Hostname: page-component-76fb5796d-5g6vh Total loading time: 0 Render date: 2024-04-25T17:03:59.471Z Has data issue: false hasContentIssue false
  • English
  • Français

Articular human joint modelling

Published online by Cambridge University Press:  07 December 2009

Ibrahim I. Esat  and
Neviman Ozada
Ibrahim I. Esat
Affiliation:
Department of Mechanical Engineering, Brunel University West London, Uxbridge, London, UK
Neviman Ozada*
Affiliation:
Department of Mechanical Engineering, Brunel University West London, Uxbridge, London, UK
*
*Corresponding author. E-mail: neriman.ozada@brunel.ac.uk
Get access Rights & Permissions [Opens in a new window]

Summary

The work reported in this paper encapsulates the theories and algorithms developed to drive the core analysis modules of the software which has been developed to model a musculoskeletal structure of anatomic joints. Due to local bone surface and contact geometry based joint kinematics, newly developed algorithms make the proposed modeller different from currently available modellers. There are many modellers that are capable of modelling gross human body motion. Nevertheless, none of the available modellers offer complete elements of joint modelling. It appears that joint modelling is an extension of their core analysis capability, which, in every case, appears to be musculoskeletal motion dynamics. It is felt that an analysis framework that is focused on human joints would have significant benefit and potential to be used in many orthopaedic applications. The local mobility of joints has a significant influence in human motion analysis, in understanding of joint loading, tissue behaviour and contact forces. However, in order to develop a bone surface based joint modeller, there are a number of major problems, from tissue idealizations to surface geometry discretization and non-linear motion analysis. This paper presents the following: (a) The physical deformation of biological tissues as linear or non-linear viscoelastic deformation, based on spring-dashpot elements. (b) The linear dynamic multibody modelling, where the linear formulation is established for small motions and is particularly useful for calculating the equilibrium position of the joint. This model can also be used for finding small motion behaviour or loading under static conditions. It also has the potential of quantifying the joint laxity. (c) The non-linear dynamic multibody modelling, where a non-matrix and algorithmic formulation is presented. The approach allows handling complex material and geometrical nonlinearity easily. (d) Shortest path algorithms for calculating soft tissue line of action geometries. The developed algorithms are based on calculating minimum ‘surface mass’ and ‘surface covariance’. An improved version of the ‘surface covariance’ algorithm is described as ‘residual covariance’. The resulting path is used to establish the direction of forces and moments acting on joints. This information is needed for linear or non-linear treatment of the joint motion. (e) The final contribution of the paper is the treatment of the collision. In the virtual world, the difficulty in analysing bodies in motion arises due to body interpenetrations. The collision algorithm proposed in the paper involves finding the shortest projected ray from one body to the other. The projection of the body is determined by the resultant forces acting on it due to soft tissue connections under tension. This enables the calculation of collision condition of non-convex objects accurately. After the initial collision detection, the analysis involves attaching special springs (stiffness only normal to the surfaces) at the ‘potentially colliding points’ and motion of bodies is recalculated. The collision algorithm incorporates the rotation as well as translation. The algorithm continues until the joint equilibrium is achieved. Finally, the results obtained based on the software are compared with experimental results obtained using cadaveric joints.

