A theoretical formulation for boundary friction in articular cartilage

Ateshian, G. A.

Affiliations

¹Department of Mechanical Engineering, Columbia University, New York, NY

Abstract

A theoretical boundary friction model is proposed for predicting the frictional behavior of articular cartilage, including its time-dependent, velocity-dependent, and load-dependent responses. This theoretical model uses the framework of the biphasic theory for articular cartilage, and provides a mathematical formulation for the principle that interstitial fluid pressurization contributes significantly to reduction of the effective friction coefficient. Several examples of the application of this theory are provided, which demonstrate that a variety of experimentally observed cartilage frictional behaviors can now be theoretically predicted.

Links

DOI: 10.1115/1.2796069

PubMed: 9083853

WoS: A1997WN86800012

History

Received: 1995-07-27

Revised: 1996-04-18

Cited Works (16)

Year	Entry
1990	Holmes MH, Mow VC. The nonlinear characteristics of soft gels and hydrated connective tissues in ultrafiltration. J Biomech. 1990;23(11):1145-1156.
1982	Armstrong CG, Mow VC. Variations in the intrinsic mechanical properties of human articular cartilage with age, degeneration, and water content. J Bone Joint Surg. 1982;64A(1):88-94.
1994	Ateshian GA, Lai WM, Zhu WB, Mow VC. An asymptotic solution for the contact of two biphasic cartilage layers. J Biomech. November 1994;27(11):1347-1360.
1995	Ateshian GA, Wang H. A theoretical solution for the frictionless rolling contact of cylindrical biphasic articular cartilage layers. J Biomech. November 1995;28(11):1341-1355.
1968	Walker PS, Dowson D, Longfield MD, Wright V. “Boosted lubrication” in synovial joints by fluid entrapment and enrichment. Ann Rheum Dis. 1968;27(6):512-520.
1980	Mow VC, Kuei SC, Lai WM, Armstrong CG. Biphasic creep and stress relaxation of articular cartilage in compression: theory and experiments. J Biomech Eng. February 1980;102(1):73-84.
1992	Jay GD. Characterization of a bovine synovial fluid lubricating factor, I: chemical, surface activity and lubricating properties. Connect Tissue Res. 1992;28(1-2):71-88.
1962	McCutchen CW. The frictional properties of animal joints. Wear. January–February 1962;5(1):1-17.
1976	Malcom LL. An Experimental Investigation of the Frictional and Deformational Responses of Articular Cartilage Interfaces to Static and Dynamic Loading [PhD thesis]. San Diego (UCSD), University of California; 1976.
1985	Swann DA, Silver FH, Slayter HS, Stafford W, Shore E. The molecular structure and lubricating activity of lubricin isolated from bovine and human synovial fluids. Biochem J. 1985;225(1):195-201.
1976	Wright V, Dowson D. Lubrication and cartilage. J Anat. February 1976;121(pt 1):107-118.
1994	Macirowski T, Tepic S, Mann RW. Cartilage stresses in the human hip joint. J Biomech Eng. February 1994;116(1):10-18.
1989	Hou JS, Holmes MH, Lai WM, Mow VC. Boundary conditions at the cartilage-synovial fluid interface for joint lubrication and theoretical verifications. J Biomech Eng. February 1989;111(1):78-87.
1970	Radin EL, Swann DA, Weisser PA. Separation of a hyaluronate-free lubricating fraction from synovial fluid. Nature. 1970;228(5269):377-378.
1976	Torzilli PA, Mow VC. On the fundamental fluid transport mechanisms through normal and pathological articular cartilage during function, I: the formulation. J Biomech. 1976;9(8):541-552.
1968	Linn FC. Lubrication of animal joints, II: the mechanism. J Biomech. August 1, 1968;1(3):193.

Cited By (34)

