Advertisement

Annals of Biomedical Engineering

, Volume 40, Issue 11, pp 2456–2474 | Cite as

Multiscale Mechanics of Articular Cartilage: Potentials and Challenges of Coupling Musculoskeletal, Joint, and Microscale Computational Models

  • J. P. Halloran
  • S. Sibole
  • C. C. van Donkelaar
  • M. C. van Turnhout
  • C. W. J. Oomens
  • J. A. Weiss
  • F. Guilak
  • A. Erdemir
Article

Abstract

Articular cartilage experiences significant mechanical loads during daily activities. Healthy cartilage provides the capacity for load bearing and regulates the mechanobiological processes for tissue development, maintenance, and repair. Experimental studies at multiple scales have provided a fundamental understanding of macroscopic mechanical function, evaluation of the micromechanical environment of chondrocytes, and the foundations for mechanobiological response. In addition, computational models of cartilage have offered a concise description of experimental data at many spatial levels under healthy and diseased conditions, and have served to generate hypotheses for the mechanical and biological function. Further, modeling and simulation provides a platform for predictive risk assessment, management of dysfunction, as well as a means to relate multiple spatial scales. Simulation-based investigation of cartilage comes with many challenges including both the computational burden and often insufficient availability of data for model development and validation. This review outlines recent modeling and simulation approaches to understand cartilage function from a mechanical systems perspective, and illustrates pathways to associate mechanics with biological function. Computational representations at single scales are provided from the body down to the microstructure, along with attempts to explore multiscale mechanisms of load sharing that dictate the mechanical environment of the cartilage and chondrocytes.

Keywords

Mechanical system Musculoskeletal Joint loading Chondrocyte Chondron Extracellular matrix Pericellular matrix Collagen Proteoglycan Continuum mechanics Microstructure Mechanobiology Locomotion Finite element analysis 

Notes

Acknowledgments

This study was supported by the National Institutes of Health grants R01EB009643 (A. Erdemir), R01AG15768 (F. Guilak), R01AR48182 (F. Guilak), R01AR48852 (F. Guilak), P01AR50245 (F. Guilak), R01GM083925 (J.A. Weiss), R01AR047369 (J.A. Weiss), and R01AR053344 (J.A. Weiss). The authors would also like to acknowledge Simbios, NIH Center for Biomedical Computation at Stanford, for hosting the project site for collaborative research.

