Development and validation of a computational multibody model of the elbow joint

  • Rahman, Munsur (Department of Civil and Mechanical Engineering, University of Missouri-Kansas City) ;
  • Cil, Akin (Department of Orthopaedic Surgery, University of Missouri-Kansas City) ;
  • Johnson, Michael (Department of Orthopaedic Surgery, University of Missouri-Kansas City) ;
  • Lu, Yunkai (Department of Civil and Mechanical Engineering, University of Missouri-Kansas City) ;
  • Guess, Trent M. (Department of Civil and Mechanical Engineering, University of Missouri-Kansas City)
  • Received : 2013.08.06
  • Accepted : 2014.08.05
  • Published : 2014.09.25


Computational multibody models of the elbow can provide a versatile tool to study joint mechanics, cartilage loading, ligament function and the effects of joint trauma and orthopaedic repair. An efficiently developed computational model can assist surgeons and other investigators in the design and evaluation of treatments for elbow injuries, and contribute to improvements in patient care. The purpose of this study was to develop an anatomically correct elbow joint model and validate the model against experimental data. The elbow model was constrained by multiple bundles of non-linear ligaments, three-dimensional deformable contacts between articulating geometries, and applied external loads. The developed anatomical computational models of the joint can then be incorporated into neuro-musculoskeletal models within a multibody framework. In the approach presented here, volume images of two cadaver elbows were generated by computed tomography (CT) and one elbow by magnetic resonance imaging (MRI) to construct the three-dimensional bone geometries for the model. The ligaments and triceps tendon were represented with non-linear spring-damper elements as a function of stiffness, ligament length and ligament zero-load length. Articular cartilage was represented as uniform thickness solids that allowed prediction of compliant contact forces. As a final step, the subject specific model was validated by comparing predicted kinematics and triceps tendon forces to experimentally obtained data of the identically loaded cadaver elbow. The maximum root mean square (RMS) error between the predicted and measured kinematics during the complete testing cycle was 4.9 mm medial-lateral translational of the radius relative to the humerus (for Specimen 2 in this study) and 5.30 internal-external rotation of the radius relative to the humerus (for Specimen 3 in this study). The maximum RMS error for triceps tendon force was 7.6 N (for Specimen 3).



Supported by : University of Missouri-Kansas City (UMKC)