Keywords

SoftwareJoint Modelling6DOFTissue wrappingforced contact based articulationunilateralbilateralconstraints
Type
Article
Information
Robotica , Volume 28 , Special Issue 2: Surgical Robotics: System Development, Application Study and Performance Analysis , March 2010 , pp. 321 - 339
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Brandt, K., Radin, E., Dieppe, P. and Van De Putte, L., “Yet more evidence that osteoarthritis is not a cartilage disease,” Ann. Rheum. Dis. 65, 1261–1264 (2006).CrossRefGoogle Scholar
2. Delp, S., Loan, J., Hoy, M., Zajac, F., Topp, E. and Rosen, J., “An interactive graphics-based model of the lower extremity to study orthopaedic surgical procedures,” IEEE Trans. Biomed. Eng. 37 (8), 757–767 (1990).CrossRefGoogle ScholarPubMed
3. Chao, E., Armiger, R., Yoshida, H., Lim, J. and Haraguchi, N., “Virtual Interactive Musculoskeletal System (VIMS) in orthopaedic research, education and clinical patient care,” J.Orthop. Surg. Res. 2 (2), (2007).CrossRefGoogle ScholarPubMed
4. Blakeley, F. M., “Cyberman,’ Chrysler Corp., Detroit, MI (1980).Google Scholar
5. Bapu, P., Evans, S., Kitka, P., Korna, M. and McDaniel, J., User's Guide for Combiman Programs, Version 4, University of Dayton Research Institute, Dayton, OH (1980).Google Scholar
6. Mi, Z., Yang, J. and Abdel-Malek, K., “Optimization based pasture prediction for human upper body,” Robotica 27, 607–620 (2009).CrossRefGoogle Scholar
7. Thalmann, D., Boulic, R., Huang, Z. and Noser, H., “Virtual and real humans interacting in the virtual world,” Proceedings of the International Conference on Virtual Systems and Multimedia '95 (1995) pp. 48–57.Google Scholar
8. Fernandez, J., Mithraratne, P., Thrupp, S., Tawhai, M. and Hunter, P., “Anatomically based geometric modelling of the musculo-skeletal system and other organs,” Biomech. Model. Mechanobiol. 2 (3), 139–155 (2004).CrossRefGoogle ScholarPubMed
9. Thalmann, N. and Cordier, F., “Construction of a human topological model from medical data,” IEEE Trans. Inform. Tech. Biomed. 4 (2), 137–149 (2000).CrossRefGoogle Scholar
10. Kupper, J., Loitz-Ramage, B., Corr, D., Hart, D. and Ronsky, J., “Measuring knee joint laxity: A review of applicable models and the need for new approaches to minimize variability,” Clin. Biomech. 22 (1), 1–13 (2007).CrossRefGoogle ScholarPubMed
11. Safran, M., McGarry, M., Shin, S., Han, S. and Lee, T., “Effects of elbow flexion and forearm rotation on valgus laxity of the elbow,” J. Bone Joint Surg. 87, 2065–2074 (2005).CrossRefGoogle ScholarPubMed
12. Jonsson, H., Karrholm, J. and Elmqvist, L., “Laxity after cruciate ligament injury in 94 knees. The KT-1000 Arthrometer versus Roentgen Stereophotogrammtry,” Acta Orthop. Scand. 64 (5), 567–570 (1993).CrossRefGoogle Scholar
13. Ganko, A., Engebretsen, L. and Ozer, H., “The Rolimeter: A new arthrometer compared with the KT-1000,” Knee Surg. Sports Traumatol. Arthrosc. 8 (1), 36–39 (2000).CrossRefGoogle ScholarPubMed
14. Habets, R., Computer assistance in orthopaedic surgery, Ph.D. Thesis (Technische Universiteit Eindhoven, 2002).Google Scholar
15. Van Der Helm, F., “Analysis of the kinematic and dynamic behaviour of the shoulder mechanism,” J. Biomech. 27 (5), 527–550 (1994).CrossRefGoogle ScholarPubMed
16. Maurel, W., 3D modelling of the human upper limb including the biomechanics of joints, muscles and soft tissues, Ph.D. Thesis (Ecole Polytechnique Federale De Lausanne, 1999).Google Scholar
