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Research Papers

Model-Based Analysis of the Stiffness of the Wrist Joint in Active and Passive Conditions

[+] Author and Article Information
Andrea Zonnino

Human Robotics Laboratory,
Department of Biomedical Engineering,
University of Delaware,
Newark, DE 19713
e-mail: zonni@udel.edu

Fabrizio Sergi

Human Robotics Laboratory,
Department of Biomedical Engineering,
University of Delaware,
Newark, DE 19713
e-mail: fabs@udel.edu

1Corresponding author.

Manuscript received March 6, 2018; final manuscript received January 18, 2019; published online February 27, 2019. Assoc. Editor: Beth A. Winkelstein.

J Biomech Eng 141(4), 041006 (Feb 27, 2019) (10 pages) Paper No: BIO-18-1121; doi: 10.1115/1.4042684 History: Received March 06, 2018; Revised January 18, 2019

The control of joint stiffness is a fundamental mechanism used to control human movements. While many studies have observed how stiffness is modulated for tasks involving shoulder and elbow motion, a limited amount of knowledge is available for wrist movements, though the wrist plays a crucial role in manipulation. We have developed a computational framework based on a realistic musculoskeletal model, which allows one to calculate the passive and active components of the wrist joint stiffness. We first used the framework to validate the musculoskeletal model against experimental measurements of the wrist joint stiffness, and then to study the contribution of different muscle groups to the passive joint stiffness. We finally used the framework to study the effect of muscle cocontraction on the active joint stiffness. The results show that thumb and finger muscles play a crucial role in determining the passive wrist joint stiffness: in the neutral posture, the direction of maximum stiffness aligns with the experimental measurements, and the magnitude increases by 113% when they are included. Moreover, the analysis of the controllability of joint stiffness showed that muscle cocontraction positively correlates with the stiffness magnitude and negatively correlates with the variability of the stiffness orientation (p < 0.01 in both cases). Finally, an exhaustive search showed that with appropriate selection of a muscle activation strategy, the joint stiffness orientation can be arbitrarily modulated. This observation suggests the absence of biomechanical constraints on the controllability of the orientation of the wrist joint stiffness.

