A Comprehensive Study of AFM Stiffness Measurements on Inclined Surfaces: Theoretical, Numerical, and Experimental Evaluation using a Hertz Approach

Abstract

In the field of cellular health assessment, the mechanical properties of cells are crucial indicators. Atomic Force Microscopy (AFM) is a prominent nanoscale technique used for its significant benefits in analyzing cell mechanics. Traditional analysis of AFM data often relies on Hertz's law, which assumes a flat surface for the biological sample. However, this assumption does not always hold true due to the diverse geometries of cells. In this study, we present a new theoretical model that includes correction coefficients in Hertz's law to consider cone-like and spherical probes, addressing the local tilt at the probe-sample interface. We validated our model through Finite Element Analysis (FEA) simulations and experimental AFM measurements on tilted polyacrylamide gels. Our findings emphasize the importance of accounting for the local tilt in probe-sample contact to ensure accurate AFM measurements. This marks a significant advancement in our understanding of cell mechanics at the nanoscale.