Journal of Computational Applied Mechanics

Contact mechanics of human knee joint: Analytical approach

Document Type : Research Paper

Authors

1 School of Mechanical Engineering KLE Technological University BVB Campus, Vidyanagar Hubballi

2 KLE technological university Hubballi Vidyanagar Hubballi

Abstract

A new methodology for modeling tibio-femoral articular contact of a knee joint based on contact models of the classical contact mechanics is established. The given analytical models of articular contact are extended to the case of contact between low strain arbitrary linear elastic tissues, i.e., cartilages and meniscus. The approach uses the geometries of contact surfaces and the generalization of the Hertzian contact theory of non-conforming bodies with frictionless contact interaction between elastic articular tissues. The normal and tangential contact displacements are determined analytically based on the exact solutions for the spherical contact between the articular tissues of the knee. The non-linear stiffness (secant and tangential stiffness) of the knee joint’s elastic half-space is derived using the analytical relationships. The method is demonstrated by exploring a case study, and the results are compared with the current literature to verify the fidelity of the proposed analytical approach. The analytical models facilitate accurate contact mechanics of the knee joint. Researchers may now use these analytical models to develop knee surrogate models in multibody dynamics.

Keywords

  1. Herzog and S. Federico, Considerations on Joint and Articular Cartilage Mechanics. Biomechanics and Modeling in Mechanobiology, 5, 64–81, 2006.
  2. Wismans, F. Veldpaus, J. Janssen, A. Huson, and P. Struben, A Three-Dimensional Mathematical Model of the Knee-Joint, Journal of Biomechanics, 13, 677–679, 681–685,1980.
  3. M. Abdel-Rahman and M.S. Hefzy, Three-Dimensional Dynamic Behaviour of the Human Knee Joint Under Impact Loading, Medical Engineering & Physics, 20, 276–290, 1998.
  4. -K. Ling, H.-Q. Guo, and S. Boersma, Analytical Study on the Kinematic and Dynamic Behaviors of a Knee Joint, Medical Engineering & Physics, 19, 29–36, 1997.
  5. Blankevoort, J.H. Kuiper, R. Huiskes, and H.J. Grootenboer, Articular Contact in a Three-Dimensional Model of the Knee, Journal of Biomechanics, 24, 1019–1031, 1991.
  6. Bei and B.J. Fregly, Multibody Dynamic Simulation of Knee Contact Mechanics. Medical Engineering & Physics, 26, 777–789, 2004.
  7. Machado, P. Flores, J.C.P. Claro, J. Ambrosio, M. Silva, A. Completo, and H.M. Lankarani, Development of a Planar Multibody Model of the Human Knee Joint, Nonlinear Dynamics, 60, 459–478, 2010.
  8. Lee, S. H., & Terzopoulos, D. (2008). Spline joints for multibody dynamics. ACM Transactions on Graphics, 27(3). https://doi.org/10.1145/1360612.1360621

 

