Skip to main content
SpringerLink
Log in

Discrete element method simulator for joint dynamics: a case study using a red-tailed hawk’s hallux digit

  • Published:
Multibody System Dynamics Aims and scope Submit manuscript

  • 1 Altmetric

Abstract

A discrete element method simulator is developed, which models all of the components (bones, tendons, and ligaments) as discrete elements. This simulator is then used to simulate the dynamics of a raptor’s hallux digit as a case study. The biomechanical linkage is constructed from computerized tomography (CT) scans of bones. The ligaments and tendons are attached to the anatomical landmarks of the bones. This model approximates the multibody dynamics of a biomechanical linkage without making kinematic assumptions on the bones’ movements in relationship to each other. The nonlinear dynamics resulting from the bones’ geometric shape and the complex distribution of forces from the soft tissue is approximated with this discrete element method simulation approach. A dynamic simulation of a hallux digit is shown, and the force distribution within the joint is also provided at different points in time. This discrete element method simulator for joint dynamics relies on few assumptions and could be readily applied to more complex biomechanical linkages. This novel method for the dynamic simulation of biomechanical linkages is very general and flexible. Since the dynamics of biomechanical linkages relies on contacting features, these systems exhibit small-scale phenomena. For this reason, the discrete element method is computationally favorable when compared to finite element methods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  1. Abraham, C.L., Maas, S.A., Weiss, J.A., Ellis, B.J., Peters, C.L., Anderson, A.E.: A new discrete element analysis method for predicting hip joint contact stresses. J. Biomech. 46(6), 1121–1127 (2013)

    Article  Google Scholar 

  2. Anderson, F.C., Pandy, M.G.: Dynamic optimization of human walking. J. Biomech. Eng. 123(5), 381–390 (2001)

    Article  Google Scholar 

  3. Anderson, D.D., Goldsworthy, J.K., Shivanna, K., Grosland, N.M., Pedersen, D.R., Thomas, T.P., Tochigi, Y., Marsh, J.L., Brown, T.D.: Intra-articular contact stress distributions at the ankle throughout stance phase–patient-specific finite element analysis as a metric of degeneration propensity. Biomech. Model. Mechanobiol. 5(2), 82–89 (2006)

    Article  Google Scholar 

  4. Anderson, A.E., Ellis, B.J., Maas, S.A., Peters, C.L., Weiss, J.A.: Validation of finite element predictions of cartilage contact pressure in the human hip joint. J. Biomech. Eng. 130(5), 051008 (2008)

    Article  Google Scholar 

  5. Arnold, A.S., Salinas, S., Hakawa, D.J., Delp, S.L.: Accuracy of muscle moment arms estimated from MRI-based musculoskeletal models of the lower extremity. Comput. Aided Surg. 5(2), 108–119 (2000)

    Article  Google Scholar 

  6. Backus, S.B., Sustaita, D., Odhner, L.U., Dollar, A.M.: Mechanical analysis of avian feet: multiarticular muscles in grasping and perching. R. Soc. Open Sci. 2(2), 140350 (2015)

    Article  Google Scholar 

  7. Bélaise, C., Blache, Y., Thouzé, A., Monnet, T., Begon, M.: Effect of wobbling mass modeling on joint dynamics during human movements with impacts. Multibody Syst. Dyn. 38(4), 345–366 (2016)

    Article  Google Scholar 

  8. Benemerito, I., Modenese, L., Montefiori, E., Mazza, C., Viceconti, M., Lacroix, D., Guo, L.: An extended discrete element method for the estimation of contact pressure at the ankle joint during stance phase. Proc. Inst. Mech. Eng., H J. Eng. Med. 234(5), 507–516 (2020)

    Article  Google Scholar 

  9. Chao, E., Inoue, N., Elias, J.J., Frassica, F.J.: Image-based computational biomechanics of the musculoskeletal system. In: Handbook of Medical Imaging, Processing and Analysis, pp. 285–298. Academic, San Diego (2000)

    Chapter  Google Scholar 

  10. Charles, J.P., Cappellari, O., Hutchinson, J.R.: A dynamic simulation of musculoskeletal function in the mouse hindlimb during trotting locomotion. Front. Bioeng. Biotechnol. 6, 61 (2018)

