Determination of the elastic modulus of adherent cells using spherical atomic force microscope probe

When the conventional Hertz formula is used to extract the elastic modulus, E, of cells based on the compression test using atomic force microscope spherical probe, the inconsistency between the actual situation and the assumption of the formula will lead to a large error. Using the ABAQUS for finite element modeling and analysis, here, a modified Hertz formula was developed to reduce the effects of cell radius, cell thickness, probe radius and compression depth on the extracted E of cells. Experimentally, the insensitivity of the extracted E to the compression region of cell and probe radius reflects the validity of the modified formula. Owing to the poor resolution of spherical probes, it's unlikely to know the actual thickness of cell at the measured point, which can lead to a huge error. Based on the modified formula, we further proposed an approach to control the effect of the uncertainty of cell thickness and ensured that a 10% difference in cell thickness does not incur over 10% variation in the obtained elastic modulus.