A bimodular polyconvex anisotropic strain energy function for articular cartilage

Journal of Biomechanical Engineering

Volumn 129, Issue 2, 2007, Pages 250-258

  Klisch, Stephen M ^a  

^a CALIFORNIA POLYTECHNIC STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; BLOOD VESSELS; MATHEMATICAL MODELS; ORTHOTICS; POISSON RATIO; STRAIN ENERGY;

ARTICULAR CARTILAGE; ORTHOTROPIC MATERIALS; STRAIN ENERGY FUNCTION;

CARTILAGE;

ANISOTROPY; ARTICLE; ARTICULAR CARTILAGE; DATA BASE; ENERGY; ENERGY CONSUMPTION; MUSCLE CELL; MUSCLE DISEASE; MUSCLE STRAIN; MUSCLE TONE; REGRESSION ANALYSIS;

ANIMALS; ANISOTROPY; CARTILAGE, ARTICULAR; ENERGY METABOLISM; HUMANS; MODELS, THEORETICAL; POISSON DISTRIBUTION; REGRESSION ANALYSIS; STRESS, MECHANICAL;

EID: 34248209005     PISSN: 01480731     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2486225     Document Type: Article

References (55)

1. Lai, W. M., Hou, J. S., and Mow, V. C., 1991, "A Triphasic Theory for the Swelling and Deformation Behaviors of Articular Cartilage," J. Biomech. Eng., 113, pp. 245-258.
2. Basser, P. J., Schneiderman, R., Bank, R. A., Wachtel, E., and Maroudas, A., 1998, "Mechanical Properties of the Collagen Network in Human Articular Cartilage as Measured by Osmotic Stress Technique," Arch. Biochem. Biophys., 351, pp. 207-219.
3. Venn, M. F., and Maroudas, A., 1977, "Chemical Composition and Swelling of Normal and Osteoarthritic Femoral Head Cartilage. I. Chemical Composition," Ann. Rheum. Dis., 36, pp. 121-129.
4. Mow, V. C., and Ratcliffe, A., 1997, "Structure and Function of Articular Cartilage and Meniscus," Basic Orthopaedic Biomechanics, V. C. Mow and W. C. Hayes, eds., Raven Press, New York, pp. 113-178.
5. Woo, S. L.-Y., Akeson, W. H., and Jemmott, G. F., 1976, "Measurements of Nonhomogeneous Directional Mechanical Properties of Articular Cartilage in Tension," J. Biomech., 9, pp. 785-791.
6. Woo, S. L.-Y., Lubock, P., Gomez, M. A., Jemmott, G. F., Kuei, S. C., and Akeson, W. H., 1979, "Large Deformation Nonhomogeneous and Directional Properties of Articular Cartilage in Uniaxial Tension," J. Biomech., 12, pp. 437-446.
7. Akizuki, S., Mow, V. C., Muller, F., Pita, J. C., Howell, D. S., and Manicourt, D. H., 1986, "Tensile Properties of Human Knee Joint Cartilage: I. Influence of Ionic Conditions, Weight Bearing, and Fibrillation on the Tensile Modulus," J. Orthop. Res., 4, pp. 379-392.
8. Soltz, M. A., and Ateshian, G. A., 2000, "A Conewise Linear Elasticity Mixture Model for the Analysis of Tension-Compression Nonlinearity in Articular Cartilage," J. Biomech. Eng., 122, pp. 576-586.
9. Laasanen, M., Toyras, J., Korhonen, R., Rieppo, J., Saarakkala, S., Nieminen, M., Hirvonen, J., and Jurvelin, J. S., 2003, "Biomechanical Properties of Knee Articular Cartilage," Biorheology, 40, pp. 133-140.
10. Wang, C. C., Chahine, N. O., Hung, C. T., and Ateshian, G. A., 2003, "Optical Determination of Anisotropic Material Properties of Bovine Articular Cartilage in Compression," J. Biomech., 36(3), pp. 339-353.
11. Donzelli, P. S., Spilker, R. L., Ateshian, G. A., and Mow, V. C., 1999, "Contact Analysis of Biphasic Transversely Isotropic Cartilage Layers and Correlations with Tissue Failure," J. Biomech., 32(10), pp. 1037-1047.
12. Krishnan, R., Park, S., Eckstein, F., and Ateshian, G. A., 2003, "Inhomogeneous Cartilage Properties Enhance Superficial Interstitial Fluid Support and Frictional Properties, but do not Provide a Homogeneous State of Stress," J. Biomech. Eng., 125(5), pp. 569-577.
13. Chang, D. G., Lottman, L. M., Chen, A. C. Schinagl, R. M., Albrecht, D. R., Pedowitz, R. A., Brossman, J., Frank, L. R., and Sah, R. L., 1999, "The Depth-Dependent, Multi-axial Properties of Aged Human Patellar Cartilage in Tension," Trans. Annu. Meet. - Orthop. Res. Soc., 24, p. 644.
14. Korhonen, R. K., Toyras, J., Nieminen, M. T., Rieppo, J., Hirvonen, J., Helminen, H. J., and Jurvelin, J. S., 2001, "Effect of Ionic Environment on the Compression-Tension Nonlinearity of Articular Cartilage in the Direction Perpendicular to Articular Surface," Trans. Annu. Meet. - Orthop. Res. Soc., 26, p. 439.