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References

Rancourt, D. , and Hogan, N. , 2001, “ Dynamics of Pushing,” J. Motor Behav., 33(4), pp. 351–362.
Bastian, A. J. , Martin, T. A. , Keating, J. G. , and Thach, W. T. , 1996, “ Cerebellar Ataxia: Abnormal Control of Interaction Torques Across Multiple Joints,” J. Neurophys., 76(1), pp. 492–509.
Bastian, A. J. , 2006, “ Learning to Predict the Future: The Cerebellum Adapts Feedforward Movement Control,” Curr. Opin. Neurobiol., 16(6), pp. 645–649. [PubMed]
Milner, T. E. , 2002, “ Contribution of Geometry and Joint Stiffness to Mechanical Stability of the Human Arm,” Exp. Brain Res., 143(4), pp. 515–519. [PubMed]
Mussa-Ivaldi, F. A. , Hogan, N. , and Bizzi, E. , 1985, “ Neural, Mechanical, and Geometric Factors Subserving Arm Posture in Humans,” J. Neurosci.: Off. J. Soc. Neurosci., 5(10), pp. 2732–2743.
Trumbower, R. D. , Krutky, M. A. , Yang, B. S. , and Perreault, E. J. , 2009, “ Use of Self-Selected Postures to Regulate Multi-Joint Stiffness During Unconstrained Tasks,” PLoS One, 4(5), p. e5411.
Hogan, N. , 1984, “ Adaptive Control of Mechanical Impedance by Coactivation of Antagonist Muscles,” IEEE Trans. Autom. Control, 29(8), pp. 681–690.
Milner, T. E. , 2002, “ Adaptation to Destabilizing Dynamics by Means of Muscle Cocontraction,” Exp. Brain Res., 143(4), pp. 406–416. [PubMed]
Rack, P. M. , and Westbury, D. R. , 1974, “ The Short Range Stiffness of Active Mammalian Muscle and Its Effect on Mechanical Properties,” J. Physiol., 240(2), pp. 331–350. [PubMed]
Morgan, D. L. , 1977, “ Separation of Active and Passive Components of Short-Range Stiffness of Muscle,” Am. J. Physiol., 232(1), pp. C45–C49. [PubMed]
Formica, D. , Charles, S. K. , Zollo, L. , Guglielmelli, E. , Hogan, N. , and Krebs, H. I. , 2012, “ The Passive Stiffness of the Wrist and Forearm,” J. Neurophysiol., 108(4), pp. 1158–1166. [PubMed]
Pando, A. L. , Lee, H. , Drake, W. B. , Hogan, N. , and Charles, S. K. , 2014, “ Position-Dependent Characterization of Passive Wrist Stiffness,” IEEE Trans. Biomed. Eng., 61(8), pp. 2235–2244. [PubMed]
Lee, H. , Ho, P. , Rastgaar, M. A. , Krebs, H. I. , and Hogan, N. , 2011, “ Multivariable Static Ankle Mechanical Impedance With Relaxed Muscles,” J. Biomech., 44(10), pp. 1901–1908. [PubMed]
Franklin, D. W. , and Milner, T. E. , 2003, “ Adaptive Control of Stiffness to Stabilize Hand Position With Large Loads,” Exp. Brain Res., 152(2), pp. 211–220. [PubMed]
McIntyre, J. , Mussa-Ivaldi, F. , and Bizzi, E. , 1996, “ The Control of Stable Postures in the Multijoint Arm,” Exp. Brain Research, 110(2), pp. 248–264.
Perreault, E. J. , Kirsch, R. F. , and Crago, P. E. , 2001, “ Effects of Voluntary Force Generation on the Elastic Components of Endpoint Stiffness,” Exp. Brain Res., 141(3), pp. 312–323. [PubMed]
Schouten, A. C. , de Vlugt, E. , van Hilten, J. J. B. , and van der Helm, F. C. T. , 2006, “ Design of a Torque-Controlled Manipulator to Analyse the Admittance of the Wrist Joint,” J. Neurosci. Methods, 154(1–2), pp. 134–141. [PubMed]
Klomp, A. , De Groot, J. H. , De Vlugt, E. , Meskers, C. G. , Arendzen, J. H. , and Van Der Helm, F. C. , 2014, “ Perturbation Amplitude Affects Linearly Estimated Neuromechanical Wrist Joint Properties,” IEEE Trans. Biomed. Eng., 61(4), pp. 1005–1014. [PubMed]
de Vlugt, E. , van Eesbeek, S. , Baines, P. , Hilte, J. , Meskers, C. G. , and de Groot, J. H. , 2011, “ Short Range Stiffness Elastic Limit Depends on Joint Velocity,” J. Biomech., 44(11), pp. 2106–2112. [PubMed]
De Serres, S. J. , and Milner, T. E. , 1991, “ Wrist Muscle Activation Patterns and Stiffness Associated With Stable and Unstable Mechanical Loads,” Exp. Brain Res., 86(2), pp. 451–458. [PubMed]