References

  1. 1.
    Abusara, Z., R. Seerattan, A. Leumann, R. Thompson, and W. Herzog. A novel method for determining articular cartilage chondrocyte mechanics in vivo. J. Biomech. 44:930–934, 2011.PubMedCrossRefGoogle Scholar
  2. 2.
    Adouni, M., and A. Shirazi-Adl. Knee joint biomechanics in closed-kinetic-chain exercises. Comput. Methods Biomech. Biomed. Engin. 12:661–670, 2009.PubMedCrossRefGoogle Scholar
  3. 3.
    Alexopoulos, L. G., L. A. Setton, and F. Guilak. The biomechanical role of the chondrocyte pericellular matrix in articular cartilage. Acta Biomater. 1:317–325, 2005.PubMedCrossRefGoogle Scholar
  4. 4.
    Alexopoulos, L. G., G. M. Williams, M. L. Upton, L. A. Setton, and F. Guilak. Osteoarthritic changes in the biphasic mechanical properties of the chondrocyte pericellular matrix in articular cartilage. J. Biomech. 38:509–517, 2005.PubMedCrossRefGoogle Scholar
  5. 5.
    Anderson, A. E., B. J. Ellis, S. A. Maas, C. L. Peters, and J. A. Weiss. Validation of finite element predictions of cartilage contact pressure in the human hip joint. J. Biomech. Eng. 130:051008, 2008.PubMedCrossRefGoogle Scholar
  6. 6.
    Anderson, A. E., B. J. Ellis, S. A. Maas, and J. A. Weiss. Effects of idealized joint geometry on finite element predictions of cartilage contact stresses in the hip. J. Biomech. 43:1351–1357, 2010.PubMedCrossRefGoogle Scholar
  7. 7.
    Anderson, D. D., K. S. Iyer, N. A. Segal, J. A. Lynch, and T. D. Brown. Implementation of discrete element analysis for subject-specific, population-wide investigations of habitual contact stress exposure. J. Appl. Biomech. 26:215–223, 2010.PubMedGoogle Scholar
  8. 8.
    Anderson, F. C., and M. G. Pandy. Individual muscle contributions to support in normal walking. Gait Posture 17:159–169, 2003.PubMedCrossRefGoogle Scholar
  9. 9.
    Arokoski, J. P., M. M. Hyttinen, T. Lapveteläinen, P. Takács, B. Kosztáczky, L. Módis, V. Kovanen, and H. Helminen. Decreased birefringence of the superficial zone collagen network in the canine knee (stifle) articular cartilage after long distance running training, detected by quantitative polarised light microscopy. Ann. Rheum. Dis. 55:253–264, 1996.PubMedCrossRefGoogle Scholar
  10. 10.
    Arokoski, J. P., J. S. Jurvelin, U. Väätäinen, and H. J. Helminen. Normal and pathological adaptations of articular cartilage to joint loading. Scand. J. Med. Sci. Sports 10:186–198, 2000.PubMedCrossRefGoogle Scholar
  11. 11.
    Ateshian, G. A. The role of interstitial fluid pressurization in articular cartilage lubrication. J. Biomech. 42:1163–1176, 2009.PubMedCrossRefGoogle Scholar
  12. 12.
    Ateshian, G. A., M. B. Albro, S. Maas, and J. A. Weiss. Finite element implementation of mechanochemical phenomena in neutral deformable porous media under finite deformation. J. Biomech. Eng. 133:081005, 2011.PubMedCrossRefGoogle Scholar
  13. 13.
    Ateshian, G. A., N. O. Chahine, I. M. Basalo, and C. T. Hung. The correspondence between equilibrium biphasic and triphasic material properties in mixture models of articular cartilage. J. Biomech. 37:391–400, 2004.PubMedCrossRefGoogle Scholar
  14. 14.
    Ateshian, G. A., B. J. Ellis, and J. A. Weiss. Equivalence between short-time biphasic and incompressible elastic material responses. J. Biomech. Eng. 129:405–412, 2007.PubMedCrossRefGoogle Scholar
  15. 15.
    Ateshian, G. A., S. Maas, and J. A. Weiss. Finite element algorithm for frictionless contact of porous permeable media under finite deformation and sliding. J. Biomech. Eng. 132:061006, 2010.PubMedCrossRefGoogle Scholar
  16. 16.
    Ateshian, G. A., and T. Ricken. Multigenerational interstitial growth of biological tissues. Biomech. Model. Mechanobiol. 9:689–702, 2010.PubMedCrossRefGoogle Scholar
  17. 17.
    Baliunas, A. J., D. E. Hurwitz, A. B. Ryals, A. Karrar, J. P. Case, J. A. Block, and T. P. Andriacchi. Increased knee joint loads during walking are present in subjects with knee osteoarthritis. Osteoarthritis Cartilage 10:573–579, 2002.PubMedCrossRefGoogle Scholar
  18. 18.
    Bathe, M., A. J. Grodzinsky, B. Tidor, and G. C. Rutledge. Optimal linearized Poisson–Boltzmann theory applied to the simulation of flexible polyelectrolytes in solution. J. Chem. Phys. 121:7557–7561, 2004.PubMedCrossRefGoogle Scholar
  19. 19.
    Besier, T. F., G. E. Gold, G. S. Beaupré, and S. L. Delp. A modeling framework to estimate patellofemoral joint cartilage stress in vivo. Med. Sci. Sports Exerc. 37:1924–1930, 2005.PubMedCrossRefGoogle Scholar
  20. 20.
    Bischof, J. E., C. E. Spritzer, A. M. Caputo, M. E. Easley, J. K. DeOrio, J. A. Nunley, 2nd, and L. E. DeFrate. In vivo cartilage contact strains in patients with lateral ankle instability. J. Biomech. 43:2561–2566, 2010.PubMedCrossRefGoogle Scholar
  21. 21.
    Brouwers, J. E. M., C. C. van Donkelaar, B. G. Sengers, and R. Huiskes. Can the growth factors PTHrP, Ihh and VEGF, together regulate the development of a long bone? J. Biomech. 39:2774–2782, 2006.PubMedCrossRefGoogle Scholar
  22. 22.
    Buckwalter, J. A. Osteoarthritis and articular cartilage use, disuse, and abuse: experimental studies. J. Rheumatol. Suppl. 43:13–15, 1995.PubMedGoogle Scholar
  23. 23.
    Buschmann, M. D., Y. A. Gluzband, A. J. Grodzinsky, and E. B. Hunziker. Mechanical compression modulates matrix biosynthesis in chondrocyte/agarose culture. J. Cell Sci. 108(Pt 4):1497–1508, 1995.PubMedGoogle Scholar
  24. 24.
    Butz, K. D., D. D. Chan, E. A. Nauman, and C. P. Neu. Stress distributions and material properties determined in articular cartilage from MRI-based finite strains. J. Biomech. 44:2667–2672, 2011.PubMedCrossRefGoogle Scholar
  25. 25.
