Computational Modelling of Diarthrodial Joints. Physiological, Pathological and Pos-Surgery Simulations

  • E. Peña
  • A. Pérez del Palomar
  • B. Calvo
  • M. A. Martínez
  • M. Doblaré
Article

Abstract

This paper provides a critical review of past and current techniques for the computational modelling of diarthrodial joints. The objective of the paper is to describe strategies for addressing the computational modelling of joint mechanics using the finite element (FE) method, differentiating between geometry, constitutive modelling of the components, computational aspects and applications. The structure and function of the main components of the joints are reviewed, with emphasis on the relationship of tissue microstructure with its continuum mechanical behavior. Applications to two diarthrodial joints (human knee and temporomandibular joint) in physiological, pathological andpos-surgery situations are presented and discussed. The paper concludes with a discussion of future research directions.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abdel-Rahman E, Hefzy MS (1993) A two-dimensional dynamic anatomical model of the human knee joint. ASME J Biomech Eng 115:357–365 Google Scholar
  2. 2.
    Akizuki S, Mow VC, Müller F, Pita JC, Howell DS, Manicourt DH (1986) Tensile properties of human knee joint cartilage:I. Influence of ionic conditions, weight bearing and fibrillation on the tensile modelus. J Orthopaed Res 4:379–392 Google Scholar
  3. 3.
    Alastrue V, Calvo B, Peña E, Doblaré M (2006) Biomechanical modelling of refractive corneal surgery. ASME J Biomech Eng 128:150–160 Google Scholar
  4. 4.
    Almeida ES, Spilker RL (1997) Mixed and penalty finite element models for the nonlinear behaviour of biphasic soft tissues in finite deformation: Part I alternate formulations. Comput Methods Appl Mech Eng 1:25–46 Google Scholar
  5. 5.
    Almeida ES, Spilker RL (1997) Mixed and penalty finite element models for the nonlinear behaviour of biphasic soft tissues in finite deformation: Part II nonlinear examples. Comput Methods Appl Mech Eng 1:151–170 Google Scholar
  6. 6.
    Almeida ES, Spilker RL (1998) Finite element formulations for hyperelastic transversely isotropic biphasic soft tissues. Comput Methods Appl Mech Eng 151:513–538 MATHGoogle Scholar
  7. 7.
    Anderson DM, Sinclair PM, McBride KM (1991) A clinical evaluation of temporomandibular joint disk plication surgery. Am J Orthod Dentofac Orthop 100 Google Scholar
  8. 8.
    Annandale T (1887) On displacement of intraarticular cartilage of the lower jaw and its treatment by operation. Lancet 1:411–412 Google Scholar
  9. 9.
    Arms S, Boyle J, Johnson R, Pope M (1995) Strain in the medial collateral ligament of the human knee: an autopsy study. J Biomech 29:199–206 Google Scholar
  10. 10.
    Armstrong CG, Lai WM, Mow VC (1984) An analisysis of the unconfined compression of articular cartilage. ASME J Biomech Eng 106:165–173 Google Scholar
  11. 11.
    Au AG, Raso VJ, Liggins AB, Otto DD, Amirfazli A (2005) A three-dimensional finite element stress analysis for the tunnel placement and buttons in anterior cruciate ligament reconstructions. J Biomech 38:827–832 Google Scholar
  12. 12.
    Bach JM, Hull ML (1998) Strain inhomogeneity in the anterior cruciate ligament under application of external and muscular loads. ASME J Biomech Eng 120:497–503 Google Scholar
  13. 13.
    Barbenel JC, Evans JH, Finlay JB (1973) Stress-strain-time relations for soft connective tissues. In: Kenedi (ed) Perspectives biomed eng. McMillan, New York, pp 165–172 Google Scholar
  14. 14.
    Beek M, Koolstra JH, van Ruijven LJ, van Eijden TMGJ (2000) Three-dimensional finite element analysis of the human temporomandibular joint disc. J Biomech 33:307–316 Google Scholar
  15. 15.
    Beek M, Koolstra JH, van Eijden TMGJ (2003) Human temporomandibular joint disc cartilage as a poroelastic material. Clin Biomech 18:69–76 Google Scholar
  16. 16.
    Beek M, Koolstra JH, van Ruijven LJ, van Eijden TMGJ (2001) Three-dimensional finite element analysis of the cartilaginous structures in the human temporomandibular joint. J Dent Res 80:1913–1918 CrossRefGoogle Scholar
  17. 17.
    Bendjaballah MZ, Shirazi-adl A, Zukor DJ (1995) Biomechanics of the human knee joint in compression: reconstruction, mesh generation and finite element analysis. Knee 2:69–79 Google Scholar
  18. 18.
    Bendjaballah MZ, Shirazi-adl A, Zukor DJ (1998) Biomechanical response of the passive human knee joint under anterior-posterior forces. Clin Biomech 13:625–633 Google Scholar
  19. 19.
    Berkovitz BKB (2000) Collagen crimping in the intra-articular disc and articular surfaces of the human temporomandibular joint. Arch Oral Biol 45:749–756 Google Scholar
  20. 20.
    Beynnon B, Yu J, Huston D, Fleming B, Johnson R, Haugh L, Pope M (1996) A sagittal plane model of the knee and cruciate ligaments with application of a sensitivity analysis. ASME J Biomech Eng 118:227–239 Google Scholar
  21. 21.
    Papadrakakis M, Topping BHV (eds) (1994) Advances in non-linear finite element methods. Civil-Comp Ltd Google Scholar
  22. 22.
    Blankevoort L, Huiskes R (1991) Ligament-bone interaction in a three-dimensional model of the knee. ASME J Biomech Eng 113:263–269 Google Scholar
  23. 23.
    Buschmann MD, Grodzinsky AJ (1995) A molecular model of proteoglycan-associated electrostatic forces in cartilage mechanics. ASME J Biomech Eng 117:179–192 Google Scholar
  24. 24.
