Modeling of the condyle elements within a biomechanical knee model


The development of a computational multibody knee model able to capture some of the fundamental properties of the human knee articulation is presented. This desideratum is reached by including the kinetics of the real knee articulation. The research question is whether an accurate modeling of the condyle contact in the knee will lead to reproduction of the complex combination of flexion/extension, abduction/adduction, and tibial rotation observed in the real knee. The model is composed by two anatomic segments, the tibia and the femur, whose characteristics are functions of the geometric and anatomic properties of the real bones. The biomechanical model characterization is developed under the framework of multibody systems methodologies using Cartesian coordinates. The type of approach used in the proposed knee model is the joint surface contact conditions between ellipsoids, representing the two femoral condyles, and points, representing the tibial plateau and the menisci. These elements are closely fitted to the actual knee geometry. This task is undertaken by considering a parameter optimization process to replicate experimental data published in the literature, namely that by Lafortune and his coworkers in 1992. Then kinematic data in the form of flexion/extension patterns are imposed on the model corresponding to the stance phase of the human gait. From the results obtained, by performing several computational simulations, it can be observed that the knee model approximates the average secondary motion patterns observed in the literature. Because the literature reports considerable inter-individual differences in the secondary motion patterns, the knee model presented here is also used to check whether it is possible to reproduce the observed differences with reasonable variations of bone shape parameters. This task is accomplished by a parameter study, in which the main variables that define the geometry of condyles are taken into account. It was observed that the data reveal a difference in secondary kinematics of the knee in flexion versus extension. The likely explanation for this fact is the elastic component of the secondary motions created by the combination of joint forces and soft tissue deformations. The proposed knee model is, therefore, used to investigate whether this observed behavior can be explained by reasonable elastic deformations of the points representing the menisci in the model.

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  1. 1.

    Bei, Y., Fregly, B.J.: Multibody dynamic simulation of knee contact mechanics. Med. Eng. Phys. 26, 777–789 (2004)

    Article  Google Scholar 

  2. 2.

    Piazza, S.J., Delp, S.C.: Three-dimensional dynamic simulation of total knee replacement motion during a step-up task. J. Biomech. Eng. 123(6), 599–606 (2001)

    Article  Google Scholar 

  3. 3.

    Blajer, W., Czaplicki, A., Dziewiecki, K., Mazur, Z.: Influence of selected modeling and computational issues on muscle force estimates. Multibody Syst. Dyn. 24, 473–492 (2010)

    MATH  Article  Google Scholar 

  4. 4.

    Mohamed, A.A., Brown, M.A., Shabana, A.A.: Study of the ligament tension and cross-section deformation using nonlinear finite element/multibody system algorithms. Multibody Syst. Dyn. 23, 227–248 (2010)

    MathSciNet  MATH  Article  Google Scholar 

  5. 5.

    Jones, M.L., Hickman, J., Knox, J.A.: Validated finite element method study of orthodontic tooth movement in the human subject. J. Orthod. 28(1), 29–38 (2001)

    Article  Google Scholar 

  6. 6.

    Halloran, J.P., Petrella, A.J., Rullkoetter, P.J.: Explicit finite element modeling of total knee replacement mechanics. J. Biomech. 38(2), 323–331 (2005)

    Article  Google Scholar 

  7. 7.

    Silva, M.P.T., Ambrósio, J.A.C.: Kinematic data consistency in the inverse dynamic analysis of biomechanical systems. Multibody Syst. Dyn. 8(2), 219–239 (2002)

    MATH  Article  Google Scholar 

  8. 8.

    Rasmussen, J., Damsgaard, M., Christensen, S., Surma, E.: Design optimization with respect to ergonomic properties. Structural and Multidisciplinan Optimization 24(2), 89–97 (2002)

    Article  Google Scholar 

  9. 9.

    Begon, M., Colloud, F., Sardain, P.: Lower limb contribution in kayak performance: modelling, simulation and analysis. Multibody Syst. Dyn. 23, 387–400 (2010)

    MathSciNet  MATH  Article  Google Scholar 

  10. 10.

