Elsevier

Acta Biomaterialia

Volume 64, December 2017, Pages 41-49
Acta Biomaterialia

Indentation mapping revealed poroelastic, but not viscoelastic, properties spanning native zonal articular cartilage

https://doi.org/10.1016/j.actbio.2017.10.003Get rights and content

Abstract

Osteoarthrosis is a debilitating disease affecting millions, yet engineering materials for cartilage regeneration has proven difficult because of the complex microstructure of this tissue. Articular cartilage, like many biological tissues, produces a time-dependent response to mechanical load that is critical to cell’s physiological function in part due to solid and fluid phase interactions and property variations across multiple length scales. Recreating the time-dependent strain and fluid flow may be critical for successfully engineering replacement tissues but thus far has largely been neglected. Here, microindentation is used to accomplish three objectives: (1) quantify a material’s time-dependent mechanical response, (2) map material properties at a cellular relevant length scale throughout zonal articular cartilage and (3) elucidate the underlying viscoelastic, poroelastic, and nonlinear poroelastic causes of deformation in articular cartilage. Untreated and trypsin-treated cartilage was sectioned perpendicular to the articular surface and indentation was used to evaluate properties throughout zonal cartilage on the cut surface. The experimental results demonstrated that within all cartilage zones, the mechanical response was well represented by a model assuming nonlinear biphasic behavior and did not follow conventional viscoelastic or linear poroelastic models. Additionally, 10% (w/w) agarose was tested and, as anticipated, behaved as a linear poroelastic material. The approach outlined here provides a method, applicable to many tissues and biomaterials, which reveals and quantifies the underlying causes of time-dependent deformation, elucidates key aspects of material structure and function, and that can be used to provide important inputs for computational models and targets for tissue engineering.

Statement of Significance

Elucidating the time-dependent mechanical behavior of cartilage, and other biological materials, is critical to adequately recapitulate native mechanosensory cues for cells. We used microindentation to map the time-dependent properties of untreated and trypsin treated cartilage throughout each cartilage zone. Unlike conventional approaches that combine viscoelastic and poroelastic behaviors into a single framework, we deconvoluted the mechanical response into separate contributions to time-dependent behavior. Poroelastic effects in all cartilage zones dominated the time-dependent behavior of articular cartilage, and a model that incorporates tension–compression nonlinearity best represented cartilage mechanical behavior. These results can be used to assess the success of regeneration and repair approaches, as design targets for tissue engineering, and for development of accurate computational models.

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

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