    Butler DL, Sheh MY, Stouffer DC, Samaranayake VA, Levy MS (1990) Surface strain variation in human patellar tendon and knee cruciate ligaments. ASME J Biomech Eng 39:38–45 Google Scholar
  25. 25.
    Carter DR, Hayes WC (1977) The compressive behavior of bone as a two-phase porous structure. J Bone Joint Surg 59:954–962 Google Scholar
  26. 26.
    Carter DR, Wong M (1988) The role of mechanical loading histories in the development od diarthrodial joints. J Orthopaed Res 6:804–816 Google Scholar
  27. 27.
    Chan SC, Seedhom BB (1995) The effect of the geometry of the tibia on prediction of the cruciate ligament forces: a theoretical analysis. J Eng Med 209:17–30 Google Scholar
  28. 28.
    Chaudhry HR, Bukiet, B, Davis A, Ritter AB, Findley T (1997) Residual stress in oscillating thoracic arteries reduce circumferential stresses and stress gradient. J Biomech 30:57–62 Google Scholar
  29. 29.
    Chen J, Buckwalter K (1993) Displacement analysis of the temporomandibular condyle from magnetic resonance images. J Biomech 26:1455–1462 Google Scholar
  30. 30.
    Chen J, Xu L (1994) A finite element analysis of the human temporomandibular joint. ASME J Biomech Eng 116:401–407 Google Scholar
  31. 31.
    Chen Y, Chen X, Hisada T (2006) Non-linear finite element analysis of mechanical electrochemical phenomena in hydrated soft tissues based on triphasic theory. Int J Numer Methods Eng 65:147–173 MATHGoogle Scholar
  32. 32.
    Cohen B, Gardner TR, Ateshian GA (1993) The influence of transverse isotropy on cartilage indentation behaviour: a study of the human humeral head. Trans Orthopaed Res Soc 39:185 Google Scholar
  33. 33.
    Cohen B, Lai WM, Chorney GS, Dick HM, Mow VV (1992) Unconfined compression of transversely isotropic biphasic tissues. Trans ASME 22:207–219 Google Scholar
  34. 34.
    Coletti JM, Akeson WH, Woo SLY (1972) A comparison of the physical behavior of normal articular cartilage and the arthroplasty surface. J Bone Joint Surg 54A:147–160 Google Scholar
  35. 35.
    Cooper B, Oberdorfer M, Rumpf D, Malakhova O, Rudman R, Mariotti A (1999) Trauma modifies strength and composition of retrodiscal tissues of the goat temporomandibular joint. Oral Dis 5(4):329–336 CrossRefGoogle Scholar
  36. 36.
    Cowin SC, Hegedus DH (1976) Bone remodeling: a theory od adaptative elasticity. J Elasticity 6:313–326 MATHMathSciNetGoogle Scholar
  37. 37.
    Currey JD (2002) Bones. Structure and mechanics. Princeton University Press, Princeton Google Scholar
  38. 38.
    DeVocht JW, Goel VK, Zeitler DL, Lew DA (1996) A study of the control of disc movement within the temporomandibular joint using the finite element technique. J Oral Maxil Surg 54:1431 Google Scholar
  39. 39.
    Doblaré M, Cueto E, Calvo B, Martínez MA, García JM, Cegoñino J (2005) On the employ of meshless methods in biomechanics. Comput Methods Appl Mech Eng 194:801–821 MATHGoogle Scholar
  40. 40.
    Doblaré M, Cueto E, Calvo B, Martínez MA, García JM, Peña E (2004) Computational bioengineering. Current trends and applications. In: An analysis of the performance of meshless methods in biomechanics. Imperial College Press, London, pp 69–100 Google Scholar
  41. 41.
    Doblaré M, García JM (2001) Application of an anisotropic bone-remodeling model based on a damage-repair theory to the analysis of the proximal femur before and after total hip replacement. J Biomech 34(9):1157–1170 Google Scholar
  42. 42.
    Doblaré M, García JM (2002) Anisotropic bone remodelling model based on a continuum damage-repair theory. J Biomech 35:1–17 Google Scholar
  43. 43.
    Haut Donahue TL, Hull ML, Rashid MM, Jacobs RC (2002) A finite element model of the human knee joint for the study of tibio-femoral contact. ASME J Biomech Eng 124:273–280 Google Scholar
  44. 44.
    Donzelli PS, Gallo LM, Spilker RL, Palla S (2004) Biphasic finite element simulation of the TMJ disc from in vivo kinematic and geometric measurements. J Biomech 37(11):1787–1791 Google Scholar
  45. 45.
    Donzelli PS, Spilker RS, Ateshian GA, Van Mow C (1999) Contact analysis of biphasic transversely isotropic cartilage layers and correlation with tissue failure. J Biomech 32:1037–1047 Google Scholar
  46. 46.
    Dworkin, SF, Huggins KH, LeResche L, VonKorff M, Howard J, Truelove E, Sommers E (1990) Epidemiology of signs and symptoms in temporomandibular disorders: clinical signs in cases and controls. J Am Dent Assoc 120(3):273–281 Google Scholar
  47. 47.
    Eberhardt AW, Lewis JL, Keer LM (1991) Contact layered elastic spheres as a model of joint contact: effect of tangential load and friction. ASME J Biomech Eng 113:107–108 Google Scholar
  48. 48.
    Van Eijden TM, Kouwenhoven E, Verbug J, Weijs WA (1986) A mathematical model of the patellofemoral joint. J Biomech 19:219–229 Google Scholar
  49. 49.
    Eisenberg SR, Grodzinsky AJ (1985) Swelling of articular cartilage and other connective tissues: electromechanochemical forces. J Orthopaed Res 3:148–159 Google Scholar
  50. 50.