17. Raikova, R., “A general approach for modelling and mathematical investigation of the human upper limb,” J. Biomech. 25 (8), 857–867 (1992).CrossRefGoogle ScholarPubMed
18. Engin, A. and Tumer, S., “Improved dynamic model of the human knee joint and its response to impact loading on the lower leg,” J. Biomech. Eng. 115, 137–143 (1993).CrossRefGoogle ScholarPubMed
19. Moeinzadeh, M., Engin, A. and Akkas, N., “Two dimensional dynamic modelling of human knee joint,” J. Biomech. 16 (4), 253–264 (1983).CrossRefGoogle ScholarPubMed
20. Ling, Z., Guo, H. and Boersma, S., “Analytical study on the kinematic and dynamic behaviours of a knee joint,” Med. Eng. Phys. 19 (1), 29–36 (1997).CrossRefGoogle Scholar
21. McLean, S., Su, A. and Van Den Bogert, J., “Development and validation of a 3d model to predict knee joint loading during dynamic movement,” J. Biomech. Eng. 125 (6), 864–874 (2003).CrossRefGoogle ScholarPubMed
22. Abdel-Rahman, E. and Hefzy, M., “Three dimensional dynamic behaviour of the human knee joint under impact loading,” Med. Eng. Phys. 20 (4), 276–290 (1998).CrossRefGoogle ScholarPubMed
23. Damsgaard, M., Rasmussen, J., Christensen, S., Surma, E. and Zee, M., “Analysis of musculoskeletal systems in the anybody modeling system,” Simulat. Model. Pract. Theor. 14 (8), 1100–1111 (2006).CrossRefGoogle Scholar
24. Delp, S. and Loan, J., “A graphics based software system to develop and analyze models of musculoskeletal structures,” Comput. Biol. Med. 25 (1), 21–34 (1995).CrossRefGoogle ScholarPubMed
25. Delp, S. and Loan, J., “A computational framework for simulating and analyzing human and animal movement,” Comput. Sci. Eng. 2, 46–55 (2000).CrossRefGoogle Scholar
26. Lifemodeller (2008). LifeMOD™. Retrieved August 20th, 2008, from http://www.lifemodeler.comGoogle Scholar
27. Chao, E., “Graphic based musculoskeletal model for biomechanical analyses and animation,” Med. Eng. Phys. 25 (3), 201–212 (2003).CrossRefGoogle ScholarPubMed
28. MSCSoftware (2008). ADAMS. Retrieved August 20th, 2008, from http://www.mscsoftware.comGoogle Scholar
29. Lin, H., Nakamura, Y., Su, F., Hashimoto, J., Nobuhara, K. and Chao, E., “Use of Virtual, Interactive, Musculoskeletal System (VIMS) in modeling and analysis of shoulder throwing activity,” J. Biomech. Eng. 127, 525–530 (2005).CrossRefGoogle ScholarPubMed
30. Davoodi, R. and Loeb, G., “A software toll for faster development of complex models of musculoskeletal systems and sensorimotor controllers in simulink,” J. Appl. Biomech. 18, 357–365 (2002).CrossRefGoogle Scholar
31. Anybody Technology (2006). The AnyBody Modeling System™, Trial Version. Retrieved December 10th, 2006, from http://www.anybodytech.comGoogle Scholar
32. Brouwer, I., Mora, V. and Laroche, D., “A viscoelastic soft tissue model for haptic surgical simulation,” EuroHaptics Conference and Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems, Tsukuba, Japan (2007).Google Scholar
33. Atkinson, T., Haut, R. and Altiero, N., “A poroelastic model that predicts some phenomenological responses of ligaments and tendons,” J. Biomech. Eng. 119 (4), 400–405 (1997).CrossRefGoogle ScholarPubMed
34. Mow, V., Kuei, S., Lai, W. and Amstrong, C., “Biphasic creep and stress relaxation of articular cartilage in compression, theory and experiments,” J. Biomech. Eng. 102 (1) 73–84 (1980).CrossRefGoogle Scholar