15. Elliot, D. M., Narmoneva, D. A., and Setton, L. A., 2002, "Direct Measurement of the Poisson's Ratio of Human Patella Cartilage in Tension," J. Biomech. Eng., 124, pp. 223-228.
16. Charlebois, M., McKee, M. D., and Buschmann, M. D., 2004, "Nonlinear Tensile Properties of Bovine Articular Cartilage and Their Variation with Age and Depth," J. Biomech. Eng., 126, pp. 129-137.
17. Chahine, N. O., Wang, C. C., Hung, C. T., and Ateshian, G. A., 2004, "Anisotropic Strain-Dependent Material Properties of Bovine Articular Cartilage in the Transitional Range From Tension to Compression," J. Biomech., 37, pp. 1251-1261.
18. Huang, C. Y., Stankiewicz, A., Ateshian, G. A., and Mow, V. C., 2005, "Anisotropy, Inhomogeneity, and Tension-Compression Nonlinearity of Human Glenohumeral Cartilage in Finite Deformation," J. Biomech., 38(4), pp. 799-809.
19. Ficklin, T., Thomas, G., Chen, A., Sah, R., Davol, A., and Klisch, S., 2006, "Development of an Experimental Protocol to Measure Anisotropic Material Properties of Bovine Articular Cartilage," Proceedings Summer Bioengineering Conference, ASME, Amelia Island, FL.
20. Curnier, A., He, Q. C., and Zysset, P., 1995, "Conewise Linear Elastic Materials," J. Elast., 37, pp. 1-38.
21. Holzapfel, G. A., Gasser, T. C., and Ogden, R. W., 2004, "Comparison of a Multi-layer Structural Model for Arterial Walls with a Fung-Type Model, and Issues of Material Stability," J. Biomech. Eng., 126(2), pp. 264-275.
22. Baer, A. E., Laursen, T. A., Guilak, F., and Setton, L. A., 2004, "The Micromechanical Environment of Intervertebral Disc Cells Determined by a Finite Deformation, Anisotropic, and Biphasic Finite Element Model," J. Biomech. Eng., 125, pp. 1-11.
23. Klisch, S. M., 2006, "A Bimodular Theory for Finite Deformations: Comparison of Orthotropic Second-order and Exponential Stress Constitutive Equations for Articular Cartilage," Biomech. Model. Mechanobiol., 5(2-3), pp. 90-101.
24. Ball, J. M., 1977, "Convexity Conditions and Existence Theorems in Non-linear Elasticity," Arch. Ration. Mech. Anal., 63, pp. 337-403.
25. Klisch, S. M., Sah, R. L., and Davol, A., 2006, "Bimodular- Orthotropic-Polyconvex Strain Energy Functions for the Collagen-Proteoglycan Solid Matrix of Articular Cartilage," Proceedings Summer Bioengineering Conference, ASME, Amelia Island, FL.
26. Schroder, J., and Neff, P., 2003, "Invariant Formulation of Hyperelastic Transverse Isotropy Based on Polyconvex Free Energy Functions," Int. J. Solids Struct., 40, pp. 401-445.
27. Itskov, M., Ehret, A. E., and Mavrilas, D., 2006, "A Polyconvex Anisotropic Strain-Energy Function for Soft Collagenous Tissues," Biomech. Model. Mechanobiol., 5(1), pp. 17-26.
28. Wagner, D. R., Reiser, K. M., and Lotz, J. C., 2006, "Glycation Increases Human Annulus Fibrosus Stiffness in Both Experimental Measurements and Theoretical Predictions," J. Biomech., 39, pp. 1021-1029.
29. Spencer, A. J. M., 1984, Continuum Theory of the Mechanics of Fibre-Reinforced Composites, Springer, New York.
30. Klisch, S. M., and Lotz, J. C., 1999, "Application of a Fiber-Reinforced Continuum Theory to Multiple Deformations of the Annulus Fibrosus," J. Biomech., 32(10), pp. 1027-1036.
31. Elliott, D. M., and Setton, L. A., 2000, "A Linear Material Model for Fiber-Induced Anisotropy of the Anulus Fibrosus," J. Biomech. Eng., 122, pp. 173-179.
32. Eberlein, R., Holzapfel, G. A., and Schulze-Bauer, C. A., 2001, "An Anisotropic Constitutive Model for Annulus Tissue and Enhanced Finite Element Analyses of Intact Lumbar Disc Bodies," Comput. Methods Biomech. Biomed. Eng., 4, pp. 209-230.
33. Spencer, A. J. M., 1971, "Theory of Invariants," Continuum Physics, A. C. Eringen, ed., Academic, New York, pp. 240-353.
34. Schroder, J., Neff, P., and Balzani, D., 2005, "A Variational Approach for Materially Stable Anisotropic Hyperelasticity," Int. J. Solids Struct., 42, pp. 4352-4371.