    Elmore SM, Sokoloff L, Norris G, Carmeci P (1963) Nature of imperfect elasticity of articular cartilage. J Appl Physiol 18:393–396 Google Scholar
  51. 51.
    Essinger JR, Leyvraz PF, Heegaard JH, Robertson DD (1989) A mathematical model for the evaluation of the behavior during flexion of condylar-type knee prostheses. J Biomech 22:1229–1241 Google Scholar
  52. 52.
    Fithian DC, Kelly MA, Van Mow C (1990) Material properties and structure-function relationship in the menisci. Clin Orthop Relat R 252:19–31 Google Scholar
  53. 53.
    Fletcher R (2001) Practical methods of optimization. Wiley Google Scholar
  54. 54.
    Flory PJ (1961) Thermodynamic relations for high elastic materials. Trans Faraday Soc 57:829–838 MathSciNetGoogle Scholar
  55. 55.
    Fortin M, Glowinski R (1983) Augmented Lagrangian methods: application to the numerical solution of boundary value problems, volume 15. North Holland, Amsterdam Google Scholar
  56. 56.
    Fox RJ, Harner CD, Sakane M, Carlin GJ, Woo SL-Y (1998) Determination of the in situ forces in the human posterior cruciate ligament using robotic technology. Am J Spors Med 26:395–401 Google Scholar
  57. 57.
    Frank CB, Jackson DW (1997) Reconstruction of the anterior cruciate ligament. J Bone Joint Surg 79-A:1556–1576 Google Scholar
  58. 58.
    Fu FH, Harner C, Vince KG (1994) Knee surgery. Willians and Wilkins, Baltimore Google Scholar
  59. 59.
    Fung YC (1973) Biorheology of soft tissues. Biorheol 10:139–155 Google Scholar
  60. 60.
    Fung YC (1993) Biomechanics. Mechanical properties of living tissues. Springer Google Scholar
  61. 61.
    Gabriel MG, Wong EK, Woo SL-Y, Yagi M, Debski RE (2004) Distribution of in situ forces in the anterior cruciate ligament in response to rotatory loads. J Orthopaed Res 22:85–89 Google Scholar
  62. 62.
    Gardiner JC, Weiss JA (2003) Subject-specific finite element analysis of the human medial collateral ligament during valgus knee loading. J Orthopaed Res 21:1098–1106 Google Scholar
  63. 63.
    Gardiner JC, Weiss JA, Rosenberg TD (2001) Strain in the human medial collateral ligament during valgus lading of the knee. Clin Orthop Relat R 391:266–274 Google Scholar
  64. 64.
    Garikipati K, Arruda EM, Grosh K, Narayanan H, Calve S (2004) A continuum treatment of growth in biological tissue: the coupling of mass transport and mechanics. J Mech Phys Solids 52(7):1595–1625 MATHMathSciNetGoogle Scholar
  65. 65.
    Glowinski R, LeTallec P (1989) Augmented Lagrangian and operator-splitting methods in nonlinear mechanics. SIAM Studies in Applied Mathematics, Philadelphia MATHGoogle Scholar
  66. 66.
    Gray H (1998) Gray’s Anatomy: The anatomical basis of medicine and surgery, volume 1, 38 edn. Harcourt Google Scholar
  67. 67.
    Grodzinsky AJ (1973) Electromechanical and physicochemical properties of connective tissue. Crit Rev Biomed Eng 9:133–199 Google Scholar
  68. 68.
    Rouviere H, Delmas A (1985) Anatomie humaine, volume 1. Masson Google Scholar
  69. 69.
    Harfe DT, Chuinard CR, Espinoza LM, Thomas KA, Solomonow M (1998) Elongation patterns of the collateral ligamnets of the human knee. Clin Biomech 13:163–175 Google Scholar
  70. 70.
    Harner CD, Giffin R, Dunteman RC, Annunziata CC, Friedman MJ (2000) Evaluation and treatment of recurrent instability after anterior cruciate ligament reconstruction. J Bone Joint Surg 82-A:1652–1663 Google Scholar
  71. 71.
    Hayes WC, Mockros LF (1971) Viscoelastic constitutive relations for human articular cartilage. J Appl Physiol 18:562–568 Google Scholar
  72. 72.
    Heegard J, Leyvraz PF, Curnier A, Rakotomana L, Huiskes R (1995) The biomechanics of the human patella during passive knee flexion. J Biomech 28:1265–1279 Google Scholar
  73. 73.
    Hefzy MS, Grood ES (1988) Review of knee models. Appl Mech Rev 41:1–13 CrossRefGoogle Scholar
  74. 74.
    Hefzy MS, Grood ES (1993) An analytical technique for modelling knee joint stiffness—Part II: Ligamentous geometric nonlinearities. ASME J Biomech Eng 105:143–145 Google Scholar
  75. 75.
    Hefzy MS, Yang H (1993) Three-dimensional anatomical model of the human patello-femoral joint to determine patello-femoralmotions and contact characteristics. ASME J Biomech Eng 15:289–302 Google Scholar
  76. 76.
    Hernandez CK, Beaupre GS, Keller TS, Carter DR (2001) The influence of bone volume fraction and this fraction on bone strength and modulus. Bone 29(1):74–78 Google Scholar
  77. 77.
    Herrmann LR, Peterson FE (1968) A numerical procedure for viscoelastic stress analysis. In: Proceedings of the seventh meeting of ICRPG mechanical behaviour working group, Orlando, 1968 Google Scholar
  78. 78.
    Hibbit, Karlsson, Sorensen, Inc (2003) Abaqus user’s manual, v. 6.4. HKS inc. Pawtucket, RI, USA Google Scholar
  79. 79.
    Hill AV (1938) The heat of shortening and the dynamic constans of muscle. Proc Roy Soc Lond B 126:136–195 Google Scholar
  80. 80.
