An axisymmetric boundary element model for determination of articular cartilage pericellular matrix properties in situ via inverse analysis of chondron deformation

Journal of Biomechanical Engineering

Volumn 132, Issue 3, 2010, Pages

  Kim, Eunjung ^a,c   Guilak, Farshid ^b   Haider, Mansoor A ^a  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

^b DUKE UNIVERSITY MEDICAL CENTER   (United States)

^c UNIVERSITY OF NOTRE DAME   (United States)

Author keywords

Aggrecan; Collagen; Inverse problem; Numerical model; Osteoarthritis; Proteoglycan

Indexed keywords

AGGRECAN; ARTICULAR CARTILAGES; AXISYMMETRIC; BIPHASIC REGION; BOUNDARY ELEMENT MODELS; CARTILAGE EXPLANTS; CARTILAGE EXTRACELLULAR MATRIXES; CELL MATRIX INTERACTIONS; CHONDROCYTES; CHONDRON; CONTINUUM MODEL; ELASTIC PROPERTIES; EXPERIMENTAL DATA; EXPERIMENTAL STUDIES; EXTRACELLULAR; FINITE ELEMENT SOLUTION; IN-SITU; INTERNAL INTERFACES; INVERSE ANALYSIS; LINEAR ELASTIC; MATERIAL PROPERTY; MECHANICAL ENVIRONMENT; MICRO-SCALES; MICROPIPETTE ASPIRATION; MICROSCOPIC SCALE; MORPHOLOGICAL CHANGES; MULTISCALES; NON-LINEAR OPTIMIZATION; NUMERICAL MODEL; NUMERICAL MODELS; PERICELLULAR MATRIX; PROTEOGLYCANS; STRUCTURE AND PROPERTIES; THEORETICAL STUDY; THREE DIMENSIONAL MORPHOLOGY; UNCONFINED COMPRESSION; YOUNG'S MODULUS;

BIOMECHANICS; BODY FLUIDS; CARTILAGE; CEMENTS; COLLAGEN; CONTINUUM MECHANICS; DEFORMATION; ELASTICITY; FINITE ELEMENT METHOD; INVERSE PROBLEMS; JOINTS (ANATOMY); LIGAMENTS; NUMERICAL METHODS; OPTIMIZATION; THREE DIMENSIONAL; TRANSFER MATRIX METHOD; ULTRASONIC MEASUREMENT;

BOUNDARY ELEMENT METHOD;

ARTICLE; ARTICULAR CARTILAGE; CARTILAGE CELL; CARTILAGE MATRIX; CELL INTERACTION; CELL STRUCTURE; CONTROLLED STUDY; ELASTIC CARTILAGE; EXTRACELLULAR MATRIX; FINITE ELEMENT ANALYSIS; MICROPIPETTE; YOUNG MODULUS; ANIMAL; BIOLOGICAL MODEL; COMPUTER SIMULATION; CYTOLOGY; HARDNESS; HUMAN; MECHANICAL STRESS; PHYSIOLOGY;

ANIMALS; CARTILAGE, ARTICULAR; CHONDROCYTES; COMPUTER SIMULATION; ELASTIC MODULUS; EXTRACELLULAR MATRIX; FINITE ELEMENT ANALYSIS; HARDNESS; HUMANS; MODELS, BIOLOGICAL; STRESS, MECHANICAL;

EID: 77953565425     PISSN: 01480731     EISSN: 15288951     Source Type: Journal    
DOI: 10.1115/1.4000938     Document Type: Article

References (50)

