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Passive Stiffness of Coupled Wrist and Forearm Rotations

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Abstract

Coordinated movement requires that the neuromuscular system account and compensate for movement dynamics. One particularly complex aspect of movement dynamics is the interaction that occurs between degrees of freedom (DOF), which may be caused by inertia, damping, and/or stiffness. During wrist rotations, the two DOF of the wrist (flexion–extension and radial–ulnar deviation, FE and RUD) are coupled through interaction torques arising from passive joint stiffness. One important unanswered question is whether the DOF of the forearm (pronation–supination, PS) is coupled to the two DOF of the wrist. Answering this question, and understanding the dynamics of wrist and forearm rotations in general, requires knowledge of the stiffness encountered during rotations involving all three DOF (PS, FE, and RUD). Here we present the first-ever measurement of the passive stiffness encountered during simultaneous wrist and forearm rotations. Using a wrist and forearm robot, we measured coupled wrist and forearm stiffness in 10 subjects and present it as a 3-by-3 stiffness matrix. This measurement of passive wrist and forearm stiffness will enable future studies investigating the dynamics of wrist and forearm rotations, exposing the dynamics for which the neuromuscular system must plan and compensate during movements involving the wrist and forearm.

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Abbreviations

DOF:

Degree(s) of freedom

sEMG:

Surface electromyogram

FE:

Flexion–extension of the wrist

MVC:

Maximum voluntary contraction

PS:

Pronation–supination of the forearm

RUD:

Radial–ulnar deviation of the wrist

References

  1. An, K.-N., R. A. Berger, and W. P. I. Cooney (eds.). Biomechanics of the Wrist Joint. New York: Springer, p. 42, 1991.

    Google Scholar 

  2. Anderton, W. and S. Charles. Kinematic coupling of wrist and forearm movements. In: Annual Meeting of the American Society of Biomechanics, Gainesville, FL, 2012.

  3. Axelson, H. W., and K. E. Hagbarth. Human motor control consequences of thixotropic changes in muscular short-range stiffness. J. Physiol. Lond. 535(1):279–288, 2001.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  4. Berens, P. CircStat: a MATLAB toolbox for circular statistics. J. Stat. Softw. 31(10):1–21, 2009.

    Google Scholar 

  5. Campbell, K. S. Short-range mechanical properties of skeletal and cardiac muscles. In: Muscle Biophysics: From Molecules to Cells, edited by D. E. Rassier. New York: Springer, 2010, pp. 223–246.

    Chapter  Google Scholar 

  6. Celestino, J. Characterization and control of a robot for wrist rehabilitation. MS, Massachusetts Institute of Technology, 2003, p. 128.

  7. Charles, S. K., and N. Hogan. The curvature and variability of wrist and arm movements. Exp. Brain Res. 203(1):63–73, 2010.

    Article  PubMed  Google Scholar 

  8. Charles, S. K., and N. Hogan. Dynamics of wrist rotations. J. Biomech. 44(4):614–621, 2011.

    Article  PubMed  Google Scholar 

  9. Charles, S. K., and N. Hogan. Stiffness, not inertial coupling, determines path curvature of wrist motions. J. Neurophysiol. 107:1230–1240, 2012.

    Article  PubMed  Google Scholar 

  10. de Leva, P. Adjustments to Zatsiorsky–Seluyanov’s segment inertia parameters. J. Biomech. 29(9):1223–1230, 1996.

    Article  PubMed  Google Scholar 

  11. de Rugy, A., R. Davoodi, and T. J. Carroll. Changes in wrist muscle activity with forearm posture: implications for the study of sensorimotor transformations. J. Neurophysiol. 108(11):2884–2895, 2012.

    Article  PubMed  Google Scholar 

  12. De Serres, S. J., and T. E. Milner. Wrist muscle activation patterns and stiffness associated with stable and unstable mechanical loads. Exp. Brain Res. 86:451–458, 1991.

    Article  PubMed  Google Scholar 

  13. Dolan, J. M., M. B. Friedman, and M. L. Nagurka. Dynamic and loaded impedance components in the maintenance of human arm posture. IEEE Trans. Syst. Man Cybern. 23(3):698–709, 1993.

    Article  Google Scholar 

  14. Formica, D., S. K. Charles, L. Zollo, E. Guglielmelli, N. Hogan, and H. I. Krebs. The passive stiffness of the wrist and forearm. J. Neurophysiol. 108:1158–1166, 2012.

    Article  PubMed Central  PubMed  Google Scholar 

  15. Fung, Y. Biomechanics: Mechanical Properties of Living Tissues. New York: Springer, 1993.

    Book  Google Scholar 

  16. Gehrmann, S. V., R. A. Kaufmann, and Z. M. Li. Wrist circumduction reduced by finger constraints. J. Hand Surg. Am. 33(8):1287–1292, 2008.

