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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 |
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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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Melzer, I.; Liebermann, D.G.; Krasovsky, T.; Oddsson, L.I.E. |
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Title |
Cognitive load affects lower limb force-time relations during voluntary rapid stepping in healthy old and young adults |
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Journal Article |
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2010 |
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The Journals of Gerontology. Series A, Biological Sciences and Medical Sciences |
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J Gerontol A Biol Sci Med Sci |
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65 |
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4 |
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400-406 |
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*Accidental Falls; Adult; Aged; Aged, 80 and over; Aging/*physiology; Attention/physiology; Cognition/*physiology; Gait/*physiology; Humans; Postural Balance/*physiology; Reaction Time |
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Abstract |
BACKGROUND: Quick step execution may prevent falls when balance is lost; adding a concurrent task delays this function. We investigate whether push-off force-time relations during the execution of rapid voluntary stepping is affected by a secondary task in older and young adults. METHODS: Nineteen healthy older adults and 12 young adults performed rapid voluntary stepping under single- and dual-task conditions. Peak power, peak force, and time to peak force during preparatory and swing phases of stepping were extracted from center of pressure and ground reaction force data. RESULTS: For dual-task condition compared with single-task condition, older adults show a longer time to reach peak force during the preparation and swing phases compared with young adults (approximately 25% vs approximately 10%, respectively). Peak power and peak force were not affected by a concurrent attention-demanding task. CONCLUSION: Older adults have difficulty allocating sufficient attention for fast muscle recruitment when concurrently challenged by an attention-demanding task. |
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Department of Physical Therapy, Faculty of Health Sciences, Ben-Gurion University of the Negev, Beer-Sheva, Israel |
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1079-5006 |
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PMID:19939911 |
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50 |
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Author |
Biess, A.; Liebermann, D.G.; Flash, T. |
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Title |
A computational model for redundant human three-dimensional pointing movements: integration of independent spatial and temporal motor plans simplifies movement dynamics |
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Journal Article |
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2007 |
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The Journal of Neuroscience : the Official Journal of the Society for Neuroscience |
Abbreviated Journal |
J Neurosci |
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27 |
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48 |
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13045-13064 |
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Analysis of Variance; Arm/physiology; Biomechanics; *Computer Simulation; Humans; *Models, Biological; Movement/*physiology; *Nonlinear Dynamics; Posture/physiology; Psychomotor Performance/*physiology; Range of Motion, Articular/physiology; Reaction Time/physiology; Space Perception/*physiology; Time Factors; Torque |
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Few computational models have addressed the spatiotemporal features of unconstrained three-dimensional (3D) arm motion. Empirical observations made on hand paths, speed profiles, and arm postures during point-to-point movements led to the assumption that hand path and arm posture are independent of movement speed, suggesting that the geometric and temporal properties of movements are decoupled. In this study, we present a computational model of 3D movements for an arm with four degrees of freedom based on the assumption that optimization principles are separately applied at the geometric and temporal levels of control. Geometric properties (path and posture) are defined in terms of geodesic paths with respect to the kinetic energy metric in the Riemannian configuration space. Accordingly, a geodesic path can be generated with less muscular effort than on any other, nongeodesic path, because the sum of all configuration-speed-dependent torques vanishes. The temporal properties of the movement (speed) are determined in task space by minimizing the squared jerk along the selected end-effector path. The integration of both planning levels into a single spatiotemporal representation simplifies the control of arm dynamics along geodesic paths and results in movements with near minimal torque change and minimal peak value of kinetic energy. Thus, the application of Riemannian geometry allows for a reconciliation of computational models previously proposed for the description of arm movements. We suggest that geodesics are an emergent property of the motor system through the exploration of dynamical space. Our data validated the predictions for joint trajectories, hand paths, final postures, speed profiles, and driving torques. |
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Department of Mathematics, Weizmann Institute of Science, 76100 Rehovot, Israel. armin.biess@weizmann.ac.il |
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0270-6474 |
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PMID:18045899 |
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35 |
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Author |
Friedman, Jason; Brown, Scott; Finkbeiner, Matthew |
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Title |
Linking cognitive and reaching trajectories via intermittent movement control |
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Journal Article |
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2013 |
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Journal of Mathematical Psychology |
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57 |
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3-4 |
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140-151 |
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Decision making; Diffusion model; Reaction times; Arm movements; Submovements |
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Theories of decision-making have traditionally been constrained by reaction time data. A limitation of reaction time data, particularly for studying the temporal dynamics of cognitive processing, is that they index only the endpoint of the decision making process. Recently, physical reaching trajectories have been used as proxies for underlying mental trajectories through decision space. We suggest that this approach has been oversimplified: while it is possible for the motor control system to access the current state of the evidence accumulation process, this access is intermittent. Instead, we demonstrate how a model of arm movements that assumes intermittent, not continuous, access to the decision process is sufficient to describe the effects of stimulus quality and viewing time in curved reaching movements. |
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