    Catt, C. J., W. Schuurman, B. G. Sengers, P. R. van Weeren, W. J. A. Dhert, C. P. Please, and J. Malda. Mathematical modelling of tissue formation in chondrocyte filter cultures. Eur. Cell. Mater. 22:377–392, 2011.PubMedGoogle Scholar
  26. 26.
    Chahine, N. O., C. T. Hung, and G. A. Ateshian. In situ measurements of chondrocyte deformation under transient loading. Eur. Cell. Mater. 13:100–111, 2007; discussion 111.PubMedGoogle Scholar
  27. 27.
    Chao, E. Y. S., K. Y. Volokh, H. Yoshida, N. Shiba, and T. Ide. Discrete element analysis in musculoskeletal biomechanics. Mol. Cell. Biomech. 7:175–192, 2010.PubMedGoogle Scholar
  28. 28.
    Chegini, S., M. Beck, and S. J. Ferguson. The effects of impingement and dysplasia on stress distributions in the hip joint during sitting and walking: a finite element analysis. J. Orthop. Res. 27:195–201, 2009.PubMedCrossRefGoogle Scholar
  29. 29.
    Chen, A. C., W. C. Bae, R. M. Schinagl, and R. L. Sah. Depth- and strain-dependent mechanical and electromechanical properties of full-thickness bovine articular cartilage in confined compression. J. Biomech. 34:1–12, 2001.PubMedCrossRefGoogle Scholar
  30. 30.
    Chen, C. S., and D. E. Ingber. Tensegrity and mechanoregulation: from skeleton to cytoskeleton. Osteoarthritis Cartilage 7:81–94, 1999.PubMedCrossRefGoogle Scholar
  31. 31.
    Choi, J. B., I. Youn, L. Cao, H. A. Leddy, C. L. Gilchrist, L. A. Setton, and F. Guilak. 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. 40:2596–2603, 2007.PubMedCrossRefGoogle Scholar
  32. 32.
    Connolly, K. D., J. L. Ronsky, L. M. Westover, J. C. Küpper, and R. Frayne. Differences in patellofemoral contact mechanics associated with patellofemoral pain syndrome. J. Biomech. 42:2802–2807, 2009.PubMedCrossRefGoogle Scholar
  33. 33.
    D’Lima, D. D., P. C. Chen, and C. W. Colwell, Jr. Osteochondral grafting: effect of graft alignment, material properties, and articular geometry. Open Orthop. J. 3:61–68, 2009.CrossRefGoogle Scholar
  34. 34.
    Delp, S. L., J. P. Loan, M. G. Hoy, F. E. Zajac, E. L. Topp, and J. M. Rosen. An interactive graphics-based model of the lower extremity to study orthopaedic surgical procedures. IEEE Trans. Biomed. Eng. 37:757–767, 1990.PubMedCrossRefGoogle Scholar
  35. 35.
    Dhaher, Y. Y., T.-H. Kwon, and M. Barry. The effect of connective tissue material uncertainties on knee joint mechanics under isolated loading conditions. J. Biomech. 43:3118–3125, 2010.PubMedCrossRefGoogle Scholar
  36. 36.
    Elias, J. J., and A. J. Cosgarea. Computational modeling: an alternative approach for investigating patellofemoral mechanics. Sports Med. Arthrosc. 15:89–94, 2007.PubMedCrossRefGoogle Scholar
  37. 37.
    Elias, J. J., M. S. Kirkpatrick, A. Saranathan, S. Mani, L. G. Smith, and M. J. Tanaka. Hamstrings loading contributes to lateral patellofemoral malalignment and elevated cartilage pressures: an in vitro study. Clin. Biomech. (Bristol, Avon) 26:841–846, 2011.CrossRefGoogle Scholar
  38. 38.
    Erdemir, A., T. M. Guess, J. Halloran, S. C. Tadepalli, and T. M. Morrison. Considerations for reporting finite element analysis studies in biomechanics. J. Biomech. 45(4):625–633, 2012.PubMedCrossRefGoogle Scholar
  39. 39.
    Erdemir, A., S. McLean, W. Herzog, and A. J. van den Bogert. Model-based estimation of muscle forces exerted during movements. Clin. Biomech. (Bristol, Avon) 22:131–154, 2007.CrossRefGoogle Scholar
  40. 40.
    Erhart-Hledik, J. C., B. Elspas, N. J. Giori, and T. P. Andriacchi. Effect of variable-stiffness walking shoes on knee adduction moment, pain, and function in subjects with medial compartment knee osteoarthritis after 1 year. J. Orthop. Res. 30(4):514–521, 2012.Google Scholar
  41. 41.
    Federico, S., A. Grillo, G. La Rosa, G. Giaquinta, and W. Herzog. A transversely isotropic, transversely homogeneous microstructural-statistical model of articular cartilage. J. Biomech. 38:2008–2018, 2005.PubMedCrossRefGoogle Scholar
  42. 42.
    Federico, S., and W. Herzog. Towards an analytical model of soft biological tissues. J. Biomech. 41:3309–3313, 2008.PubMedCrossRefGoogle Scholar
  43. 43.
    Fernandez, J. W., M. Akbarshahi, K. M. Crossley, K. B. Shelburne, and M. G. Pandy. Model predictions of increased knee joint loading in regions of thinner articular cartilage after patellar tendon adhesion. J. Orthop. Res. 29:1168–1177, 2011.PubMedCrossRefGoogle Scholar
  44. 44.
    Fernandez, J. W., and M. G. Pandy. Integrating modelling and experiments to assess dynamic musculoskeletal function in humans. Exp. Physiol. 91:371–382, 2006.PubMedCrossRefGoogle Scholar
  45. 45.
    Fischer, K. J., J. E. Johnson, A. J. Waller, T. E. McIff, E. B. Toby, and M. Bilgen. MRI-based modeling for radiocarpal joint mechanics: validation criteria and results for four specimen-specific models. J. Biomech. Eng. 133:101004, 2011.PubMedCrossRefGoogle Scholar
  46. 46.
    Fitzpatrick, C. K., M. A. Baldwin, P. J. Laz, D. P. FitzPatrick, A. L. Lerner, and P. J. Rullkoetter. Development of a statistical shape model of the patellofemoral joint for investigating relationships between shape and function. J. Biomech. 44:2446–2452, 2011.PubMedCrossRefGoogle Scholar
  47. 47.
    Foolen, J., C. C. van Donkelaar, and K. Ito. Intracellular tension in periosteum/perichondrium cells regulates long bone growth. J. Orthop. Res. 29:84–91, 2011.PubMedCrossRefGoogle Scholar
  48. 48.
    Fregly, B. J., T. F. Besier, D. G. Lloyd, S. L. Delp, S. A. Banks, M. G. Pandy, and D. D. D’Lima. Grand challenge competition to predict in vivo knee loads. J. Orthop. Res. 30:503–513, 2012.PubMedCrossRefGoogle Scholar
  49. 49.
    Galban, C. J., and B. R. Locke. Analysis of cell growth in a polymer scaffold using a moving boundary approach. Biotechnol. Bioeng. 56:422–432, 1997.PubMedCrossRefGoogle Scholar
