0
Research Papers

A Quantitative Interpretation of the Response of Articular Cartilage to Atomic Force Microscopy-Based Dynamic Nanoindentation Tests

[+] Author and Article Information
Matteo Taffetani

MOX, Politecnico di Milano and Fondazione
CEN–Centro Europeo di Nanomedicina,
Piazza Leonardo da Vinci, 32,
Milano 20133, Italy
e-mail: matteo.taffetani@polimi.it

Roberto Raiteri

Department of Informatics, Bioengineering,
Robotics, and System Engineering,
Università di Genova,
via Opera pia, 13,
Genova 16145, Italy
e-mail: roberto.raiteri@unige.it

Riccardo Gottardi

Ri.MED Foundation,
Palermo 90133, Italy
Department of Orthopaedic Surgery,
University of Pittsburgh,
Pittsburgh, PA 15260
e-mail: RIG10@pitt.edu

Dario Gastaldi

Department of Chemistry,
Materials and Chemical Engineering,
Politecnico di Milano,
Piazza Leonardo da Vinci, 32,
Milano 20133, Italy
e-mail: Dario.gastialdi@polimi.it

Pasquale Vena

Mem. ASME
Department of Chemistry Materials
and Chemical Engineering,
Politecnico di Milano,
Piazza Leonardo da Vinci, 32,
Milano 20133, Italy
IRCCS—Istituto OrtopedicoGaleazzi,
P.zzaR.Galeazzi4,
Milano 20161, Italy
e-mail: pasquale.vena@polimi.it

1Corresponding author.

Manuscript received December 9, 2014; final manuscript received March 15, 2015; published online June 2, 2015. Assoc. Editor: Amir Abbas Zadpoor.

J Biomech Eng 137(7), 071005 (Jul 01, 2015) (8 pages) Paper No: BIO-14-1615; doi: 10.1115/1.4030175 History: Received December 09, 2014; Revised March 15, 2015; Online June 02, 2015

In this paper, a quantitative interpretation for atomic force microscopy-based dynamic nanoindentation (AFM-DN) tests on the superficial layers of bovine articular cartilage (AC) is provided. The relevant constitutive parameters of the tissue are estimated by fitting experimental results with a finite element model in the frequency domain. Such model comprises a poroelastic stress–strain relationship for a fibril reinforced tissue constitution, assuming a continuous distribution of the collagen network orientations. The identification procedure was first validated using a simplified transversely isotropic constitutive relationship; then, the experimental data were manually fitted by using the continuous distribution fibril model. Tissue permeability is derived from the maximum value of the phase shift between the input harmonic loading and the harmonic tissue response. Tissue parameters related to the stiffness are obtained from the frequency response of the experimental storage modulus and phase shift. With this procedure, an axial to transverse stiffness ratio (anisotropy ratio) of about 0.15 is estimated.

FIGURES IN THIS ARTICLE
<>
Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.