35. Drapaca, C., Sivaloganathan, S. and Tenti, G., “Nonlinear constitutive laws in viscoelasticity,” Math. Mech. Solid 12, 475–501 (2007).CrossRefGoogle Scholar
36. Viidik, A. and Ekholm, R., “Light and electron microscopic studies of collagen fibers under strain,” Anat. Embryol. 127 (2), 154–164 (1968).Google Scholar
37. Fung, Y., Biomechanics: Mechanical Properties of Living Tissues, 2nd ed. (Springer-Verlag, New York, 1993).CrossRefGoogle Scholar
38. Ogden, R., Non-Linear Elastic Deformations (Ellis Horwood, New York, 1984).Google Scholar
39. Funk, J., Hall, G., Crandall, J. and Pilkey, W., “Linear and quasi-linear viscoelastic characterization of ankle ligaments,” J. Biomech. Eng. 122, 15–22 (2000).CrossRefGoogle ScholarPubMed
40. Cowin, S. and Doty, S., Tissue Mechanics, 2nd ed. (Springer, New York, 2007).CrossRefGoogle Scholar
41. Weiss, J. and Gardiner, J., “Computational modeling of ligament mechanics,” Clin. Rev. Biomed. Eng. 29 (4), 1–70 (2001).Google ScholarPubMed
42. Loocke, M., Lyons, C. and Simms, C., “Viscoelastic properties of passive skeletal muscle in compression: Stress-relaxation behaviour and constitutive modelling,” J. Biomech. 41, 1555–1565 (2008).CrossRefGoogle ScholarPubMed
43. Hill, A., “The heat of shortening and the dynamic constants of muscle,” Proc. Roy. Soc. Lond. Ser. B, Biol. Sci. 126 (843), 136–195 (1938).Google Scholar
44. Blum, E., Haun, C. and Ryan, J., “A musculo-skeletal model of rat ankle motion and its experimental test on rat,” J. Biomech. 40 (4), 891–899 (2007).CrossRefGoogle ScholarPubMed
45. Winters, J. and Wang, Y., “Integrating hill-based and neuro-fuzzy adaptive models to estimate history-dependent muscle mechanical behaviour,” 5th World Congress of Biomechanics 39 (1) (2006) p. S41.CrossRefGoogle Scholar
46. Zajac, F., Topp, E. and Stevenson, P., “A dimensionless musculotendon model,” 8th Annual Conference IEEE Engineering in Medicine and Biology Society (1986) pp. 601–604.Google Scholar
47. Huxley, H., “The mechanism of muscular contraction,” Science 164 (3886), 1356–1366 (1969).CrossRefGoogle ScholarPubMed
48. Krogt, M., Doorenbosch, C. and Harlaar, J., “Muscle length and lengthening velocity in voluntary crouch gait,” Gait Posture 26 (4), 532–538 (2007).CrossRefGoogle ScholarPubMed
49. Pandy, M., “Moment arm of a muscle force,” Exerc. Sport Sci. Rev. 27, 79–118 (1999).CrossRefGoogle ScholarPubMed
50. An, K., Takahashi, K., Harrigan, T. and Chao, E., “Determination of muscle orientations and moment arms,” J. Biomech. Eng. 106 (3), 280–282 (1984).CrossRefGoogle ScholarPubMed
51. Marai, G., Laidlaw, D., Demiralp, D., Andrews, C., Grimm, C. and Crisco, J., “Estimating joint contact areas and ligament lengths from bone kinematics and surfaces,” IEEE Trans. Biomed. Eng. 51 (5), 790–799 (2003).CrossRefGoogle Scholar
52. Marai, G., Data driven predictive modeling of diarthrodial joints, Ph.D. Thesis (Brown University, 2007).Google Scholar
53. Buford, W. Jr., Andersen, C., Elder, K. and Patterson, R., “Verification of spline-path muscle models for a 3D simulation of the extremities,” Proceedings ISB, Zurich (2001) p. 206.Google Scholar
54. Spoor, C., van Leeuwen, J., Meskers, C., Titulaer, A. and Huson, A., “Estimation of instantaneous moment arms of lower-leg muscles,” J. Biomech. 23 (12), 1247–1259 (1990).CrossRefGoogle ScholarPubMed
