Iranian Journal of Biomedical Engineering (IJBME)
نشریه علمی مهندسی پزشکی زیستی

Development of a Planar Multibody Model of the Knee Joint with Contact Mechanics

Document Type : Full Research Paper

Authors

Amirhosein Javanfar 1
Mahdi Bamdad 2

1 Ph.D. Student, School of Mechanical and Mechatronics Engineering, Shahrood University of Technology, Shahrood, Iran

2 Associate Professor, Corrective Exercise and Rehabilitation Laboratory, School of Mechanical and Mechatronics Engineering, Shahrood University of Technology, Shahrood, Iran

https://doi.org/10.22041/ijbme.2022.555148.1775
Abstract
Biomechanical modeling of human joints has been considered for a long time by researchers due to its high importance and application. Therefore, methods of modeling joints, and kinematic and dynamic analysis of human movement have continuously been developing. In this paper, a biomechanical human knee model is developed, and a generic procedure for dynamic analysis of contact problems in combination with the musculoskeletal model is introduced. The development of this knee dynamic model includes the geometric expression of collision curves and an algorithm for determining collision points. This presentation addresses cartilage penetration depth and contact force calculation through nonlinear discontinuous contact law. Therefore, the femur and tibia's relative motion is modeled through the combined collision reactions of cartilage and bone in the knee. Moreover, two knee models, the novel curve fitted-plane contact model, and the spherical-plane contact model, have been compared, and a personalized model has been developed for such cases as knee osteoarthritis. There is a difference (average 12%) between the results of the enhanced model and the sphere on the plane model in the cartilage penetration. In the simulation, maximum penetration depth in a healthy knee is reported to be 0.705 mm, while in a 75% KOA is 0.521 mm, including 0.5 mm cartilage-cartilage contact and 0.021 mm bone-bone contact. The contact force is not increased in KOA despite the general belief. The cartilage penetration depth exceeds cartilage thickness, and the bone-bone contact leads to pain. It is a suitable tool for the analysis and control of the auxiliary device in order to control the relative motion of the tibia femur and their separation in patients with osteoarthritis of the knee.

Keywords

Forward Dynamics
Nonlinear Discontinuous
Contact Model
Osteoarthritis
Musculoskeletal Modeling
Cartilage
Penetration Depth

