Contact creep of biphasic cartilage layers

Journal of Applied Mechanics, Transactions ASME

Volumn 66, Issue 1, 1999, Pages 137-145

  Kelkar, R ^a   Ateshian, G A ^a  

^a Columbia University ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIPHASIC CARTILAGE LAYERS; SOLID COLLAGEN PROTEOGLYCAN MATRIX;

CARTILAGE; CREEP; INTEGRAL EQUATIONS; INTERFACES (MATERIALS); MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; PROBLEM SOLVING; STRESS ANALYSIS; SUBSTRATES;

BIOMECHANICS;

EID: 0033098444     PISSN: 00218936     EISSN: 15289036     Source Type: Journal    
DOI: 10.1115/1.2789140     Document Type: Article

References (50)

1. Agbezuge, L. K., and Deresiewicz, H., 1974, “On the Indentation of a Consolidating Half-Space,” hr. J. Tech., Vol. 12, pp. 322-338.
2. Armstrong, C. G., 1986, “An Analysis of the Stresses in a Thin Layer of Articular Cartilage in a Synovial Joint,” Eng. Med., Vol. 15, pp. 55-61.
3. Armstrong, C. G., Mow, V. C., and Wirth, C. R., 1985, “Biomechanics of Impact-Induced Microdamage to Articular Cartilage: A Possible Genesis for Chondromalacia Patella,” AAOS Symposium on Sports Medicine: The Knee, G. A. M. Finerman, ed., C. V. Mosby Co., St. Louis, MO, pp. 70-84.
4. Ateshian, G. A., 1995, “Continuity Requirements Across a Contact Interface in the Formulation of a Boundary Friction Model for Biphasic Articular Cartilage,” Bioengineering Conference, ASME, New York, BED-Vol. 29, pp. 147-148.
5. Ateshian, G. A., 1997, “A Theoretical Formulation for Boundary Friction in Articular Cartilage,” ASME Journal of Biomechanical Engineering, Vol. 119, pp. 81-86.
6. Ateshian, G. A., Lai, W. M., Zhu, W. B., and Mow, V. C., 1992, “A Biphasic Model for Contact in Diarthrodial Joints,” Adv. Bioeng., ASME, New York, BED-Vol. 22, pp. 191-194.
7. Ateshian, G. A., Lai, W. M., Zhu, W. B., and Mow, V. C., 1994, “An Asymptotic Solution for the Contact of Two Biphasic Cartilage Layers,” J. Biomech., Vol. 27, pp. 1347-1360.
8. Ateshian, G. A., and Wang, H., 1995, “A Theoretical Solution for the Moving Contact of Cylindrical Biphasic Articular Cartilage Layers,” J. Biomech., Vol. 28, pp. 1341-1355.
9. Athanasiou, K. A., Rosenwasser, M. P., Buckwalter, J. A., Malinin, T. I., and Mow, V. C., 1991, “Interspecies Comparisons of in situ Intrinsic Mechanical Properties of Distal Femoral Cartilage,” J. Orthop. Res., Vol. 9, pp. 330-340.
10. Bachrach, N. W., Mow, V. C., and Guilak, F., 1998, “Incompressibility of the Solid Matrix of Articular Cartilage Under Hydrostatic Load,” J. Biomech., Vol. 31, pp. 445-451.
11. Biot, M. A., 1962, “Mechanics of Deformation of Acoustic Propagation in Porous Media,” J. Appl. Phys., Vol. 33, pp. 1482-1498.
12. Bowen, R. M., 1976, Continuum Physics, Vol. 3, A. E. Eringen, ed., Academic Press, San Diego, CA, pp. 1-127.
13. Brown, T. D., Radin, E. L., Martin, R. B., and Burr, D., 1984, “Finite Element Studies of Some Juxtarticular Stress Changes due to Localized Subchondral Stiffening,” J. Biomech., Vol. 17, pp. 11-24.
14. Donzelli, P. S., 1995, “A Mixed-Penalty Contact Finite Element Formulation for Biphasic Soft Tissues,” Ph.D. thesis, Department of Mechanical, Aeronautical Engineering and Mechanics, Rensselaer Polytechnic Institute, Troy, New York.
15. Donzelli, P. S., and Spilker, R. L., 1994, “A Mixed-Penalty Contact Finite Element Formulation With Applications to the Biphasic Tissues of the Knee,” Adv. Bioeng., ASME, New York, BED-Vol. 28, pp. 13-14.
