Biomechanics and Modeling in Mechanobiology

, Volume 14, Issue 6, pp 1167–1180 | Cite as

Effects of osteoarthritis and pathological walking on contact stresses in femoral cartilage

  • J. Mabuma
  • M. Schwarze
  • C. Hurschler
  • B. Markert
  • W. Ehlers
Original Paper


Osteoarthritis is a widespread abnormality in synovial joints leading to increasing pain and potential work disability in middle-aged and older populations. A primary cause of osteoarthritis is related to damages from high local stresses combined with insufficient self-healing of cartilage. In this framework, it is the goal of the present contribution to offer a thermodynamically consistent simulation of a highly anisotropic, heterogeneous, osmotic swelling and poroviscoelastic model of healthy and osteoarthritic articular cartilage based on the Theory of Porous Media. Physiological and pathological loading patterns are included by means of multi-body system calculations on patients. The contact stresses at the cartilage surface are represented by means of three-dimensional and simplified stereographic views of the femoral head. For normal walking, the stress peaks are higher in the degenerated case than in the healthy case. Interestingly, pathological walking combined with degenerated cartilage tissue minimises the occurrence of high local stresses.


Articular cartilage Theory of Porous Media Osteoarthritis Multi-body system Contact stress Pathological load 



The authors like to acknowledge the funding by the DFG grants MA 2233/4 and HU 873/4-1. Besides, the MRI scans of the femoral head were obtained by courtesy of Fritz Schick (University Hospital of Tübingen).


  1. Abraham CL, Maas SA, Weiss JA, Ellis BJ, Peters CL, Anderson AE (2013) A new discrete element analysis method for predicting hip joint contact stresses. J Biomech 46:1121–1127CrossRefGoogle Scholar
  2. Acartürk A (2009) Simulation of charged hydrated porous materials. Dissertation thesis, Report No. II-18, Institute of Applied Mechanics (CE), University of StuttgartGoogle Scholar
  3. Adam G, Läuger P, Stark G (1995) Physikalische Chemie und Biophysik, 3rd edn. Springer, BerlinCrossRefGoogle Scholar
  4. Andersen MS, Damsgaard M, MacWilliams B, Rasmussen J (2010) A computationally efficient optimisation-based method for parameter identification of kinematically determinate and over-determinate biomechanical systems. Comput Method Biomech 13:171–183CrossRefGoogle Scholar
  5. Anderson AE, Ellis BJ, Maas SA, Weiss JA (2010) Effects of idealized joint geometry on finite element predictions of cartilage contact stresses in the hip. J Biomech 43:1351–1357CrossRefGoogle Scholar
  6. Azuma T, Nakai R, Takizawa O, Tsutsumi S (2009) In vivo structural analysis of articular cartilage using diffusion tensor magnetic resonance imaging. Magn Reson Imaging 27:1242–1248CrossRefGoogle Scholar
  7. Bachrach NM, Mow VC, Guilak F (1998) Incompressibility of the solid matrix of articular cartilage under high hydrostatic pressures. J Biomech 31:445–451CrossRefGoogle Scholar
  8. Bae WC, Wong VW, Hwang J, Antonacci JM, Nugent-Derfus GE, Blewis ME, Temple-Wong MM, Sah RL (2008) Wear-lines and split-lines of human patellar cartilage: relation to tensile biomechanical properties. Osteoarthr Res Soc Int 16:841–845CrossRefGoogle Scholar
  9. Benninghoff A (1925) Spaltlinien am Knochen, eine Methode zur Ermittlung der Architektur platter Knochen. Verhandlungen der Anatomischen Gesellschaft 34:189–206Google Scholar
  10. Bergmann G, Graichen F, Siraky J, Jendrzynski H, Rohlmann A (1988) Multichannel strain gauge telemetry for orthopaedic implants. J Biomech 21:169–176CrossRefGoogle Scholar
  11. Bergmann G, Deuretzbacher G, Heller M, Graichen F, Rohlmann A, Strauss J, Duda GN (2001) Hip contact forces and gait patterns from routine activities. J Biomech 34:859–871CrossRefGoogle Scholar