    Hirokawa S, Tsuruno R (1997) Hyperelastic model analysis of anterior cruciate ligament. Med Eng Phys 19:637–651 Google Scholar
  81. 81.
    Hirokawa S, Tsuruno R (2000) Three-dimensional deformation and stress distribution in an analytical/computational model of the anterior cruciate ligament. J Biomech 33:1069–1077 Google Scholar
  82. 82.
    Hirsch C (1944) A contribution to the pathogenesis chondromalacia of the patella. Acta Chir Scand 90:1–106 Google Scholar
  83. 83.
    Holmes MH (1986) Finite deformation of soft tissue: analysis of a mixture model in uni-axial compression. ASME J Biomech Eng 108:372–381 Google Scholar
  84. 84.
    Holzapfel GA (2000) Nonlinear solid mechanics. Wiley, New York MATHGoogle Scholar
  85. 85.
    Holzapfel GA, Gasser TC, Ogden RW (2000) A new constitutive framework for arterial wall mechanics and a comparative study of material models. J Elasticity 61:1–48 MATHMathSciNetGoogle Scholar
  86. 86.
    Holzapfel GA, Gasser TC (2001) A viscoelastic model for fiber-reinforced composites at finite strains: continuum basis, computational aspects and applications. Comput Methods Appl Mech Eng 190:4379–4403 Google Scholar
  87. 87.
    Holzapfel GA, Gasser TC, Stadler M (2002) A structural model for the viscoelastic behaviour of arterial walls: continuum formulation and finite element analysis. Eur J Mech A/Solid 21:441–463 MATHGoogle Scholar
  88. 88.
    Hu K, Qiguo R, Fang J, Mao JJ (2003) Effects of condylar fibrocartilage on the biomechanical loading of the human temporomandibular joint in a three-dimensional, nonlinear finite element model. Med Eng Phys 25:107–113 Google Scholar
  89. 89.
    Huberti HH, Hayes WC (1984) Patellofemoral contact pressures. J Bone Joint Surg 66-A:715–724 Google Scholar
  90. 90.
    Hughes TJR (2000) The finite element method: linear static and dynamic finite analysis. Dover, New York MATHGoogle Scholar
  91. 91.
    Hull ML, Berns GS, Varma H, Patterson A (1995) Strain in the medial collateral ligament of the human knee under single and combined loads. J Biomech 29:199–206 Google Scholar
  92. 92.
    Humphrey JD (2002) Continuum biomechanics of soft biological tissues. Proc Roy Soc Lond A 175:1–44 Google Scholar
  93. 93.
    Huxley AF (1957) Muscle structure and theories of contraction. Prog Biophys Biophysic Chem 173:257–318 Google Scholar
  94. 94.
    Jackson JP (1968) Degenerative changes in the knee after meniscectomy. Br Med J 2:525 Google Scholar
  95. 95.
    Jacobs CR (1994) Numerical simulation of bone adaption to mechanical loading. PhD thesis, Stanford University, Stanford, California Google Scholar
  96. 96.
    Jalani A, Shirazi-adl A, Bendjaballah MZ (1997) Biomechanics of human tibio-femoral joint in axial rotation. Knee 4:203–213 Google Scholar
  97. 97.
    Jurvelin JS, Arokoski JP, Hunziker EB (1997) Optical and mechanical determination of Poisson’s ratio of adult bovine articular cartilage. J Biomech 33:235–241 Google Scholar
  98. 98.
    Kastelic J, Galeski A (1978) The multicomposite structure of tendon. J Connect Tissue R 6:11–23 CrossRefGoogle Scholar
  99. 99.
    Kempson GE, Freeman MAR, Swanson SA (1971) The determination of a creep modulus for articular cartilage form indentation tests on the human femoral head. J Biomech 4:239–250 Google Scholar
  100. 100.
    Keyac JH (2001) Improved prediction of proximal femoral fracture load using nonlinear finite element models. Med Eng Phys 23:165–173 Google Scholar
  101. 101.
    Khalsa PS, Eisenberg SR (1997) Compressive behavior of articular cartilage is not completely explained by proteoglycan osmotic pressure. J Biomech 30:589–594 Google Scholar
  102. 102.
    Koolstra JH, van Eijden TMGJ (1995) Biomechanical analysis of Jaw-closing movements. J Dent Res 74:1564–1570 Google Scholar
  103. 103.
    Koolstra JH, van Eijden TMGJ (1999) Three-dimensional dynamical capabilities of the human masticatory muscles. J Biomech 32:145–152 Google Scholar
  104. 104.
    Koolstra JH, van Eijden TMGJ (2004) Functional significance of the coupling between head and jaw movements. J Biomech 37:1387–1392 Google Scholar
  105. 105.
    Korhonen RM, Laasanen MS, Töyräs J, Lappalainen R, Helminen HJ, Jurvelin JS (2003) Fibril reinforced poroelastic model predicts specifically mechanical behavior of normal proteoglycan depleted and collagen degraded articular cartilage. J Biomech 36:1373–1379 Google Scholar
  106. 106.
    Kurita H, Ohtsuka A, Kobayashi H, Kurashina K (2001) Resorption of the lateral pole of the mandibular condyle in temporomandibular disc displacement. Dentomaxillofac Rad 30:88–91 Google Scholar
  107. 107.
    Lai WM, Mow VC, Roth V (1986) Effects of a nonlinear strain-dependent permeability and rate of compression on the stress behavior of articular cartilage. ASME J Biomech Eng 108:123–130 Google Scholar
  108. 108.
    Lanir Y (1979) A structural theory for the homogeneous biaxial stress-strain relationship in flat collageneous tissues. J Biomech 12:423–436 Google Scholar
  109. 109.
    Lanir Y (1983) Constitutive equations for fibrous connective tissues. J Biomech 16:1–12 Google Scholar
  110. 110.
