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A new method for computing the uniaxial modulus of articular cartilages using modified inhomogeneous triphasic model

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Abstract

It is well known that subtle changes in structure and tissue composition of articular cartilage can lead to its degeneration. The present paper puts forward a modified layered inhomogeneous triphasic model with four parameters based on the inhomogeneous triphasic model proposed by Narmoneva et al. Incorporating a piecewise fitting optimization criterion, the new model was used to obtain the uniaxial modulus Ha, and predict swelling pattern for the articular cartilage based on ultrasound-measured swelling strain data. The results show that the new method can be used to provide more accurate estimation on the uniaxial modulus than the inhomogeneous triphasic model with three parameters and the homogeneous mode, and predict effectively the swelling strains of highly nonuniform distribution of degenerated articular cartilages. This study can provide supplementary information for exploring mechanical and material properties of the cartilage, and thus be helpful for the diagnosis of osteoarthritis-related diseases.

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References

  1. Mow V.C., Ratcliffe A., Poole A.R.: Cartilage and diarthrodial joints as paradigms for hierarchical materials and structures. Biomaterials 13, 67–97 (1992)

    Article  Google Scholar 

  2. Mow V.C., Gu W.Y., Chen F.H.: Structure and function of articular cartilage and meniscus. In: Mow, V.C., Huiskes, R. (eds) Basic Orthopaedic Biomechanics and Mechano-biology, 3rd edn, Lippincott Williams & Wilkins, Philadelphia (2005)

    Google Scholar 

  3. Wang, Q.: Ultrasonic characterization of transient and inhomogeneous swelling behavior and progressive degeneration of articular cartilage. [Phd Thesis], Hongkong Polytechnic University, Hongkong, China (2007)

  4. Mow V.C., Guo X.E.: Mechano-electrochemical properties of articular cartilage: their inhomogeneities and anisotropies. Annu. Rev. Biomed. Eng. 4, 175–209 (2002)

    Article  Google Scholar 

  5. Brandt K., Doherty M., Lohmander S.: Osteoarthritis Cartilage. Oxford University Press, London (1998)

    Google Scholar 

  6. Kempson G.E.: The Joints and Synovial Fluid, vol. II, pp. 177–238. Academic Press, New York (1980)

    Google Scholar 

  7. Mow V.C., Zhu W., Ratcliffe A.: Basic othopaedic biomechanics: structure and function of articular cartilage and meniscus. In: Mow, V.C., Hayes, W.C. (eds) Basic Orthopaedic Biomechanics, pp. 143–198. Raven Press, New York (1991)

    Google Scholar 

  8. Maroudas A.: Balance between swelling pressure and collagen tension in normal and degenerate cartilage. Nature 260, 808–809 (1976)

    Article  Google Scholar 

  9. Lai W.M., Hou J.S., Mow V.C.: A triphasic theory for the swelling and deformation behaviors of articular cartilage. J. Biomech. Eng. 113, 245–258 (1991)

    Article  Google Scholar 

  10. Maroudas A.: Transport of solutes through cartilage—permeability to large molecules. J. Anat. 122, 335–347 (1976)

    Google Scholar 

  11. Narmoneva D.A., Wang J.Y., Setton L.A.: Nonuniform swelling-induced residual strains in articular cartilage. J. Biomech. 32, 401–408 (1999)

    Article  Google Scholar 

  12. Mow V.C., Kuer S.C., Lai W.M., Armstrong C.G.: Biphasic creep and stress relaxation of articular cartilage in compression: theory and experiments. J. Biomech. Eng. 102, 73–84 (1980)

    Article  Google Scholar 

  13. Mak A.F.: The apparent viscoelastic behavior of articular cartilage—the contributions from the intrinsic matrix viscoelasticity and interstitial fluid flows. J. Biomech. Eng. 108, 123–130 (1986)

    Article  Google Scholar 

  14. Narmoneva, D.A.: Material property determination for normal and osteoarthritic articular cartilage using triphasic mechano-chemical theoretical model of osmotic loading. [Phd Thesis], Duke University, Durham, North Carolina (2000)

  15. Chen W.Y., Zhang Q.Y., Wei X.C., Wang X.H., Li X.N.: Viscoelastic properties of chondrocytes isolated from normal and osteoarthritic rabbit knee cartilage. Chin. J. Theo. Appl. Mech. 39, 517–521 (2007)

    Google Scholar 

  16. Zheng Y.P., Mak A.F.T., Lau K.P., Qin L.: An ultrasonic measurement for in vitro depth-dependent equilibrium strains of articular cartilage in compression. Phys. Med. Biol. 47, 3165–3180 (2002)

    Article  Google Scholar 

  17. Zheng Y.P., Niu H.J., Wang Q., Mak A.F.T.: Extraction of mechanical properties of articular cartilage from osmotic swelling behavior monitored using high frequency ultrasound. J. Biomech. Eng. 129, 413–422 (2007)

    Article  Google Scholar 

  18. Niu H.J., Wang Q., Zheng Y.P., Pu F.: Computation of uniaxial modulus of the normal and degenerated articular cartilage using inhomogeneous triphasic model. Lect. Notes Comput. Sci. Int. Conf. Life Syst. Model. Simul. 4689, 104–110 (2007)

    Google Scholar 

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Correspondence to Yubo Fan.

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The project was supported by the National Natural Science Foundation of China (10772018, 30872720).

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Niu, H., Wang, Q., Zheng, Y. et al. A new method for computing the uniaxial modulus of articular cartilages using modified inhomogeneous triphasic model. Acta Mech Sin 26, 121–126 (2010). https://doi.org/10.1007/s10409-009-0287-x

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  • DOI: https://doi.org/10.1007/s10409-009-0287-x

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