An analytical poroelastic model for laboratorial mechanical testing of the articular cartilage (AC)

doi:10.1007/s10483-018-2334-9

Abstract

Abstract:

The articular cartilage (AC) can be seen as a biphasic poroelastic material. The cartilage deformation under compression mainly leads to an interstitial fluid flow in the porous solid phase. In this paper, an analytical poroelastic model for the AC under laboratorial mechanical testing is developed. The solutions of interstitial fluid pressure and velocity are obtained. The results show the following facts. (i) Both the pressure and fluid velocity amplitudes are proportional to the strain loading amplitude. (ii) Both the amplitudes of pore fluid pressure and velocity in the AC depend more on the loading amplitude than on the frequency. Thus, in order to obtain the considerable fluid stimulus for the AC cell responses, the most effective way is to increase the loading amplitude rather than the frequency. (iii) Both the interstitial fluid pressure and velocity are strongly affected by permeability variations. This model can be used in experimental tests of the parameters of AC or other poroelastic materials, and in research of mechanotransduction and injury mechanism involved interstitial fluid flow.

Key words: laboratorial mechanical test, transversely isotropy, elastic layer, point force solution, Fourier Transformation, articular cartilage (AC), poroelasticity, interstitial fluid flow, injury mechanism

2010 MSC Number:

74L15
92C10

Xiaogang WU, Kuijun CHEN, Zhaowei WANG, Ningning WANG, Teng ZHAO, Yanan XUE, Yanqin WANG, Weiyi CHEN. An analytical poroelastic model for laboratorial mechanical testing of the articular cartilage (AC). Applied Mathematics and Mechanics (English Edition), 2018, 39(6): 813-828.