    LeRoux MA, Setton LA (2002) Experimental and biphasic FEM determinations of the material properties and hydraulic permeability of the meniscus in tension. ASME J Biomech Eng 124:315–321 Google Scholar
  111. 111.
    Lewis JL, Lew WD, Hill JA, Hanley P, Ohland K, Kirstukas S, Hunter RE (1989) Knee joint motion and ligament forces before and after ACL reconstruction. ASME J Biomech Eng 111:97–106 CrossRefGoogle Scholar
  112. 112.
    Li G, Gil J, Kanamori A, Woo SL (1999) A validated three-dimensional computational model of a human joint. ASME J Biomech Eng 121:657–662 Google Scholar
  113. 113.
    Li G, Lopez O, Rubash H (2001) Variability of a three-dimensional finite element model constructed using magnetic resonance images of a knee for joint contact stress analysis. ASME J Biomech Eng 123:341–346 MATHGoogle Scholar
  114. 114.
    Limbert G, Middleton J (2004) A tranversely isotropic viscohyperelastic material. Application to the modeling of biological soft connective tissues. Int J Solids Struct 41:4237–4260 MATHGoogle Scholar
  115. 115.
    Limbert G, Middleton J, Taylor M (2004) Finite element analysis of the human ACL subjected to passive anterior tibial loads. Comput Methods Biomech Biomed Eng 7:1–8 Google Scholar
  116. 116.
    Linn FC, Sokoloff L (1965) Movement and composition of interstitial fluid of cartilage. Arthritis Rheum 8:481–494 Google Scholar
  117. 117.
    Van Loocke M, Lyons CG, Simms C (2004) Stress-strain-time relations for soft connective tissues. In: Prendergast PJ, McHugh PE (eds) Topics in bio-mechanical engineering. Trinity centre for bioengineering & National Centre for Biomedical Engineering Science, pp 216–234 Google Scholar
  118. 118.
    Lotz JC, Gerhart TN, Hayes WC (1991) Mechanical properties of metaphyseal bone in the proximal femur. J Biomech 24:317–329 Google Scholar
  119. 119.
    Li LP, Bushmann MD, Shirazi-Adl A (2000) A fibril reinforced nonhomogeneous poroelastic model for articular cartilage: inhomogeneous response in unconfined compression. J Biomech 33:1533–1541 Google Scholar
  120. 120.
    Li LP, Soulhat J, Bushmann MD, Shirazi-Adl A (1999) Nonlinear analysis of cartilage in unconfined ramp compression usinga fibril reinforced poroelastic model. Clin Biomech 14:673–682 Google Scholar
  121. 121.
    Luenberger DE (1989) Programacion lineal y no lineal. Addison-Wesley Iberoamericana Google Scholar
  122. 122.
    Macnicol MF, Thomas NP (2000) The knee after menisctomy. J Bone Joint Surg 82-B:157–159 Google Scholar
  123. 123.
    Mak A (1986) The apparent viscoelastic behaviour of articular cartilage. The contributions from the intrinsic matrix viscoelastocity and intersticial fluid flows. ASME J Biomech Eng 108:123–130 Google Scholar
  124. 124.
    Maroudas A (1976) Balance between swelling pressures and collagen tension in normal and degenerate cartilage. Nature 260:808–809 Google Scholar
  125. 125.
    Marsden JE, Hughes TJR (1994) Mathematical foundations of elasticity. Dover, New York Google Scholar
  126. 126.
    Martins JAC, Pires EB, Salvado R, Dinis PB (1998) A numerical model of passive and active behavior of skeletal muscles. Comput Methods Appl Mech Eng 151:419–433 MATHGoogle Scholar
  127. 127.
    Matthews LS, Sonstegard DA, Henke JA (1977) Load bearing characteristics of the patello-femoral joint. Acta Orthop Scand 48:511–516 CrossRefGoogle Scholar
  128. 128.
    Moeinzadeh M-H, Engin AE, Akkas N (1983) Two-dimensional dynamic modelling of human knee joint. J Biomech 16:253–264 Google Scholar
  129. 129.
    Mogo KE, Shirazi-Adl A (2004) Cruciate coupling and screw-home mechanics in passive knee joint during extension-flexion. J Biomech (in press) Google Scholar
  130. 130.
    Mow CV, Kuei SC, Lai WM, Amstrong CG (1980) Biphasic creep and stress relaxation of articular cartilage in compression: theory and experiments. ASME J Biomech Eng 102:73–84 Google Scholar
  131. 131.
    Mow VC, Holmes MH, Lai WM (1984) Fluid transport and mechanical properties of articular cartilage: a review. J Biomech 17:377–394 Google Scholar
  132. 132.
    Mow VC, Kwan MK, Lai WM, Armstrong CG (1985) A finite deformation theory for nonlinearity permeable soft hydrated biological tissues. In: Frontiers in biomechanics. Springer Google Scholar
  133. 133.
    Mow VC, Guo XE (2003) Mechano-electrochemical properties of articular cartilage: their inhomogeneities and anisotropies. Annu Rev Biomed Eng 4:175–209 Google Scholar
  134. 134.
    Mow VC, Ratcliffe A (1997) Structure and function of articular cartilage and meniscus, 2nd edn. Lippincott-Raven, Philadelphia, pp 113–177 Google Scholar
  135. 135.
    Mow VC, Soslowsky LJ (1991) Basic orthopeadics biomechanics. In: Friction, lubrication and wear of diarthrodial joints. Raven Press, New York, pp 245–292 Google Scholar
  136. 136.
    Murakami T (1990) The lubrication in natural synovial joints and joint protheses. JSME Int J Vib Sys 33:465–474 Google Scholar
  137. 137.
    Nagahara K, Murata S, Nakamura S, Tsuchiya T (1999) Displacement and stress distribution in the temporomandibular joint during clenching. Angle Orthod 69:372 Google Scholar
  138. 138.