    Article  Google Scholar 

  11. Chitsazan, A., Rouhi, G., Abbasi, M., Pezeshki, S., Tavakoli, S.A.H.: Assessment of stress distribution in ankle joint: simultaneous application of experimental and finite element methods. Int. J. Exp. Comput. Biomech. 3(1), 45–61 (2015)

    Article  Google Scholar 

  12. Cignoni, P., Callieri, M., Corsini, M., Dellepiane, M., Ganovelli, F., Ranzuglia, G.: MeshLab: an open-source mesh processing tool. In: Scarano, V., Chiara, R.D., Erra, U. (eds.) Eurographics Italian Chapter Conference. The Eurographics Association, Salerno, Italy (2008). https://doi.org/10.2312/LocalChapterEvents/ItalChap/ItalianChapConf2008/129-136

    Chapter  Google Scholar 

  13. Cundall, P.A., Strack, O.D.: A discrete numerical model for granular assemblies. Geotechnique 29(1), 47–65 (1979)

    Article  Google Scholar 

  14. Delp, S.L., Anderson, F.C., Arnold, A.S., Loan, P., Habib, A., John, C.T., Guendelman, E., Thelen, D.G.: Opensim: open-source software to create and analyze dynamic simulations of movement. IEEE Trans. Biomed. Eng. 54(11), 1940–1950 (2007)

    Article  Google Scholar 

  15. Dhaher, Y.Y., Kahn, L.E.: The effect of vastus medialis forces on patello-femoral contact: a model-based study. J. Biomech. Eng. 124(6), 758–767 (2002)

    Article  Google Scholar 

  16. Doyle, C.E., Bird, J.J., Isom, T.A., Kallman, J.C., Bareiss, D.F., Dunlop, D.J., King, R.J., Abbott, J.J., Minor, M.A.: An avian-inspired passive mechanism for quadrotor perching. IEEE/ASME Trans. Mechatron. 18(2), 506–517 (2012)

    Article  Google Scholar 

  17. Galton, P.M., Shepherd, J.D.: Experimental analysis of perching in the European starling (Sturnus vulgaris: Passeriformes; Passeres), and the automatic perching mechanism of birds. J. Exp. Zool. Part A: Ecol. Genet. Physiol. 317(4), 205–215 (2012)

    Article  Google Scholar 

  18. Goslow, G.E.: The attack and strike of some North American raptors. The Auk 88(4), 815–827 (1971)

    Article  Google Scholar 

  19. Goslow, G.E.: Adaptive mechanisms of the raptor pelvic limb. The Auk 89(1), 47–64 (1972)

    Article  Google Scholar 

  20. Guo, J., Huang, H., Yu, Y., Liang, Z., Ambrósio, J., Zhao, Z., Ren, G., Ao, Y.: Modeling muscle wrapping and mass flow using a mass-variable multibody formulation. Multibody Syst. Dyn. 49(3), 315–336 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  21. Hainisch, R., Gfoehler, M., Zubayer-Ul-Karim, M., Pandy, M.G.: Method for determining musculotendon parameters in subject-specific musculoskeletal models of children developed from MRI data. Multibody Syst. Dyn. 28(1), 143–156 (2012)

    Article  Google Scholar 

  22. Harris, M.D., Anderson, A.E., Henak, C.R., Ellis, B.J., Peters, C.L., Weiss, J.A.: Finite element prediction of cartilage contact stresses in normal human hips. J. Orthop. Res. 30(7), 1133–1139 (2012)

    Article  Google Scholar 

  23. Haut Donahue, T.L., Hull, M., Rashid, M.M., Jacobs, C.R.: A finite element model of the human knee joint for the study of tibio-femoral contact. J. Biomech. Eng. 124(3), 273–280 (2002)

    Article  Google Scholar 

  24. Heers, A.M., Rankin, J.W., Hutchinson, J.R.: Building a bird: musculoskeletal modeling and simulation of wing-assisted incline running during avian ontogeny. Front. Bioeng. Biotechnol. 6, 140 (2018)

    Article  Google Scholar 

  25. Henak, C.R., Ateshian, G.A., Weiss, J.A.: Finite element prediction of transchondral stress and strain in the human hip. J. Biomech. Eng. 136(2), 021021 (2014)

