Poroelasticity of Cartilage at the Nanoscale

Abstract

Atomic-force-microscopy-based oscillatory loading was used in conjunction with finite element modeling to quantify and predict the frequency-dependent mechanical properties of the superficial zone of young bovine articular cartilage at deformation amplitudes, δ, of ∼15 nm; i.e., at macromolecular length scales. Using a spherical probe tip (R ∼ 12.5 μm), the magnitude of the dynamic complex indentation modulus, |E*|, and phase angle, φ, between the force and tip displacement sinusoids, were measured in the frequency range f ∼ 0.2–130 Hz at an offset indentation depth of δ[subscript 0] ∼ 3 μm. The experimentally measured |E*| and φ corresponded well with that predicted by a fibril-reinforced poroelastic model over a three-decade frequency range. The peak frequency of phase angle, f[subscript peak], was observed to scale linearly with the inverse square of the contact distance between probe tip and cartilage, [1 over d[superscript 2]], as predicted by linear poroelasticity theory. The dynamic mechanical properties were observed to be independent of the deformation amplitude in the range δ = 7–50 nm. Hence, these results suggest that poroelasticity was the dominant mechanism underlying the frequency-dependent mechanical behavior observed at these nanoscale deformations. These findings enable ongoing investigations of the nanoscale progression of matrix pathology in tissue-level disease.