Subjects

  1. S. Hoo, G. D’Onofrio, and G. Figueroa, "Knee Dislocations and Fractures," Clinical Guide to Musculoskeletal Medicine, pp. 451-457: Springer, 2022.
  2. M. Ayati Najafabadi, A. Hashemi Oskouei, and S. M. Rafiaei, “Using changes in the center of mass to measure the balance in people with different leg lengths when climbing stairs,” Iranian Journal of Biomedical Engineering, vol. 15, no. 2, pp. 131-140, 2021.
  3. R. Budarick, B. E. MacKeil, S. Fitzgerald et al., “Design evaluation of a novel Multicompartment unloader knee brace,” Journal of Biomechanical Engineering, vol. 142, no. 1, 2020.
  4. A. Segal, “Bracing and orthoses: a review of efficacy and mechanical effects for tibiofemoral osteoarthritis,” PM&R, vol. 4, no. 5, pp. S89-S96, 2012.
  5. A. Block, and N. Shakoor, “Lower limb osteoarthritis: biomechanical alterations and implications for therapy,” Current opinion in rheumatology, vol. 22, no. 5, pp. 544-550, 2010.
  6. Miyazaki, M. Wada, H. Kawahara et al., “Dynamic load at baseline can predict radiographic disease progression in medial compartment knee osteoarthritis,” Annals of the rheumatic diseases, vol. 61, no. 7, pp. 617-622, 2002.
  7. Johnson, P. Scarrow, and W. Waugh, “Assessments of loads in the knee joint,” Medical and Biological Engineering and Computing, vol. 19, no. 2, pp. 237-243, 1981.
  8. Salehi Amini, S. Kazemirad, S. Mohammadi et al., “Design, Analysis and Function Simulation of a Simple and Effective Driving Mechanism for Gait Trainer,” Iranian Journal of Biomedical Engineering, vol. 7, no. 2, pp. 121-132, 2013.
  9. Bahraminasab, “Effect of Femoral Component Interface Design on Biomechanical Performance of Knee Prosthesis,” Iranian Journal of Biomedical Engineering, vol. 10, no. 1, pp. 25-40, 2016.
  10. M. F. Machado, “A multibody approach to the contact dynamics: a knee joint application,” 2013.
  11. Martínez-Solís, A. Claudio-Sánchez, J. M. Rodríguez-Lelis et al., “A portable system with sample rate of 250 Hz for characterization of knee and hip angles in the sagittal plane during gait,” BioMedical Engineering OnLine, vol. 13, no. 1, pp. 1-21, 2014.
  12. Machado, P. Flores, J. Claro et al., “Development of a planar multibody model of the human knee joint,” Nonlinear Dynamics, vol. 60, no. 3, pp. 459-478, 2010.
  13. L. Landon, M. W. Hast, and S. J. Piazza, “Robust contact modeling using trimmed NURBS surfaces for dynamic simulations of articular contact,” Computer Methods in Applied Mechanics and Engineering, vol. 198, no. 30-32, pp. 2339-2346, 2009.
  14. Strasser, Lehrbuch der Muskel-und Gelenkmechanik: Рипол Классик, 1908.
  15. Menschik, Biometrie: das Konstruktionsprinzip des Kniegelenks, des Hüftgelenks, der Beinlänge und der Körpergrösse: Springer-Verlag, 2013.
  16. H. Moeinzadeh, and A. E. Engin, “Response of a two-dimensional dynamic model of the human knee to the externally applied forces and moments,” Journal of biomedical engineering, vol. 5, no. 4, pp. 281-291, 1983.
  17. Abdel-Rahman, M. Hefzy, and T. Cooke, "Determination of the ligamentous and contact forces in the human tibio-femoral joint using a three-dimensional dynamic anatomical model." pp. 373-376.
  18. M. Abdel-Rahman, and M. S. Hefzy, “Three-dimensional dynamic behaviour of the human knee joint under impact loading,” Medical engineering & physics, vol. 20, no. 4, pp. 276-290, 1998.
  19. Hirokawa, “Three-dimensional mathematical model analysis of the patellofemoral joint,” Journal of biomechanics, vol. 24, no. 8, pp. 659-671, 1991.
  20. Hertz, “Ueber die Berührung fester elastischer Körper,” 1882.
  21. G. Pandy, K. Sasaki, and S. Kim, “A three-dimensional musculoskeletal model of the human knee joint. Part 1: theoretical construction,” Computer Methods in Biomechanics and Bio Medical Engineering, vol. 1, no. 2, pp. 87-108, 1997.
  22. M. Guess, H. Liu, S. Bhashyam et al., “A multibody knee model with discrete cartilage prediction of tibio-femoral contact mechanics,” Computer methods in biomechanics and biomedical engineering, vol. 16, no. 3, pp. 256-270, 2013.
  23. R. Smith, K. Won Choi, D. Negrut et al., “Efficient computation of cartilage contact pressures within dynamic simulations of movement,” Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization, vol. 6, no. 5, pp. 491-498, 2018.
  24. Esrafilian, L. Stenroth, M. E. Mononen et al., “An EMG-assisted muscle-force driven finite element analysis pipeline to investigate joint-and tissue-level mechanical responses in functional activities: Towards a rapid assessment toolbox,” bioRxiv, 2021.
