Poroelasticity is the dominant energy dissipation mechanism in cartilage at the nano-scale

Abstract

Recent studies of micro- and nano-scale mechanics of cartilage and chondrocyte pericellular matrix have begun to relate matrix molecular structure to its mechanical response. AFM-based indentation has revealed rate-dependent stiffness at the micro-scale. While multi-scale elastic behavior has been studied, and poro-viscoelastic properties have been extensively documented at the tissue-level, time-dependent behavior and energy dissipation mechanisms of cartilage matrix at the nano-scale are not well understood. Here, we used AFM-based dynamic compression in conjunction with poroelastic finite element modeling to study the frequency-dependent behavior of cartilage using nano-scale oscillatory displacement amplitudes. We introduce the characteristic frequency f[subscript peak] at which the maximum energy dissipation occurs as an important parameter to characterize matrix time-dependent behavior. Use of micron-sized AFM probe tips with nano-scale oscillatory displacements over a 3-decade frequency range enabled clear identification of this characteristic frequency f[subscript peak]. The length-scale dependence of poroelastic behavior combined with judicious choice of probe tip geometry revealed flow-dependent and flow-independent behavior during matrix displacement amplitudes on the order of macromolecular dimensions and intermolecular pore-sizes.