Determination of the linear elastic regime in AFM nanoindentation experiments on cells

Atomic force microscopy nanoindentation method has been extensively used for the determination of cells' mechanical properties. The data processing is usually performed using contact mechanics models at the linear elastic regime such as the Hertz model. It should be noted that the cells' response can be considered as linearly elastic only for a limited range of indentation depths. Although there are in literature proposed values of the maximum allowed nanoindentation depth for most of the cell types, these values have been mostly derived empirically. As a result, the use of these empirically obtained findings can result in significant errors regarding Young's modulus calculations. A large number of measurements, using spherical and conical indenters, showed errors in the range of 4-10% with respect to the Young's modulus calculation. In this paper, a new mathematical approach is proposed that enables the identification of the optimum load - indentation data range for the application of the Hertz contact theory. The results presented in this paper indicate that the optimum choice of the maximum indentation depth can vary greatly even in the same sample. For example, 64 load indentation curves on the same cell using a spherical indenter showed that the maximum indentation depth is (553 +/- 43)nm (mean value +/- standard deviation). As a consequence, the determination of a specific maximum indentation depth for indentation experiments on a specific cell will lead to significant errors regarding Young's modulus values. Hence, the selection of the linear elastic regime must be performed individually for each load-indentation curve to accurately determine the cell's mechanical response.