    Article  PubMed  Google Scholar 

  17. Gielen, C., and J. C. Houk. Nonlinear viscosity of human wrist. J. Neurophysiol. 52(3):553–569, 1984.

    CAS  PubMed  Google Scholar 

  18. Given, J. D., J. P. A. Dewald, and W. Z. Rymer. Joint dependent passive stiffness in paretic and contralateral limbs of spastic patients with hemiparetic stroke. J. Neurol. Neurosurg. Psychiatry 59(3):271–279, 1995.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  19. Hogan, N. The mechanics of multi-joint posture and movement control. Biol. Cybern. 52:315–331, 1985.

    Article  CAS  PubMed  Google Scholar 

  20. Hollerbach, J. M., and T. Flash. Dynamic interactions between limb segments during planar arm movement. Biol. Cybern. 44(1):67–77, 1982.

    Article  CAS  PubMed  Google Scholar 

  21. Ives, J. C., and J. K. Wigglesworth. Sampling rate effects on surface EMG timing and amplitude measures. Clin. Biomech. 18(6):543–552, 2003.

    Article  Google Scholar 

  22. Krebs, H., B. T. Volpe, D. Williams, J. Celestino, S. Charles, D. Lynch, and N. Hogan. Robot-aided neurorehabilitation: a robot for the wrist rehabilitation. IEEE Trans. Neural Syst. Rehabil. Eng. 15(3):327–335, 2007.

    Article  PubMed Central  PubMed  Google Scholar 

  23. Lariviere, C., A. Delisle, and A. Plamondon. The effect of sampling frequency on EMG measures of occupational mechanical exposure. J. Electromyogr. Kinesiol. 15(2):200–209, 2005.

    Article  PubMed  Google Scholar 

  24. Leger, A. B., and T. E. Milner. Passive and active wrist joint stiffness following eccentric exercise. Eur. J. Appl. Physiol. 82(5–6):472–479, 2000.

    Article  CAS  PubMed  Google Scholar 

  25. Lehman, S. L., and B. M. Calhoun. An identified model for human wrist movements. Exp. Brain Res. 81(1):199–208, 1990.

    Article  CAS  PubMed  Google Scholar 

  26. Mussa-Ivaldi, F. A., N. Hogan, and E. Bizzi. Neural, mechanical, and geometric factors subserving arm posture in humans. J. Neurosci. 5(10):2732–2743, 1985.

    CAS  PubMed  Google Scholar 

  27. Ochi, E., K. Nakazato, and N. Ishii. Effects of eccentric exercise on joint stiffness and muscle connectin (titin) isoform in the rat hindlimb. J. Physiol. Sci. 57(1):1–6, 2007.

    Article  CAS  PubMed  Google Scholar 

  28. Rijnveld, N. and H. I. Krebs. Passive wrist joint impedance in flexion–extension and abduction-adduction. In: International Conference on Rehabilitation Robotics, Noordwijk, Netherlands, 2007.

  29. Whitehead, N. P., D. L. Morgan, J. E. Gregory, and U. Proske. Rises in whole muscle passive tension of mammalian muscle after eccentric contractions at different lengths. J. Appl. Physiol. 95(3):1224–1234, 2003.

    CAS  PubMed  Google Scholar 

  30. Whitehead, N. P., N. S. Weerakkody, J. E. Gregory, D. L. Morgan, and U. Proske. Changes in passive tension of muscle in humans and animals after eccentric exercise. J. Physiol. 533(Pt 2):593–604, 2001.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  31. Williams, D. A Robot for Wrist Rehabilitation. MS, Massachusetts Institute of Technology, 2001, p. 59–62.

  32. Wu, G., F. C. T. van der Helm, H. E. J. Veeger, M. Makhsous, P. Van Roy, C. Anglin, J. Nagels, A. R. Karduna, K. McQuade, X. G. Wang, F. W. Werner, and B. Buchholz. ISB recommendation on definitions of joint coordinate systems of various joints for the reporting of human joint motion—Part II: shoulder, elbow, wrist and hand. J. Biomech. 38(5):981–992, 2005.

    Article  CAS  PubMed  Google Scholar 

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Acknowledgments

We’d like to thank Dr. Dennis Eggett (BYU Statistical Consulting Center) for technical assistance with the statistical analysis.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Brigham Young University, Provo, UT, 84602, USA

    Will B. Drake

  2. Department of Mechanical Engineering and Neuroscience Center, Brigham Young University, 435 CTB, Provo, UT, 84602, USA

    Steven K. Charles

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  1. Will B. Drake
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  2. Steven K. Charles
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Correspondence to Steven K. Charles.

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Associate Editor Michael R. Torry oversaw the review of this article.

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Drake, W.B., Charles, S.K. Passive Stiffness of Coupled Wrist and Forearm Rotations. Ann Biomed Eng 42, 1853–1866 (2014). https://doi.org/10.1007/s10439-014-1054-0

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  • DOI: https://doi.org/10.1007/s10439-014-1054-0

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