On the Interplay Between Roughness and Elastic Modulus at the Nanoscale: A Methodology Study with Bone as Model Material.

Abstract

Atomic force microscopy (AFM)-based nanoindentation enables investigation of the mechanical response of biological materials at a subcellular scale. However, quantitative estimates of mechanical parameters such as the elastic modulus (E) remain unreliable because the influence of sample roughness on E measurements at the nanoscale is still poorly understood. This study re-examines the interpretation of roughness from a more rigorous perspective and validates an experimental methodology to extract roughness at each nanoindentation site-i.e., the local roughness γ_s-with which the corresponding E value can be accurately correlated. Cortical regions of a murine tibia cross-section, characterized by complex nanoscale morphology, were selected as a testbed. Eighty non-overlapping nanoindentations were performed using two different AFM tips, maintaining a maximum penetration depth of 10 nm for each measurement. Our results show a slight decreasing trend of E versus γ_s (Spearman's rank correlation coefficient ρ = -0.27187). A total of 90% of the E values are reliable when γ_s < 10 nm (coefficient of determination R² > 0.90), although low γ_s values are associated with significant dispersion around E (γ_s = 0) = E₀ = 1.18 GPa, with variations exceeding 50%. These findings are consistent with a qualitative tip-to-sample contact model that accounts for the pronounced roughness heterogeneity typical of bone topography at the nanoscale.