    Article  Google Scholar 

  26. Jin, C., Olsen, B.C., Luber, E.J., Buriak, J.M.: van der Waals epitaxy of soft twisted bilayers: lattice relaxation and mass density waves. ACS Nano 14(10), 13441–13450 (2020)

    Article  Google Scholar 

  27. Kern, A.M., Anderson, D.D.: Expedited patient-specific assessment of contact stress exposure in the ankle joint following definitive articular fracture reduction. J. Biomech. 48(12), 3427–3432 (2015)

    Article  Google Scholar 

  28. Kessens, C.C., Horowitz, M., Liu, C., Dotterweich, J., Yim, M., Edge, H.L.: Toward lateral aerial grasping & manipulation using scalable suction. In: 2019 International Conference on Robotics and Automation (ICRA), pp. 4181–4186. IEEE, Montreal, Canada (2019)

    Chapter  Google Scholar 

  29. Malone, K.F., Xu, B.H.: Determination of contact parameters for discrete element method simulations of granular systems. Particuology 6(6), 521–528 (2008)

    Article  Google Scholar 

  30. Marieswaran, M., Sikidar, A., Goel, A., Joshi, D., Kalyanasundaram, D.: An extended OpenSim knee model for analysis of strains of connective tissues. Biomed. Eng. Online 17(1), 1–13 (2018)

    Article  Google Scholar 

  31. Mishra, B., Rajamani, R.K.: The discrete element method for the simulation of ball mills. Appl. Math. Model. 16(11), 598–604 (1992)

    Article  MATH  Google Scholar 

  32. Modenese, L., Phillips, A.T.: Prediction of hip contact forces and muscle activations during walking at different speeds. Multibody Syst. Dyn. 28(1), 157–168 (2012)

    Article  Google Scholar 

  33. Moissenet, F., Cheze, L., Dumas, R.: Individual muscle contributions to ground reaction and to joint contact, ligament and bone forces during normal gait. Multibody Syst. Dyn. 40(2), 193–211 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  34. Moitra, A., Chabalko, C., Balachandran, B.: Studies of extreme energy localizations with smoothed particle hydrodynamics. In: International Conference on Offshore Mechanics and Arctic Engineering, vol. 56550, p. V007T06A080. American Society of Mechanical Engineers, St. John’s, Newfoundland, Canada (2015)

    Google Scholar 

  35. Morales-Orcajo, E., Souza, T.R., Bayod, J., de Las Casas, E.B.: Non-linear finite element model to assess the effect of tendon forces on the foot-ankle complex. Med. Eng. Phys. 49, 71–78 (2017)

    Article  Google Scholar 

  36. Nelson, A.J., Hall, P.T., Saul, K.R., Crouch, D.L.: Effect of mechanically passive, wearable shoulder exoskeletons on muscle output during dynamic upper extremity movements: a computational simulation study. J. Appl. Biomech. 36(2), 59–67 (2020)

    Article  Google Scholar 

  37. Popek, K.M., Johannes, M.S., Wolfe, K.C., Hegeman, R.A., Hatch, J.M., Moore, J.L., Katyal, K.D., Yeh, B.Y., Bamberger, R.J.: Autonomous grasping robotic aerial system for perching (AGRASP). In: 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 1–9. IEEE, Madrid, Spain (2018)

    Google Scholar 

  38. Quinn, T.H., Baumel, J.J.: The digital tendon locking mechanism of the avian foot (Aves). Zoomorphology 109(5), 281–293 (1990)

    Article  Google Scholar 

  39. Renani, M.S., Rahman, M., Cil, A., Stylianou, A.P.: Calibrating multibody ulno-humeral joint cartilage using a validated finite element model. Multibody Syst. Dyn. 44(1), 81–91 (2018)

    Article  Google Scholar 

  40. Ribeiro, A., Rasmussen, J., Flores, P., Silva, L.F.: Modeling of the condyle elements within a biomechanical knee model. Multibody Syst. Dyn. 28(1), 181–197 (2012)

    Article  MathSciNet  Google Scholar 

  41. Richardson, F.: Adaptive Modifications for Tree-Trunk Foraging in Birds, vol. 44. University of California Press, Berkeley (1942)

    Google Scholar 

  42. Roux, A., Laporte, S., Lecompte, J., Gras, L.L., Iordanoff, I.: Influence of muscle–tendon complex geometrical parameters on modeling passive stretch behavior with the discrete element method. J. Biomech. 49(2), 252–258 (2016)

