Is it mathematically correct to fit AFM data (obtained on biological materials) to equations arising from Hertzian mechanics?

When testing soft biological samples using the Atomic Force Microscopy (AFM) nanoindentation method, the force-indentation data is usually fitted to the equations provided by Hertzian mechanics. Nevertheless, a significant question remains up to date; is this a correct approach from a mathematical perspective? Biological materials are heterogeneous, so 'what do we calculate' when using a classic fitting approach? In this paper, conclusive answers to the abovementioned questions are provided. In addition, a new tool for the nanomechanical characterization of biological samples, the depth-dependent mechanical properties maps, is introduced.

Automated summary

This paper provides conclusive answers to the mathematical question regarding the fitting approach in testing soft biological samples and introduces a new tool, depth-dependent mechanical properties maps, for nanomechanical characterization of biological samples.