A simple and robust method for characterizing the power-law rheology behavior of biological cells through...

For biological cells, their viscoelastic properties play critical roles in both physiological and pathological processes, and indentation has emerged as a key technique to extract mechanical properties. If purely elastic behavior is assumed, the achieved elastic moduli become depth-dependent and highly scattered, underscoring the need to account for cellular viscoelasticity. However, the complexity of existing methods poses significant challenges for the practical extraction of viscoelastic parameters from standard indentations. In this work, we formulate explicit expressions describing spherical and conical indentation responses for viscoelastic cells elucidated by power-law rheology (PLR) model. Combining Lee and Radok's approach and traditional Hertzian and Sneddon's contact models, the relations between apparent modulus and loading time are obtained analytically, which are independent of loading velocity. Notably, the linear dependence of the normalized apparent modulus on loading time on a logarithmic scale can be utilized as a signature of the PLR behavior of cells, and its explicit expression can be directly adopted to accurately extract the viscoelastic parameters of cells. Applications of this approach to standard indentations enable robust extraction of viscoelastic parameters, with high consistency demonstrated across both virtual numerical experiments and actual experiments. This work presents a straightforward and reliable approach to accurately determine the viscoelastic properties of biological cells from standard indentations, without the need for complex fitting procedures or velocity-dependent corrections.