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Biomech Model Mechanobiol. 2017 Feb;16(1):297-311. doi: 10.1007/s10237-016-0817-y. Epub 2016 Aug 23.

A combined experimental atomic force microscopy-based nanoindentation and computational modeling approach to unravel the key contributors to the time-dependent mechanical behavior of single cells.

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Department of Applied Physics, University of Eastern Finland, POB 1627, 70211, Kuopio, Finland.
Department of Applied Physics, University of Eastern Finland, POB 1627, 70211, Kuopio, Finland.
Department of Integrative Medical Biology, Umeå University, POB 843, 90187, Umeå, Sweden.
School of Public Health, Health Science Center of Xi'an Jiaotong University, Key Laboratory of Trace Elements and Endemic Diseases, National Health and Family Planning Commission, Xi'an, China.
School of Engineering and Technology, Savonia University of Applied Sciences, POB 1188, 70201, Kuopio, Finland.
Diagnostic Imaging Center, Kuopio University Hospital, Kuopio, Finland.


Cellular responses to mechanical stimuli are influenced by the mechanical properties of cells and the surrounding tissue matrix. Cells exhibit viscoelastic behavior in response to an applied stress. This has been attributed to fluid flow-dependent and flow-independent mechanisms. However, the particular mechanism that controls the local time-dependent behavior of cells is unknown. Here, a combined approach of experimental AFM nanoindentation with computational modeling is proposed, taking into account complex material behavior. Three constitutive models (porohyperelastic, viscohyperelastic, poroviscohyperelastic) in tandem with optimization algorithms were employed to capture the experimental stress relaxation data of chondrocytes at 5 % strain. The poroviscohyperelastic models with and without fluid flow allowed through the cell membrane provided excellent description of the experimental time-dependent cell responses (normalized mean squared error (NMSE) of 0.003 between the model and experiments). The viscohyperelastic model without fluid could not follow the entire experimental data that well (NMSE = 0.005), while the porohyperelastic model could not capture it at all (NMSE = 0.383). We also show by parametric analysis that the fluid flow has a small, but essential effect on the loading phase and short-term cell relaxation response, while the solid viscoelasticity controls the longer-term responses. We suggest that the local time-dependent cell mechanical response is determined by the combined effects of intrinsic viscoelasticity of the cytoskeleton and fluid flow redistribution in the cells, although the contribution of fluid flow is smaller when using a nanosized probe and moderate indentation rate. The present approach provides new insights into viscoelastic responses of chondrocytes, important for further understanding cell mechanobiological mechanisms in health and disease.


Atomic force microscopy; Cell mechanics; Chondrocyte; Finite element analysis; Nanoindentation; Poroviscohyperelastic; Stress relaxation

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