1. Mow, V. C., Ratcliffe, A., and Poole, A. R., 1992, "Cartilage and Diarthrodial Joints as Paradigms for Hierarchical Materials and Structures," Biomaterials, 13, pp. 67-97.
2. Urban, J. P., Maroudas, A., Bayliss, M. T., and Dillon, J., 1979, "Swelling Pressures of Proteoglycans at the Concentrations Found in Cartilaginous Tissues," Biorheology, 16, pp. 447-464. (Pubitemid 10097135)
3. Stockwell, R. A., 1979, Biology of Cartilage Cells, Cambridge University Press, Cambridge, UK.
4. Hunziker, E. B., Michel, M., and Studer, D., 1997, "Ultrastructure of Adult Human Articular Cartilage Matrix After Cryotechnical Processing," Microsc. Res. Tech., 37, pp. 271-284.
5. Poole, C. A., Flint, M. H., and Beaumont, B. W., 1987, "Chondrons in Cartilage: Ultrastructural Analysis of the Pericellular Microenvironment in Adult Human Articular Cartilages," J. Orthop. Res., 5, pp. 509-522.
6. Benninghoff, A., 1925, "Form und Bau der Gelenkknorpel in ihren Beziehungen zur Funktion Erste Mitteilung: Die Modellierenden und Formerhaltenden Faktoren des Knorpelreliefs," Anat. Embryol., 76(1-3), pp. 43-63.
7. Poole, C. A., Ayad, S., and Gilbert, R. T., 1992, "Chondrons From Articular Cartilage. V. Immunohistochemical Evaluation of Type VI Collagen Organisation in Isolated Chondrons by Light, Confocal and Electron Microscopy," J. Cell. Sci., 103, pp. 1101-1110.
8. Poole, C. A., Ayad, S., and Schofield, J. R., 1988, "Chondrons From Articular Cartilage: I. Immunolocalization of Type VI Collagen in the Pericellular Capsule of Isolated Canine Tibial Chondrons," J. Cell. Sci., 90, pp. 635-643.
9. Alexopoulos, L. G., Youn, I., Bonaldo, P., and Guilak, F., 2009, "Developmental and Osteoarthritic Changes in Col6a1 Knockout Mice: The Biomechanics of Collagen VI in the Cartilage Pericellular Matrix," Arthritis Rheum., 60, pp. 771-779.
10. Lee, G. M., Paul, T. A., Slabaugh, M., and Kelley, S. S., 2000, "The Incidence of Enlarged Chondrons in Normal and Osteoarthritic Human Cartilage and Their Relative Matrix Density," Osteoarthritis Cartilage, 8, pp. 44-52.
11. Szirmai, J. A., 1974, "The Concept of the Chondron as a Biomechanical Unit, 87," Biopolymer und Biomechanik von Bindegewebssystemen, F. Hartmann, ed., Academic, Berlin.
12. Guilak, F., Alexopoulos, L. G., Upton, M. L., Youn, I., Choi, J. B., Cao, L., Setton, L. A., and Haider, M. A., 2006, "The Pericellular Matrix as a Transducer of Biomechanical and Biochemical Signals in Articular Cartilage," Ann. N.Y. Acad. Sci., 1068, pp. 498-512.
13. Alexopoulos, L. G., Setton, L. A., and Guilak, F., 2005a, "The Biomechanical Role of the Chondrocyte Pericellular Matrix in Articular Cartilage," Acta Biomater., 1, pp. 317-325.
14. Guilak, F., and Mow, V. C., 2000, "The Mechanical Environment of the Chondrocyte: A Biphasic Finite Element Model of Cell-Matrix Interactions in Articular Cartilage," J. Biomech., 33, pp. 1663-1673.
15. Haider, M. A., 2004, "A Radial Biphasic Model for Local Cell-Matrix Mechanics in Articular Cartilage," SIAM J. Appl. Math., 64, pp. 1588-1608.
16. Kim, E., Guilak, F., and Haider, M. A., 2008, "The Dynamic Mechanical Environment of the Chondrocyte: A Biphasic Finite Element Model of Cell-Matrix Interactions Under Cyclic Compressive Loading," ASME J. Biomech. Eng., 130, p. 061009.