  25. Küçük, “The effect of modeling cartilage on predicted ligament and contact forces at the knee,” Computers in Biology and Medicine, vol. 36, no. 4, pp. 363-375, 2006.
  26. Masouros, A. Bull, and A. Amis, “(i) Biomechanics of the knee joint,” Orthopaedics and Trauma, vol. 24, no. 2, pp. 84-91, 2010.
  27. Singh, H. Chaudhary, and A. K. Singh, “A novel gait-based synthesis procedure for the design of 4-bar exoskeleton with natural trajectories,” Journal of orthopaedic translation, vol. 12, pp. 6-15, 2018.
  28. -M. Lee, and J. Guo, “Kinematic and dynamic analysis of an anatomically based knee joint,” Journal of biomechanics, vol. 43, no. 7, pp. 1231-1236, 2010.
  29. -M. Lee, and D. Wang, "Design analysis of a passive weight-support lower-extremity-exoskeleton with compliant knee-joint." pp. 5572-5577.
  30. C. Chapra, and R. P. Canale, Numerical methods for engineers: Mcgraw-hill New York, 2011.
  31. OpenfMRI, Available: https://legacy.openfmri.org.
  32. Zeighami, “Tibiofemoral contact areas and contact forces in healthy and osteoarthritic subjects,” École de technologie supérieure, 2018.
  33. Sharf, and Y. Zhang, “A contact force solution for non-colliding contact dynamics simulation,” Multibody System Dynamics, vol. 16, no. 3, pp. 263-290, 2006.
  34. S. Andersen, D. L. Benoit, M. Damsgaard et al., “Do kinematic models reduce the effects of soft tissue artefacts in skin marker-based motion analysis? An in vivo study of knee kinematics,” Journal of biomechanics, vol. 43, no. 2, pp. 268-273, 2010.
  35. Q. Liu, F. C. Anderson, M. H. Schwartz et al., “Muscle contributions to support and progression over a range of walking speeds,” Journal of biomechanics, vol. 41, no. 15, pp. 3243-3252, 2008.
  36. Feikes, J. O'Connor, and A. Zavatsky, “A constraint-based approach to modelling the mobility of the human knee joint,” Journal of biomechanics, vol. 36, no. 1, pp. 125-129, 2003.
  37. L. Delp, F. C. Anderson, A. S. Arnold et al., “OpenSim: open-source software to create and analyze dynamic simulations of movement,” IEEE transactions on biomedical engineering, vol. 54, no. 11, pp. 1940-1950, 2007.
  38. L. Delp, J. P. Loan, M. G. Hoy et al., “An interactive graphics-based model of the lower extremity to study orthopaedic surgical procedures,” IEEE Transactions on Biomedical engineering, vol. 37, no. 8, pp. 757-767, 1990.
  39. Y. Park, “Breastfeeding for one month or longer is associated with higher risk of osteoarthritis in older adults: NHANES 1999–2012,” Clinical nutrition research, vol. 6, no. 4, pp. 277-284, 2017.
  40. L. Wise, J. Niu, M. Yang et al., “Patterns of compartment involvement in tibiofemoral osteoarthritis in men and women and in whites and African Americans,” Arthritis care & research, vol. 64, no. 6, pp. 847-852, 2012.
  41. H. Miller, R. L. Krupenevich, A. L. Pruziner et al., “Medial knee joint contact force in the intact limb during walking in recently ambulatory service members with unilateral limb loss: a cross-sectional study,” PeerJ, vol. 5, pp. e2960, 2017.
  42. N. Findley, and F. A. Davis, Creep and relaxation of nonlinear viscoelastic materials: Courier corporation, 2013.
  43. R. Winby, G. L. David, F. B. Thor, and T. B. Kirk. 2009, “Muscle and external load contribution to knee joint contact loads during normal gait,” Journal of biomechanics, 42 (14): 2294-2300.
  44. E. Richards, M. S. Andersen, J. Harlaar et al., “Relationship between knee joint contact forces and external knee joint moments in patients with medial knee osteoarthritis: effects of gait modifications,” Osteoarthritis and Cartilage, vol. 26, no. 9, pp. 1203-1214, 2018.
  45. Li, and K. Gu, “Reconsideration on the use of elastic models to predict the instantaneous load response of the knee joint,” Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine, vol. 225, no. 9, pp. 888-896, 2011.
  46. Hu, H. Xin, Z. Chen et al., “The role of menisci in knee contact mechanics and secondary kinematics during human walking,” Clinical Biomechanics, vol. 61, pp. 58-63, 2019.
  47. Wilson, C. Van Donkelaar, R. Van Rietbergen et al., “The role of computational models in the search for the mechanical behavior and damage mechanisms of articular cartilage,” Medical engineering & physics, vol. 27, no. 10, pp. 810-826, 2005.
Iranian Journal of Biomedical Engineering (IJBME)
Volume 16, Issue 2
Summer 2022
Pages 133-145

  • Receive Date 05 June 2022
  • Revise Date 19 July 2022
  • Accept Date 29 July 2022

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