  50. 50.
    Geers, M. G. D., V. G. Kouznetsova, and W. A. M. Brekelmans. Multi-scale computational homogenization: trends and challenges. J. Comput. Appl. Math. 234:2175–2182, 2010.CrossRefGoogle Scholar
  51. 51.
    Goldsmith, A. A., A. Hayes, and S. E. Clift. Application of finite elements to the stress analysis of articular cartilage. Med. Eng. Phys. 18:89–98, 1996.PubMedCrossRefGoogle Scholar
  52. 52.
    Grodzinsky, A. J., M. E. Levenston, M. Jin, and E. H. Frank. Cartilage tissue remodeling in response to mechanical forces. Annu. Rev. Biomed. Eng. 2:691–713, 2000.PubMedCrossRefGoogle Scholar
  53. 53.
    Gu, K. B., and L. P. Li. A human knee joint model considering fluid pressure and fiber orientation in cartilages and menisci. Med. Eng. Phys. 33:497–503, 2011.PubMedCrossRefGoogle Scholar
  54. 54.
    Guess, T. M., H. Liu, S. Bhashyam, and G. Thiagarajan. A multibody knee model with discrete cartilage prediction of tibio-femoral contact mechanics. Comput. Methods Biomech. Biomed. Engin., 2011. doi: 10.1080/10255842.2011.617004.
  55. 55.
    Guilak, F. Compression-induced changes in the shape and volume of the chondrocyte nucleus. J. Biomech. 28:1529–1541, 1995.PubMedCrossRefGoogle Scholar
  56. 56.
    Guilak, F. Biomechanical factors in osteoarthritis. Best Pract. Res. Clin. Rheumatol. 25:815–823, 2011.PubMedCrossRefGoogle Scholar
  57. 57.
    Guilak, F., L. G. Alexopoulos, M. L. Upton, I. Youn, J. B. Choi, L. Cao, L. A. Setton, and M. A. Haider. The pericellular matrix as a transducer of biomechanical and biochemical signals in articular cartilage. Ann. N. Y. Acad. Sci. 1068:498–512, 2006.PubMedCrossRefGoogle Scholar
  58. 58.
    Guilak, F., and C. T. Hung. Physical regulation of cartilage metabolism. In: Basic Orthopaedic Biomechanics and Mechanobiology, edited by V. C. Mow, and R. Huiskes. Philadelphia: Lippincott Williams & Wilkins, 2005, pp. 259–300.Google Scholar
  59. 59.
    Guilak, F., and V. C. Mow. The mechanical environment of the chondrocyte: a biphasic finite element model of cell–matrix interactions in articular cartilage. J. Biomech. 33:1663–1673, 2000.PubMedCrossRefGoogle Scholar
  60. 60.
    Guilak, F., J. R. Tedrow, and R. Burgkart. Viscoelastic properties of the cell nucleus. Biochem. Biophys. Res. Commun. 269:781–786, 2000.PubMedCrossRefGoogle Scholar
  61. 61.
    Haider, M. A., and F. Guilak. Application of a three-dimensional poroelastic BEM to modeling the biphasic mechanics of cell–matrix interactions in articular cartilage (revision). Comput. Methods Appl. Mech. Eng. 196:2999–3010, 2007.PubMedCrossRefGoogle Scholar
  62. 62.
    Halloran, J. P., M. Ackermann, A. Erdemir, and A. J. van den Bogert. Concurrent musculoskeletal dynamics and finite element analysis predicts altered gait patterns to reduce foot tissue loading. J. Biomech. 43:2810–2815, 2010.PubMedCrossRefGoogle Scholar
  63. 63.
    Halloran, J. P., A. Erdemir, and A. J. van den Bogert. Adaptive surrogate modeling for efficient coupling of musculoskeletal control and tissue deformation models. J. Biomech. Eng. 131:011014, 2009.PubMedCrossRefGoogle Scholar
  64. 64.
    Han, S.-K., S. Federico, A. Grillo, G. Giaquinta, and W. Herzog. The mechanical behaviour of chondrocytes predicted with a micro-structural model of articular cartilage. Biomech. Model. Mechanobiol. 6:139–150, 2007.PubMedCrossRefGoogle Scholar
  65. 65.
    Han, S.-K., S. Federico, and W. Herzog. A depth-dependent model of the pericellular microenvironment of chondrocytes in articular cartilage. Comput. Methods Biomech. Biomed. Engin. 14:657–664, 2011.PubMedCrossRefGoogle Scholar
  66. 66.
    Han, L., A. J. Grodzinsky, and C. Ortiz. Nanomechanics of the cartilage extracellular matrix. Annu. Rev. Mater. Res. 41:133–168, 2011.PubMedCrossRefGoogle Scholar
  67. 67.
    Harris, M. D., A. E. Anderson, C. R. Henak, B. J. Ellis, C. L. Peters, and J. A. Weiss. Finite element prediction of cartilage contact stresses in normal human hips. J. Orthop. Res. 30(7):1133–1139, 2012.PubMedCrossRefGoogle Scholar
  68. 68.
    Harris, J. D., K. K. Solak, R. A. Siston, A. Litsky, J. Richards, and D. C. Flanigan. Contact pressure comparison of proud osteochondral autograft plugs versus proud synthetic plugs. Orthopedics 34:97, 2011.PubMedGoogle Scholar
  69. 69.
    Haut Donahue, T. L., M. L. Hull, M. M. Rashid, and C. R. Jacobs. How the stiffness of meniscal attachments and meniscal material properties affect tibio-femoral contact pressure computed using a validated finite element model of the human knee joint. J Biomech 36:19–34, 2003.PubMedCrossRefGoogle Scholar
  70. 70.
    Heinegård, D., and A. Oldberg. Structure and biology of cartilage and bone matrix noncollagenous macromolecules. FASEB J. 3:2042–2051, 1989.PubMedGoogle Scholar
  71. 71.
    Helminen, H. J., M. M. Hyttinen, M. J. Lammi, J. P. Arokoski, T. Lapveteläinen, J. Jurvelin, I. Kiviranta, and M. I. Tammi. Regular joint loading in youth assists in the establishment and strengthening of the collagen network of articular cartilage and contributes to the prevention of osteoarthrosis later in life: a hypothesis. J. Bone Miner. Metab. 18:245–257, 2000.PubMedCrossRefGoogle Scholar
  72. 72.
    Henninger, H. B., S. P. Reese, A. E. Anderson, and J. A. Weiss. Validation of computational models in biomechanics. Proc. Inst. Mech. Eng. H 224:801–812, 2010.PubMedCrossRefGoogle Scholar
  73. 73.
    Herzog, W., and S. Federico. Considerations on joint and articular cartilage mechanics. Biomech. Model. Mechanobiol. 5:64–81, 2006.PubMedCrossRefGoogle Scholar
  74. 74.