Year	Entry
2003	Ateshian GA, Hung CT. Functional properties of native articular cartilage. In: Guilak F, Butler DL, Goldstein SA, Mooney DJ, eds. Functional Tissue Engineering. New York, NY: Inc., Springer-Verlag; 2003:46-68.
2000	Soltz MA, Ateshian GA. Interstitial fluid pressurization during confined compression cyclical loading of articular cartilage. Ann Biomed Eng. February 2000;28(2):150-159.
2002	Mow VC, Guo XE. Mechano-electrochemical properties of articular cartilage: their inhomogeneities and anisotropies. Annu Rev Biomed Eng. 2002;4:175-209.
1998	Soltz MA, Ateshian GA. Experimental verification and theoretical prediction of cartilage interstitial fluid pressurization at an impermeable contact interface in confined compression. J Biomech. October 1998;31(10):927-934.
2003	Park S, Krishnan R, Nicoll SB, Ateshian GA. Cartilage interstitial fluid load support in unconfined compression. J Biomech. December 2003;36(12):1785-1796.
2004	Park S, Costa KD, Ateshian GA. Microscale frictional response of bovine articular cartilage from atomic force microscopy. J Biomech. November 2004;37(11):1679-1687.
2009	Ateshian GA. The role of interstitial fluid pressurization in articular cartilage lubrication. J Biomech. June 19, 2009;42(9):1163-1176.
1999	Torzilli PA, Grigiene R, Borrelli J Jr, Helfet DL. Effect of impact load on articular cartilage: cell metabolism and viability, and matrix water content. J Biomech Eng. October 1999;121(5):433-441.
2002	LeRoux MA, Setton LA. Experimental and biphasic FEM determinations of the material properties and hydraulic permeability of the meniscus in tension. J Biomech Eng. June 2002;124(3):315-321.
2003	Krishnan R, Park S, Eckstein F, Ateshian GA. Inhomogeneous cartilage properties enhance superficial interstitial fluid support and frictional properties, but do not provide a homogeneous state of stress. J Biomech Eng. October 2003;125(5):569-577.
2004	Krishnan R, Kopacz M, Ateshian GA. Experimental verification of the role of interstitial fluid pressurization in cartilage lubrication. J Orthop Res. May 2004;22(3):565-570.
1998	Ateshian GA, Wang H, Lai WM. The role of interstitial fluid pressurization and surface porosities on the boundary friction of articular cartilage. J Tribol. April 1998;120(2):241-248.
2007	Moutos FT, Freed LE, Guilak F. A biomimetic three-dimensional woven composite scaffold for functional tissue engineering of cartilage. Nat Mater. February 2007;6(2):162-167.
2015	Whitney GA. Characterization of the Frictional-Shear Damage Properties of Scaffold-Free Engineered Cartilage and Reduction of Damage Susceptibility by Upregulation of Collagen Content [PhD thesis]. Cleveland, OH: Case Western Reserve University; January 2015.
1997	Wang X. The Frictional Role of Interstitial Fluid Viscosity At the Interface of Deformable Porous Media [PhD thesis]. Columbia University; 1997.
1997	Wang H. Boundary Lubrication of Articular Cartilage: The Role of Interstitial Fluid Pressure, Surface Porosities and Equilibrium Friction Coefficient [PhD thesis]. Columbia University; 1997.
2000	Soltz MA. Investigation of a Boundary Friction Model for Articular Cartilage: Effects of Interstitial Fluid Pressurization and Surface Topography [PhD thesis]. Columbia University; 2000.
2004	Krishnan R. Role of Interstitial Fluid Pressurization in Articular Cartilage Lubrication [PhD thesis]. Columbia University; 2004.
2005	Park S. Interstitial Fluid Flow-Dependent and Flow-Independent Mechanical and Tribological Response of Articular Cartilage [PhD thesis]. Columbia University; 2005.
2006	Basalo Perez-Luna IM. Effects of Enzymatic Degradation and Supplementation of Chrondroitin Sulfate on the Frictional Properties of Articular Cartilage [PhD thesis]. Columbia University; 2006.
2008	Lima EG. The Tissue-Engineering of Functional Osteochondral Constructs for Cartilage Repair [PhD thesis]. Columbia University; 2008.
2009	Canal Guterl C. Contact Mechanics of Articular Layers: 2D Strain Fields and Their Relation to Tissue Inhomogeneity [PhD thesis]. Columbia University; 2009.
2010	Caligaris M. Migrating Contact Area Promotes Low Friction and Wear in Articular Joints [PhD thesis]. Columbia University; 2010.
2020	Zimmerman BKL. Mechanically Mediated Fatigue Failure in Articular Cartilage: Experimental, Theoretical, and Computational Models [PhD thesis]. Columbia University; 2020.
2022	Wang C. Assessment of Crosslink Density in Collagen Models and Ultrafast Laser Crosslinking of Corneal and Cartilage Tissues as Novel Treatment Modalities [PhD thesis]. Columbia University; 2022.
2008	Gleghorn JP. Boundary Mode Frictional Properties of Articular Cartilage: Functional Implications of Lubricin Localization [PhD thesis]. Ithaca, NY: Cornell University; January 2008.
2009	Moutos FT. Biomimetic Composite Scaffolds for the Functional Tissue Engineering of Articular Cartilage [PhD thesis]. Duke University; 2009.
2013	McGann ME. Wear Characteristics and Crosslinked Properties of Articular Cartilage [PhD thesis]. University of Notre Dame; April 2013.
2017	Irvine AD. Modulating Mechanical Cues and Oxygen Availability to Regulate Chondrogenesis Within MSC Laden Hydrogels [PhD thesis]. Trinity College Dublin; June 2017.
2005	Adeeb SM. Load-Bearing Across Diaiihrodial Joints With Special Reference to Peripheral Structures and the Menisci of the Knee [PhD thesis]. Calgary, AB: University of Calgary; January 2005.
2010	Tapper JE. Dynamic in Vivo Kinematics in an Ovine Stifle Joint Model of Osteoarthritis [PhD thesis]. Calgary, AB: University of Calgary; March 2010.
2005	Klein TJ. Cartilage Tissue Engineering: Biophysical Modulation of Functional Depth-Dependent Properties [PhD thesis]. San Diego (UCSD), University of California; 2005.
2006	Schmidt TA. Proteoglycan 4 Metabolism and Boundary Lubrication of Articular Cartilage [PhD thesis]. San Diego (UCSD), University of California; 2006.
2005	Guerin HAL. A Nonlinear Anisotropic Continuum Model of Human Annulus Fibrosus Mechanical Behavior [PhD thesis]. Philadelphia, PA: University of Pennsylvania; 2005.