17. Ateshian, G. A., Warden, W. H., Kim, J. J., Grelsamer, R. P., and Mow, V. C., 1997, "Finite Deformation Biphasic Material Properties of Bovine Articular Cartilage From Confined Compression Experiments," J. Biomech., 30, pp. 1157-1164.
18. 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., 9, pp. 330-340.
19. Mow, V. C., Kuei, S. C., Lai, W. M., and Armstrong, C. G., 1980, "Biphasic Creep and Stress Relaxation of Articular Cartilage in Compression: Theory and Experiments," ASME J. Biomech. Eng., 102, pp. 73-84.
20. Trickey, W. R., Lee, G. M., and Guilak, F., 2000, "Viscoelastic Properties of Chondrocytes From Normal and Osteoarthritic Human Cartilage," J. Orthop. Res., 18, pp. 891-898.
21. Darling, E. M., Topel, M., Zauscher, S., Vail, T. P., and Guilak, F., 2008, "Viscoelastic Properties of Human Mesenchymally-Derived Stem Cells and Primary Osteoblasts, Chondrocytes, and Adipocytes," J. Biomech., 41, pp. 454-464.
22. Darling, E. M., Zauscher, S., and Guilak, F., 2006, "Viscoelastic Properties of Zonal Articular Chondrocytes Measured by Atomic Force Microscopy," Osteoarthritis Cartilage, 14, pp. 571-579. (Pubitemid 43758550)
23. Koay, E. J., Shieh, A. C., and Athanasiou, K. A., 2003, "Creep Indentation of Single Cells," ASME J. Biomech. Eng., 125, pp. 334-341.
24. Shieh, A. C., and Athanasiou, K. A., 2006, "Biomechanics of Single Zonal Chondrocytes," J. Biomech., 39, pp. 1595-1602.
25. Alexopoulos, L. G., Haider, M. A., Vail, T. P., and Guilak, F., 2003, "Alterations in the Mechanical Properties of the Human Chondrocyte Pericellular Matrix With Osteoarthritis," ASME J. Biomech. Eng., 125, pp. 323-333.
26. Guilak, F., Alexopoulos, L. G., Haider, M. A., Ting-Beall, H. P., and Setton, L. A., 2005, "Zonal Uniformity in Mechanical Properties of the Chondrocyte Pericellular Matrix: Micropipette Aspiration of Canine Chondrons Isolated by Cartilage Homogenization," Ann. Biomed. Eng., 33, pp. 1312-1318.
27. Alexopoulos, L. G., Williams, G. M., Upton, M. L., Setton, L. A., and Guilak, F., 2005, "Osteoarthritic Changes in the Biphasic Mechanical Properties of the chondrocyte Pericellular Matrix in Articular Cartilage," J. Biomech., 38, pp. 509-517. (Pubitemid 40126462)
28. Michalek, A. J., and Iatridis, J. C., 2007, "A Numerical Study to Determine Pericellular Matrix Modulus and Evaluate Its Effects on the Micromechanical Environment of Chondrocytes," J. Biomech., 40, pp. 1405-1409.
29. Guilak, F., Jones, W. R., Ting-Beall, H. P., and Lee, G. M., 1999, "The Deformation Behavior and Mechanical Properties of Chondrocytes in Articular Cartilage," Osteoarthritis Cartilage, 7, pp. 59-70.
30. Hing, W. A., Sherwin, A. F., and Poole, C. A., 2002, "The Influence of the Pericellular Microenvironment on the Chondrocyte Response to Osmotic Challenge," Osteoarthritis Cartilage, 10, pp. 297-307.
31. Guilak, F., Ratcliffe, A., and Mow, V. C., 1995, "Chondrocyte Deformation and Local Tissue Strain in Articular Cartilage: A Confocal Microscopy Study," J. Orthop. Res., 13, pp. 410-421.
32. Buschmann, M. D., Gluzband, Y. A., Grodzinsky, A. J., and Hunziker, E. B., 1995, "Mechanical Compression Modulates Matrix Biosynthesis in Chondrocyte/Agarose Culture," J. Cell Sci., 108, pp. 1497-1508.
33. Quinn, T. M., Grodzinsky, A. J., Buschmann, M. D., Kim, Y. J., and Hunziker, E. B., 1998, "Mechanical Compression Alters Proteoglycan Deposition and Matrix Deformation Around Individual Cells in Cartilage Explants," J. Cell. Sci., 111, pp. 573-583.