    Hodge, W. A., R. S. Fijan, K. L. Carlson, R. G. Burgess, W. H. Harris, and R. W. Mann. Contact pressures in the human hip joint measured in vivo. Proc. Natl. Acad. Sci. USA 83:2879–2883, 1986.PubMedCrossRefGoogle Scholar
  75. 75.
    Hopewell, B., and J. P. G. Urban. Adaptation of articular chondrocytes to changes in osmolality. Biorheology 40:73–77, 2003.PubMedGoogle Scholar
  76. 76.
    Hudelmaier, M., C. Glaser, J. Hohe, K. H. Englmeier, M. Reiser, R. Putz, and F. Eckstein. Age-related changes in the morphology and deformational behavior of knee joint cartilage. Arthritis Rheum. 44:2556–2561, 2001.PubMedCrossRefGoogle Scholar
  77. 77.
    Huyghe, J. M., W. Wilson, and K. Malakpoor. On the thermodynamical admissibility of the triphasic theory of charged hydrated tissues. J. Biomech. Eng. 131:044504, 2009.PubMedCrossRefGoogle Scholar
  78. 78.
    Hyttinen, M. M., J. P. Arokoski, J. J. Parkkinen, M. J. Lammi, T. Lapveteläinen, K. Mauranen, K. Király, M. I. Tammi, and H. J. Helminen. Age matters: collagen birefringence of superficial articular cartilage is increased in young guinea-pigs but decreased in older animals after identical physiological type of joint loading. Osteoarthritis Cartilage 9:694–701, 2001.PubMedCrossRefGoogle Scholar
  79. 79.
    Idowu, B. D., M. M. Knight, D. L. Bader, and D. A. Lee. Confocal analysis of cytoskeletal organisation within isolated chondrocyte sub-populations cultured in agarose. Histochem. J. 32:165–174, 2000.PubMedCrossRefGoogle Scholar
  80. 80.
    Julkunen, P., W. Wilson, J. S. Jurvelin, and R. K. Korhonen. Composition of the pericellular matrix modulates the deformation behaviour of chondrocytes in articular cartilage under static loading. Med. Biol. Eng. Comput. 47:1281–1290, 2009.PubMedCrossRefGoogle Scholar
  81. 81.
    Julkunen, P., W. Wilson, J. S. Jurvelin, J. Rieppo, C.-J. Qu, M. J. Lammi, and R. K. Korhonen. Stress-relaxation of human patellar articular cartilage in unconfined compression: prediction of mechanical response by tissue composition and structure. J. Biomech. 41:1978–1986, 2008.PubMedCrossRefGoogle Scholar
  82. 82.
    Jurvelin, J., M. Buschmann, and E. Hunziker. Optical and mechanical determination of Poisson’s ratio of adult bovine humeral articular cartilage. J. Biomech. 30:235–241, 1997.PubMedCrossRefGoogle Scholar
  83. 83.
    Kang, H. G., and J. B. Dingwell. Dynamics and stability of muscle activations during walking in healthy young and older adults. J. Biomech. 42:2231–2237, 2009.PubMedCrossRefGoogle Scholar
  84. 84.
    Karamanidis, K., and A. Arampatzis. Evidence of mechanical load redistribution at the knee joint in the elderly when ascending stairs and ramps. Ann. Biomed. Eng. 37:467–476, 2009.PubMedCrossRefGoogle Scholar
  85. 85.
    Kazemi, M., L. P. Li, M. D. Buschmann, and P. Savard. Partial meniscectomy changes fluid pressurization in articular cartilage in human knees. J. Biomech. Eng. 134:021001, 2012.PubMedCrossRefGoogle Scholar
  86. 86.
    Kerrigan, D. C., P. O. Riley, T. J. Nieto, and U. Della Croce. Knee joint torques: a comparison between women and men during barefoot walking. Arch. Phys. Med. Rehabil. 81:1162–1165, 2000.PubMedCrossRefGoogle Scholar
  87. 87.
    Khoshgoftar, M., C. C. van Donkelaar, and K. Ito. Mechanical stimulation to stimulate formation of a physiological collagen architecture in tissue-engineered cartilage: a numerical study. Comput. Methods Biomech. Biomed. Engin. 14:135–144, 2011.PubMedCrossRefGoogle Scholar
  88. 88.
    Kim, E., F. Guilak, and M. A. Haider. The dynamic mechanical environment of the chondrocyte: a biphasic finite element model of cell–matrix interactions under cyclic compressive loading. J. Biomech. Eng. 130:061009, 2008.PubMedCrossRefGoogle Scholar
  89. 89.
    Kim, E., F. Guilak, and M. A. Haider. An axisymmetric boundary element model for determination of articular cartilage pericellular matrix properties in situ via inverse analysis of chondron deformation. J. Biomech. Eng. 132:031011, 2010.PubMedCrossRefGoogle Scholar
  90. 90.
    Klisch, S. M., A. Asanbaeva, S. R. Oungoulian, K. Masuda, E. J.-M. Thonar, A. Davol, and R. L. Sah. A cartilage growth mixture model with collagen remodeling: validation protocols. J. Biomech. Eng. 130:031006, 2008.PubMedCrossRefGoogle Scholar
  91. 91.
    Kock, L. M., A. Ravetto, C. C. van Donkelaar, J. Foolen, P. J. Emans, and K. Ito. Tuning the differentiation of periosteum-derived cartilage using biochemical and mechanical stimulations. Osteoarthritis Cartilage 18:1528–1535, 2010.PubMedCrossRefGoogle Scholar
  92. 92.
    Koolstra, J. H., and T. M. G. J. van Eijden. Combined finite-element and rigid-body analysis of human jaw joint dynamics. J. Biomech. 38:2431–2439, 2005.PubMedCrossRefGoogle Scholar
  93. 93.
    Korhonen, R. K., S.-K. Han, and W. Herzog. Osmotic loading of in situ chondrocytes in their native environment. Mol. Cell. Biomech. 7:125–134, 2010.PubMedGoogle Scholar
  94. 94.
    Korhonen, R. K., and W. Herzog. 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. 41:480–485, 2008.PubMedCrossRefGoogle Scholar
  95. 95.
    Korhonen, R. K., P. Julkunen, J. Rieppo, R. Lappalainen, Y. T. Konttinen, and J. S. Jurvelin. Collagen network of articular cartilage modulates fluid flow and mechanical stresses in chondrocyte. Biomech. Model. Mechanobiol. 5:150–159, 2006.PubMedCrossRefGoogle Scholar
  96. 96.
    Korhonen, R. K., P. Julkunen, W. Wilson, and W. Herzog. Importance of collagen orientation and depth-dependent fixed charge densities of cartilage on mechanical behavior of chondrocytes. J. Biomech. Eng. 130:021003, 2008.PubMedCrossRefGoogle Scholar
  97. 97.
    Krishnan, R., E. N. Mariner, and G. A. Ateshian. Effect of dynamic loading on the frictional response of bovine articular cartilage. J. Biomech. 38:1665–1673, 2005.PubMedCrossRefGoogle Scholar