Shadmehr, R. , Mussa-Ivaldi, F. A. , and Bizzi, E. , 1993, “ Postural Force Fields of the Human Arm and Their Role in Generating Multijoint Movements,” J. Neurosci.: Off. J. Soc. Neurosci., 13(1), pp. 45–62.
Weiss, P. , Hunter, I. , and Kearney, R. , 1988, “ Human Ankle Joint Stiffness Over the Full Range of Muscle Activation Levels,” J. Biomech., 21(7), pp. 539–544. [PubMed]
Bennett, D. J. , Hollerbach, J. M. , Xu, Y. , and Hunter, I. W. , 1992, “ Time-Varying Stiffness of Human Elbow Joint During Cyclic Voluntary Movement,” Exp. Brain Res., 88(2), pp. 433–442. [PubMed]
Osu, R. , Franklin, D. W. , Kato, H. , Gomi, H. , Domen, K. , Yoshioka, T. , and Kawato, M. , 2002, “ Short- and Long-Term Changes in Joint Co-Contraction Associated With Motor Learning as Revealed From Surface EMG,” J. Neurophysiol., 88(2), pp. 991–1004. [PubMed]
Burdet, E. , Osu, R. , Franklin, D. W. , Milner, T. E. , and Kawato, M. , 2001, “ The Central Nervous System Stabilizes Unstable Dynamics by Learning Optimal Impedance,” Nature, 414(6862), pp. 446–449. [PubMed]
Franklin, D. , Liaw, G. , Milner, T. , Osu, R. , Burdet, E. , and Kawato, M. , 2007, “ Endpoint Stiffness of the Arm is Directionally Tuned to Instability in the Environment,” J. Neurosci.: Off. J. Soc. Neurosci., 27(29), pp. 7705–7716.
Franklin, D. , So, U. , Kawato, M. , and Milner, T. , 2004, “ Impedance Control Balances Stability With Metabolically Costly Muscle Activation,” J. Neurophysiol., 26(9), pp. 2468–2477.
Kadiallah, A. , Liaw, G. , Kawato, M. , Franklin, D. W. , and Burdet, E. , 2011, “ Impedance Control is Selectively Tuned to Multiple Directions of Movement,” J. Neurophysiol., 106(5), pp. 2737–2748. [PubMed]
Perreault, E. J. , Kirsch, R. F. , and Crago, P. E. , 2002, “ Voluntary Control of Static Endpoint Stiffness During Force Regulation Tasks,” J. Neurophysiol., 87(6), pp. 2808–2816. [PubMed]
Gomi, H. , and Osu, R. , 1998, “ Task-Dependent Viscoelasticity of Human Multijoint Arm and Its Spatial Characteristics for Interaction With Environments,” J. Neurosci.: Off. J. Soc. Neurosci., 18(21), pp. 8965–8978.
Darainy, M. , 2004, “ Learning to Control Arm Stiffness Under Static Conditions,” J. Neurophysiol., 92(6), pp. 3344–3350. [PubMed]
Charles, S. K. , and Hogan, N. , 2011, “ Dynamics of Wrist Rotations,” J. Biomech., 44(4), pp. 614–621. [PubMed]
Milner, T. E. , and Cloutier, C. , 1993, “ Compensation for Mechanically Unstable Loading in Voluntary Wrist Movement,” Exp. Brain Res., 94(3), pp. 522–532. [PubMed]
Milner, T. E. , and Cloutier, C. , 1998, “ Damping of the Wrist Joint During Voluntary Movement,” Exp. Brain Res., 122(3), pp. 309–317. [PubMed]
Halaki, M. , O'Dwyer, N. , and Cathers, I. , 2006, “ Systematic Nonlinear Relations Between Displacement Amplitude and Joint Mechanics at the Human Wrist,” J. Biomech., 39(12), pp. 2171–2182. [PubMed]
Deshpande, A. D. , Gialias, N. , and Matsuoka, Y. , 2012, “ Contributions of Intrinsic Visco-Elastic Torques During Planar Index Finger and Wrist Movements,” IEEE Trans. Biomed. Eng., 59(2), pp. 586–594. [PubMed]
Inouye, J. M. , and Valero-Cuevas, F. J. , 2016, “ Muscle Synergies Heavily Influence the Neural Control of Arm Endpoint Stiffness and Energy Consumption,” PLoS Comput. Biol., 12(2), p. e1004737. [PubMed]
Hu, X. , Murray, W. M. , and Perreault, E. J. , 2011, “ Muscle Short-Range Stiffness Can Be Used to Estimate the Endpoint Stiffness of the Human Arm,” J. Neurophysiol., 105(4), pp. 1633–1641. [PubMed]
Valero-Cuevas, F. J. , Johanson, M. E. , and Towles, J. D. , 2003, “ Towards a Realistic Biomechanical Model of the Thumb: The Choice of Kinematic Description May Be More Critical Than the Solution Method or the Variability/Uncertainty of Musculoskeletal Parameters,” J. Biomech., 36(7), pp. 1019–1030. [PubMed]
