Annals of Biomedical Engineering

, Volume 33, Issue 4, pp 494–501 | Cite as

Large Deformation Finite Element Analysis of Micropipette Aspiration to Determine the Mechanical Properties of the Chondrocyte

  • Frank P. T. Baaijens
  • Wendy R. Trickey
  • Tod A. Laursen
  • Farshid Guilak


Chondrocytes, the cells in articular cartilage, exhibit solid-like viscoelastic behavior in response to mechanical stress. In modeling the creep response of these cells during micropipette aspiration, previous studies have attributed the viscoelastic behavior of chondrocytes to either intrinsic viscoelasticity of the cytoplasm or to biphasic effects arising from fluid–solid interactions within the cell. However, the mechanisms responsible for the viscoelastic behavior of chondrocytes are not fully understood and may involve one or both of these phenomena. In this study, the micropipette aspiration experiment was modeled using a large strain finite element simulation that incorporated contact boundary conditions. The cell was modeled using finite strain incompressible and compressible elastic models, a two-mode compressible viscoelastic model, or a biphasic elastic or viscoelastic model. Comparison of the model to the experimentally measured response of chondrocytes to a step increase in aspiration pressure showed that a two-mode compressible viscoelastic formulation accurately captured the creep response of chondrocytes during micropipette aspiration. Similarly, a biphasic two-mode viscoelastic analysis could predict all aspects of the cell’s creep response to a step aspiration. In contrast, a biphasic elastic formulation was not capable of predicting the complete creep response, suggesting that the creep response of the chondrocytes under micropipette aspiration is predominantly due to intrinsic viscoelastic phenomena and is not due to the biphasic behavior.