  1. Bei, Y., and Fregly, B.J. (2004), "Multibody dynamic simulation of knee contact mechanics", Med. Eng. Phys., 26(9), 777-789.
  2. Blankevoort, L., Kuiper, J.H., Huiskes, R., and Grootenboer, H. J. (1991), "Articular contact in a three-dimensional model of the knee", J. Biomech., 24(11), 1019-1031.
  3. Bloemker, K.H., Guess, T.M., Maletsky, L., and Dodd, K. (2012), "Computational knee ligament modeling using experimentally determined zero-load lengths", Open Biomed. Eng. J., 6, 33-41.
  4. Buchanan, T.S., Delp, S.L., and Solbeck, J.A. (1998), "Muscular resistance to varus and valgus loads at the elbow", J. Biomech. Eng., 120(5), 634-639.
  5. de Haan, J., Schep, N.W., Eygendaal, D., Kleinrensink, G.J., Tuinebreijer, W.E., and den Hartog, D. (2011), "Stability of the elbow joint: relevant anatomy and clinical implications of in vitro biomechanical studies", Open Orthop. J., 5, 168-176.
  6. Degreef, I., and De Smet, L. (2011), "The arthroscopic ulnohumeral arthroplasty: from mini-open to arthroscopic surgery", Minim. Invasive Surg., 798084.
  7. Donahue, T.L., Hull, M.L., Rashid, M.M., and Jacobs, C.R. (2002), "A finite element model of the human knee joint for the study of tibio-femoral contact", J. Biomech. Eng., 124(3), 273-280.
  8. Ferreira, L.M., King, G.J., and Johnson, J.A. (2011), "Motion-derived coordinate systems reduce inter-subject variability of elbow flexion kinematics", J. Orthop. Res., 29(4), 596-601.
  9. Fisk, J. P., and Wayne, J.S. (2009), "Development and validation of a computational musculoskeletal model of the elbow and forearm", Ann. Biomed. Eng., 37(4), 803-812.
  10. Garner, B.A., and Pandy, M.G. (2001), "Musculoskeletal model of the upper limb based on the visible human male dataset", Comput. Methods Biomech. Biomed. Eng., 4(2), 93-126.
  11. Gonzalez, R.V., Abraham, L.D., Barr, R.E., and Buchanan, T.S. (1999), "Muscle activity in rapid multi-degree-of-freedom elbow movements: solutions from a musculoskeletal model", Biol. Cybern., 80(5), 357-367.
  12. Gonzalez, R.V., Hutchins, E.L., Barr, R.E., and Abraham, L.D. (1996), "Development and evaluation of a musculoskeletal model of the elbow joint complex", J. Biomech. Eng., 118(1), 32-40.
  13. Guess, T.M. (2012), "Forward dynamics simulation using a natural knee with menisci in the multibody framework", Multibody Syst. Dyn., 28(1-2), 37-53.
  14. Guess, T.M., Liu, H., Bhashyam, S., and Thiagarajan, G. (2013), "A multibody knee model with discrete cartilage prediction of tibio-femoral contact mechanics", Comput. Methods Biomech. Biomed. Eng., 16(3), 256-270.
  15. Guess, T.M., Thiagarajan, G., Kia, M., and Mishra, M. (2010), "A subject specific multibody model of the knee with menisci", Med. Eng. Phys., 32(5), 505-515.
  16. Holzbaur, K.R., Murray, W.M., and Delp, S.L. (2005), "A model of the upper extremity for simulating musculoskeletal surgery and analyzing neuromuscular control", Ann. Biomed. Eng., 33(6), 829-840.
  17. Hunt, K.H., and Crossley, F.R.E. (1975), "Coefficient of Restitution Interpreted as Damping in Vibroimpact", J. Appl. Mech., 42(2), 440.
  18. Kwak, S.D., Blankevoort, L., and Ateshian, G.A. (2000), "A Mathematical Formulation for 3D Quasi-Static Multibody Models of Diarthrodial Joints", Comput. Methods Biomech. Biomed. Eng., 3(1), 41-64.
  19. Lemay, M.A., and Crago, P.E. (1996), "A dynamic model for simulating movements of the elbow, forearm, an wrist", J. Biomech., 29(10), 1319-1330.
  20. Li, G., Gil, J., Kanamori, A., and Woo, S.L. (1999), "A validated three-dimensional computational model of a human knee joint", J. Biomech. Eng., 121(6), 657-662.
  21. Liacouras, P.C., and Wayne, J.S. (2007), "Computational modeling to predict mechanical function of joints: application to the lower leg with simulation of two cadaver studies", J. Biomech. Eng., 129(6), 811-817.
  22. Morrey, B.F., and Chao, E.Y. (1976), "Passive motion of the elbow joint", J. Bone Joint Surg. Am., 58(4), 501-508.
  23. Raikova, R. (1992), "A general approach for modelling and mathematical investigation of the human upper limb", J. Biomech., 25(8), 857-867.
  24. Regan, W.D., Korinek, S.L., Morrey, B.F., and An, K.N. (1991), "Biomechanical study of ligaments around the elbow joint", Clin. Orthop. Relat. Res., 271, 170-179.
  25. Schuind, F., An, K.N., Berglund, L., Rey, R., Cooney, W.P., 3rd, Linscheid, R.L., and Chao, E.Y. (1991), "The distal radioulnar ligaments: a biomechanical study", J. Hand Surg. Am., 16(6), 1106-1114.
  26. Spratley, E.M., and Wayne, J.S. (2011), "Computational model of the human elbow and forearm: application to complex varus instability", Ann. Biomed. Eng., 39(3), 1084-1091.
  27. Stylianou, A.P., Guess, T.M., and Cook, J.L. (2012), "Development and validation of a multi-body model of the canine stifle joint", Comput. Methods Biomech. Biomed. Eng., doi: 10.1080/10255842.2012.684243
  28. Triolo, R.J., Werner, K.N., and Kirsch, R. F. (2001), "Modeling the postural disturbances caused by upper extremity movements", IEEE Trans. Neural. Syst. Rehabil. Eng., 9(2), 137-144.
  29. Wismans, J., Veldpaus, F., Janssen, J., Huson, A., and Struben, P. (1980), "A three-dimensional mathematical model of the knee-joint", J. Biomech., 13(8), 677-685.
  30. Zielinska, B., and Donabue, T. L. (2006), "3D finite element model of meniscrectomy: changes in joint contact behavior", J. Biomech. Eng., 128(1), 115-123.

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