  1. Lee, K. M., & Guo, J. (2010). Kinematic and dynamic analysis of an anatomically based knee joint. Journal of Biomechanics, 43(7), 1231–1236. https://doi.org/10.1016/j.jbiomech.2010.02.001
  2. Wilson, C. C. van Donkelaar, R. van Rietberger, and R. Huiskes, The Role of Computational Models in the Search for the Mechanical Behaviour and Damage Mechanisms of Articular Cartilage, Medical Engineering and Physics 27, 810–826, 2005.
  3. Z. Wu, W. Herzog, and M. Epstein, Evaluation of the Finite Element Software ABAQUS for Biomechanical Modelling of Biphasic Tissues, Journal of Biomechanics, 31, 165–169, 1997.
  4. Caruntu and M.S. Hefzy, 3-D Anatomically Based Dynamic Modeling of the Human Knee to Include Tibio-Femoral and Patello-Femoral joints, Journal of Biomechanical Engineering, 126, 44–53, 2004.
  5. P´erez-Gonzalez, C. Fenollosa-Esteve, J.L. Sancho-Bru, F.T. Sanchez-Marin, M. Vergara, and P.J. Rodriguez-Cervantes, A Modified Elastic Foundation Contact Model for Application in 3D Models of the Prosthetic Knee, Medical Engineering & Physics, 30, 387–398, 2008.
  6. -Ch. Lin, R.T. Haftka, N.V. Queipo, and B.J. Fregly, Surrogate Articular Contact Models for Computationally Efficient Multibody Dynamic Simulations, Medical Engineering & Physics, 32, 584–594, 2010.
  7. Ilan, Eskinazi., & Benjamin, J, Fregly. (2016). An open-source toolbox for surrogate modeling of joint contact mechanics. IEEE transactions on biomedical engineering, vol.63, No. 2.
  8. Roman, Pryazhevskiy., Ildar, Akhtyamov., Anna, Morgunova., Helo, Mohammad, Jihad., & Andrey, Nevzorov. (2020). Springer Nature Switzerland AG 2020, IHIET, AISC 1018, pp.612-617.
  9. Popov, V. L., Heß, M., Willert, E., Popov, V. L., Heß, M., & Willert, E. (2019). Normal Contact Without Adhesion. In Handbook of Contact Mechanics. https://doi.org/10.1007/978-3-662-58709-6_2
  10. Lee, E. H. (1955). Stress analysis in visco-elastic bodies. Quarterly of Applied Mathematics, 13(2), 183–190. https://doi.org/10.1090/qam/69741.
  11. LD Landau, E.M. Lifschitz, Theory of elasticity (Theoretical Physics, Vol7), 3rd edition, 1999, Butterworth-Heinemann, Oxford, 8,9.
  12. Caruntu and M.S. Hefzy, 3-D Anatomically Based Dynamic Modeling of the Human Knee to Include Tibio-Femoral and Patello-Femoral joints, Journal of Biomechanical Engineering, 126, 44–53, 2004.
  13. Zielinska, B., & Donahue, T. L. H. (2006). 3D finite element model of meniscectomy: Changes in joint contact behavior. Journal of Biomechanical Engineering, 128(1), 115–123.
  14. Anderson, A. E., et al. (2005). Subject-specific finite element model of the pelvis: development, validation and sensitivity studies. Journal of Biomechanical Engineering, 127(3), 364–373.
  15. Halonen, K. S., et al. (2014). Deformation of articular cartilage during static loading of a knee joint–experimental and finite element analysis. Journal of Biomechanics, 47(10), 2467–2474.
  16. Wang, Y., Fan, Y., & Zhang, M. (2014). Comparison of stress on knee cartilage during kneeling and standing using finite element models. Medical Engineering & Physics, 36(4), 439–447.
  17. Adouni, M., Shirazi-Adl, A., & Shirazi, R. (2012). Computational biodynamics of human knee joint in gait: from muscle forces to cartilage stresses. Journal of Biomechanics, 45(12), 2149– 2156.
  18. Adams, C. R., et al. (2007). Effects of rotator cuff tears on muscle moment arms: A computational study. Journal of Biomechanics, 40(15), 3373–3380.
  19. Zheng, K. K., et al. (2014). Magnetic resonance imaging (MRI) based finite element modeling for analyzing the influence of material properties on menisci responses. In Applied Mechanics and Materials (pp. 305–309). Trans Tech Publications.
  20. N. Sneddon, The Relation between Load and Penetration in the Axisymmetric Boussinesq Problem for a Punch of Arbitrary Profile. Int. J. Eng. Sci.,1965, v. 3, pp. 47–57.
  21. L. Johnson, Contact mechanics. Cambridge University Press, Ninth printing 2003.
  22. Popov, V. L., Heß, M., Willert, E., Popov, V. L., Heß, M., & Willert, E. (2019). Normal Contact Without Adhesion. In Handbook of Contact Mechanics. https://doi.org/10.1007/978-3-662-58709-6_2
  23. Halonen, K. S., et al. (2014). Deformation of articular cartilage during static loading of a knee joint–experimental and finite element analysis. Journal of Biomechanics, 47(10), 2467–2474.
  24. Wang, Y., Fan, Y., & Zhang, M. (2014). Comparison of stress on knee cartilage during kneeling and standing using finite element models. Medical Engineering & Physics, 36(4), 439–447.
  25. Hu, J., Chen, Z., Xin, H., Zhang, Q., & Jin, Z. (2018). Musculoskeletal multibody dynamics simulation of the contact mechanics and kinematics of a natural knee joint during a walking cycle. Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine, 232(5), 508–519. https://doi.org/10.1177/0954411918767695
  26. Lee, K. M., & Guo, J. (2010). Kinematic and dynamic analysis of an anatomically based knee joint. Journal of Biomechanics, 43(7), 1231–1236. https://doi.org/10.1016/j.jbiomech.2010.02.001
  27. Duraisamy, Shriram., Gideon, Praveen, Kumar., Fangsen, Cui., Yee, Han, Dave, Lee., & Karuppasamy, Subburaj. (2017). Evaluating the effects of material properties of artificial meniscal implant in the human knee joint using finite element analysis. Scintific reports, 7:6011, DOI:10.1038/s41598-017-06271-3
  28. Lee, E. H. (1955). Stress analysis in visco-elastic bodies. Quarterly of Applied Mathematics, 13(2), 183–190. https://doi.org/10.1090/qam/69741.
  29. LD Landau, E.M. Lifschitz, Theory of elasticity (Theoretical Physics, Vol7), 3rd edition, 1999, Butterworth-Heinemann, Oxford, 8,9.
  30. Radok, J. R. M. (1957). Visco-elastic stress analysis. Quarterly of Applied Mathematics, 15(2), 198–202. https://doi.org/10.1090/qam/92453
  31. Fernandes, D. J. C. (2014). Finite element analysis of the ACL-deficient knee. Ph.D. thesis, IST, Universidade de Lisboa, Portugal.
  32. Halonen, K.S., et al., deformation of articular cartilage during static loading of a knee joint – Experimental and finite element analysis. Journal of Biomechanics (2014), http://dx.doi.org/10.1016/j.jbiomech.2014.04.013
  33. Chan, D., Cai, L., Butz, K. et al. In vivo articular cartilage deformation: non-invasive quantification of intratissue strain during joint contact in the human knee. Sci Rep 6, 19220 (2016). https://doi.org/10.1038/srep19220
Journal of Computational Applied Mechanics
Volume 52, Issue 4
December 2021
Pages 553-569
  • Receive Date: 30 June 2021
  • Revise Date: 04 December 2021
  • Accept Date: 10 December 2021