    Nickel JC, McLachlan KR (1994) In vivo measurement of the frictional properties of the temporomandibular joint disc. Arch Oral Biol 39(4) Google Scholar
  139. 139.
    Nitzan DW (2001) The process of lubrication impairment and its involvement in temporomandibular joint disc displacement: a theoretical concept. J Oral Maxil Surg 59:36–45 Google Scholar
  140. 140.
    Oomens CWJ, Maenhout M, van Oijen CH, Drost MR, Baaijens FP (2003) Finite element modelling of contracting skeletal muscle. Phil Trans Roy Soc Lond B 358:1453–1460 Google Scholar
  141. 141.
    Osborn JW (1993) A model to describe how ligaments may control symmetrical jaw opening movements in man. J Oral Rehabil 20:585–604 Google Scholar
  142. 142.
    Park S, Krishnan R, Nicoll SB, Ateshian GA (2003) Cartilage interstitial fluid support in unconfined compression. J Biomech 36:1785–1796 Google Scholar
  143. 143.
    Parsons JR, Black J (1977) The viscoelastic shear behavior of normal Rabbit Articular Cartilage. J Biomech 10:21–29 Google Scholar
  144. 144.
    Peña E, Calvo B, Martinez MA, Palanca D, Doblaré M (2006) Influence of the tunnel angle in acl reconstructions on the biomechanics of the knee joint. Clin Biomech 21(5):508–516 Google Scholar
  145. 145.
    Peña E, Calvo B, Martinez MA, Doblaré M (2006) A three-dimensional finite element analysis of the combined behavior of ligaments and menisci in the healthy human knee joint. J Biomech 39:1686–1701 Google Scholar
  146. 146.
    Peña E, Calvo B, Martinez MA, Palanca D, Doblaré M (2005) Finite element analysis of the effect of meniscal tears and meniscectomy on human knee biomechanics. Clin Biomech 20:498–507 Google Scholar
  147. 147.
    Peña E, Calvo B, Martinez MA, Palanca D, Doblaré M (2006) Why lateral meniscectomy is more dangerous than medial meniscectomy? a finite element study. J Orthopaed Res 24:1001–1010 Google Scholar
  148. 148.
    Peña E, Calvo B, Martínez MA, Doblaré M (2007) An anisotropic visco-hyperelastic model for ligaments at finite strains: formulation and computational aspects. Int J Solid Struct 44:760–778 MATHGoogle Scholar
  149. 149.
    Peña E, Martinez MA, Calvo B, Doblaré M (2006) On the numerical treatment of initial strains in soft biological tissues. Int J Numer Meth Eng 68:836–860 MATHGoogle Scholar
  150. 150.
    Peña E, Martinez MA, Calvo B, Palanca D, Doblaré M (2005) A finite element simulation of the effect of graft stiffness and graft tensioning in ACL reconstruction. Clin Biomech 20:636–644 Google Scholar
  151. 151.
    Peck C, Langenbach GEJ, Hannam AG (2000) Dynamic simulation of muscle and articular properties during human wide jaw opening. Arch Oral Biol 45:963–982 Google Scholar
  152. 152.
    Pérez-Palomar A (2004) Three dimensional finite element simulation of the temporomandibular joint. PhD thesis, University of Zaragoza, Spain (in Spanish) Google Scholar
  153. 153.
    Pérez-Palomar A, Doblaré M (2006) On the numerical simulation of the mechanical behaviour of articular cartilage. Int J Numer Meth Eng 67:1244–1271 Google Scholar
  154. 154.
    Pérez-Palomar A, Doblaré M (2006) 3D Finite Element simulation of the opening movement of the mandible in healthy and pathologic situations. ASME J Biomech Eng 128:242–249 Google Scholar
  155. 155.
    Pérez-Palomar A, Doblaré M (2006) Finite Element Analysis of the Temporomandibular Joint during lateral excursions of the mandible. J Biomech 39:1244–1271 Google Scholar
  156. 156.
    Pérez-Palomar A, Doblaré M (2006) The effect of collagen reinforcement in the behaviour of the temporomandibular joint disc. J Biomech 39:1075–1085 Google Scholar
  157. 157.
    Pioletti D (1997) Viscoelastic properties of soft tissues. PhD thesis, The University of Lausanne Google Scholar
  158. 158.
    Pioletti DP, Rakotomanana L (2000) Finite element model of the anterior cruciate ligament. Eur J Mech A/Solids 19:749–759 MATHGoogle Scholar
  159. 159.
    Pioletti DP, Rakotomanana L, Leyvraz PF, Benvenuti JF (1997) Finite element model of the anterior cruciate ligament. Comput Methods Biomech Biomed Eng Google Scholar
  160. 160.
    Pioletti DP, Rakotomanana LR, Benvenuti J-F, Leyvraz P-F (1998) Viscoelastic constitutive law in large deformations: application to human knee ligaments and tendons. J Biomech 31:753–757 Google Scholar
  161. 161.
    Powell MJD (1969) Optimization. In: A method for nonlinear constraints in minimization problems. Academic, New York, pp 283–298 Google Scholar
  162. 162.
    Prater ME, Bailey BJ, and Quinn FB (1998) Temporomandibular joint disorders. The University of Texas Medical Branch Google Scholar
  163. 163.
    Périé D, Hobatho MC (1998) In vivo determination of contact areas and pressure of the femorotibial joint using non-linear finite element analysis. Clin Biomech 13:394–402 Google Scholar
  164. 164.
    Puso MA, Weiss JA (1998) Finite element implementation of anisotropic quasilinear viscoelasticity. ASME J Biomech Eng 120:162–170 Google Scholar
  165. 165.
    Puxkandl R, Zizak I, Paris O, Tesch W, Bernstorff S, Purslow P, Fratzll P (2002) Viscoelastic properties of collagen: synchrotron radiation investigations and structural model. Phil Trans Roy Soc Lond B 357:191–197 Google Scholar
  166. 166.
