Uncoupled poroelastic and intrinsic viscoelastic dissipation in cartilage

https://doi.org/10.1016/j.jmbbm.2018.04.024Get rights and content

Highlights

  • Poroelasticity and intrinsic viscoelasticity were decoupled.

  • Poroelasticity increased dissipation over baseline intrinsic viscoelasticity.

  • Cartilage energy dissipation was superior to isotropic poroelastic materials.

  • Substantial loss of fluid decreased intrinsic viscoelasticity.

  • Poroelastic and viscoelastic properties were measured at microscale lengths.

Abstract

This paper studies uncoupled poroelastic (flow-dependent) and intrinsic viscoelastic (flow-independent) energy dissipation mechanisms via their dependence on characteristic lengths to understand the root of cartilage's broadband dissipation behavior. Phase shift and dynamic modulus were measured from dynamic microindentation tests conducted on hydrated cartilage at different contact radii, as well as on dehydrated cartilage. Cartilage weight and thickness were recorded during dehydration. Phase shifts revealed poroelastic- and viscoelastic-dominant dissipation regimes in hydrated cartilage. Specifically, phase shift at a relatively small radius was governed by poroviscoelasticity, while phase shift at a relatively large radius was dominantly governed by intrinsic viscoelasticity. The uncoupled dissipation mechanisms demonstrated that intrinsic viscoelastic dissipation provided sustained broadband dissipation for all length scales, and additional poroelastic dissipation increased total dissipation at small length scales. Dehydration decreased intrinsic viscoelastic dissipation of cartilage. The findings demonstrated a possibility to measure poroelastic and intrinsic viscoelastic properties of cartilage at similar microscale lengths. Also they encouraged development of broadband cartilage like-dampers and provided important design parameters to maximize their performance.

Introduction

Articular cartilage is a connective tissue that functions as a load-bearing and dissipative material over a broadband spectrum of loading frequency. Cartilage has a heterogeneous structure composed of the dense solid matrix (e.g., collagen fibrils and proteoglycans) and fluid (Mow et al., 1992). Fluid is the largest constituent (about 60 – 85% of wet weight), and it plays an important role in swelling interfibriliar space (about 30% of total water) and extrafibriliar space (Maroudas et al., 1991, Mow et al., 1992, Torzilli, 1985). Cartilage dehydrate and rehydrate due to pressure-induced exudation of fluid through the solid matrix under normal loading conditions in vivo. Time-dependent properties of cartilage are from coupled mechanisms of the solid matrix and fluid flow. The mechanisms have been characterized as poroelasticity and intrinsic viscoelasticity, resulting in efficient and sustained broadband dissipative properties (Nia et al., 2011, Nia et al., 2013, Fulcher et al., 2009, Lawless et al., 2017).

Previous studies have provided evidence on poroelasticity and intrinsic viscoelasticity of cartilage, but the relative contributions of the two are unclear. Poroelasticity-driven dissipation and response originates from solid-fluid frictional (viscous drag) interaction, and therefore is flow-dependent (Nia et al., 2011, Nia et al., 2015). Previous studies showed that poroelasticity-driven dissipation was dominant at relatively small length scales (about 5–6 µm) under oscillatory loading (Nia et al., 2011, Nia et al., 2013). Intrinsic viscoelasticity-driven dissipation is associated with delay due to molecular friction and rearrangement of a solid matrix (Nia et al., 2011, Nia et al., 2015), and therefore is flow-independent (June et al., 2009, Lai and Hu, 2017, Mak, 1986). Previous work measured intrinsic viscoelasticity of cartilage by employing macroscale compression tests (Fulcher et al., 2009, June et al., 2009, Lawless et al., 2017, Mak, 1986) and small magnitude shear loading (Henak et al., 2016). Although a few studies have individually measured poroelasticity (Nia et al., 2011, Nia et al., 2013) and intrinsic viscoelasticity of cartilage (Fulcher et al., 2009, Lawless et al., 2017) over a wide spectrum of frequency, their relative contributions have not been uncoupled from each other. Also, it is difficult to utilize previously reported results to uncouple the mechanisms because test length scales (about 5–6 µm for poroelasticity (local) versus about 5 mm for intrinsic viscoelasticity (full-thickness)) are polarized, and therefore depth-dependent heterogeneous structure (e.g., collagen direction and diameter) of cartilage cannot be compared precisely.