  12. de Boer R (1998) Theory of porous media—past and present. Zamm-Z Angw Math Me 78:441–466CrossRefzbMATHGoogle Scholar
  13. de Boer R (2000) Theory of porous media. Springer, BerlinCrossRefzbMATHGoogle Scholar
  14. de Boer R (2005) Trends in continuum mechanics of porous media. Volume 18 of theory and applications of transport in porous media. Springer, DodrechtCrossRefGoogle Scholar
  15. Bowen RM (1976) Theory of mixtures. In: Eringen AC (ed) Continuum physics, vol III. Academic Press, New York, pp 1–127Google Scholar
  16. Bowen RM (1980) Incompressible porous media models by use of the theory of mixtures. Int J Eng Sci 18:1129–1148CrossRefzbMATHGoogle Scholar
  17. Brinckmann P, Frobin W, Hierholzer E (1981) Stress on the articular surface of the hip joint in healthy adults and persons with idiopathic osteoarthrosis of the hip joint. J Biomech 14:149–156CrossRefGoogle Scholar
  18. Broom ND, Myers DD (1984) Further insights into the structural principles governing the function of articular cartilage. J Anat 139:275–294Google Scholar
  19. Brown TD, Shawn DT (1983) In vitro contact stress distributions in the natural human hip. J Biomech 16:373–384CrossRefGoogle Scholar
  20. Ciavarella M, Strozzi A, Baldini A, Giacopini M (2007) Normalisation of load and clearance effects in ball in socket-like replacements. Proc Inst Mech Eng Part H J Eng Med 221:601–611CrossRefGoogle Scholar
  21. Daniel M, Iglic A, Kralj-Iglic V (2005) The shape of acetabular cartilage optimizes hip contact stress distribution. J Anat 207:85–91CrossRefGoogle Scholar
  22. Day WH, Swanson SAV, Freeman MAR (1975) Contact Pressures in the Loaded Human Cadaver Hip. J Bone Joint Surg Br 57:302–313Google Scholar
  23. Diebels S, Ellsiepen P, Ehlers W (1999) Error-controlled Runge-Kutta time integration of a viscoplastic hybrid two-phase model. Technische Mechanik 19:19–27Google Scholar
  24. Donnan FG (1911) Theorie der Membrangleichgewichte und Membranpotentiale bei Vorhandensein von nicht dialysierenden Elektrolyten. Ein Beitrag zur physikalisch-chemischen Physiologie. Z Elektrochem Angew P 17:572–581Google Scholar
  25. Ehlers W (1989) Poröse Medien - ein kontinuumsmechanisches Modell auf der Basis der Mischungstheorie. Report No. II-21 of the Institute of Applied Mechanics, University of Stuttgart 2011 (Reproduction of “Forschungsberichte aus dem Fachbereich Bauwesen”, Heft 47, Universität-GH-Essen)Google Scholar
  26. Ehlers W (1993a) Compressible, incompressible and hybrid two-phase models in porous media theories. In: Angel YC (ed) Anisotropy and inhomogeneity in elasticity and plasticity, AMD-Vol. 158. ASME, New York, pp 25–38Google Scholar
  27. Ehlers W (1993b) Constitutive equations for granular materials in geomechanical context. In: Hutter K (ed) Continuum mechanics in environmental sciences and geophysics, CISM courses and lecture notes no. 337. Springer, Berlin, pp 313–402CrossRefGoogle Scholar
  28. Ehlers W (1996) Grundlegende Konzepte in der Theorie Poröser Medien. Technische Mechanik 16:63–76Google Scholar
  29. Ehlers W (2002) Foundations of multiphasic and porous materials. In: Ehlers W, Bluhm J (eds) Porous media: theory, experiments and numerical applications. Springer, Berlin, pp 3–86CrossRefGoogle Scholar
  30. Ehlers W (2009) Challenges of porous media models in geo- and biomechanical engineering including electro-chemically active polymers and gels. Int J Adv Eng Sci Appl Math 1:1–24CrossRefGoogle Scholar
  31. Ehlers W (2014) Vector and tensor calculus: an introduction. Lecture notes, Institute of Applied Mechanics, Chair of Continuum Mechanics, University of StuttgartGoogle Scholar
  32. Ehlers W, Ellsiepen P, Blome P, Mahnkopf D, Markert B (1999) Theoretische und numerische Studien zur Lösung von Rand- und Anfangswertproblemen in der Theorie Poröser Medien, Forschungsbericht zum DFG-Projekt Eh 107/6-2. Report No. 99-II-1, Institute of Applied Mechanics (CE), University of StuttgartGoogle Scholar