  98. 98.
    Lai, W. M., J. S. Hou, and V. C. Mow. A triphasic theory for the swelling and deformation behaviors of articular cartilage. J. Biomech. Eng. 113:245–258, 1991.PubMedCrossRefGoogle Scholar
  99. 99.
    Li, L. P., J. T. M. Cheung, and W. Herzog. Three-dimensional fibril-reinforced finite element model of articular cartilage. Med. Biol. Eng. Comput. 47:607–615, 2009.PubMedCrossRefGoogle Scholar
  100. 100.
    Lin, Y.-C., J. P. Walter, S. A. Banks, M. G. Pandy, and B. J. Fregly. Simultaneous prediction of muscle and contact forces in the knee during gait. J. Biomech. 43:945–952, 2010.PubMedCrossRefGoogle Scholar
  101. 101.
    Maas, S. A., B. J. Ellis, G. A. Ateshian, and J. A. Weiss. FEBio: finite elements for biomechanics. J. Biomech. Eng. 134:011005, 2012.PubMedCrossRefGoogle Scholar
  102. 102.
    McLean, S. G., A. Su, and A. J. van den Bogert. Development and validation of a 3-D model to predict knee joint loading during dynamic movement. J. Biomech. Eng. 125:864–874, 2003.PubMedCrossRefGoogle Scholar
  103. 103.
    Michalek, A. J., and J. C. Iatridis. A numerical study to determine pericellular matrix modulus and evaluate its effects on the micromechanical environment of chondrocytes. J. Biomech. 40:1405–1409, 2007.PubMedCrossRefGoogle Scholar
  104. 104.
    Miller, E. J., R. F. Riemer, T. L. Haut Donahue, and K. R. Kaufman. Experimental validation of a tibiofemoral model for analyzing joint force distribution. J. Biomech. 42:1355–1359, 2009.PubMedCrossRefGoogle Scholar
  105. 105.
    Mononen, M. E., P. Julkunen, J. Töyräs, J. S. Jurvelin, I. Kiviranta, and R. K. Korhonen. Alterations in structure and properties of collagen network of osteoarthritic and repaired cartilage modify knee joint stresses. Biomech. Model. Mechanobiol. 10:357–369, 2011.PubMedCrossRefGoogle Scholar
  106. 106.
    Mononen, M. E., M. T. Mikkola, P. Julkunen, R. Ojala, M. T. Nieminen, J. S. Jurvelin, and R. K. Korhonen. Effect of superficial collagen patterns and fibrillation of femoral articular cartilage on knee joint mechanics—A 3D finite element analysis. J. Biomech. 45(3):579–587, 2012.PubMedCrossRefGoogle Scholar
  107. 107.
    Mow, V. C., G. A. Ateshian, and R. L. Spilker. Biomechanics of diarthrodial joints: a review of twenty years of progress. J. Biomech. Eng. 115:460–467, 1993.PubMedCrossRefGoogle Scholar
  108. 108.
    Mow, V. C., W. Y. Gu, and F. H. Chen. Structure and function of articular cartilage and meniscus. In: Basic Orthopaedic Biomechanics and Mechanobiology, edited by V. C. Mow, and R. Huiskes. Philadelphia: Lippincott Williams & Wilkins, 2005, pp. 181–258.Google Scholar
  109. 109.
    Mow, V. C., M. H. Holmes, and W. M. Lai. Fluid transport and mechanical properties of articular cartilage: a review. J. Biomech. 17:377–394, 1984.PubMedCrossRefGoogle Scholar
  110. 110.
    Mow, V. C., S. C. Kuei, W. M. Lai, and C. G. Armstrong. Biphasic creep and stress relaxation of articular cartilage in compression? Theory and experiments. J. Biomech. Eng. 102:73–84, 1980.PubMedCrossRefGoogle Scholar
  111. 111.
    Mündermann, A., C. O. Dyrby, D. E. Hurwitz, L. Sharma, and T. P. Andriacchi. Potential strategies to reduce medial compartment loading in patients with knee osteoarthritis of varying severity: reduced walking speed. Arthritis Rheum. 50:1172–1178, 2004.PubMedCrossRefGoogle Scholar
  112. 112.
    Muthuri, S. G., D. F. McWilliams, M. Doherty, and W. Zhang. History of knee injuries and knee osteoarthritis: a meta-analysis of observational studies. Osteoarthritis Cartilage 19:1286–1293, 2011.PubMedCrossRefGoogle Scholar
  113. 113.
    Nam, J., P. Perera, J. Liu, L. C. Wu, B. Rath, T. A. Butterfield, and S. Agarwal. Transcriptome-wide gene regulation by gentle treadmill walking during the progression of monoiodoacetate-induced arthritis. Arthritis Rheum. 63:1613–1625, 2011.PubMedCrossRefGoogle Scholar
  114. 114.
    Nap, R. J., and I. Szleifer. Structure and interactions of aggrecans: statistical thermodynamic approach. Biophys. J. 95:4570–4583, 2008.PubMedCrossRefGoogle Scholar
  115. 115.
    Nikolaev, N. I., B. Obradovic, H. K. Versteeg, G. Lemon, and D. J. Williams. A validated model of GAG deposition, cell distribution, and growth of tissue engineered cartilage cultured in a rotating bioreactor. Biotechnol. Bioeng. 105:842–853, 2010.PubMedGoogle Scholar
  116. 116.
    Nonaka, H., K. Mita, M. Watakabe, K. Akataki, N. Suzuki, T. Okuwa, and K. Yabe. Age-related changes in the interactive mobility of the hip and knee joints: a geometrical analysis. Gait Posture 15:236–243, 2002.PubMedCrossRefGoogle Scholar
  117. 117.
    Obradovic, B., J. H. Meldon, L. E. Freed, and G. Vunjak-Novakovic. Glycosaminoglycan deposition in engineered cartilage: experiments and mathematical model. AIChE J. 46:1860–1871, 2000.CrossRefGoogle Scholar
  118. 118.
    Ofek, G., and K. Athanasiou. Micromechanical properties of chondrocytes and chondrons: relevance to articular cartilage tissue engineering. J. Mech. Mater. Struct. 2:1059–1086, 2007.CrossRefGoogle Scholar
  119. 119.
    Ofek, G., R. M. Natoli, and K. A. Athanasiou. In situ mechanical properties of the chondrocyte cytoplasm and nucleus. J. Biomech. 42:873–877, 2009.PubMedCrossRefGoogle Scholar
  120. 120.
    Peña, E., B. Calvo, M. A. Martínez, and M. Doblaré. Effect of the size and location of osteochondral defects in degenerative arthritis. A finite element simulation. Comput. Biol. Med. 37:376–387, 2007.PubMedCrossRefGoogle Scholar
  121. 121.
    Peña, E., B. Calvo, M. A. Martínez, and M. Doblaré. Computer simulation of damage on distal femoral articular cartilage after meniscectomies. Comput. Biol. Med. 38:69–81, 2008.PubMedCrossRefGoogle Scholar
