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Volume 2017 (2017), Article ID 8519539, 11 pages
Research Article

Axisymmetric Contact Problem for a Flattened Cell: Contributions of Substrate Effect and Cell Thickness to the Determination of Viscoelastic Properties by Using AFM Indentation

1School of Engineering, University of Warwick, Coventry CV4 7AL, UK
2International Research Centre for Nano Handling and Manufacturing of China, Changchun University of Science and Technology, Changchun 130022, China

Correspondence should be addressed to X. Liu

Received 31 July 2017; Revised 22 October 2017; Accepted 1 November 2017; Published 20 December 2017

Academic Editor: Kun Wang

Copyright © 2017 Xinyao Zhu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Nanoindentation technology has proven to be an effective method to investigate the viscoelastic properties of biological cells. The experimental data obtained by nanoindentation are frequently interpreted by Hertz contact model. However, in order to validate Hertz contact model, some studies assume that cells have infinite thickness which does not necessarily represent the real situation. In this study, a rigorous contact model based upon linear elasticity is developed for the interpretation of indentation tests of flattened cells. The cell, normally bonded to the Petri dish, is initially treated as an elastic layer of finite thickness perfectly fixed to a rigid substrate. The theory of linear elasticity is utilized to solve this contact issue and then the solutions are extended to viscoelastic situation which is regarded as a good indicator for mechanical properties of biological cells. To test the present model, AFM-based creep test has been conducted on living human hepatocellular carcinoma cell (SMMC-7721 cell) and its fullerenol-treated counterpart. The results indicate that the present model could not only describe very well the creep behavior of SMMC-7721 cells, but also curb overestimation of the mechanical properties due to substrate effect.