Indentation mapping revealed poroelastic, but not viscoelastic, properties spanning native zonal articular cartilage
Graphical abstract
Introduction
Biological tissues, e.g. cartilage, present significant property differences over small (i.e., nano- to micrometer) length scales and marked time-dependent behavior. Accurate determination of properties and their variation throughout tissues is vital to engineer materials that effectively recapitulate the property gradients that are present in native tissues, e.g. to match cellular level strains particularly under dynamic mechanical loading and to provide appropriate mechanical cues to cells. Much work thus far has focused on creating simple constructs that match bulk tissue properties at very slow loading rates, yet this approach neglects the dramatically different properties observed at higher physiological loading rates and the complex, hierarchical organization of most tissues that spans multiple length scales (e.g., nanometers to centimeters).
Articular cartilage is particularly compelling due to the prevalence of osteoarthritis and as a complex material possessing significant mechanical property variation, underlying chemistry, and extracellular matrix organization from the articular surface to the underlying bone [1], [2], [3], [4], [5], [6], [7]. While articular cartilage possesses a pronounced time-dependent response [8], [9], classic methods for mechanical property assessment [10], [11] and evaluating fluid-structure interactions [12], [13], [14] poorly assess behavior within small regions of tissue, e.g., within individual cartilage zones. Displacements of chondrocytes in cartilage sections have been mapped via digital image correlation [5], [6], [15], or through the use of displacement-encoded magnetic resonance imaging [16], [17]; however, these methods apply loads to bulk sections of tissue and prevent direct loading of specific cartilage zones. Thus, while inverse methods have been applied to estimate properties, the quantification of time-dependent mechanisms remains daunting and prone to error. In contrast, microindentation provides a facile way to directly observe the mechanical response of cartilage in situ without altering the zonal arrangement, while enabling investigation of both elastic and time-dependent material behaviors.
The time-dependent response in articular cartilage has been attributed to viscoelasticity, poroelasticity, or a combination of these phenomenon [18], [19], [20], [21], [22], [23]. Yet it is likely that these behaviors vary with the underlying chemistry and extracellular matrix organization in zonal cartilage. Indentation of the articular surface has evaluated equilibrium properties of native, diseased, and repair cartilage [24], [25], [26], [27], [28] and begun to explore the time-dependent response [9], [22], [29], [30]. Results were combined with finite element models [21], [31] and correlated with chemistry in maps spanning osteochondral tissues [32], [33], [34]. However, much work remains to establish time-dependent material properties for each cartilage zone.
Microindentation uniquely provides the ability to assess both time-dependent behavior in small tissue volumes and the underlying causes of this deformation at length scales relevant to cells. Because viscoelastic models assume that materials act as a continuum, mechanical response is assumed to be independent of indenter probe radius if the applied strain and strain rates are kept constant [35]. Thus if the rise (i.e., indentation) time and the ratio of indenter depth to indenter radius are maintained, then the measured material parameters should not vary with indenter size. On the other hand, because poroelastic models assume that a time-dependent response is due to fluid transport, the size of the indenter has a nonlinear impact on the behavior of the tested material. For this poroelastic case, a characteristic rise time can be established which is proportional to the square of the indentation radius if relative indentation depth is kept constant [36], [37]. Thus, testing at various indentation rates using multiple sizes of indenter probes with rates matched via viscoelastic or poroelastic assumptions can determine whether time-dependent material behavior is due to physical arrangement of the solid material (i.e., viscoelasticity) or fluid transport (i.e., poroelasticity). With data obtained by performing experiments using multiple sized probes, we can now evaluate whether viscoelastic [38] or poroelastic [9], [36] models better represent cartilage behavior in each zone.
Using a novel microindentation-based approach, we test the hypothesis that a nonlinear biphasic model [9] best represents the time-dependent mechanical behavior of articular cartilage. Trypsin treatment was also employed to increase permeability through glycosaminoglycan (GAG) depletion [39], [40] to evaluate changes in the time-dependent mechanical response, with increased permeability of cartilage, with the goal of deconvoluting viscoelastic and poroelastic behavior. In this work we performed indentation using multiple sized indenters and multiple initial loading rates for untreated cartilage, trypsin treated cartilage, and agarose. The indentation modulus was obtained from the initial portion of the load/displacement response and used to determine the dominant time dependent mechanism (poroelastic vs. viscoelastic). The load relaxation data was then fit using the appropriate class of material models. Additionally the nonlinear biphasic model was fit using a multiple indent approach to compensate for finite loading rates. Evaluating zonal material properties provides an important target for tissue engineering to match deformations and fluid flows experienced by cells in native tissue, to improve accuracy of computational finite element models of cartilage, and may provide novel insight into osteoarthritis progression.
Section snippets
Materials
Agarose, a material with known poroelastic behavior [41], samples were prepared (Sigma, A9539) to 10% (w/w), dissolved into phosphate buffered saline (PBS) with a pH of 7.4, heated to 90 °C in a double boiler while being continuously mixed with a magnetic stir rod, and centrifuged (2500 RPM, 5 min) to eliminate bubbles. Eight specimens were sectioned using a vibratome (Technical Products International, Vibratome 1000) to 1 mm thick slices and mounted to 1 mm thick steel testing pucks using a thin
Results
Initial indentation modulus was used to compare matched strain rates (i.e., viscoelastic assumptions) or matched characteristic poroelastic indentation rate (i.e., poroelastic assumptions [36], [37], see supplemental material) using two cono-spherical indenters of different radii. Mean R ^ 2 values for the Hertzian fitting of the indentation data demonstrated validity of this approach as follows: Untreated – 0.993 ± 0.017, Trypsin Treated – 0.988 ± 0.017, and Agarose – 0.998 ± 0.0028. Indentation of
Discussion
Biological and biomimetic materials frequently present significant property differences over small length scales and a pronounced time-dependent response producing vastly different mechanical properties at physiological loading rates compared to equilibrium properties. The approach presented herein represents a systematic method to investigate and quantify these properties to provide invaluable information for those seeking to recapitulate native mechanosensory cues for cells. Using
Conclusion
This study demonstrated a method to measure the time-dependent behavior of biological and biomimetic materials. This understanding is important to recreate the mechanical environment of native tissue and stimulate cells with physiologically relevant strains and fluid flow. Using indentation, we mapped property variation over cell relevant length scales within a tissue. Further, this approach illuminated the underlying poroelastic and or viscoelastic causes of time-dependence in articular
Conflict of interest
The authors do not have any conflicts of interest to disclose.
