Effects of membrane pre-stress and intrinsic viscoelasticity on nanoindentation of cells using AFM

Abstract

Nanoindentation using atomic force microscopy (AFM) has found a wide range of applications in characterizing the mechanical properties of cells. However, both conventional Hertz theory and Sneddon's solution face difficulties in interpreting cell indentation data due to lack of considerations of the bilayered structure of cells, the pre-stress of cell membranes and the intrinsic viscoelasticity of cell interior phases. In the present study, the indentation of a cell using AFM is modelled as that of a pre-tensed elastic shell supported by a viscoelastic half-space. Analytical solutions are derived for the shallow indentation of the elastic counterpart of the bilayered structure and then extended to moderate-depth indentation. The cell membrane and its pre-tension are important in interpreting the indentation data if a small indenter is used. Based on the elastic solutions, viscoelastic solutions are derived for creep tests, relaxation tests and linear loading tests, and verified by finite element analysis. Parametric studies were performed to investigate the effects of the membrane pre-stress and the intrinsic viscoelasticity of the cell on the relation between the indentation load vs. indentation depth. In addition, an inverse analysis was performed to extract the viscoelastic parameters of the cell interior phase and the uniqueness of the extraction was assessed.