A Quantitative Interpretation of the Response of Articular Cartilage to Atomic Force Microscopy Based Dynamic Nanoindentation Tests

Abstract

In this paper, a quantitative interpretation for atomic force microscopybased dynamic nanoindentation (AFMDN) tests on the superficial layers of bovine articular cartilage (AC) is provided. The relevant constitutive parameters of the tissue are estimated by fitting experimental results with a finite element model in the frequency domain. Such model comprises a poroelastic stress–strain relationship for a fibril reinforced tissue constitution, assuming a continuous distribution of the collagen network orientations. The identification procedure was first validated using a simplified transversely isotropic constitutive relationship; then, the experimental data were manually fitted by using the continuous distribution fibril model. Tissue permeability is derived from the maximum value of the phase shift between the input harmonic loading and the harmonic tissue response. Tissue parameters related to the stiffness are obtained from the frequency response of the experimental storage modulus and phase shift. With this procedure, an axial to transverse stiffness ratio (anisotropy ratio) of about 0.15 is estimated.