    Article  Google Scholar 

  43. Sachdeva, P., Sueda, S., Bradley, S., Fain, M., Pai, D.K.: Biomechanical simulation and control of hands and tendinous systems. ACM Trans. Graph. 34(4), 1–10 (2015)

    Article  MATH  Google Scholar 

  44. Schmitz, A., Piovesan, D.: Development of an open-source, discrete element knee model. IEEE Trans. Biomed. Eng. 63(10), 2056–2067 (2016)

    Article  Google Scholar 

  45. Seth, A., Sherman, M., Reinbolt, J.A., Delp, S.L.: OpenSim: a musculoskeletal modeling and simulation framework for in silico investigations and exchange. Proc. IUTAM 2, 212–232 (2011)

    Article  Google Scholar 

  46. Shelburne, K.B., Torry, M.R., Pandy, M.G.: Effect of muscle compensation on knee instability during ACL-deficient gait. Med. Sci. Sports Exerc. 37(4), 642–648 (2005)

    Article  Google Scholar 

  47. Sikidar, A., Marieswaran, M., Kalyanasundaram, D.: Estimation of forces on anterior cruciate ligament in dynamic activities. Biomech. Model. Mechanobiol. 20(4), 1533–1546 (2021)

    Article  Google Scholar 

  48. Townsend, K.C., Thomas-Aitken, H.D., Rudert, M.J., Kern, A.M., Willey, M.C., Anderson, D.D., Goetz, J.E.: Discrete element analysis is a valid method for computing joint contact stress in the hip before and after acetabular fracture. J. Biomech. 67, 9–17 (2018)

    Article  Google Scholar 

  49. Van Houcke, J., Audenaert, E.A., Atkins, P.R., Anderson, A.E.: A combined geometric morphometric and discrete element modeling approach for hip cartilage contact mechanics. Front. Bioeng. Biotechnol. 8, 318 (2020)

    Article  Google Scholar 

  50. Volokh, K., Chao, E., Armand, M.: On foundations of discrete element analysis of contact in diarthrodial joints. Mol. Cell. Biomech. 4(2), 67 (2007)

    Google Scholar 

  51. Ward, A.B., Weigl, P.D., Conroy, R.M.: Functional morphology of raptor hindlimbs: implications for resource partitioning. The Auk 119(4), 1052–1063 (2002)

    Article  Google Scholar 

  52. Yoshida, H., Faust, A., Wilckens, J., Kitagawa, M., Fetto, J., Chao, E.Y.S.: Three-dimensional dynamic hip contact area and pressure distribution during activities of daily living. J. Biomech. 39(11), 1996–2004 (2006)

    Article  Google Scholar 

Download references

Acknowledgements

Partial support for this project from DARPA’s Young Faculty Award is greatly appreciated. Research was sponsored by the Army Research Office and was accomplished under Grant Number W911NF-20-1-0336. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Office or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.

Author information

Authors and Affiliations

  1. LAB2701, Mechanical & Aerospace Engineering Department, North Carolina State University, Raleigh, NC, 27695, USA

    Tushar Mollik, Scott Kennedy, Md Raf E Ul Shougat, XiaoFu Li & Edmon Perkins

  2. Mechanical & Aerospace Engineering Department, North Carolina State University, Raleigh, NC, 27695, USA

    Larry Silverberg

  3. Mechanical Engineering Department, Gonzaga University, Spokane, WA, 99258, USA

    Timothy Fitzgerald

  4. Scarlet Imaging, Murray, UT, 84157, USA

    Scott Echols & Nick Kirk

Authors
  1. Tushar Mollik
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Scott Kennedy
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Md Raf E Ul Shougat
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. XiaoFu Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Timothy Fitzgerald
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Scott Echols
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Nick Kirk
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Larry Silverberg
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Edmon Perkins
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tushar Mollik.

Ethics declarations

Conflict of Interest

The authors have no conflicts of interest to declare that are relevant to the content of this article.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mollik, T., Kennedy, S., Shougat, M.R.E.U. et al. Discrete element method simulator for joint dynamics: a case study using a red-tailed hawk’s hallux digit. Multibody Syst Dyn 55, 453–473 (2022). https://doi.org/10.1007/s11044-022-09828-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11044-022-09828-x

Keywords

Search

Navigation