    Rachev A, Hayashi K (1999) Theoretical study of the effects of vascular smooth muscle contraction on strain and stress distributions in arteries. Ann Biomed Eng 27(4):459–468 Google Scholar
  167. 167.
    Raminaraka NA, Terrier A, Theumann N, Siegrist O (2005) Effects of the posterior cruciate ligament reconstruction on the biomechanics of the knee joint: a finite element analysis. Clin Biomech 20:434–442 Google Scholar
  168. 168.
    Sanjeevi RA (1982) A viscoelastic model for the mechanical properties of biological materials. J Biomech 15:107–109 Google Scholar
  169. 169.
    Sasaki N, Odajima S (1996) Stress-strain curve and Young’s modulus of a collagen molecule as determined by X-ray diffraction technique. J Biomech 29:655–658 Google Scholar
  170. 170.
    Sathasivam S, Walker PS (1997) A computer model with surface friction for the prediction of total knee kinematics. J Biomech 30:177–184 Google Scholar
  171. 171.
    Sato H, Ström D, Carlsson GE (1995) Controversies on anatomy and function of the ligaments associated with the temporomandibular joint: a literature survey. J Orofac Pain 9:308–316 Google Scholar
  172. 172.
    Scheller G, Sobau C, Bülow JU (2001) Arthroscopic partial lateral meniscectomy in an otherwise normal knee: clinical, functional and radiographic results of a long-term follow-up study. Arthrosc 17:946–952 Google Scholar
  173. 173.
    Setton L, Elliott DM, Mow VC (1999) Altered mechanics of cartilage with osteoarthritis: human osteoarthritis and an experimental model of joint degeneration. Osteoarthr Cartilage 7:2–14 Google Scholar
  174. 174.
    Shengyi T, Yinghua X (1991) Biomechanical properties and collagen fiber orientation of TMJ discs in dogs: Part I. Gross anatomy and collagen fiber orientation of the discs. J Craniomandib Disord 5:28–34 Google Scholar
  175. 175.
    Simmons R, Howell S, Hull ML (2003) Effect of angle of the femoral and tibial tunnels in the coronal plane and incremental excision of the posterior cruciate ligament on tension of an anterior cruciate ligament graft: an in vitro study. J Bone Joint Surg 85-A:1018–1029 Google Scholar
  176. 176.
    Simo JC (1987) On a fully three-dimensional finite-strain viscoelastic damage model: Formulation and computational aspects. Comput Methods Appl Mech Eng 60:153–173 MATHMathSciNetGoogle Scholar
  177. 177.
    Simo JC, Hughes TJR (1998) Computational inelasticity. Springer, New York MATHGoogle Scholar
  178. 178.
    Simo JC, Taylor RL (1985) Consistent tangent operators for rate-independent elastoplasticity. Comput Methods Appl Mech Eng 48:101–118 MATHGoogle Scholar
  179. 179.
    Simo JC, Taylor RL (1991) Quasi-incompresible finite elasticity in principal stretches. Continuum basis and numerical algorithms. Comput Methods Appl Mech Eng 85:273–310 MATHMathSciNetGoogle Scholar
  180. 180.
    Simo JC, Taylor RL, Pister KS (1985) Variational and projection methods for the volume constraint in finite deformation elasto-plasticity. Comput Methods Appl Mech Eng 51:177–208 MATHMathSciNetGoogle Scholar
  181. 181.
    Simo JC, Taylor R (1991) Quasi-incompressible finite elasticity in principal stretches. Continuum basis and numerical algorithm. Comput Methods Appl Mech Eng 85(3) Google Scholar
  182. 182.
    Sokoloff L (1963) Elasticity of articular cartilage: effect of ions and viscous solutions. Sci 141:1055–1056 Google Scholar
  183. 183.
    Song Y, Debski RE, Musahl V, Thomas M, Woo SL-Y (2004) A three-dimensional finite element model of the human anterior cruciate ligament: a computational analysis with experimental validation. J Biomech 37:383–390 Google Scholar
  184. 184.
    Soulhat J, Buschman MD, Shirazi-Adl A (1999) A fibril-network reinforced biphasic model of cartilage in unconfined compression. ASME J Biomech Eng 121:340–347 Google Scholar
  185. 185.
    Spencer AJM (1954) Theory of invariants. In: Continuum physics. Academic, New York, pp 239–253 Google Scholar
  186. 186.
    Spilker RL, Suh JK (1990) Formulation and evaluation of a finite element model for the biphasic model of hydrated soft tissue. Comput Struct 35(4):425–439 MATHGoogle Scholar
  187. 187.
    Suggs J, Wang C, Li G (2003) The effect of graft stiffnes on knee joint biomechanics after ACL reconstruction: a 3D computational simulation. Clin Biomech 18:35–43 Google Scholar
  188. 188.
    Suh JK, Spilker RL, Holmes MR (1991) A penalty finite element analysis for non-linear mechanics of biphasic hydrated soft tissue under large deformation. Int J Numer Methods Eng 32:1411–1439 MATHGoogle Scholar
  189. 189.
    Suh JK, Bai S (1997) Biphasic poroviscoelastic behavior of cartilage in creep indentation test. In: Transactions 43rd annual meeting of the orthopaedic research society, San Francisco, 1997 Google Scholar
  190. 190.
    Tanaka E, Rodrigo P, Tanaka M, Kawaguchi A, Shibazaji T, Tanne K (2001) Stress analysis in the TMJ during jaw opening by use of a three dimensional finite element model based on magnetic resonance images. Int J Oral Maxil Surg 30:421–430 Google Scholar
  191. 191.
    Tanaka E, Tanne K, Sakuda MA (1994) A three dimensional finite element model of the mandible including the TMJ and its application to stress analysis in the TMJ during clenching. Med Eng Phys 16:316–322 Google Scholar
  192. 192.