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References

[1] Robinson, D. L., Kersh, M. E., Walsh, N. C., Ackland, D. C., de Steiger, R. N., and Pandy, M. G. Mechanical properties of normal and osteoarthritic human articular cartilage. Journal of the Mechanical Behavior of Biomedical Materials, 61, 96-109(2016)
[2] Mow, V. C., Kuei, S., Lai, W. M., and Armstrong, C. G. Biphasic creep and stress relaxation of articular cartilage in compression:theory and experiments. Journal of Biomechanical Engineering, 102, 73-84(1980)
[3] Frank, E. H. and Grodzinsky, A. J. Cartilage electromechanics-Ⅱ, a continuum model of cartilage electrokinetics and correlation with experiments. Journal of Biomechanics, 20, 629-639(1987)
[4] Ateshian, G. A., Warden, W. H., Kim, J. J., Grelsamer, R. P., and Mow, V. C. Finite deformation biphasic material properties of bovine articular cartilage from confined compression experiments. Journal of Biomechanics, 30, 1157-1164(1997)
[5] Soulhat, J., Buschmann, M. D., and Shiraziadl, A. A fibril-network-reinforced biphasic model of cartilage in unconfined compression. Journal of Biomechanical Engineering, 121, 340-347(1999)
[6] Cohen, B., Lai, W. M., and Mow, V. C. A transversely isotropic biphasic model for unconfined compression of growth plate and chondroepiphysis. Journal of Biomechanical Engineering, 120, 491-496(1998)
[7] Cohen, B., Gardner, T., and Ateshian, G. The influence of transverse isotropy on cartilage indentation behavior-a study of the human humeral head. Orthopaedic Research Society, 18, 185(1993)
[8] Mow, V., Good, P., and Gardner, T. A new method to determine the tensile properties of articular cartilage using the indentation test. Orthopaedic Research Society, 25, 0103(2000)
[9] Lai, W. M., Hou, J., and Mow, V. C. A triphasic theory for the swelling and deformation behaviors of articular cartilage. Journal of Biomechanical Engineering, 113, 245-258(1991)
[10] Gu, W., Lai, W., and Mow, V. Transport of multi-electrolytes in charged hydrated biological soft tissues. Porous Media:Theory and Experiments, Springer, Berlin (1999)
[11] Linn, F. C. and Sokoloff, L. Movement and composition of interstitial fluid of cartilage. Arthritis and Rheumatology, 8, 481-494(1965)
[12] Greene, G. W., Zappone, B., Söderman, O., Topgaard, D., Rata, G., Zeng, H., and Israelachvili, J. N. Anisotropic dynamic changes in the pore network structure, fluid diffusion and fluid flow in articular cartilage under compression. Biomaterials, 31, 3117-3128(2010)
[13] Mow, V. C., Wang, C. C., and Hung, C. T. The extracellular matrix, interstitial fluid and ions as a mechanical signal transducer in articular cartilage. Osteoarthr and Cartilage, 7, 41-58(1999)
[14] Makela, J. T. and Korhonen, R. K. Highly nonlinear stress-relaxation response of articular cartilage in indentation:importance of collagen nonlinearity. Journal of Biomechanics, 49, 1734-1741(2016)
[15] Guo, H. and Torzilli, P. A. Shape of chondrocytes within articular cartilage affects the solid but not the fluid microenvironment under unconfined compression. Acta Biomaterialia, 29, 170-179(2016)
[16] Cilingir, A. C. Effect of rotational and sliding motions on friction and degeneration of articular cartilage under dry and wet friction. Journal of Bionic Engineering, 12, 464-472(2015)
[17] Fujie, H. and Imade, K. Effects of low tangential permeability in the superficial layer on the frictional property of articular cartilage. Biosurface and Biotribology, 1, 124-129(2015)
[18] Speirs, A. D., Beaulé, P. E., Ferguson, S. J., and Frei, H. Stress distribution and consolidation in cartilage constituents is influenced by cyclic loading and osteoarthritic degeneration. Journal of Biomechanics, 47, 2348-2353(2014)
[19] Ateshian, G. A. and Wang, H. A theoretical solution for the frictionless rolling contact of cylindrical biphasic articular cartilage layers. Journal of Biomechanics, 28, 1341-1355(1995)
[20] Soltz, M. A. and Ateshian, G. A. Experimental verification and theoretical prediction of cartilage interstitial fluid pressurization at an impermeable contact interface in confined compression. Journal of Biomechanics, 31, 927-934(1998)
[21] Cheng, A. D. Material coefficients of anisotropic poroelasticity. International Journal of Rock Mechanics and Mining Sciences, 34, 199-205(1997)
[22] Abousleiman, Y. and Cui, L. Poroelastic solutions in transversely isotropic media for wellbore and cylinder. International Journal of Solids and Structures, 35, 4905-4929(1998)
[23] Cowin, S. C. Bone poroelasticity. Journal of Biomechanics, 32, 217-238(1999)
[24] Lian, Q., Chen, C., Uwayezu, M. C., Zhang, W., Bian, W., Wang, J., and Jin, Z. Biphasic mechanical properties of in vivo repaired cartilage. Journal of Bionic Engineering, 12, 473-482(2015)
[25] Ateshian, G. A. and Wang, H. A theoretical solution for the frictionless rolling contact of cylindrical biphasic articular cartilage layers. Journal of Biomechanics, 28, 1341-1355(1995)
[26] Soltz, M. A. and Ateshian, G. A. Experimental verification and theoretical prediction of cartilage interstitial fluid pressurization at an impermeable contact interface in confined compression. Journal of Biomechanics, 31, 927-934(1998)
[27] Bachrach, N. M., Mow, V. C., and Guilak, F. Incompressibility of the solid matrix of articular cartilage under high hydrostatic pressures. Journal of Biomechanics, 31, 445-451(1998)
[28] Fujie, H. and Imade, K. Effects of low tangential permeability in the superficial layer on the frictional property of articular cartilage. Biosurface and Biotribology, 1, 124-129(2015)
[29] Wu, X. G. and Chen, W. Y. A hollow osteon model for examining its poroelastic behaviors:mathematically modeling an osteon with different boundary cases. European Journal of MechanicsA/Solids, 40, 34-49(2013)
[30] Cen, H. P., Wu, X. G., Yu, M. L., Liu, Q. Z., and Jia, Y. M. Effects of the microcrack shape, size and direction on the poroelastic behaviors of a single osteon:a finite element study. Acta of Bioengineering and Biomechanics/Wroclaw University of Technology, 18, 3-10(2016)
[31] Wu, X. G., Yu, W. L., Cen, H. P., Wang, Y. Q., Guo, Y., and Chen, W. Y. Hierarchical model for strain generalized streaming potential induced by the canalicular fluid flow of an osteon. Acta Mechanica Sinica, 31, 112-121(2015)