    Meireles, F., Machado, M., Silva, M., Flores, P.: Dynamic modeling and analysis of human locomotion using multibody system methodologies. Int. J. Comput. Vis. Biomech. 2(2), 199–206 (2009)

    Google Scholar 

  11. 11.

    Kłodowski, A., Rantalainen, T., Mikkola, A., Heinonen, A., Sievänen, H.: Flexible multibody approach in forward dynamic simulation of locomotive strains in human skeleton with flexible lower body bones. Multibody Syst. Dyn. 25(4), 395–409 (2001)

    Article  Google Scholar 

  12. 12.

    Nikravesh, P.E.: Computer-Aided Analysis of Mechanical Systems. Prentice-Hall, Englewood Cliffs (1988)

    Google Scholar 

  13. 13.

    Schiehlen, W.: Multibody Systems Handbook. Springer, Berlin (1990)

    Google Scholar 

  14. 14.

    Shabana, A.A.: Dynamics of Multibody Systems. Wiley, New York (1989)

    Google Scholar 

  15. 15.

    Ambrosio, J.: Rigid and flexible multibody dynamics tools for the simulation of systems subjected to contact and impact conditions. Eur. J. Mech. A, Solids 19, S23–44 (2000)

    Google Scholar 

  16. 16.

    TNO, 1998, MADYMO™ Theoretical manual, Version 5.3, TNO, Delft, The Netherlands

  17. 17.

    AnyBody™Technology, Computer Aided Ergonomics & Biomechanics (

  18. 18.

    Monteiro, N.M.B., Silva, M.P.T., Folgado, J.O.M.G., Melancia, J.P.L.: Structural analysis of the intervertebral discs adjacent to an interbody fusion using multibody dynamics and finite element cosimulation. Multibody Syst. Dyn. 25(2), 245–270 (2011)

    Article  Google Scholar 

  19. 19.

    Pandy, M.G.: Computer modeling and simulation of human movement. Annu. Rev. Biomed. Eng. 3, 245–273 (2001)

    Article  Google Scholar 

  20. 20.

    Cappozzo, A., Gazzani, F.: Joint kinematic assessement during physical exercise. In: Berme, N., Cappozzo, A. (eds.) Biomechanics of Human Movement: Applications in Rehabilitation, Sports and Ergonomics, pp. 263–274. Bertec, Worthington (1990)

    Google Scholar 

  21. 21.

    Steven, N.K.: Geared six-bar design. In: Proceedings of the Second Applied Mechanisms Conference, Oklahoma State University, October 1971, Paper No. 25 (1971)

  22. 22.

    Steven, N.K., Kramer, N., Srinivasan, S.: Design of a knee mechanism for a knee disarticulation prosthesis. In: Proceedings of the ASME Mechanisms Conference, Minneapolis, September 1994, DE-Vol. 71, pp. 455–462 (1994)

  23. 23.

    Flores, P., Ambrósio, J., Claro, J.C.P., Lankarani, H.M.: Dynamics of multibody systems with spherical clearance joints. J. Comput. Nonlinear Dyn. 1(3), 240–247 (2006)

    Article  Google Scholar 

  24. 24.

    Flores, P., Ambrósio, J., Claro, J.C.P.: Dynamic analysis for planar multibody mechanical systems with lubricated joints. Multibody Syst. Dyn. 12(1), 47–74 (2004)

    MATH  Article  Google Scholar 

  25. 25.

    Tian, Q., Liu, C., Machado, M., Flores, P.: A new model for dry and lubricated cylindrical joints with clearance in spatial flexible multibody systems. Nonlinear Dyn. 64(1–2), 25–47 (2011)

    Article  Google Scholar 

  26. 26.

    Flores, P., Ambrósio, J., Claro, J.C.P., Lankarani, H.M.: Translational joints with clearance in rigid multibody systems. J. Comput. Nonlinear Dyn. 3(1), 0110071-10 (2008)

    Article  Google Scholar 

  27. 27.