35. Wagner, D. R., 2002, "A Mechanistic Strain Energy Function and Experimental Results for the Human Annulus Fibrosus," Ph.D. thesis, U. C. Berkeley, Berkeley, CA.
36. Itskov, M., and Aksel, N., 2004, "A Class of Orthotropic and Transversely Isotropic Hyperelastic Constitutive Models Based on a Polyconvex Strain Energy Function," Int. J. Solids Struct., 41, pp. 3833-3848.
37. Chang, D. G., 1999, "Structure and Function Relationships of Articular Cartilage in Osteoarthritis," Ph.D. thesis, University of California, San Diego, La Jolla, CA.
38. Jurvelin, J. S., Buschmann, M. D., and Hunziker, E. B., 1997, "Optical and Mechanical Determination of Poisson's Ratio of Adult Bovine Humeral Articular Cartilage," J. Biomech., 30, pp. 235-241.
39. Wong, M., Ponticiello, M., Kovanen, V., and Jurvelin, J. S., 2000, "Volumetric Changes of Articular Cartilage During Stress Relaxation in Unconfined Compression," J. Biomech., 33(9), pp. 1049-1054.
40. Williamson, A. K., Chen, A. C., Masuda, K., Thonar, E. J.-M. A., and Sah, R. L., 2003, "Tensile Mechanical Properties of Bovine Articular Cartilage: Variations with Growth and Relationships to Collagen Network Components," J. Orthop. Res., 21, pp. 872-880.
41. Broom, N. D., and Poole, C. A., 1983, "Articular Cartilage Collagen and Proteoglycans. Their Functional Interdependency," Arthritis Rheum., 26(9), pp. 1111-1119.
42. Vynios, D. H., Papageorgakopoulou, N., Sazakli, H., and Tsiganos, C. P., 2001, "The Interactions of Cartilage Proteoglycans with Collagens are Determined by Their Structures," Biochimie, 83, pp. 899-906.
43. Hendrickx, S., Thomas, P., Preston, B., and Stanton, P., 2001, "Partial Characterization of Matrix Components Interacting with Cartilage Proteoglycans," Arch. Biochem. Biophys., 390(2), pp. 186-194.
44. Jeffery, A. K., Blunn, G. W., Archer, C. W., and Bentley, G., 1991, "Three-Dimensional Collagen Architecture in Bovine Articular Cartilage," J. Bone Jt. Surg., Br. Vol. 73-B, 795-801.
45. Benninghoff, A., 1925, "Form und Bau der Gelenkknorpel in Ihren Beziehungen zur Funktion. Zweiter Teil: der Aufbau des Gelenkknorpels in Seinen Beziehungen zur Funktion," Z. Zellforsch Mikrosk Anat., 2, pp. 783-862.
46. Lanir, Y., 1983, "Constitutive Equations for Fibrous Connective Tissues," J. Biomech., 16, pp. 1-12.
47. Gasser, T. C., Ogden, R. W., and Holzapfel, G. A., 2006, "Hyperelastic Modelling of Arterial Layers with Distributed Collagen Fibre Orientations," J. R. Soc., Interface, 3, pp. 15-35.
48. Anderson, A. F., Ellis, B. J., Maas, S. A., Peters, C. L., Ateshian, G. A., and Weiss, J. A., 2006, "Experimental Measurement and Finite Element Prediction of Cartilage Contact Pressures in the Human Hip," Proceedings ASME Summer Bioengineering Conference, Amelia Island, FL.
49. Klisch, S. M., Sah, R. L., and Hoger, A., 2000, "A Growth Mixture Theory for Cartilage," Mechanics in Biology, J. Casey and G. Bao, eds., ASME, AMD-242, New York, pp. 229-242.
50. Klisch, S. M., Van Dyke, T., and Hoger, A., 2001, "A Theory of Volumetric Growth for Compressible Elastic Materials," Math. Mech. Solids, 6, pp. 551-575.
51. Klisch, S. M., and Hoger, A., 2003, "Volumetric Growth of Thermoelastic Materials and Mixtures," Math. Mech. Solids, 8, pp. 377-402.
52. Klisch, S. M., Chen, S. S., Sah, R. L., and Hoger, A., 2003, "A Growth Mixture Theory for Cartilage with Applications to Growth-Related Experiments on Cartilage Explants," J. Biomech. Eng., 125, pp. 169-179.
53. Klisch, S. M., Sah, R. L., and Hoger, A., 2005, "A Cartilage Growth Mixture Model for Infinitesimal Strains: Solutions of Boundary-Value Problems Related to In Vitro Growth Experiments," Biomech. Model. Mechanobiol., 3(4), pp. 209-223.
54. Davol, A., Bingham, M. S., Sah, R. L., and Klisch, S. M., 2007, "A Nonlinear Finite Element Model of Cartilage Growth," Biomech. Model. Mechanobiol., in press.
55. Smith, G. D., Knutsen, G., and Richardson, J. B., 2005, "A Clincial Review of Cartilage Repair Techniques," J. Bone Jt. Surg., Am. Vol. 87B(4), pp. 445-449.