Valero-Cuevas, F. J. , 2005, “ An Integrative Approach to the Biomechanical Function and Neuromuscular Control of the Fingers,” J. Biomech., 38(4), pp. 673–684. [PubMed]
Valero-Cuevas, F. J. , Hoffmann, H. , Kurse, M. U. , Kutch, J. J. , and Theodorou, E. A. , 2011, “ Computational Models for Neuromuscular Function,” IEEE Rev. Biomed. Eng., 2, pp. 110–135.
Saul, K. R. , Hu, X. , Goehler, C. M. , Vidt, M. E. , Daly, M. , Velisar, A. , and Murray, W. M. , 2014, “ Benchmarking of Dynamic Simulation Predictions in Two Software Platforms Using an Upper Limb Musculoskeletal Model,” Comput. Methods Biomech. Biomed. Eng., 18(13), pp. 1445–1458.
Delp, S. L. , Anderson, F. C. , Arnold, A. S. , Loan, P. , Habib, A. , John, C. T. , Guendelman, E. , and Thelen, D. G. , 2007, “ OpenSim: Open Source to Create and Analyze Dynamic Simulations of Movement,” IEEE Trans. Bio-Med. Eng., 54(11), pp. 1940–1950.
Sherman, M. A. , Seth, A. , and Delp, S. L. , 2013, “ What is a Moment Arm? Calculating Muscle Effectiveness in Biomechanical Models Using Generalized Coordinates,” ASME Paper No. DETC2013-13633.
Hill, A. V. , 1938, “ The Heat of Shortening and the Dynamic Constants of Muscle,” Proc. R. Soc. London B, 126(843), pp. 136–195.
Millard, M. , Uchida, T. , Seth, A. , and Delp, S. L. , 2013, “ Flexing Computational Muscle: Modeling and Simulation of Musculotendon Dynamics,” ASME J. Biomech. Eng., 135(2), p. 21005.
Cui, L. , Perreault, E. J. , Maas, H. , and Sandercock, T. G. , 2008, “ Modeling Short-Range Stiffness of Feline Lower Hindlimb Muscles,” J. Biomech., 41(9), pp. 1945–1952. [PubMed]
van Eesbeek, S. , de Groot, J. H. , van der Helm, F. C. T. , and de Vlugt, E. , 2010, “ In Vivo Estimation of the Short-Range Stiffness of Cross-Bridges From Joint Rotation,” J. Biomech., 43(13), pp. 2539–2547. [PubMed]
Zonnino, A. , and Sergi, F. , 2017, “ Using Musculoskeletal Models to Estimate the Passive Joint Stiffness,” 41st Annual Meeting of the American Society of Biomechanics, Boulder, CO, Aug. 8–11, pp. 8–9.
Dornay, M. , Mussa-Ivaldi, F. A. , McIntyre, J. , and Bizzi, E. , 1993, “ Stability Constraints for the Distributed Control of Motor Behavior,” Neural Networks, 6(8), pp. 1045–1059.
Perreault, E. J. , Kirsch, R. F. , and Acosta, A. M. , 1999, “ Multiple-Input, Multiple-Output System Identification for Characterization of Limb Stiffness Dynamics,” Biol. Cybern., 80(5), pp. 327–337. [PubMed]
Seth, A. , Sherman, M. , Reinbolt, J. A. , and Delp, S. L. , 2011, “ OpenSim: A Musculoskeletal Modeling and Simulation Framework for in Silico Investigations and Exchange,” Procedia IUTAM, 2, pp. 212–232. [PubMed]
Berens, P. , 2009, “ CircStat: A MATLAB Toolbox for Circular Statistics,” J. Stat. Software, 31(10), pp. 1–21.
Seegmiller, D. B. , Eggett, D. L. , and Charles, S. K. , 2016, “ The Effect of Common Wrist Orthoses on the Stiffness of Wrist Rotations,” J. Rehabil. Res. Develop., 53(6), pp. 1151–1166.
Park, K. , Chang, P. H. , and Kang, S. H. , 2017, “ In Vivo Estimation of Human Forearm and Wrist Dynamic Properties,” IEEE Trans. Neural Syst. Rehabil. Eng., 25(5), pp. 436–446. [PubMed]
Drake, W. B. , and Charles, S. K. , 2014, “ Passive Stiffness of Coupled Wrist and Forearm Rotations,” Ann. Biomed. Eng., 42(9), pp. 1853–1866. [PubMed]
Johns, R. J. , and Wright, V. , 1963, “ Relative Importance of Various Tissues in Joint Stiffness,” J. Am. Med. Assoc., 183(2), p. 189.
Kuo, P. H. , and Deshpande, A. D. , 2012, “ Muscle-Tendon Units Provide Limited Contributions to the Passive Stiffness of the Index Finger Metacarpophalangeal Joint,” J. Biomech., 45(15), pp. 2531–2538. [PubMed]