16. Donzelli, P. S., and Spilker, R. L., 1995, “Iterative Contact Detection Algorithm for a Mixed-Penalty Biphasic Finite Element,” Bioengineering Conference, ASME New York, BED-Vol. 29, pp. 169-170.
17. Eberhardt, A. W., Keer, L. M., Lewis, J. L., and Vithoontien, V., 1990, “An Analytical Model of Joint Contact,” ASME Journal of Biomechanical Engineering, Vol. 112, pp. 407-413.
18. Gray, M. L., Pizzanelli, A. M., Grodzinsky, A. J., and Lee, R. C., 1988, “Mechanical and Physicochemical Determinants of the Chondrocyte Biosynthetic Response,” J. Orthop. Res., Vol. 6, pp. 777-792.
19. Guilak, F., Hou, J. S., Ratcliffe, A., and Mow, V. C., “Articular Cartilage» Under Hydrostatic Loading,” Adv. Bioeng., ASME, New York, Vol. BED-Vol. 8, pp. 183-186.
20. Guilak, F., Meyer, B. C., Ratcliffe, A., and Mow, V. C., 1994, “The Effects of Matrix Compression on Proteoglycan Metabolism in Articular Cartilage Explants,” Osteoarthritis and Cartilage, Vol. 2, pp. 91-101.
21. Guilak, F., Ratcliffe, A., Lane, N., Rossenwasser, M. P., and Mow, V. C., 1994, “Mechanical and Biochemical Changes in the Superficial Zone of Articular Cartilage in a Canine Model of Osteoarthritis,” J. Orthop. Res., Vol. 12, pp. 474-484.
22. Hayes, W. C., Keer, L. M., Herrmann, G., and Mockros, L. F., 1992, “A Mathematical Analysis for Indentation Tests of Articular Cartilage,” J. Biomech., Vol. II, pp. 407-419.
23. Hirsch, C., 1944, “The Pathogenesis of Chondromalacia of the Patella,” Acta. Chir. Scand. SuppL, Vol. 83, pp. 1-106.
24. Holmes, M. H., 1986, “Finite Deformation of Soft Tissue: Analysis of a Mixture Model in Uni-axial Compression,” ASME Journal of Biomechanical Engineering, Vol. 108, pp. 372-381.
25. Hou, J. S., Holmes, M. H., Lai, W. M., and Mow, V. C., 1989, “Boundary Conditions at the Cartilage-Synovial Fluid Interface for Joint Lubrication and Theoretical Verifications,” ASME Journal of Biomechanical Engineering, Vol. III, pp. 78-87.
26. Johnson, K. L., 1985, Contact Mechanics, Cambridge University Press, Cambridge, UK, pp. 302-306.
27. Jones, I. L., Klamfeldt, A., and Sanstrom, T., “The Effect of Continuous Mechanical Pressure Upon the Turnover of Articular Cartilage Proteoglycans in Vitro,” Clin. Orthop., Vol. 165, pp. 283-289.
28. Kelkar, R., 1996, “Normal and Abnormal Mechanics of the Shoulder: Studies of Articular Geometry, Contact and Kinematics, Ph.D. thesis, Columbia University, New York, pp. 250-251.
29. Kelkar, R., and Ateshian, G. A., “Contact Creep Response Between a Rigid Impermeable Cylinder and a Biphasic Cartilage Layer Using Integral Transform,” Bioengineering Conference, ASME, New York, BED-Vol. 29, pp. 313-314.
30. Kelly, P. A., and O’Connor, J. J., 1996, “Transmission of Rapidly Applied Loads Through Articular Cartilage, Part I: Uncracked Cartilage,” Proc. Inst. Mech. Engrs., Vol. 210, pp. 27-37.
31. Kempson, G. E., Freeman, M. A. R., and Swanson, S. A. V., 1971, “The Determination of a Creep Modulus for Articular Cartilage From Indentation Tests on the Human Femoral Head,” J. Biomech., Vol. 4, pp. 239-250.
32. Kenyon, D. E., 1976, “The Theory of an Incompressible Solid-Fluid Mixture,” Arch. Rat. Mech. Anal., Vol. 62, pp. 131-147.