References

Pearle, A., Warren, R., and Rodeo, S., 2005, “Basic Science of Articular Cartilage and Osteoarthritis,” Clin. Sports Med., 24(1), pp. 1–12. [CrossRef] [PubMed]
Mankin, H., Mow, V., and Buckwalter, J., 1999, “Articular Cartilage Structure, Composition and Function,” Orthopaedic Basic Science: Biology and Biomechanics of the Musculoskeletal System, American Academy of Orthopaedic Surgeons, Rosemont, IL, pp. 443–470.
Poole, A., Kojima, T., Yasuda, T., Mwale, F., Kobayashi, M., and Laverty, S., 2001, “Composition and Structure of Articular Cartilage: A Template for Tissue Repair,” Clin. Orthop. Relat. Res., 391(Suppl.), pp. S26–S33. [CrossRef] [PubMed]
Schinagl, R., Gurskis, D., Chen, A., and Sah, R., 1997, “Depth-Dependent Confined Compression Modulus of Full Thickness Bovine Articular Cartilage,” J. Orthop. Res., 15(4), pp. 499–506. [CrossRef] [PubMed]
Appleyard, R., Burkhardt, D., Ghosh, P., Read, R., Cake, M., Swain, M., and Murrel, G., 2003, “Topographical Analysis of the Structural, Biochemical and Dynamical Biomechanical Properties of Cartilage in an Ovine Model of Osteoarthritis,” Osteoarthritis Cartilage, 11(1), pp. 65–77. [CrossRef] [PubMed]
Huang, C., Mow, V., and Ateshian, G., 2001, “The Role of Flow Independent Viscoelasticity in the Biphasic Tensile and Compressive Responses of Articular Cartilage,” ASME J. Biomech. Eng., 123(5), pp. 410–418. [CrossRef]
Hu, Y., Zhao, X., Vlassak, J., and Suo, Z., 2010, “Using Indentation to Characterize the Poroelasticity of Gels,” Appl. Phys. Lett., 96(12), p. 121904. [CrossRef]
Ebenstein, D., and Pruitt, L., 2006, “Nanoindentation of Biological Materials,” Nano Today, 1(3), pp. 26–33. [CrossRef]
Stolz, M., Gottardi, R., Raiteri, R., Miot, S., Martin, I., Imer, R., Staufer, U., Raducanu, A., Duggelin, M., Baschong, W., Daniels, A., Friederich, N., Aszodi, A., and Aebi, U., 2009, “Early Detection of Aging Cartilage and Osteoarthritis in Mice and Patient Samples Using Atomic Force Microscopy,” Nat. Nanotechnol., 4(3), pp. 186–192. [CrossRef] [PubMed]
Armstrong, C., Lai, V., and Mow, V., 1984, “An Analysis of the Unconfined Compression of Articular Cartilage,” ASME J. Biomed. Eng., 106(2), pp. 165–173. [CrossRef]
Li, C., Pruitt, L., and King, K., 2006, “Nanoindentation Differentiates Tissue-Scale Functional Properties of Native Articular Cartilage,” J. Biomed. Mater. Res., Part A, 78(4), pp. 729–758. [CrossRef]
Stolz, M., Raiteri, R., Daniels, A., van Landingham, M., Baschong, W., and Aebi, U., 2004, “Dynamic Elastic Modulus of Porcine Articular Cartilage Determined at Two Different Levels of Tissue Organization by Indentation-Type Atomic Force Microscopy,” Biophys. J., 85(5), pp. 3269–3683. [CrossRef]
Loparic, M., Wirtz, D., Daniels, A., Raiteri, R., van Landingham, M., Guex, G., Martin, I., Aebi, U., and Stolz, M., 2010, “Micro- and Nanomechanical Analysis of Articular Cartilage by Indentation-Type Atomic Force Microscopy: Validation With a Gel–Microfiber Composite,” Biophys. J., 98(11), pp. 2731–2740. [CrossRef] [PubMed]
Simha, N., Jin, H., Hall, M., Chiravarambath, S., and Lewis, J., 2007, “Effect of Indenter Size on Elastic Modulus of Cartilage Measured by Indentation,” ASME J. Biomech. Eng., 129(5), pp. 767–775. [CrossRef]
Franke, O., Goken, M., Meyers, M., Durst, K., and Hodge, A., 2011, “Dynamic Nanoindentation of Articular Porcine Cartilage,” Mater. Sci. Eng. C, 31(4), pp. 789–795. [CrossRef]
Han, L., Frank, E., Greene, J., Lee, H., Hung, H., Grodzinsky, A., and Ortiz, C., 2011, “Time-Dependent Nanomechanics of Cartilage,” Biophys. J., 100(7), pp. 1846–1854. [CrossRef] [PubMed]
Taffetani, M., Bertarelli, E., Gottardi, R., Raiteri, R., and Vena, P., 2012, “Modelling of the Frequency Response to Dynamic Nanoindentation of Soft Hydrated Anisotropic Materials: Application to Articular Cartilage,” Comput. Model. Eng. Sci., 87(5), pp. 433–460. [CrossRef]
Taffetani, M., Griebel, M., Gastaldi, D., Klisch, S., and Vena, P., 2014, “Poroviscoelastic Finite Element Model Including Continuous Fiber Distribution for the Simulation of Nanoindentation Tests on Articular Cartilage,” J. Mech. Behav. Biomed. Mater., 32(1), pp. 17–30. [CrossRef] [PubMed]
Hutter, J., and Bechhoefer, J., 1993, “Calibration of Atomic Force Microscope Tips,” Rev. Sci. Instrum., 64(7), pp. 1868–1876. [CrossRef]
Raiteri, R., Preuss, M., Grattarola, M., and Butt, H., 1998, “Preliminary Results on the Electrostatic Double Layer Force Between Two Surface With High Surface Potential,” Colloid Surf. A, 136(1–2), pp. 195–201. [CrossRef]
Johnson, K., 1985, Contact Mechanics, Cambridge University, Cambridge, UK. [CrossRef]
Field, J., and Swain, M., 1993, “A Simple Predictive Model for Spherical Indentation,” J. Mater. Res., 8(2), pp. 297–306. [CrossRef]
Cowin, S., and Doty, S., 2006, Tissue Mechanics, Springer Verlag, New York. [CrossRef]
Ateshian, G., Rajan, V., Chahine, N., Canal, C., and Hung, C., 2009, “Modeling the Matrix of Articular Cartilage Using a Continuous Fiber Angular Distribution Predicts Many Observed Phenomena,” ASME J. Biomech. Eng., 131(6), p. 061003. [CrossRef]
Stender, M. E., Raub, C. B., Yamauchi, K. A., Shirazi, R., Vena, P., Sah, R. L., Hazelwood, S. J., and Klisch, S. M., 2013, “Integrating qPLM and Biomechanical Test Data With an Anisotropic Fiber Distribution Model and Predictions of TGF-β 1 and IGF-1 Regulation of Articular Cartilage Fiber Modulus,” Biomech. Model. Mechanobiol., 12(6), pp. 1073–1088. [CrossRef] [PubMed]
Cheng, Y., Ni, W., and Cheng, C., 2006, “Nonlinear Analysis of Oscillatory Indentation in Elastic and Viscoelastic Solids,” Phys. Rev. Lett., 97(7), p. 075506. [CrossRef] [PubMed]
Buschmann, M., and Grodzinsky, A., 1995, “A Molecular Model of Proteoglycan-Associated Electrostatic Forces in Cartilage Mechanics,” ASME J. Biomech. Eng., 117(2), pp. 179–192. [CrossRef]
Korhonen, R., Wong, M., Arokoski, J., Lindgern, R., Helminen, H., Hunziker, E., and Jurvelin, J., 2002, “Importance of the Superficial Tissue Layer for the Indentation Stiffness of Articular Cartilage,” Med. Eng. Phys., 24(2), pp. 99–108. [CrossRef] [PubMed]
Buckwalter, J., 2002, “Articular Cartilage Injuries,” Clin. Orthop. Relat. Res., 402(1), pp. 21–37. [CrossRef] [PubMed]
Nia, H., Han, L., Li, Y., Ortiz, C., and Grodzinsky, A., 2011, “Poroelasticity of Cartilage at the Nanoscale,” Biophys. J., 101(9), pp. 2304–2313. [CrossRef] [PubMed]
Lu, X., Wan, L., Guo, X., and Mow, V., 2010, “A Linearized Formulation of Triphasic Mixture Theory for Articular Cartilage and Its Application to Indentation Analysis,” J. Biomech., 43(4), pp. 673–679. [CrossRef] [PubMed]
Chen, A., Bae, W., Schinagl, R., and Sah, R., 2001, “Depth- and Strain-Dependent Mechanical and Electromechanical Properties of Full-Thickness Bovine Articular Cartilage in Confined Compression,” J. Biomech., 34(1), pp. 1–12. [CrossRef] [PubMed]
Williamson, A., Chen, A., and Sah, R., 2001, “Compressive Properties and Function-Composition Relationships of Developing Bovine Articular Cartilage,” J. Orthop. Res., 19(6), pp. 1113–1121. [CrossRef] [PubMed]
Lu, X., and Mow, V., 2008, “Biomechanics of Articular Cartilage and Determination of Material Properties,” Med. Sci. Sports Exercises, 40(2), pp. 193–199. [CrossRef]
Chahine, N., Chen, F., Hung, C., and Ateshian, G., 2005, “Direct Measurement of Osmotic Pressure of Glycosaminoglycan Solutions by Membrane Osmometry at Room Temperature,” Biophys. J., 89(3), pp. 1543–1550. [CrossRef] [PubMed]