  122. 122.
    Peña, E., B. Calvo, M. A. Martinez, D. Palanca, and M. Doblaré. Why lateral meniscectomy is more dangerous than medial meniscectomy. A finite element study. J. Orthop. Res. 24:1001–1010, 2006.PubMedCrossRefGoogle Scholar
  123. 123.
    Pierce, D. M., W. Trobin, S. Trattnig, H. Bischof, and G. A. Holzapfel. A phenomenological approach toward patient-specific computational modeling of articular cartilage including collagen fiber tracking. J. Biomech. Eng. 131:091006, 2009.PubMedCrossRefGoogle Scholar
  124. 124.
    Prodromos, C. C., T. P. Andriacchi, and J. O. Galante. A relationship between gait and clinical changes following high tibial osteotomy. J. Bone Joint Surg. Am. 67:1188–1194, 1985.PubMedGoogle Scholar
  125. 125.
    Sah, R. L., Y. J. Kim, J. Y. Doong, A. J. Grodzinsky, A. H. Plaas, and J. D. Sandy. Biosynthetic response of cartilage explants to dynamic compression. J. Orthop. Res. 7:619–636, 1989.PubMedCrossRefGoogle Scholar
  126. 126.
    Sengers, B. G., H. K. Heywood, D. A. Lee, C. W. J. Oomens, and D. L. Bader. Nutrient utilization by bovine articular chondrocytes: a combined experimental and theoretical approach. J. Biomech. Eng. 127:758–766, 2005.PubMedCrossRefGoogle Scholar
  127. 127.
    Sengers, B. G., C. W. Oomens, and F. P. Baaijens. An integrated finite-element approach to mechanics, transport and biosynthesis in tissue engineering. J. Biomech. Eng. 126:82–91, 2004.PubMedCrossRefGoogle Scholar
  128. 128.
    Sengers, B. G., C. W. J. Oomens, T. Q. D. Nguyen, and D. L. Bader. Computational modeling to predict the temporal regulation of chondrocyte metabolism in response to various dynamic compression regimens. Biomech. Model. Mechanobiol. 5:111–122, 2006.PubMedCrossRefGoogle Scholar
  129. 129.
    Sengers, B. G., C. C. Van Donkelaar, C. W. J. Oomens, and F. P. T. Baaijens. The local matrix distribution and the functional development of tissue engineered cartilage, a finite element study. Ann. Biomed. Eng. 32:1718–1727, 2004.PubMedCrossRefGoogle Scholar
  130. 130.
    Sengers, B. G., C. C. van Donkelaar, C. W. J. Oomens, and F. P. T. Baaijens. Computational study of culture conditions and nutrient supply in cartilage tissue engineering. Biotechnol. Prog. 21:1252–1261, 2005.PubMedCrossRefGoogle Scholar
  131. 131.
    Sharma, L., D. E. Hurwitz, E. J. Thonar, J. A. Sum, M. E. Lenz, D. D. Dunlop, T. J. Schnitzer, G. Kirwan-Mellis, and T. P. Andriacchi. Knee adduction moment, serum hyaluronan level, and disease severity in medial tibiofemoral osteoarthritis. Arthritis Rheum. 41:1233–1240, 1998.PubMedCrossRefGoogle Scholar
  132. 132.
    Shelburne, K. B., M. R. Torry, and M. G. Pandy. Muscle, ligament, and joint-contact forces at the knee during walking. Med. Sci. Sports Exerc. 37:1948–1956, 2005.PubMedCrossRefGoogle Scholar
  133. 133.
    Shirazi, R., and A. Shirazi-Adl. Computational biomechanics of articular cartilage of human knee joint: effect of osteochondral defects. J. Biomech. 42:2458–2465, 2009.PubMedCrossRefGoogle Scholar
  134. 134.
    Shirazi-Adl, A., and K. E. Moglo. Effect of changes in cruciate ligaments pretensions on knee joint laxity and ligament forces. Comput. Methods Biomech. Biomed. Engin. 8:17–24, 2005.PubMedCrossRefGoogle Scholar
  135. 135.
    Sibole, S. C., and A. Erdemir. Chondrocyte deformations as a function of tibiofemoral joint loading predicted by a generalized high-throughput pipeline of multi-scale simulations. PLoS ONE 7(5):e37538, 2012. doi: 10.1371/journal.pone.0037538.
  136. 136.
    Soltz, M. A., and G. A. Ateshian. Experimental verification and theoretical prediction of cartilage interstitial fluid pressurization at an impermeable contact interface in confined compression. J. Biomech. 31:927–934, 1998.PubMedCrossRefGoogle Scholar
  137. 137.
    Soulhat, J., M. D. Buschmann, and A. Shirazi-Adl. A fibril-network-reinforced biphasic model of cartilage in unconfined compression. J. Biomech. Eng. 121:340–347, 1999.PubMedCrossRefGoogle Scholar
  138. 138.
    Stolz, M., R. Raiteri, A. U. Daniels, M. R. VanLandingham, W. Baschong, and U. Aebi. Dynamic elastic modulus of porcine articular cartilage determined at two different levels of tissue organization by indentation-type atomic force microscopy. Biophys. J . 86:3269–3283, 2004.PubMedCrossRefGoogle Scholar
  139. 139.
    Temple, M. M., W. C. Bae, M. Q. Chen, M. Lotz, D. Amiel, R. D. Coutts, and R. L. Sah. Age- and site-associated biomechanical weakening of human articular cartilage of the femoral condyle. Osteoarthritis Cartilage 15:1042–1052, 2007.PubMedCrossRefGoogle Scholar
  140. 140.
    Torzilli, P. A., M. Bhargava, S. Park, and C. T. C. Chen. Mechanical load inhibits IL-1 induced matrix degradation in articular cartilage. Osteoarthritis Cartilage 18:97–105, 2010.PubMedCrossRefGoogle Scholar
  141. 141.
    Torzilli, P. A., X.-H. Deng, and M. Ramcharan. Effect of compressive strain on cell viability in statically loaded articular cartilage. Biomech. Model. Mechanobiol. 5:123–132, 2006.PubMedCrossRefGoogle Scholar
  142. 142.
    Urban, J. P. Present perspectives on cartilage and chondrocyte mechanobiology. Biorheology 37:185–190, 2000.PubMedGoogle Scholar
  143. 143.
    van Donkelaar, C. C., G. Chao, D. L. Bader, and C. W. J. Oomens. A reaction-diffusion model to predict the influence of neo-matrix on the subsequent development of tissue-engineered cartilage. Comput. Methods Biomech. Biomed. Engin. 14:425–432, 2011.PubMedCrossRefGoogle Scholar
  144. 144.
    van Donkelaar, C. C., and W. Wilson. Mechanics of chondrocyte hypertrophy. Biomech. Model. Mechanobiol. 11(5):655–664, 2012.PubMedCrossRefGoogle Scholar
  145. 145.