55. Murray, W., Arnold, A., Salinas, S., Durbhakula, M., Buchanan, T. and Delp, S., “Building biomechanical models based on medical image data: An assessment of model accuracy,” Book Chapter-Medical Image Computing and Computer-Assisted Intervention – MICCAI 1496 (1998) pp. 539–549.Google Scholar
56. An, K., Hui, F., Morrey, B., Linscheid, R. and Chao, E., “Muscles across the elbow joint: A biomechanical analysis,” J. Biomech. 14 (10), 659–669 (1981).CrossRefGoogle ScholarPubMed
57. Jensen, R. and Davy, D., “An investigation of muscle lines of action about the hip: A centroid line approach vs the straight line approach,” J. Biomech. 8 (2) 103–110 (1975).CrossRefGoogle ScholarPubMed
58. Murray, W., Buchanan, T. and Delp, S., “Scaling of peak moment arms of elbow muscles with upper extremity bone dimensions,” J. Biomech. 35 (1) 19–26 (2002).CrossRefGoogle ScholarPubMed
59. Buford, W. and Anderson, C., “Predicting moment arms in diarthroidal joints-3D computer simulation capability and muscle-tendon model validation,” Proceedings of the 28th IEEE EMBS Annual International Conference, New York, USA (2006).Google Scholar
60. Garner, B. and Pandy, M., “The obstacle set method for representing muscle path in musculoskeletal models,” Comput. Meth. Biomech. Biomed. Eng. 3 (1), 1–30 (2000).CrossRefGoogle ScholarPubMed
61. Carman, A. and Milburn, P., “Dynamic coordinate data for describing muscle–tendon paths: A mathematical approach,” J. Biomech. 38 (4), 943–951 (2005).CrossRefGoogle ScholarPubMed
62. Charlton, I. and Johnson, G., “Application of spherical and cylindrical wrapping algorithm in a musculoskeletal model of the upper limb,” J. Biomech. 34 (9) 1209–1216 (2001).CrossRefGoogle Scholar
63. Gao, F., Damsgaard, M., Rasmussen, J. and Christensen, S., “Computational method for muscle-path representation in musculoskeletal models,” Biol. Cybern. 87 (3), 199–210 (2002).CrossRefGoogle ScholarPubMed
64. Audenaert, A. and Audenaert, E., “Global optimization method for combined spherical-cylindrical wrapping in musculoskeletal upper limb modelling,” Comput. Meth. Programs Biomed. 92 (1) 8–19 (2008).CrossRefGoogle ScholarPubMed
65. Marsden, S. and Swailes, D., “A novel approach to the prediction of musculotendon paths,” J. Eng. Med. 222 (1), 51–61 (2008).CrossRefGoogle Scholar
66. Gatti, C., Dickerson, C., Chadwick, E., Mell, A. and Hughes, R., “Comparison of model predicted and measured moment arms for the rotator cuff muscles,” Clin. Biomech. 22 (6) 639–644 (2007).CrossRefGoogle ScholarPubMed
67. Lin, M. and Manocha, D., “Collision and proximity queries,” In: Goodman, J. and O'Rourke, J. (Eds.), Handbook of discrete and computational geometry (2nd ed., pp. 787–807). New York: CRC Press (2003).Google Scholar
68. Chung, K. and Wang, W., “Quick collision detection of polytopes in virtual environments,” Proceedings of the ACM Symposium, Virtual Reality Software and Technology, Hong Kong (1996).Google Scholar
69. Cameron, S., “Enhancing GJK: Computing penetration distance between convex polyhedra,” Proceedings of the IEEE International Conference on Robotics and Automation 4 (1997) pp. 3112–3117.CrossRefGoogle Scholar
70. Bajaj, C. and Dey, T., “Convex decomposition of polyhedra and robustness,” SIAM J. Comput. 21 (2), 339–364 (1992).CrossRefGoogle Scholar
