (b) 100.5, (c) 100, (d) 10−0.5, and (e) 10−1Hz and amplitudes of indentation: (a) 0.5, (b) 0.75, and (c) 1μm. The fit obtained by the nonlinear viscoelastic model is also shown (dashed curves).

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Figure 6

Orthogonal projections of an undeformed cell (a) and a compressed cell with initial strain ϵz(t0)=12% (b). (c) and (d) show images of the same cell during dynamic experiments at axial strains of ϵz(t)=30% and 55%, respectively. The cell in (d) shows the ruptured membrane of the cell.

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