    van Turnhout, M. C., S. Kranenbarg, and J. L. van Leeuwen. Contribution of postnatal collagen reorientation to depth-dependent mechanical properties of articular cartilage. Biomech. Model. Mechanobiol. 10:269–279, 2011.PubMedCrossRefGoogle Scholar
  146. 146.
    Vaziri, A., H. Nayeb-Hashemi, A. Singh, and B. A. Tafti. Influence of meniscectomy and meniscus replacement on the stress distribution in human knee joint. Ann. Biomed. Eng. 36:1335–1344, 2008.PubMedCrossRefGoogle Scholar
  147. 147.
    Wan, L. Q., X. E. Guo, and V. C. Mow. A triphasic orthotropic laminate model for cartilage curling behavior: fixed charge density versus mechanical properties inhomogeneity. J. Biomech. Eng. 132:024504, 2010.PubMedCrossRefGoogle Scholar
  148. 148.
    Williams, G. M., E. F. Chan, M. M. Temple-Wong, W. C. Bae, K. Masuda, W. D. Bugbee, and R. L. Sah. Shape, loading, and motion in the bioengineering design, fabrication, and testing of personalized synovial joints. J. Biomech. 43:156–165, 2010.PubMedCrossRefGoogle Scholar
  149. 149.
    Wilson, W., J. M. Huyghe, and C. C. van Donkelaar. A composition-based cartilage model for the assessment of compositional changes during cartilage damage and adaptation. Osteoarthritis Cartilage 14:554–560, 2006.PubMedCrossRefGoogle Scholar
  150. 150.
    Wilson, W., J. M. Huyghe, and C. C. van Donkelaar. Depth-dependent compressive equilibrium properties of articular cartilage explained by its composition. Biomech. Model. Mechanobiol. 6:43–53, 2007.PubMedCrossRefGoogle Scholar
  151. 151.
    Wilson, W., C. C. van Donkelaar, and J. M. Huyghe. A comparison between mechano-electrochemical and biphasic swelling theories for soft hydrated tissues. J. Biomech. Eng. 127:158–165, 2005.PubMedCrossRefGoogle Scholar
  152. 152.
    Wilson, W., C. C. van Donkelaar, B. van Rietbergen, and R. Huiskes. A fibril-reinforced poroviscoelastic swelling model for articular cartilage. J. Biomech. 38:1195–1204, 2005.PubMedCrossRefGoogle Scholar
  153. 153.
    Wilson, W., C. C. van Donkelaar, R. van Rietbergen, and R. Huiskes. The role of computational models in the search for the mechanical behavior and damage mechanisms of articular cartilage. Med. Eng. Phys. 27:810–826, 2005.PubMedCrossRefGoogle Scholar
  154. 154.
    Wilson, W., C. C. van Donkelaar, B. van Rietbergen, K. Ito, and R. Huiskes. Stresses in the local collagen network of articular cartilage: a poroviscoelastic fibril-reinforced finite element study. J. Biomech. 37:357–366, 2004.PubMedCrossRefGoogle Scholar
  155. 155.
    Winby, C. R., D. G. Lloyd, T. F. Besier, and T. B. Kirk. Muscle and external load contribution to knee joint contact loads during normal gait. J. Biomech. 42:2294–2300, 2009.PubMedCrossRefGoogle Scholar
  156. 156.
    Wong, B. L., and R. L. Sah. Mechanical asymmetry during articulation of tibial and femoral cartilages: local and overall compressive and shear deformation and properties. J. Biomech. 43:1689–1695, 2010.PubMedCrossRefGoogle Scholar
  157. 157.
    Wu, J. Z., and W. Herzog. Analysis of the mechanical behavior of chondrocytes in unconfined compression tests for cyclic loading. J. Biomech. 39:603–616, 2006.PubMedCrossRefGoogle Scholar
  158. 158.
    Wu, J. Z., W. Herzog, and M. Epstein. Modelling of location- and time-dependent deformation of chondrocytes during cartilage loading. J. Biomech. 32:563–572, 1999.PubMedCrossRefGoogle Scholar
  159. 159.
    Yang, N. H., P. K. Canavan, and H. Nayeb-Hashemi. The effect of the frontal plane tibiofemoral angle and varus knee moment on the contact stress and strain at the knee cartilage. J. Appl. Biomech. 26:432–443, 2010.PubMedGoogle Scholar
  160. 160.
    Yang, N., H. Nayeb-Hashemi, and P. K. Canavan. The combined effect of frontal plane tibiofemoral knee angle and meniscectomy on the cartilage contact stresses and strains. Ann. Biomed. Eng. 37:2360–2372, 2009.PubMedCrossRefGoogle Scholar
  161. 161.
    Yang, N. H., H. Nayeb-Hashemi, P. K. Canavan, and A. Vaziri. Effect of frontal plane tibiofemoral angle on the stress and strain at the knee cartilage during the stance phase of gait. J. Orthop. Res. 28:1539–1547, 2010.PubMedCrossRefGoogle Scholar
  162. 162.
    Yao, J., A. D. Salo, J. Lee, and A. L. Lerner. Sensitivity of tibio-menisco-femoral joint contact behavior to variations in knee kinematics. J. Biomech. 41:390–398, 2008.PubMedCrossRefGoogle Scholar
  163. 163.
    Ytterberg, S. R., M. L. Mahowald, and H. E. Krug. Exercise for arthritis. Baillieres Clin. Rheumatol. 8:161–189, 1994.PubMedCrossRefGoogle Scholar
  164. 164.
    Zielinska, B., and T. L. H. Donahue. 3D finite element model of meniscectomy: changes in joint contact behavior. J. Biomech. Eng. 128:115–123, 2006.PubMedCrossRefGoogle Scholar

Copyright information

© Biomedical Engineering Society 2012

Authors and Affiliations

  • J. P. Halloran
    • 1
    • 2
  • S. Sibole
    • 1
    • 2
  • C. C. van Donkelaar
    • 3
  • M. C. van Turnhout
    • 3
  • C. W. J. Oomens
    • 3
  • J. A. Weiss
    • 4
    • 5
    • 6
  • F. Guilak
    • 7
  • A. Erdemir
    • 1
    • 2
  1. 1.Department of Biomedical EngineeringLerner Research Institute, Cleveland ClinicClevelandUSA
  2. 2.Computational Biomodeling (CoBi) CoreLerner Research Institute, Cleveland ClinicClevelandUSA
  3. 3.Department of Biomedical EngineeringEindhoven University of TechnologyEindhovenThe Netherlands
  4. 4.Department of BioengineeringUniversity of UtahSalt Lake CityUSA
  5. 5.Scientific Computing and Imaging InstituteUniversity of UtahSalt Lake CityUSA
  6. 6.Department of OrthopaedicsUniversity of UtahSalt Lake CityUSA
  7. 7.Department of Orthopaedic SurgeryDuke University Medical CenterDurhamUSA

Personalised recommendations