Cartilage Osteoarthritis Cytoskeleton Biomechanics Poroelastic Poroviscoelastic Nonlinear 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Baaijens, F. An U-ALE formulation of 3-D unsteady viscoelastic flow. Int. J. Numer. Methods Eng. 36:1115–1143, 1993.Google Scholar
  2. 2.
    Bachrach, N., W. Valhmu, E. Stazzone, A. Ratcliffe, W. Lai, and V. Mow. Changes in proteoglycan synthesis of chondrocytes in articular cartilage are associated with the time-dependent changes in their mechanical environment. J. Biomech. 28:1561–1570, 1995.CrossRefPubMedGoogle Scholar
  3. 3.
    Guilak, F. Compression-induced changes in the shape and volume of the chondrocyte nucleus. J. Biomech. 28:1529–1542, 1995.CrossRefPubMedGoogle Scholar
  4. 4.
    Guilak, F., G. Erickson, and H. Ting-Beall. The effects of osmotic stress on the viscoelastic and physical properties of articular chondrocytes. Biophys. J. 82:720–727, 2002.PubMedGoogle Scholar
  5. 5.
    Guilak, F., and V. Mow. The mechanical environment of the chondrocyte: A biphasic finite element model of cell–matrix interactions in articular cartilage. J. Biomech. 33:1663–1673, 2000.CrossRefPubMedGoogle Scholar
  6. 6.
    Guilak, F., R. L. Sah, and L. A. Setton. Physical Regulation of Cartilage Metabolism, In: Mow VC, Hayes W. C., Editors. Basic Orthopaedic Biomechanics. 2nd ed. Philadelphia: Lippincott-Raven; 1997, p. 179–207.Google Scholar
  7. 7.
    Haider, M., and F. Guilak. An axisymmetric boundary integral model for incompressible linear viscoelasticity: Application to the micropipette aspiration contact problem. J. Biomech. Eng. 122:236–244, 2000.CrossRefPubMedGoogle Scholar
  8. 8.
    Haider, M., and F. Guilak. An axisymmetric boundary integral model for assessing elastic cell properties in the micropipette aspiration contact problem. J. Biomech. Eng. 124:586–595, 2002.CrossRefPubMedGoogle Scholar
  9. 9.
    Hochmuth, R. Micropipette aspiration of living cells. J. Biomech. 33:15–22, 2000.CrossRefPubMedGoogle Scholar
  10. 10.
    Hung, C., K. Costa, and X. Guo. Apparent and transient mechanical properties of chondrocytes during osmotic loading using triphasic theory and afm indentation. ASME Bioeng. Conf. BED-50:625–626, 2001.Google Scholar
  11. 11.
    Jones, W., H. Ting-Beall, G. Lee, S. Kelley, R. Hochmuth, and F. Guilak. Alterations in the young’s modulus and volumetric properties of chondrocytes isolated from normal and osteoarthritic human cartilage. J. Biomech. 32:119–127, 1999.CrossRefPubMedGoogle Scholar
  12. 12.
    Koay, E., A. Shien, and K. Athanasiou. Creep indentation of single cells. J. Biomech. Eng. 125(3):334–341, 2003.CrossRefPubMedGoogle Scholar
  13. 13.
    Mow, V., S. Kuei, W. Lai, and C. Armstrong. Biphasic creep and stress relaxation of articular cartilage in compression: Theory and experiments. J. Biomech. Eng. 102:73–84, 1980.PubMedGoogle Scholar
  14. 14.
    Mow, V., D. Sun, X. Guo, C. Hung, and W. Lai. Chondrocyte-extracellular matrix interactions during osmotic swelling. ASME Bioeng. Conf. BED42:133–134, 1999.Google Scholar
  15. 15.
    Poole, R. Imbalances of Anabolism and Catabolism of Cartilage Matrix Components in Osteoarthritis. In: Keuttner, K. E., Goldberg, V. M., eds. Osteoarthritic Disorders. AAOS Press, Rosemont, Illinois, USA, 1995, p. 247–260.Google Scholar
  16. 16.
    Sato, M., D. Theret, L. Wheeler, N. Ohshima, and R. Nerem. Application of the micropipette technique to the measurement of cultured porcine aortic endothelial cell viscoelastic properties. J. Biomech. Eng. 112:263–268, 1990.PubMedGoogle Scholar
  17. 17.
    Sengers, B., C. Oomens, and F. Baaijens. An integrated finite element approach to mechanics, transport and biosynthesis in tissue engineering. J. Biomech. Eng. 126:82–91, 2004.CrossRefPubMedGoogle Scholar
  18. 18.
    Setton, L., W. Zhu, and V. Mow. The biphasic poroviscoelastic behavior of articular cartilage: Role of the surface zone in governing the compressive behavior. J. Biomech. 26:581–592, 1993.CrossRefPubMedGoogle Scholar
  19. 19.
    Shin, D., and K. Athanasiou. Cytoindentation for obtaining cell biomechanical properties. J. Orthop. Res. 17:880–890, 1999.PubMedGoogle Scholar
  20. 20.
    Theret, D., M. Levesque, M. Sato, R. Nerem, and L. Wheeler. The application of a homogeneous half-space model in the analysis of endothelial cell micropipette measurements. J. Biomech. Eng. 110:190–199, 1988.PubMedGoogle Scholar
  21. 21.
    Trickey, W., F. Baaijens, T. Laursen, L. Alexopoulos, and F. Guilak. Determination of the Poisson’s ratio of the cell: Recovery properties of chondrocytes after release from complete micropipette aspiration. J. Biomech. (Submitted), 2004a.Google Scholar
  22. 22.
    Trickey, W., G. Lee, and F. Guilak. Viscoelastic properties of chondrocytes from normal and osteoarthritic human cartilage. J. Orthop. Res. 18:891–898, 2000.PubMedGoogle Scholar
  23. 23.
    Trickey, W., T. Vail, and F. Guilak. The role of the cytoskeleton in the viscoelastic properties of human articular chondrocytes. J. Orthop. Res. 22:131–139, 2004b.Google Scholar
  24. 24.
    Wilkes, R., and K. Athanasiou. The intrinsic incompressibility of osteoblast-like cells. Tissue Eng. 2:167–181, 1996.Google Scholar
  25. 25.
    Wu, J., W. Herzog, and M. Epstein. Modelling of location- and time-dependent deformation of chondrocytes during cartilage loading. J. Biomech. 32:563–572, 1999.PubMedGoogle Scholar

Copyright information

© Biomedical Engineering Society 2005

Authors and Affiliations

  • Frank P. T. Baaijens
    • 1
  • Wendy R. Trickey
    • 2
  • Tod A. Laursen
    • 3
  • Farshid Guilak
    • 2
  1. 1.Department of Biomedical EngineeringEindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Departments of Surgery and Biomedical EngineeringDuke University Medical CenterDurham
  3. 3.Department of Civil and Environmental EngineeringDuke UniversityDurham

Personalised recommendations