Atomic force microscopy (AFM) has become one of the most used techniques for quantifying the mechanical properties of soft materials such as living cells. AFM force-indentation curves are conventionally fitted with a Hertzian model to extract elastic properties. The elastic properties solely are, however, insufficient to describe the mechanical properties of cells. Hence, extending the quantification to assess, in addition, the viscous behavior, is necessary for a more adequate characterization of the mechanical properties. Here, we expand the analysis capabilities to describe the viscoelastic behavior of the probed materials while using the same conventional AFM force-indentation curves. Our model gives an explicit relation of force and indentation and extracts physically meaningful cell mechanical parameters. We first validated the model on simulated forceindentation curves of a viscoelastic half-infinite space. Then, we applied the fitting model to the force-indentation curves of two hydrogels with different crosslinking mechanisms, polyacrylamide and agarose. We demonstrated that the viscoelastic properties extracted using our fitting model reflected adequately the distinct nature of these hydrogels. Finally, we characterized HeLa cells in two different cell cycle phases, interphase and mitosis and showed that mitotic cells have a higher apparent elasticity and a lower apparent viscosity when compared to interphase cells. Our study provides a simple and rapid method, which can be directly integrated into the standard AFM framework, for extracting the viscoelastic properties of materials. This facilitates the exploration of advanced material properties in general and the understanding of complex biophysical processes in particular.
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