Determination of viscoelastic properties of living cells from the time-dependent interpretation of Hertz model

Abstract

In this master’s thesis, we present a modified version of the Hertz contact theory, providing not only the elastic, but also the viscous characteristics of living cells. The Hertzian model imposes limitations when applied to complex scenarios involving larger deformations, non-ideal surfaces, and adhesive interactions. Despite its limitations, the Hertz model provides quick estimations and initial assessments of mechanical properties in a variety of experimental setups. However, when dealing with larger deformations, nonlinear effects, and adhesive interactions, more sophisticated models and techniques might be required to accurately understand the viscoelastic properties of biological samples. In this sense, conventional Hertz equation’s Young’s modulus is reformulated as a time-dependent function, enabling the analysis of the viscoelasticity. Thus, in order to prove our model experimentally, we used the atomic force microscopy (AFM) technique to explore the mechanical properties of L929 fibroblastic and OFCOL II osteoblastic cells. Furthermore, the proposed model was rigorously tested in various conditions, simulating different geometries of the indenter (conical, flat, and spherical), with minimal disparity of the estimated Young’s moduli obtained from the power-law and Hertz models fitted to actual cell stiffness.