  33. Ehlers W, Karajan N, Markert B (2009) An extended biphasic model for charged hydrated tissues with application to the intervertebral disc. Biomech Model Mech 8:233–251CrossRefGoogle Scholar
  34. Eipper G (1998) Theorie und Numerik finiter elastischer Deformationen in fluidgesättigten porösen Festkörpern. Dissertation thesis, Report No. II-1, Institute of Applied Mechanics (CE), University of StuttgartGoogle Scholar
  35. Ellsiepen P (1999) Zeit- und ortsadaptive Verfahren angewandt auf Mehrphasenprobleme poröser Medien. Dissertation, Bericht Nr. II-3 aus dem Institut für Mechanik (Bauwesen), Universität StuttgartGoogle Scholar
  36. Federico S, Herzog W (2008) On the permeability of fibre-reinforced porous materials. Int J Solids Struct 45:2160–2172CrossRefzbMATHGoogle Scholar
  37. Forcheimer P (1901) Wasserbewegung durch Boden. Z Ver Dtsch Ing 50:1–34Google Scholar
  38. Genda E, Iwasaki N, Li G, MacWilliams BA, Barrance PJ, Chao EYS (2001) Normal hip joint contact pressure distribution in single-leg standing-effect of gender and anatomic parameters. J Biomech 34:895–905CrossRefGoogle Scholar
  39. Gonzalez-Perez I, Iserte JL, Fuentes A (2011) Implementation of Hertz theory and validation of a finite element model for stress analysis of gear drives with localized bearing contact. Mech Mach Theory 46:765–783CrossRefzbMATHGoogle Scholar
  40. Grodzinsky AJ, Roth V, Myers E, Grossman WK, Mow VV (1981) The significance of electromechanical and osmotic forces in the nonequilibrium swelling behavior of articular cartilage in tension. J Biomech Eng-T ASME 103:221–232CrossRefGoogle Scholar
  41. Gründer W (2006) MRI assessment of cartilage ultrastructure. NMR Biomed 19:855–876CrossRefGoogle Scholar
  42. Hassanizadeh SM, Gray WG (1987) High velocity flow in porous media. Transp Porous Med 2:521–531CrossRefGoogle Scholar
  43. Hayes WC, Keer LM, Herrmann G, Mockros LF (1972) A mathematical analysis for indentation tests of articular cartilage. J Biomech 5:541–551CrossRefGoogle Scholar
  44. Hill A (1938) The heat of shortening and the dynamic constants of muscle. Proc R Soc Lond B Bio 126:136–195CrossRefGoogle Scholar
  45. Hipp JA, Sugano N, Millis MB, Murphy SB (1999) Planning acetabular redirection osteotomies based on joint contact pressures. Clin Orthop Relat Res 364:134–143CrossRefGoogle Scholar
  46. Hodge WA, Fijan RS, Carlson KL, Burgess RG, Harris WH, Mann RW (1986) Contact pressures in the human hip joint measured in vivo. Proc Natl Acad Sci USA 83:2879–2883CrossRefGoogle Scholar
  47. Iglic A, Antolic V, Srakar F (1993) Biomechanical analysis of various operative hip joint rotation center shifts. Arch Orthop Traum Surg 112:124–126CrossRefGoogle Scholar
  48. Johnson KL (1985) Contact mechanics. Cambridge University Press, CambridgeCrossRefzbMATHGoogle Scholar
  49. Juszczyk MM, Cristofolini L, Viceconti M (2011) The human proximal femur behaves linearly elastic up to failure under physiological loading conditions. J Biomech 44:2259–2266CrossRefGoogle Scholar
  50. Karajan N (2009) An extended biphasic description of the inhomogeneous and anisotropic intervertebral disc. Dissertation thesis, Report No. II-19, Institute of Applied Mechanics (CE), University of StuttgartGoogle Scholar
  51. Kellgren JH, Bier F (1956) Radiological signs of rheumatoid arthritis: a study of observer differences in the reading of hand films. Ann Rheum Dis 15:55–60CrossRefGoogle Scholar
  52. Kellgren JH, Lawrence F (1957) Radiological assessment of osteo-arthritis. Ann Rheum Dis 16:494–500CrossRefGoogle Scholar
  53. Klotz IM, Rosenberg RM (2000) Chemical thermodynamics: basic theory and methods, 6th edn. Wiley, New YorkGoogle Scholar
  54. Knupp PM, Lage JL (1995) Generalization of the Forchheimer-extended Darcy flow model to the tensor permeability case via a variational principle. J Fluid Mech 299:97–104MathSciNetCrossRefzbMATHGoogle Scholar