Acknowledgements
The National Science Foundation [NSF #1055989 and #1338154], National Institutes of Health [1R01AR069060-01A1] and the Univ. of Colorado Innovative Grants supported this work. Imaging performed at the Univ. of Colorado Anschutz Advanced Light Microscopy Core was supported by NIH/NCATS [UL1 TR001082]. We also thank Drs. Michelle Oyen and David Burris for providing Matlab code and spreadsheets used for data analysis. Specific commercial equipment, instruments, and materials identified in this
References (68)
- et al.
Depth-dependent biomechanical and biochemical properties of fetal, newborn, and tissue-engineered articular cartilage
J. Biomech.
(2007) - et al.
Depth-dependent anisotropy of the micromechanical properties of the extracellular and pericellular matrices of articular cartilage evaluated via atomic force microscopy
J. Biomech.
(2013) - et al.
Depth-dependent compressive properties of normal aged human femoral head articular cartilage: relationship to fixed charge density
Osteoarthr. Cartilage
(2001) - et al.
Zonal changes in the three-dimensional morphology of the chondron under compression: The relationship among cellular, pericellular, and extracellular deformation in articular cartilage
J. Biomech.
(2007) - et al.
Mechanical response of bovine articular cartilage under dynamic unconfined compression loading at physiological stress levels
Osteoarthr. Cartilage
(2004) - et al.
Fluid load support during localized indentation of cartilage with a spherical probe
J. Biomech.
(2012) - et al.
Lai, Fluid transport and mechanical properties of articular cartilage: a review
J. Biomech.
(1984) - et al.
A fiber reinforced poroelastic model of nanoindentation of porcine costal cartilage: a combined experimental and finite element approach
J. Mech. Behav. Biomed. Mater.
(2009) - et al.
Poroelastic response of articular cartilage by nanoindentation creep tests at different characteristic lengths
Med. Eng. Phys.
(2014) - et al.
Stresses in the local collagen network of articular cartilage: a poroviscoelastic fibril-reinforced finite element study
J. Biomech.
(2004)
Mechanical properties of hyaline and repair cartilage studied by nanoindentation
Acta Biomater.
Nanoindentation of biological materials
Nano Today
Dynamic nanoindentation of articular porcine cartilage
Mater. Sci. Eng. C.
Use of microindentation to characterize the mechanical properties of articular cartilage: comparison of biphasic material properties across length scales
Osteoarthr. Cartilage
Poroviscoelastic finite element model including continuous fiber distribution for the simulation of nanoindentation tests on articular cartilage
J. Mech. Behav. Biomed. Mater.
Two different correlations between nanoindentation modulus and mineral content in the bone–cartilage interface
J. Struct. Biol.
Poroviscoelastic characterization of particle-reinforced gelatin gels using indentation and homogenization
J. Mech. Behav. Biomed. Mater.
Nanoindentation of viscoelastic solids: a critical assessment of experimental methods
Curr. Opin. Solid State Mater. Sci.
An analytical model to predict interstitial lubrication of cartilage in migrating contact areas
J. Biomech.
Experimental characterization of biphasic materials using rate-controlled Hertzian indentation
Tribol. Int.
Optical and mechanical determination of poisson’s ratio of adult bovine humeral articular cartilage
J. Biomech.
Cartilage interstitial fluid load support in unconfined cmaompression
J. Biomech.
Anisotropy, inhomogeneity, and tension–compression nonlinearity of human glenohumeral cartilage in finite deformation
J. Biomech.
Anisotropic strain-dependent material properties of bovine articular cartilage in the transitional range from tension to compression
J. Biomech.
The changing role of the superficial region in determining the dynamic compressive properties of articular cartilage during postnatal development
Osteoarthr. Cartil. OARS Osteoarthr. Res. Soc.
The tensile properties of the cartilage of human femoral condyles related to the content of collagen and glycosaminoglycans
Biochim. Biophys. Acta BBA – Gen. Subj.
Synthesis and characterization of a lubricin mimic (mLub) to reduce friction and adhesion on the articular cartilage surface
Biomaterials
Mechano-electrochemical properties of articular cartilage: Their inhomogeneities and anisotropies
Annu. Rev. Biomed. Eng.
Depth-dependent confined compression modulus of full-thickness bovine articular cartilage
J. Orthop. Res.
Video microscopy to quantitate the inhomogeneous equilibrium strain within articular cartilage during confined compression
Ann. Biomed. Eng.
Comparative study of the intrinsic mechanical properties of the human acetabular and femoral head cartilage
J. Orthop. Res. Off. Publ. Orthop. Res. Soc.
Biomechanical properties of knee articular cartilage
Biorheology
Transport of solutes through cartilage: permeability to large molecules
J. Anat.
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