33. Lai, W. M., and Mow, V. C., 1980, “Drag-Induced Compression of Articular Cartilage During a Permeation Experiment,” Biorheology, Vol. 17, pp. 111-123.
34. Macirowski, T., Tepic, S., and Mann, R. W., 1994, “Cartilage Stresses in the Human Hip Joint,” ASME Journal of Biomechanical Engineering, Vol. 116, pp. 10-18.
35. Mak, A. F., Lai, W. M., and Mow, V. C., 1987, “Biphasic Indentation of Articular Cartilage. Part I: Theoretical Analysis,” J. Biomech., Vol. 20, pp. 703-714.
36. Malcom, L. L., 1976, “An Experimental Investigation of the Frictional and Deformational Responses of Articular Cartilage Interfaces to Static and Dynamic Loading,” Ph.D. thesis, University of California, San Diego, La Jolla, CA.
37. McCutchen, C. W., 1962, “The Frictional Properties of Animal Joints,” Wear, Vol. 5, pp. 1-17.
38. McNamee, J., and Gibson, R. E., 1960, “Displacement Functions and Linear Transforms Applied to Diffusion Through Porous Elastic Media,” Quart. J. Mech. Appl. Math., Vol. 13, pp. 98-111.
39. Meachim, G., and Bentley, G., 1978, “Horizontal Splitting in Patellar Articular Cartilage,” Arth. Rheum., Vol. 21, pp. 669-674.
40. Mow, V. C., Gibbs, M. C., Lai, W. M., Zhu, W. B., and Athanasiou, K. A., 1989, “Biphasic Indentation of Articular Cartilage, Part II: A Numerical Algorithm and an Experimental Study,” J. Biomech., Vol. 22, pp. 853-861.
41. Mow, V. C., Kuei, S. C., Lai, W. M., and Armstrong, C. G., 1980, “Biphasic Creep and Stress Relaxation of Articular Cartilage: Theory and Experiment,” ASME Journal of Biomechanical Engineering, Vol. 102, Vol. 73-84.
42. Mow, V. C., and Lai, W. M., 1980, “Recent Developments in Synovial Joint Biomechanics,” SIAM Review, Vol. 22, pp. 275-317.
43. Mow, V. C., Ratcliffe, A., and Poole, A. R., “Cartilage and Diarthrodial Joints as Paradigms for Hierarchical Materials and Structures,” Biomaterials, Vol. 13, pp. 67-97.
44. Palmoski, M. J., and Brandt, K. D., 1984, “Effect of Static and Cyclic Compressive Loading on Articular Cartilage Plugs in Vitro,” Arthritis Rheum., Vol. 27, pp. 675-681.
45. Radin, E. L., Martin, R. B., Burr, D. B., Caterson, B., Boyd, R. D., and Goodwin, C., 1984, “Effects of Mechanical Loading on the Tissues of the Rabbit Knee,” J. Orthop. Res., Vol. 2, pp. 221-234.
46. Setton, L. A., Mow, V. C., Muller, F. J., Pita, J. C., and Howell, D. S., 1994, “Mechanical Properties of Canine Articular Cartilage are Significantly Altered Following Transection of the Anterior Cruciate Ligament,” J. Orothop. Res., Vol. 12, pp. 451-463.
47. Sokoloff, L., 1966, “Elasticity of Aging Cartilage,” Fed. Proc. Am. Socs. Exp. Biol., Vol. 25, pp. 1089-1095.
48. Spilker, R. L., Suh, J. K., and Mow, V. C., 1992, “A Finite Element Analysis of the Indentation Stress-Relaxation Response of Linear Biphasic Articular Cartilage,” ASME Journal of Biomechanical Engineering, Vol. 114, pp. 191-201.
49. Suh, J. K., and Spilker, R. L., 1994, “Indentation Analysis of Biphasic Articular Cartilage: Nonlinear Phenomena Under Finite Deformation,” ASME Journal of Biomechanical Engineering, Vol. 116, pp. 1-9.
50. van der Voet, A. F., Shrive, N. G., and Schachar, N. S., 1993, “Numerical Modelling of Articular Cartilage in Synovial Joints: Poroelasticity and Boundary Conditions,” Recent Advances in Computer Methods in Biomechanics and Biomedical Engineering, J. Middleton, G. N. Pande, K. R. Williams, eds., Books & Journals International, Ltd., UK, pp. 200-209.