Poroelasticity-driven dissipation is length-dependent, while intrinsic viscoelasticity-driven dissipation is not. This difference provides a means to distinguish the contributions of the two. Poroelastic dissipation is flow-dependent, and therefore is associated with characteristic poroelastic diffusion time. The diffusion time is proportional to the squared of a characteristic length (e.g., contact radius) (Lai and Hu, 2017, Nia et al., 2011). Consequently, a characteristic length can govern poroelasticity-driven dissipation. A poroelasticity-driven dissipation spectrum moves toward a low frequency range as a characteristic length increases, and its peak frequency, fporo, can be estimated with poroelastic diffusion time (Fig. 1) (Lai and Hu, 2017, Nia et al., 2011). In contrast, intrinsic viscoelastic dissipation is flow-independent (June et al., 2009, Lai and Hu, 2017, Mak, 1986). Accordingly, an intrinsic viscoelasticity-driven dissipation spectrum and its peak frequency, fvisco, are independent of a characteristic length (Fig. 1). Consequently, the two dissipation mechanisms can be distinguished over a broad frequency range by carefully selecting characteristic lengths.

The main aim of this study is to understand the origin of cartilage's broadband dissipation behavior by uncoupling the poroelastic and intrinsic viscoelastic dissipation mechanisms through their dependence on characteristic lengths. Phase shifts, a measure of dissipation, were measured at three different contact radii (characteristic lengths). Results of phase shifts were compared to uncouple the dissipation mechanisms. Dynamic moduli were also measured to examine dynamic response of cartilage based on the uncoupled dissipation mechanisms. In addition, phase shift and dynamic modulus of dehydrated cartilage were measured to further investigate the effect of fluid loss on broadband dissipative and mechanical properties.

Section snippets

Sample preparation

Full-thickness cartilage samples were harvested from patellae of porcine joints (12 animals, 5–6 months old, gender unknown and assumed random). Cylindrical samples with a diameter of 6 mm were obtained using a biopsy punch and a scalpel. Subchondral bone was trimmed using a microtome to create a level articular surface for indentation testing. The deep zone of each sample was adhered to the center of a glass petri dish (Loctite 495, Henkel, Germany). Dulbecco's phosphate-buffered saline (DPBS)

Results

Phase shifts of hydrated cartilage from asmall were significantly different from those from a large contact radius (i.e., amedium and alarge) (p < 0.05) (Fig. 3a). Phase shift from asmall gradually decreased from 5 Hz to 100 Hz, and its dependence on frequency was significant (p < 0.05). The maximum and minimum values were 30.50±2.19 degrees at 5 Hz and 13.74±1.28 degrees at 100 Hz, respectively. Phase shift from amedium was steady over the frequency range, and it was not significantly

Discussion

Intrinsic viscoelasticity provided baseline of dissipation over the broadband frequency, and poroelasticity additionally increased overall dissipation (Figs. 3a and 6). Phase shifts from asmall and large contact radii (i.e., amedium and alarge) originate from poroviscoelastic dissipation and intrinsic viscoelastic dominant dissipation, respectively (Fig. 3a). Therefore, the difference between phase shifts with asmall and amedium was from the contribution of poroelasticity-driven dissipation;

Conclusions

In this study, dissipative properties due to poroelasticity and intrinsic viscoelasticity of cartilage were investigated over physiological loading frequencies. Uncoupling between poroelasticity and intrinsic viscoelasticity was achieved via dependence of poroelastic relaxation on characteristic lengths (contact radii in dynamic indentation tests). The uncoupled dissipation mechanisms provided novel information on origins of efficient and sustained broadband dissipation of cartilage; intrinsic

Acknowledgment

Funding from the National Science Foundation (CMMI-DCSD-1662456) is gratefully acknowledged. The authors are grateful to Shannon K. Walsh and Sunjung Kim for helpful discussions on statistical analysis.

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