Quantitative mechanical analysis of indentations on layered, soft elastic materials

Area of Science:

• Biophysics
• Materials Science
• Cell Mechanics

Background:

• Atomic force microscopy (AFM) is crucial for cell mechanics studies.
• Current AFM analysis tools struggle with mechanically heterogeneous biological samples.
• Accurate elastic modulus determination is vital for understanding cell behavior.

Purpose of the Study:

• To develop a quantitative model for AFM indentation analysis of two-layered elastic materials.
• To account for mechanical heterogeneity in biological samples during AFM indentation.
• To provide a guideline for designing and interpreting AFM indentation experiments.

Main Methods:

• Numerical calculation of force-indentation curves using an analytic model for two-layered elastic materials.
• Development of a phenomenological model for indentation force on layered materials.
• Verification using finite element analysis (FEA) simulations.
• Validation through AFM microindentation and macroindentation experiments.

Main Results:

• The effect of the substrate on indentation is predictable based on elastic modulus mismatch and layer height.
• A closed-form equation accurately predicts indentation force for significant Young's modulus mismatches (up to two orders of magnitude) when contact radius is less than layer height.
• The model successfully deconvolutes the Young's modulus of individual layers in heterogeneous samples.

Conclusions:

• The developed model accurately quantifies mechanical properties of layered elastic materials.
• This approach significantly enhances the analysis of AFM indentation data from heterogeneous biological samples.
• The model serves as a valuable tool for experimental design and interpretation in cell mechanics research.