Figures

Grahic Jump Location
Fig. 1

Schematic side-view of the AFM-DN setup representing the microcantilever, the spherical indenter, and the soft sample. The controlled displacement of the fixed end of the cantilever (h0), the cantilever deflection (hc), and the indentation depth (hs) are reported.

Grahic Jump Location
Fig. 2

Overview of the numerical approach based on two models working in sequence and described in the central column: the abaqus model, where the equilibrium indentation depth is reached through a nonlinear simulation, and the matlab model, where the harmonic displacement is applied using a linearized constitutive relationship. The lateral columns report the AC constitutive equations used to feed the models: the transversely isotropic model and the continuum mixture model, respectively. It is worth noting that, for both the constitutive relationships, the two steps share the same mesh; in the case of the continuum mixture model, also the stiffness tangent matrix obtained at the end of the abaqus step is passed to the integration points in the matlab step.

Grahic Jump Location
Fig. 3

Experimental data in terms of (a) the storage modulus versus frequency and (b) the tangent of the phase shift versus frequency for the three indentation depths analyzed. Mean values and standard deviation bars are plotted.

Grahic Jump Location
Fig. 4

Best fitting results for all the analyzed experimental data, in terms of (a) E'*(f) and (b) tan(φf) when the transversely isotropic model is used. Data for the three penetration depths are reported: black lines indicate the numerical results and gray lines represent the experimental data (mean curves only).

Grahic Jump Location
Fig. 5

Best fitting results for all the analyzed experimental data, in terms of (a) E'*(f) and (b) tan(φf) when the fibril distribution model is used. Gray lines define experimental data (mean curves only) whereas black lines indicate the numerical results obtained by using the parameters of model AFIBERS.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In