71. Lin, M. and Gottschalk, S., “Collision detection between geometric models: A survey,” Proceedings of IMA Conference on Mathematics of Surfaces (1998).Google Scholar
72. Jimenez, P., Thomas, F. and Torras, C., “3D collision detection: A survey,” Comput. Graph. 25 (2), 269–285 (2001).CrossRefGoogle Scholar
73. Gottschalk, S., Lin, M. and Manocha, D., “OBB-tree: A hierarchical structure for rapid interference detection,” 30th Annual Conference Series Computer Graphics (30) (1996) pp. 171–180.Google Scholar
74. GAMMA (2008). Geometric Algorithms for Modeling, Motion, and Animation/Software and Models. Retrieved March 1st, 2008, from http://gamma.cs.unc.eduGoogle Scholar
75. Pfeiffer, F. and Glocker, C., Multibody Dynamics with Unilateral Contacts (Wiley Series in Nonlinear Science) (Wiley, New York, 1996).CrossRefGoogle Scholar
76. Drumwright, E., “Fast and stable penalty method for rigid simulation,” IEEE Trans. Vis. Comput. Graph. 14 (1), 231–240 (2008).CrossRefGoogle ScholarPubMed
77. Ferris, M., Mangasarian, O. and Pang, J., “Complementarity: Applications, algorithms and extensions,” Kluwer Academic Publishers, Netherlands (2001).Google Scholar
78. Trinkle, J., “Formulation of multibody dynamics as complementarity problems,” ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Chicago, Illinois (2003).Google Scholar
79. Pang, J. and Trinkle, J., “Complementarity formalisms and existence of solutions of dynamic multi-rigid contact problems with coulomb friction,” Math. Programming 73, 199–226 (1996).CrossRefGoogle Scholar
80. Duriez, C., Andriot, C. and Kheddar, A., “Signorini's contact model for deformable objects in haptic simulations,” IEEE/RSJ International Conferences on Intelligent Robotics and Systems, Sendai, Japan (2004).Google Scholar
81. Berrenberg, S. and Krause, R., “Efficient parallel simulation of biphasic materials in biomechanics,” 6th International Congress on Industrial Applied Mathematics (ICIAM07) and GAMM Annual Meeting, Zurich 7 (1), 1121101–1121102 (2007).Google Scholar
82. Bei, Y. and Fregly, B., “Multibody dynamic simulation of knee contact mechanics,” Med. Eng. Phys. 26 (9), 777–789 (2004).CrossRefGoogle ScholarPubMed
83. Han, S., Federico, S., Epstein, M. and Herzog, W., “An articular cartilage contact model based on real surface geometry,” J. Biomech. 38, 179–184 (2005).CrossRefGoogle ScholarPubMed
84. Lenarcic, J. and Klopcar, N., “Positional kinematics of humanoid arms,” Robotica 24, 105–112 (2006).CrossRefGoogle Scholar
85. Garner, B. and Pandy, M., “Estimation of musculotendon properties in the human upper limb,” Annu. Biomed. Eng. 31, 207–220 (2003).CrossRefGoogle ScholarPubMed
86. Holzbaur, K., Murray, W. and Delp, S., “A model of the upper extremity for simulating musculoskeletal surgery and analysing neuromuscular control,” Annu. Biomed. Eng. 33 (6), 829–840 (2005).CrossRefGoogle Scholar
87. Langenderfer, J., Jerabek, S., Thangamani, V., Kuhn, J. and Hughes, R., “Musculoskeletal parameters of muscles crossing the shoulder and elbow and the effect of sarcomere length sample size on estimation of optimal muscle length,” Clin. Biomech. 19, 664–670 (2004).CrossRefGoogle ScholarPubMed
88. Butler, D., Grood, E. and Noyes, F., “Biomechanics of ligaments and tendons,” Exerc. Sport Sci. Rev. 6, 125–181 (1978).Google ScholarPubMed
89. Mihelj, M., “Human arm kinematics for robot based rehabilitation,” Robotica 24, 377–383 (2006).CrossRefGoogle Scholar