  55. Lai WM, Hou JS, Mow VC (1991) A triphasic theory for the swelling and deformation behaviours of articular cartilage. J Biomech Eng-T ASME 113:245–258CrossRefGoogle Scholar
  56. Lanir Y (1987) Biorheology and fluid flux in swelling tissues. I. Bicomponent theory for small deformations, including concentration effects. Biorheology 24:173–187Google Scholar
  57. Lee EH (1969) Elastic-plastic deformation at finite strains. J Appl Mech 36:1–6CrossRefzbMATHGoogle Scholar
  58. Lee EH, Liu DT (1967) Finite-strain elastic–plastic theory with application to plane wave analysis. Jpn J Appl Phys 38:19–27CrossRefGoogle Scholar
  59. Lieser B (2003) Morphologische und biomechanische eigenschaften des hüftgelenks (articulatio coxae) des hundes (canis familiaris). Dissertation thesis, Institut für Tieranatomie, Ludwig-Maximilians-Universität MünchenGoogle Scholar
  60. Lilledahl MB, Pierce DM, Ricken T, Holzapfel GA, de Lange Davies C (2011) Structural analysis of articular cartilage using multiphoton microscopy: input for biomechanical modeling. IEEE T Med Imaging 30:1635–1648CrossRefGoogle Scholar
  61. Lipshitz H, Etheridge R, Glimcher M (1975) In vitro wear of articular cartilage. J Bone Joint Surg 57:527–537Google Scholar
  62. Machado M, Moreira P, Flores P, Lankarani HM (2012) Compliant contact force models in multibody dynamics: evolution of the Hertz contact theory. Mech Mach Theory 53:99–121CrossRefGoogle Scholar
  63. Malo MKH, Rohrbach D, Isaksson H, Töyräs J, Jurvelin JS, Tamminen IS, Kröger H, Raum K (2013) Longitudinal elastic properties and porosity of cortical bone tissue vary with age in human proximal femur. Bone 53:451–458CrossRefGoogle Scholar
  64. Markert B (2005) Porous media viscoelasticity with application to polymeric foams. Dissertation thesis, Report No. II-12, Institute of Applied Mechanics (CE), University of StuttgartGoogle Scholar
  65. Markert B (2007) A constitutive approach to 3-d nonlinear fluid flow through finite deformable porous continua with application to a high-porosity polyurethane foam. Transp Porous Med 70:427–450MathSciNetCrossRefGoogle Scholar
  66. Markert B (2008) A biphasic continuum approach for viscoelastic high-porosity foams: comprehensive theory, numerics, and application. Arch Comput Method E 15:371–446MathSciNetCrossRefzbMATHGoogle Scholar
  67. Markert B, Ehlers W, Karajan N (2005) A general polyconvex strain-energy function for fiber-reinforced materials. Proc Appl Math Mech 5(1):245–246CrossRefGoogle Scholar
  68. Maroudas A (1968) Physicochemical properties of cartilage in the light of ion exchange theory. Biophys J 8:575–595CrossRefGoogle Scholar
  69. Maroudas A (1975) Biophysical chemistry of cartilaginous tissues with special reference to solute and fluid transport. J Biorheol 12:233–248Google Scholar
  70. Maroudas A, Bannon C (1981) Measurement of swelling pressure in cartilage and comparison with the osmotic pressure of constituent proteoglycans. Biorheology 18:619–632Google Scholar
  71. Mavcic B, Iglic A, Kralj-Iglic V, Brand RA, Vengust R (2008) Cumulative hip contact stress predicts osteoarthritis in DDH. Clin Orthop Relat Res 467:682–691Google Scholar
  72. Maxian TA, Brown TD, Weinstein SL (1995) Chronic stress tolerance levels for human articular cartilage: two nonuniform contact models applied to long-term follow-up of CDH. J Biomech 28:159–166CrossRefGoogle Scholar
  73. Mow VC, Kuei SC, Lai WM, Armstrong CG (1980) Biphasic creep and relaxation of articular cartilage in compression: theory and experiments. J Biomech Eng-T ASME 102:73–84CrossRefGoogle Scholar
  74. Ogden RW (1972) Large deformation isotropic elasticity—on the correlation of theory and experiment for incompressible rubberlike solids. Proc R Soc Lond A-Conta 326:565–584CrossRefzbMATHGoogle Scholar
