Uncoupled poroelastic and intrinsic viscoelastic dissipation in cartilage
Graphical abstract
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 degrees at 5 Hz and 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.
References (44)
- et al.
Characterization of polymeric structural foams under compressive impact loading by means of energy-absorption diagram
Int. J. Impact Eng.
(2001) - et al.
The structure and mechanical properties of articular cartilage are highly resilient towards transient dehydration
Acta Biomater.
(2016) - et al.
Fluid load support during localized indentation of cartilage with a spherical probe
J. Biomech.
(2012) - et al.
A numerical investigation of damping in fuzzy oscillators with poroelastic coating attached to a host structure
J. Sound Vib.
(2018) - et al.
Effects of sustained interstitial fluid pressurization under migrating contact area, and boundary lubrication by synovial fluid, on cartilage friction
Osteoarthr. Cartil. OARS Osteoarthr. Res. Soc.
(2008) - et al.
Tendon exhibits complex poroelastic behavior at the nanoscale as revealed by high-frequency AFM-based rheology
J. Biomech.
(2017) - et al.
The measurement of shock waves following heel strike while running
J. Biomech.
(1985) - et al.
Anisotropic dynamic changes in the pore network structure, fluid diffusion and fluid flow in articular cartilage under compression
Biomaterials
(2010) - et al.
Cartilage stress-relaxation proceeds slower at higher compressive strains
Arch. Biochem. Biophys.
(2009) - et al.
Viscoelasticity of articular cartilage: analysing the effect of induced stress and the restraint of bone in a dynamic environment
J. Mech. Behav. Biomed. Mater.
(2017)
A broadband damper design inspired by cartilage-like relaxation mechanisms
J. Sound Vib.
The effect of osmotic and mechanical pressures on water partitioning in articular cartilage
Biochim. Biophys. Acta BBA - Gen. Subj.
Cartilage and diarthrodial joints as paradigms for hierarchical materials and structures
Biomaterials
Poroelasticity of cartilage at the nanoscale
Biophys. J.
High-bandwidth AFM-based rheology reveals that cartilage is most sensitive to high loading rates at early stages of impairment
Biophys. J.
Care during freeze-drying of bovine pericardium tissue to be used as a biomaterial: a comparative study
Cryobiology
Matrix and cell injury due to sub-impact loading of adult bovine articular cartilage explants: effects of strain rate and peak stress
J. Orthop. Res.
Mechanical properties of collagen fibrils
Biophys. J.
Structure–mechanics relationships of collagen fibrils in the osteogenesis imperfecta mouse model
J. R. Soc. Interface
Correlation between apparent diffusion coefficient and viscoelasticity of articular cartilage in a porcine model
Skelet. Radiol.
Localization of viscous behavior and shear energy dissipation in articular cartilage under dynamic shear loading
J. Biomech. Eng.
A transversely isotropic biphasic model for unconfined compression of growth plate and chondroepiphysis
J. Biomech. Eng.
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