Axisymmetric contact problem for a flattened cell : contributions of substrate effect and cell thickness to the determination of viscoelastic properties by using AFM indentation

摘要

Nanoindentation technology has proven 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 facilitate the application of Hertz contact model, a mass of studies assume 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 which represent a factual morphology. The cell, normally bonded to the petri dish, is initially treated as an elastic layer of finite thickness perfectly fixed to a rigid substrate, and the conic indenter is assumed to be frictionless. 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, an 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 can also curb overestimation of the mechanical properties due to substrate effect. Moreover, the present model could identify the difference between the control and treated SMMC-7721 cells in terms of the extracted viscoelastic parameters, suggesting its potential in revealing the biomechanical effects of fullerenol-like drug treatment on cancerous cells.