Application of a layered model for determination of the elasticity of biological systems

Elasticity of biological systems is considered to be an important property that might be related to functional or pathological changes. Therefore, careful study and detailed understanding of cell and tissue elasticity is crucial for correct description of their functioning. Atomic Force Microscopy (AFM) is a powerful technique, which allows for determination of the physical properties, such as elasticity, of soft-matter systems in nano-scale. An important step in AFM elasticity studies is a proper interpretation of experimental data. Two most frequently used theoretical schemes applied to determine elasticity are due to Hertz and Sneddon, which are effectively one-parameter models. In this work, we go beyond this approach. Firstly, as elasticity is a local property, we extract from the slope of experimental force-indentation curve an elasticity parameter, which varies with indentation depth. Then secondly, we find best approximation of this parameter by applying the two-layer model with four effective parameters, as proposed by Kovalev. This method is employed to the experimental data taken on murine liver sinusoidal endothelial cells in non-alcoholic fatty liver disease model. The obtained results show additional effects, not seen within the traditional, simplified scheme. Namely, the elasticity of the first layer does not change its value in the model of non-alcoholic fatty liver disease, but the increase of stiffness is noticed in second layer. The second goal of this article is to reveal and discuss the differences between traditional approaches and the one being presented. The deviations from the original assumptions are analysed and the corresponding restrictions on utility of theoretical models are presented.