Figures

Grahic Jump Location
Fig. 1

Representation of the musculoskeletal system (left) and the musculotendon unit (right) used in the simulations

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Fig. 2

Block diagram of the framework used to calculate the passive (A) and active (B) joint stiffness. The analyses presented in this manuscript always assumed a null desired joint torque (τ=0).

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Fig. 3

Measurements of the passive stiffness of the wrist (left). Model-based estimates of the passive stiffness when different groups of muscles are included (right). All values are obtained with the wrist in the neutral posture. Units of stiffness in the polar plot are Nm/rad. PM1-5 are the five passive models (see Sec. 2.5.1).

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Fig. 4

Map of the passive stiffness of the wrist joint in multiple postures

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Fig. 5

Polar histogram representing the distribution of the orientation of the passive stiffness of the wrist joint in the joint angle domain considered. Note that the distribution is symmetric about the origin so peaks at 120 deg and 300 deg represent the same group of ellipses, as well as the peaks at 90 deg and 270 deg.

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Fig. 6

Set of admissible stiffness values established via systematic search when all muscles (left) can cocontract, or when only the wrist muscles (center), or only the finger and thumb muscles (right) can cocontract. The values refer to the neutral posture and to a null desired net torque. The smallest ellipse represents the passive stiffness, while the black represents the stiffness that corresponds to the activation vector that minimize GAL, selected within the subset A(0). Units of stiffness in the polar plot are N·m/rad. In each of the three polar plots only 500 ellipses, equally spaced in terms of GAL have been represented.

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Fig. 7

(Top) the plot represents the relationship between the magnitude of the achievable joint stiffness and the GAL; the small dots represent the set of achievable stiffness value (decimated 1000 times), while the line is the fit obtained from linear regression. (Bottom) the plot represents the relationship between the orientation of the achievable joint stiffness and seven equally spaced groups of GAL; the bars represent the mean value of orientation for the ellipses within each group, while the error bars show the standard deviation within each group. The big dots in the Y-axis represent the values obtained in the passive condition.

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Fig. 8

The plots represent the distribution of the achievable magnitude (top) and orientation (center), and eccentricity (bottom), when different groups of muscles cocontract. Please note the logarithmic scale used for the vertical axis, which allows one to appreciate the presence of a small number of feasible solutions for several values of magnitude, orientation, and eccentricity.

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