34. Freeman, P. M., Natarajan, R. N., Kimura, J. H., and Andriacchi, T. P., 1994, "Chondrocyte Cells Respond Mechanically to Compressive Loads," J. Orthop. Res., 12, pp. 311-320.
35. Knight, M. M., Ross, J. M., Sherwin, A. F., Lee, D. A., Bader, D. L., and Poole, C. A., 2001, "Chondrocyte Deformation Within Mechanically and Enzymatically Extracted Chondrons Compressed in Agarose," Biochim. Biophys. Acta, 1526, pp. 141-146.
36. Choi, J. B., Youn, I., Cao, L., Leddy, H. A., Gilchrist, C. L., Setton, L. A., and Guilak, F., 2007, "Zonal Changes in the Three-Dimensional Morphology of the Chondron Under Compression: The Relationship Among Cellular, Pericellular, and Extracellular Deformation in Articular Cartilage," J. Biomech., 40, pp. 2596-2603.
37. Haider, M. A., and Guilak, F., 2002, "An Axisymmetric Boundary Integral Model for Assessing Elastic Cell Properties in the Micropipette Aspiration Contact Problem," ASME J. Biomech. Eng., 124, pp. 586-595.
38. Benedict, B. A., 2008, "Axisymmetric Poroelastic Boundary Element Methods for Biphasic Mechanics of Articular Cartilage," Ph.D. thesis, Department of Mathematics, North Carolina State University, Raleigh, NC.
39. Guilak, F., 2000, "The Deformation Behavior and Viscoelastic Properties of Chondrocytes in Articular Cartilage," Biorheology, 37, pp. 27-44. (Pubitemid 30353533)
40. Haider, M. A., and Guilak, F., 2007, "Application of a Three-Dimensional Poroelastic BEM to Modeling the Biphasic Mechanics of Cell-Matrix Interactions in Articular Cartilage," Comput. Methods Appl. Mech. Eng., 196, pp. 2999-3010.
41. Korhonen, R. K., and Herzog, W., 2008, "Depth-Dependent Analysis of the Role of Collagen Fibrils, Fixed Charges and Fluid in the Pericellular Matrix of Articular Cartilage on Chondrocyte Mechanics," J. Biomech., 41, pp. 480-485.
42. Wu, J. Z., and Herzog, W., 2006, "Analysis of the Mechanical Behavior of Chondrocytes in Unconfined Compression Tests for Cyclic Loading," J. Biomech., 39, pp. 603-616.
43. Armstrong, C. G., Lai, W. M., and Mow, V. C., 1984, "An Analysis of the Unconfined Compression of Articular Cartilage," ASME J. Biomech. Eng., 106, pp. 165-173.
44. Bakr, A. A., 1986, The Boundary Integral Equation Method in Axisymmetric Stress Analysis Problems, Springer-Verlag, Berlin.
45. Stroud, A. H., and Secrest, D., 1966, Gaussian Quadrature Formulas, Prentice-Hall, Englewood Cliffs, NJ.
46. Haider, M. A., and Guilak, F., 2000, "An Axisymmetric Boundary Integral Model for Incompressible Linear Elasticity: Application to the Micropipette Aspiration Problem," ASME J. Biomech. Eng., 122, pp. 236-244.
47. Guiggiani, M., and Casalini, P., 1987, "Direct Computation of Cauchy Principal Value Integrals in Advanced Boundary Elements," Int. J. Numer. Methods Eng., 24, pp. 1711-1720.
48. Nelder, J., and Mead, R., 1965, "A Simplex Method for Function Minimization," Comput. J., 7, pp. 308-313.
49. Kelley, C. T., 1999, Iterative Methods for Optimization, SIAM, Philadelphia.
50. Allen, D. M., and Mao, J. J., 2004, "Heterogeneous Nanostructural and Nanoelastic Properties of Pericellular and Interterritorial Matrices of Chondrocytes by Atomic Force Microscopy," J. Struct. Biol., 145, pp. 196-204.