Skip to main content

Advertisement

Springer Nature Link
Log in

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

  • Published:
Annals of Biomedical Engineering Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3

Similar content being viewed by others

References

  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.

    Article  PubMed  CAS  Google Scholar 

  2. Adouni, M., and A. Shirazi-Adl. Knee joint biomechanics in closed-kinetic-chain exercises. Comput. Methods Biomech. Biomed. Engin. 12:661–670, 2009.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    PubMed  Google Scholar 

  8. Anderson, F. C., and M. G. Pandy. Individual muscle contributions to support in normal walking. Gait Posture 17:159–169, 2003.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  11. Ateshian, G. A. The role of interstitial fluid pressurization in articular cartilage lubrication. J. Biomech. 42:1163–1176, 2009.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  16. Ateshian, G. A., and T. Ricken. Multigenerational interstitial growth of biological tissues. Biomech. Model. Mechanobiol. 9:689–702, 2010.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  22. Buckwalter, J. A. Osteoarthritis and articular cartilage use, disuse, and abuse: experimental studies. J. Rheumatol. Suppl. 43:13–15, 1995.

    PubMed  CAS  Google Scholar 

  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.

    PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    PubMed  CAS  Google Scholar 

  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.

    PubMed  CAS  Google Scholar 

  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.

    PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  30. Chen, C. S., and D. E. Ingber. Tensegrity and mechanoregulation: from skeleton to cytoskeleton. Osteoarthritis Cartilage 7:81–94, 1999.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  36. Elias, J. J., and A. J. Cosgarea. Computational modeling: an alternative approach for investigating patellofemoral mechanics. Sports Med. Arthrosc. 15:89–94, 2007.

    Article  PubMed  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  Google Scholar 

  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. 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.

    Article  PubMed  Google Scholar 

  42. Federico, S., and W. Herzog. Towards an analytical model of soft biological tissues. J. Biomech. 41:3309–3313, 2008.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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. Guilak, F. Compression-induced changes in the shape and volume of the chondrocyte nucleus. J. Biomech. 28:1529–1541, 1995.

    Article  PubMed  CAS  Google Scholar 

  56. Guilak, F. Biomechanical factors in osteoarthritis. Best Pract. Res. Clin. Rheumatol. 25:815–823, 2011.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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. 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.

    Article  PubMed  CAS  Google Scholar 

  60. Guilak, F., J. R. Tedrow, and R. Burgkart. Viscoelastic properties of the cell nucleus. Biochem. Biophys. Res. Commun. 269:781–786, 2000.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  66. Han, L., A. J. Grodzinsky, and C. Ortiz. Nanomechanics of the cartilage extracellular matrix. Annu. Rev. Mater. Res. 41:133–168, 2011.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  70. Heinegård, D., and A. Oldberg. Structure and biology of cartilage and bone matrix noncollagenous macromolecules. FASEB J. 3:2042–2051, 1989.

    PubMed  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  73. Herzog, W., and S. Federico. Considerations on joint and articular cartilage mechanics. Biomech. Model. Mechanobiol. 5:64–81, 2006.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  75. Hopewell, B., and J. P. G. Urban. Adaptation of articular chondrocytes to changes in osmolality. Biorheology 40:73–77, 2003.

    PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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. 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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  114. Nap, R. J., and I. Szleifer. Structure and interactions of aggrecans: statistical thermodynamic approach. Biophys. J. 95:4570–4583, 2008.

    Article  PubMed  CAS  Google Scholar 

  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.

    PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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. 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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  142. Urban, J. P. Present perspectives on cartilage and chondrocyte mechanobiology. Biorheology 37:185–190, 2000.

    PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  144. van Donkelaar, C. C., and W. Wilson. Mechanics of chondrocyte hypertrophy. Biomech. Model. Mechanobiol. 11(5):655–664, 2012.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  163. Ytterberg, S. R., M. L. Mahowald, and H. E. Krug. Exercise for arthritis. Baillieres Clin. Rheumatol. 8:161–189, 1994.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

Download references

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.

Author information

Authors and Affiliations

  1. Department of Biomedical Engineering, Lerner Research Institute, Cleveland Clinic, Cleveland, OH, USA

    J. P. Halloran, S. Sibole & A. Erdemir

  2. Computational Biomodeling (CoBi) Core, Lerner Research Institute, Cleveland Clinic, Cleveland, OH, USA

    J. P. Halloran, S. Sibole & A. Erdemir

  3. Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands

    C. C. van Donkelaar, M. C. van Turnhout & C. W. J. Oomens

  4. Department of Bioengineering, University of Utah, Salt Lake City, UT, USA

    J. A. Weiss

  5. Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT, USA

    J. A. Weiss

  6. Department of Orthopaedics, University of Utah, Salt Lake City, UT, USA

    J. A. Weiss

  7. Department of Orthopaedic Surgery, Duke University Medical Center, Durham, NC, USA

    F. Guilak

Authors
  1. J. P. Halloran
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. S. Sibole
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. C. C. van Donkelaar
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. M. C. van Turnhout
    View author publications

    You can also search for this author inPubMed Google Scholar

  5. C. W. J. Oomens
    View author publications

    You can also search for this author inPubMed Google Scholar

  6. J. A. Weiss
    View author publications

    You can also search for this author inPubMed Google Scholar

  7. F. Guilak
    View author publications

    You can also search for this author inPubMed Google Scholar

  8. A. Erdemir
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to A. Erdemir.

Additional information

Associate Editor Michael R. King oversaw the review of this article.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Halloran, J.P., Sibole, S., van Donkelaar, C.C. et al. Multiscale Mechanics of Articular Cartilage: Potentials and Challenges of Coupling Musculoskeletal, Joint, and Microscale Computational Models. Ann Biomed Eng 40, 2456–2474 (2012). https://doi.org/10.1007/s10439-012-0598-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10439-012-0598-0

Keywords