  75. Rasmussen J, Damsgaard M, Voigt M (2001) Muscle recruitment by the min/max criterion—a comparative numerical study. J Biomech 34:409–415CrossRefGoogle Scholar
  76. Rasmussen J, Zee MD, Damsgaard M, Marek C, Siebertz K (2005) A general method for scaling musculoskeletal models. Proc Int Symp Comput Simul Biomech 24:755–756Google Scholar
  77. Ratcliffe AR, Mow VC (1996) Articular cartilage. In: Comper WD (ed) Extracellular matrix. Harwood Academic Publishers, UK, pp 234–302Google Scholar
  78. Ricken T, Bluhm J (2010) Remodeling and growth of living tissue: a multiphase theory. Arch Appl Mech 80:453–465CrossRefzbMATHGoogle Scholar
  79. Saarakkala S, Laasanen MS, Jurvelin JS, Törrönen K, Lammi MJ, Lappalainen R, Töyräs J (2003) Ultrasound indentation of normal and spontaneously degenerated bovine articular cartilage. Osteoarthr Cartil 11:697–705CrossRefGoogle Scholar
  80. Saarakkala S, Julkunen P, Kiviranta P, Mäkitalo J, Jurvelin JS, Korhonen RK (2010) Depth-wise progression of osteoarthritis in human articular cartilage:investigation of composition, structure and biomechanics. Osteoarthr Cartil 18:73–81CrossRefGoogle Scholar
  81. Seifzadeh A, Oguamanam DCD, Papini M (2012) Evaluation of the constitutive properties of native, tissue engineered, and degenerated articular cartilage. Clin Biomech 27:852–858CrossRefGoogle Scholar
  82. Simo JC, Ortiz M (1985) A unified approach to finite deformation elastoplastic analysis based on the use of hyperelastic constitutive equations. Comput Method Appl Mech 45:221–245CrossRefGoogle Scholar
  83. Skempton AW (1960) Significance of Terzaghi’s concept of effective stress (Terzaghi’s discovery of effective stress). In: Bjerrum L, Casagrande A, Peck RB, Skempton AW (eds) From theory to practice in soil mechanics. Wiley, New York, pp 42–53Google Scholar
  84. Sun Z, Hao C (2012) Conformal contact problems of ball-socket and ball. Phys Proc 25:209–214CrossRefGoogle Scholar
  85. Vetterling W, Press W (1992) Routine implementing the simplex method. In: Press W (ed) Numerical recipes in C: the art of scientific computing. Cambridge University Press, Cambridge, pp 439–443Google Scholar
  86. Wilson W, Huyghe JM, van Donkelaar C (2007) Depth-dependent compressive equilibrium properties of articular cartilage explained by its composition. Biomech Model Mech 6:43–53CrossRefGoogle Scholar
  87. Wu G, Siegler S, Allard P, Kirtley C, Leardini A, Rosenbaum D, Whittle M, D’Lima DD, Cristofolini L, Witte H, Schmid O, Stokes I (2002) ISB recommendation on definition of joint coordinate system of various joints for the reporting of human joint motion-part I: ankle, hip, and spine. J Biomech 35:543–548CrossRefGoogle Scholar
  88. Wu JZ, Herzog W, Epstein M (2000) Joint contact mechanics in the early stages of osteoarthritis. Med Eng Phys 22:1–12CrossRefGoogle Scholar
  89. Yoshida H, Faust A, Wilckens J, Kitagawa M, Fetto J, Chao EYS (2006) Three-dimensional dynamic hip contact area and pressure distribution during activities of daily living. J Biomech 39:1996–2004CrossRefGoogle Scholar
  90. Yosibash Z, Padan R, Joskowicz L, Milgrom C (2007) A CT-based high-order finite element analysis of the human proximal femur compared to in-vitro experiments. J Biomech Eng-T ASME 129:297–309CrossRefGoogle Scholar
  91. Zhupanska OI (2011) Contact problem for elastic spheres: applicability of the Hertz theory to non-small contact areas. Int J Eng Sci 49:576–588MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • J. Mabuma
    • 1
  • M. Schwarze
    • 2
  • C. Hurschler
    • 2
  • B. Markert
    • 3
  • W. Ehlers
    • 1
  1. 1.Institute of Applied Mechanics (Civil Engineering)University of StuttgartStuttgartGermany
  2. 2.Laboratory for Biomechanics and BiomaterialsMedical School of HannoverHannoverGermany
  3. 3.Institute of General MechanicsRWTH Aachen UniversityAachenGermany

Personalised recommendations