    Fialho, J.C., Fernandes, P.R., Eça, L., Folgado, J.: Computational hip joint simulator for wear and heat generation. J. Biomech. 40, 2358–2366 (2007)

    Article  Google Scholar 

  28. 28.

    Machado, M., Flores, P., Claro, J.C.P., Ambrósio, J., Silva, M., Completo, A., Lankarani, H.M.: Development of a planar multibody model of the human knee joint. Nonlinear Dyn. 60(3), 459–478 (2010)

    MATH  Article  Google Scholar 

  29. 29.

    Ottoboni, A., Parenti-Castelli, V., Sancisi, N., Belvedere, C., Leardini, A.: Articular surface approximation in equivalent spatial parallel mechanism models of the human knee joint. Proc. Inst. Mech. Eng. Part. H, J. Eng. Med. 224(9), 1121–1132 (2010)

    Article  Google Scholar 

  30. 30.

    Ribeiro, A.: A biomechanical multibody knee model based on ellipsoids: modeling, simulation and analysis. MSc Thesis, University of Minho, Portugal (2010)

  31. 31.

    Strasser, H.: Lehrbuch der muskel und gelenkmechanik. Springer, Berlin (1917)

    Google Scholar 

  32. 32.

    Menschik, A.: Mechanik des kniegelenkes Teil 1. Z. Orthoped. 112, 481 (1974)

    Google Scholar 

  33. 33.

    Crowninshield, R., Pope, M.H., Johnson, R.J.: An analytical model of the knee. J. Biomech. 9, 397–405 (1976)

    Article  Google Scholar 

  34. 34.

    Wismans, J., Veldpaus, F., Janssen, J., Huson, A., Struben, P.: A three-dimensional mathematical model of the knee-joint. J. Biomech. 13(8), 677–685 (1980)

    Article  Google Scholar 

  35. 35.

    Moeinzadeh, M.H., Engin, A.E., Akkas, N.: Two-dimensional dynamic modeling of human knee joint. J. Biomech. 316(4), 253–264 (1983)

    Article  Google Scholar 

  36. 36.

    Abdel-Rahman, E.M., Hefzy, M.S.: A two-dimensional dynamic anatomical model of the human knee joint. J. Biomech. Eng. 115, 357–365 (1993)

    Article  Google Scholar 

  37. 37.

    Abdel-Rahman, E.M., Hefzy, M.S.: Three-dimensional dynamic behaviour of the human knee joint under impact loading. Med. Eng. Phys. 20, 276–290 (1998)

    Article  Google Scholar 

  38. 38.

    Piazza, S.J., Delp, S.L.: Three-dimensional dynamic simulation of total knee replacement motion during a step-up task. J. Biomech. Eng. 123, 599–606 (2001)

    Article  Google Scholar 

  39. 39.

    Flores, P., Leine, R., Glocker, C.: Modeling and analysis of rigid multibody systems with translational clearance joints based on the nonsmooth dynamics approach. Multibody Syst. Dyn. 23(2), 165–190 (2010)

    MathSciNet  Article  Google Scholar 

  40. 40.

    Guess, T.M.: Forward dynamics simulation using a natural knee with menisci in the multibody framework. In: Ambrósio, J., et al. (eds.) Proceedings of the EUROMECH Colloquium 511 on Biomechanics of Human Motion, Ponta Delgada, Azores, Portugal, March 9–12 (2011), 15 p.

    Google Scholar 

  41. 41.

    Hirokova, S.: Three-dimensional mathematical model analysis of the patella-femoral joint. J. Biomech. 24, 659–671 (1991)

    Article  Google Scholar 

  42. 42.

    Heegard, J., Leyvraz, P.F., Curnier, A., Rakotomanana, L., Huiskes, R.: Biomechanics of the human patella during passive knee flexion. J. Biomech. 28(11), 1265–1279 (1995)

    Article  Google Scholar 

  43. 43.

