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Author  |
Biess, A.; Flash, T.; Liebermann, D.G. |
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Title |
Riemannian geometric approach to human arm dynamics, movement optimization, and invariance |
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Journal Article |
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Year |
2011 |
Publication |
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics |
Abbreviated Journal |
Phys Rev E Stat Nonlin Soft Matter Phys |
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83 |
Issue |
3 Pt 1 |
Pages |
031927 |
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Keywords |
Arm/*physiology; Biomechanics; Computer Simulation; Humans; Kinetics; Male; Models, Biological; Models, Statistical; Models, Theoretical; *Movement; Psychomotor Performance/*physiology; Range of Motion, Articular/physiology; Reaction Time/physiology; Space Perception/*physiology; Torque |
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Abstract |
We present a generally covariant formulation of human arm dynamics and optimization principles in Riemannian configuration space. We extend the one-parameter family of mean-squared-derivative (MSD) cost functionals from Euclidean to Riemannian space, and we show that they are mathematically identical to the corresponding dynamic costs when formulated in a Riemannian space equipped with the kinetic energy metric. In particular, we derive the equivalence of the minimum-jerk and minimum-torque change models in this metric space. Solutions of the one-parameter family of MSD variational problems in Riemannian space are given by (reparameterized) geodesic paths, which correspond to movements with least muscular effort. Finally, movement invariants are derived from symmetries of the Riemannian manifold. We argue that the geometrical structure imposed on the arm's configuration space may provide insights into the emerging properties of the movements generated by the motor system. |
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Bernstein Center for Computational Neuroscience, DE-37073 Gottingen, Germany. armin@nld.ds.mpg.de |
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1539-3755 |
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PMID:21517543 |
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29 |
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Author |
Berman, S.; Liebermann, D.G.; McIntyre, J. |
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Title |
Constrained Motion Control on a Hemispherical Surface – Path Planning |
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Journal Article |
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Year |
2014 |
Publication |
Journal of Neurophysiology |
Abbreviated Journal |
J Neurophysiol |
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Volume |
111 |
Issue |
5 |
Pages |
954-968 |
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Keywords |
Constrained motion; geodesics; path planning |
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Surface-constrained motion, i.e., motion constraint by a rigid surface, is commonly found in daily activities. The current work investigates the choice of hand paths constrained to a concave hemispherical surface. To gain insight regarding the paths and their relationship with task dynamics, we simulated various control policies. The simulations demonstrated that following a geodesic path is advantageous not only in terms of path length, but also in terms of motor planning and sensitivity to motor command errors. These stem from the fact that the applied forces lie in a single plane (that of the geodesic path itself). To test whether human subjects indeed follow the geodesic, and to see how such motion compares to other paths, we recorded movements in a virtual haptic-visual environment from eleven healthy subjects. The task was comprised of point-to-point motion between targets at two elevations (30 degrees and 60 degrees ). Three typical choices of paths were observed from a frontal plane projection of the paths: circular arcs, straight lines, and arcs close to the geodesic path for each elevation. Based on the measured hand paths, we applied k-means blind separation to divide the subjects into three groups and compared performance indicators. The analysis confirmed that subjects who followed paths closest to the geodesic produced faster and smoother movements, compared to the others. The 'better' performance reflects the dynamical advantages of following the geodesic path, as shown by the simulations, and may also reflect invariant features of the control policies used to produce such a surface-constrained motion. |
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Ben-Gurion University of the Negev |
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0022-3077 |
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PMID:24259548 |
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72 |
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Banina, M.C.; Molad, R.; Solomon, J.S.; Berman, S.; Soroker, N.; Frenkel-Toledo, S.; Liebermann, D.G.; Levin, M.F. |
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Title |
Exercise intensity of the upper limb can be enhanced using a virtual rehabilitation system |
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Journal Article |
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Year |
2020 |
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Disability and Rehabilitation. Assistive Technology |
Abbreviated Journal |
Disabil Rehabil Assist Technol |
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1-7 |
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Stroke; difficulty; exercise therapy; intensity; personalized exercise; upper limb; virtual reality |
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Purpose: Motor recovery of the upper limb (UL) is related to exercise intensity, defined as movement repetitions divided by minutes in active therapy, and task difficulty. However, the degree to which UL training in virtual reality (VR) applications deliver intense and challenging exercise and whether these factors are considered in different centres for people with different sensorimotor impairment levels is not evidenced. We determined if (1) a VR programme can deliver high UL exercise intensity in people with sub-acute stroke across different environments and (2) exercise intensity and difficulty differed among patients with different levels of UL sensorimotor impairment.Methods: Participants with sub-acute stroke (<6 months) with Fugl-Meyer scores ranging from 14 to 57, completed 10 approximately 50-min UL training sessions using three unilateral and one bilateral VR activity over 2 weeks in centres located in three countries. Training time, number of movement repetitions, and success rates were extracted from game activity logs. Exercise intensity was calculated for each participant, related to UL impairment, and compared between centres.Results: Exercise intensity was high and was progressed similarly in all centres. Participants had most difficulty with bilateral and lateral reaching activities. Exercise intensity was not, while success rate of only one unilateral activity was related to UL severity.Conclusion: The level of intensity attained with this VR exercise programme was higher than that reported in current stroke therapy practice. Although progression through different activity levels was similar between centres, clearer guidelines for exercise progression should be provided by the VR application.Implications for rehabilitationVR rehabilitation systems can be used to deliver intensive exercise programmes.VR rehabilitation systems need to be designed with measurable progressions through difficulty levels. |
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Center for Interdisciplinary Research in Rehabilitation of Greater Montreal (CRIR), Feil and Oberfeld Research Centre, Jewish Rehabilitation Hospital, Laval, Canada |
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1748-3107 |
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PMID:32421460 |
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Call Number |
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106 |
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