    Tanne K, Tanaka E, Sakuda M (1991) The elastic modulus of the temporomandibular joint disc from adult dogs. J Dent Res 70:1545 Google Scholar
  193. 193.
    Taskaya-Yilmaz N, Ogutcen-Toller M (2001) Magnetic resonance imaging evaluation of temporomandibular joint disc deformities in relation to type of disc displacement. J Oral Maxil Surg 59:860–865 Google Scholar
  194. 194.
    Timoshenko S, Goodier JN (1972) Teoría de la elasticidad. Editorial Urmo Google Scholar
  195. 195.
    Mow VC, Hayes WC (1991) Basic orthopaedic biomechanics. Raven Press, New York Google Scholar
  196. 196.
    Vedi V, Williams A, Tennant SJ, Spouse E (1999) Meniscal movement. J Bone Joint Surg 81-B:37–41 Google Scholar
  197. 197.
    De Vita R, Slaughter WS (2005) A structural constitutive model for the strain rate-dependent behavior of anterior cruciate ligaments. Int J Solids Struct (in press) Google Scholar
  198. 198.
    Vose GP, Kubala AL (1959) Bone strength, its relationship tox-ray-determined ash content. Human Biol 31:261–270 Google Scholar
  199. 199.
    Walker PS, Erkman MJ (1975) The role of the menisci in force transmission across the knee. Clin Orthop Relat R 109:184–192 Google Scholar
  200. 200.
    Weinberg S, Lapointe, H (1987) Cervical extension-flexion injury (whiplash) and internal derangement of the temporomandibular joint. J Oral Maxil Surg 45(8):653–656 Google Scholar
  201. 201.
    Weiss J, Gardiner JC (2001) Computational modelling of ligament mechanics. Crit Rev Biomed Eng 29:1–70 Google Scholar
  202. 202.
    Weiss J, Gardiner JC, Bonifasi-Lista C (2002) Ligament material behavior is nonlinear, viscoelastic and rate-independent under shear loading. J Biomech 35:943–950 Google Scholar
  203. 203.
    Weiss JA, Gardiner JC, Ellis BJ, Lujan TJ, Phatak NS (2005) Three-dimensional finite element modeling of ligaments: technical aspects. Med Eng Phys 27:845–861 Google Scholar
  204. 204.
    Weiss JA, Maker BN, Govindjee S (1996) Finite element implementation of incompressible, transversely isotropic hyperelasticity. Comput Methods Appl Mech Eng 135:107–128 MATHGoogle Scholar
  205. 205.
    Weiss JA, Maker BN, Schauer DA (1995) Treatment of initial stress in hyperelastic finite element models of soft tissues. In: Beaver Creek CO (ed) ASME summer bioengineering conference, 1995 Google Scholar
  206. 206.
    Weiss JA, Maker BN, Govindjee S (1996) Finite element implementation of incompressible, transversely isotropic hyperelasticity. Comput Methods Appl Mech Eng 135:107–128 MATHGoogle Scholar
  207. 207.
    Wilkes CH (1978) Arthrography of the temporomandibular joint in patients with the TMJ pain-dysfunction syndrome. Minn Med 61(11):645–652 Google Scholar
  208. 208.
    Wilkes CH (1978) Structural and functional alterations of the temporomandibular joint. Northwest Dent 57(5):287–294 MathSciNetGoogle Scholar
  209. 209.
    Wilson W, van Donkelaar CC, van Rietbergen B, Huiskes R (2003) Pathways of load-induced cartilage damage causing degeneration in the knee after meniscectomy. J Biomech 36:845–851 Google Scholar
  210. 210.
    Winters JM (1990) Hill-based muscle models: a system engineering perspective. In: Winters JM, Woo S (eds) Multyple muscle system. Springer, New York, pp 165–172 Google Scholar
  211. 211.
    Woo SL, Lubock P, Gómez MA, Jemmott G, Kuei SC, Akeson WH (1979) Large deformation nonhomogeneous and directional properties of articular cartilage in uniaxial tension. J Biomech 12:437–446 Google Scholar
  212. 212.
    Wriggers P (1995) Finite element algorithms for contact problems. Arch Comput Methods Eng 2:1–49 MathSciNetGoogle Scholar
  213. 213.
    Yasunaga T, Kimura M, Kikuchi S (2001) Histologic change of the meniscus and cartilage tissue after meniscal suture. Clin Orthop Relat R 387:232–240 Google Scholar
  214. 214.
    Yoshiya M, Kurosaka M, Yamada M (1991) Optimal orientation of bone tunnels in the anterior cruciate ligament reconstruction. Trand ORS 16:602 Google Scholar
  215. 215.
    Zahalak GI (1981) A distributed moment approximation for kinetic theories of muscular contraction. Math Biosci 55:89–114 MATHGoogle Scholar
  216. 216.
    Zahalak GI, Ma SP (1990) Muscle activation and contraction: constitutive relations based on cross-bridge kinetics. ASME J Biomech Eng 112:52–62 Google Scholar
  217. 217.
    Zajac FE (1989) Muscle and tendon: properties, models, scaling and application ti biomechanics and motor control. Crit Rev Biomed Eng 17:359–411 Google Scholar
  218. 218.
    Zienkiewicz OC, Taylor RL (1994) The finite element method, volume 1: basic formulation and linear problems. McGraw-Hill Google Scholar

Copyright information

© CIMNE, Barcelona, Spain 2007

Authors and Affiliations

  • E. Peña
    • 1
  • A. Pérez del Palomar
    • 1
  • B. Calvo
    • 1
  • M. A. Martínez
    • 1
  • M. Doblaré
    • 1
  1. 1.Group of Structural Mechanics and Materials Modeling, Aragón Institute of Engineering ResearchUniversity of ZaragozaZaragozaSpain

Personalised recommendations