    Essinger, J.R., Leyvraz, P.F., Heegard, J.H., Robertson, D.D.: Mathematical model for the evaluation of the behavior during flexion of condylar-type knee prostheses. J. Biomech. 22, 1229–1241 (1989)

    Article  Google Scholar 

  44. 44.

    DeFrate, L.E., Papannagari, R., Gill, T.J., Moses, J.M., Pathare, N.P., Li, G.: The 6 degrees of freedom kinematics of the knee after anterior cruciate ligament deficiency: an in vivo imaging analysis. Am. J. Sports Med. 34, 1240–1246 (2006)

    Article  Google Scholar 

  45. 45.

    Lafortune, M.A., Cavanagh, P.R., Sommer, H.J., Kalenak, A.: Three-dimensional kinematics of the human knee during walking. J. Biomech. 25(4), 347–357 (1992)

    Article  Google Scholar 

  46. 46.

    Sancisi, N., Paenti-Castelli, V.: On the role of ligaments in the guidance of the human knee passive motion. In: Ambrósio, J., et al. (eds.) Proceedings of the Euromech Colloquium 511 on Biomechanics of Human Motion, Ponta Delgada, Azores, Portugal, March 9–12 (2011), 9 p.

    Google Scholar 

  47. 47.

    Benoit, D., Ramsey, D., Lamontagne, M., Xu, L., Wretenberg, P., Renström, P.: Effect of skin movement artifact on knee kinematics during gait and cutting motions measured in vivo. Gait Posture 24(2), 152–164 (2005)

    Article  Google Scholar 

  48. 48.

    Andersen, M., Benoit, D., Damsgaard, M., Ramsey, D., Rasmussen, J.: Do kinematic models reduce the effects of soft tissue artefacts in skin marker-based motion analysis? An in vivo study of knee kinematics. J. Biomech. 43, 268–273 (2010)

    Article  Google Scholar 

  49. 49.

    Winter, D.A.: Biomechanics and Motor Control of Human Movement, 3rd edn. Wiley, Toronto (2005)

    Google Scholar 

  50. 50.

    Damsgaard, M., Rasmussen, J., Christensen, S.T., Surma, E., Zee, M.D.: Analysis of musculoskeletal systems in the AnyBody Modeling System™. Simul. Model. Pract. Theory 14(8), 1100–1111 (2006)

    Article  Google Scholar 

  51. 51.

    Li, K., Tashman, S., Fu, F., Harner, C., Zhang, X.: Automating analysis of the distal femur articular geometry based on three-dimensional surface data. Ann. Biomed. Eng. 48, 2928–2936 (2010)

    Article  Google Scholar 

  52. 52.

    Shaffer, B., Kennedy, S., Klmikiewicz, J., Yao, L.: Preoperactive sizing of meniscal allografts in meniscus transplantation. Am. J. Sports Med. 28(4), 524–533 (2000)

    Google Scholar 

  53. 53.

    Li, Z.M.: Functional degrees of freedom. Motor Control 10, 301–310 (2006)

    Google Scholar 

  54. 54.

    Li, Z.M., Tang, J.: Coordination of thumb joints during opposition. J. Biomech. 40, 502–510 (2007)

    Article  Google Scholar 

  55. 55.

    Page, A., Galvez, J.A., Baydal-Bertomeu, J.M., Mata, V., Belda-Lois, J.M.: Functional degrees of freedom of neck movements: linear models may overestimate variability. Gait Posture 28, S56 (2008)

    Article  Google Scholar 

  56. 56.

    Page, A., Rosário, H., Gálvez, J.A., Mata, V.: Representation of planar motion of complex joints by means of rolling pairs. Application to neck motion. J. Biomech. 44, 747–750 (2011)

    Article  Google Scholar 

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Correspondence to Paulo Flores.

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Ribeiro, A., Rasmussen, J., Flores, P. et al. Modeling of the condyle elements within a biomechanical knee model. Multibody Syst Dyn 28, 181–197 (2012).

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  • Knee modeling
  • Stance phase
  • Condyles
  • Multibody methodologies