Quasi-linear viscoelastic properties of PC-12 neuron-like cells measured using atomic force microscopy

Atomic force microscopy has been widely used to measure the mechanical properties of living cells. Models based on Hertz theory are often utilized to estimate the Young's modulus of cells. In practice, the nonlinear viscoelastic behavior of cells can often be observed in indentation experiments. In this article, the quasi-linear viscoelasticity (QLV) theory, which has been successfully applied to many biological tissues, was employed to construct the constitutive equation of neuron-like PC-12 cells. The values of Young's modulus obtained via our proposed method were one or two orders of magnitude, depending on the indenting rate, less than those obtained using methods based on the modified Hertzian model. The Kelvin model was also introduced to describe the solid and liquid behavior of cells. The prediction error of the Kelvin model was larger than that of the proposed QLV model, especially at the peak force and the toe portion of the force response. The results revealed that the Young's modulus estimated by the QLV model was less affected by indenting rates than that estimated by the modified Hertzian model or the Kelvin model. The proposed QLV model accounting for the indenting conditions was capable of describing both the nonlinear elastic response and relaxation behavior and, therefore, was more appropriate for modeling the biomechanical behaviors of PC-12 cells than the nonlinear elastic model or the linear viscoelastic model.