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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 |
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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Year |
2007 |
Publication |
The Journal of Neuroscience : the Official Journal of the Society for Neuroscience |
Abbreviated Journal |
J Neurosci |
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27 |
Issue |
48 |
Pages |
13045-13064 |
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Keywords |
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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Hoffman, J.R.; Liebermann, D.; Gusis, A. |
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Title |
Relationship of leg strength and power to ground reaction forces in both experienced and novice jump trained personnel |
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Journal Article |
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Year |
1997 |
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Aviation, Space, and Environmental Medicine |
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Aviat Space Environ Med |
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68 |
Issue |
8 |
Pages |
710-714 |
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*Aerospace Medicine; *Aviation; Biomechanics; Humans; Leg/*physiology; Male; Military Personnel/*education; *Physical Education and Training; Physical Fitness/*physiology; Range of Motion, Articular; Wounds and Injuries/etiology/*prevention & control |
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METHODS: There were 14 male soldiers who participated in this study examining the relationship of leg strength and power on landing performance. Subjects were separated into two groups. The first group (E, n = 7) were parachute training instructors and highly experienced in parachute jumping. The second group of subjects (N, n = 7) had no prior parachute training experience and were considered novice jumpers. All subjects were tested for one-repetition maximum (1 RM) squat strength and maximal jump power. Ground reaction forces (GRF) and the time to peak force (TPF) at landing were measured from jumps at four different heights (95 cm, 120 cm, 145 cm, and 170 cm). All jumps were performed from a customized jump platform onto a force plate. RESULTS: No differences were seen between E and N in either IRM squat strength or in MJP. In addition, no differences were seen between the groups for time to peak force at any jump height. However, significantly greater GRF were observed in E compared to N. Moderate to high correlations between maximal jump power and GRF (r values ranging from 0.62-0.93) were observed in E. Although maximal jump power and the TPF was significantly correlated (r = -0.89) at only 120 cm for E, it was interesting to note that the correlations between MJP and the time to peak force in E were all negative and that the correlations between these variables in N were all positive. CONCLUSIONS: These results suggest that experienced parachutists may use a different landing strategy than novice jumpers. This difference may be reflected by differences in GRF generated during impact and a more efficient utilization of muscle power during the impact phase of the landing. |
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Aeromedical Center, Physiological Training Unit, Israel Air Force, Israel |
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0095-6562 |
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PMID:9262813 |
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60 |
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Krasovsky, T.; Berman, S.; Liebermann, D.G. |
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Title |
Kinematic features of continuous hand reaching movements under simple and complex rhythmical constraints |
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Journal Article |
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2010 |
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Journal of Electromyography and Kinesiology : Official Journal of the International Society of Electrophysiological Kinesiology |
Abbreviated Journal |
J Electromyogr Kinesiol |
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20 |
Issue |
4 |
Pages |
636-641 |
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*Acoustic Stimulation; Adult; Biomechanics; *Cues; Female; Hand/*physiology; Humans; Male; Movement/*physiology |
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BACKGROUND: Auditory cues are known to alter movement kinematics in healthy people as well as in people with neurological conditions (e.g., Parkinson's disease or stroke). Pacing movement to rhythmical constraints is known to change both the spatial and temporal features of movement. However, the effect of complexity of pacing on the spatial and temporal kinematic properties is still poorly understood. The current study investigated spatial and temporal aspects of movement (path and speed, respectively) and their integration while subjects followed simple isochronous or complex non-isochronous rhythmical constraints. Spatiotemporal decoupling was expected under the latter constraint. METHODS: Ten subjects performed point-to-point hand movements towards visual targets on the surface of a hemisphere, while following continuous auditory cues of different pace and meter. The spatial and temporal properties of movement were compared to geodesic paths and unimodal bell-shaped speed profiles, respectively. Multiple two-way RM-ANOVAs (pace [1-2 Hz] x meter [duple-triple]) were performed on the different kinematic variables calculated to assess hand deviations from the model data (p< or = 0.05). RESULTS: As expected, increasing pace resulted in straighter hand paths and smoother speed profiles. Meter, however, affected only the path (shorter and straighter under triple) without significantly changing speed. Such an effect was observed at the slow pace only. CONCLUSIONS: Under simple rhythmic cues, an increase in pace causes spontaneous adjustments in spatial features (straighter hand paths) while preserving temporal ones (maximally-smoothed hand speeds). Complex rhythmical cues in contrast perturb spatiotemporal coupling and challenge movement control. These results may have important practical implications in motor rehabilitation. |
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Department of Physical and Occupational Therapy, Faculty of Medicine, McGill University, Canada |
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1050-6411 |
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PMID:20382031 |
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32 |
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Author |
Liebermann, D.G.; Goodman, D. |
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Title |
Effects of visual guidance on the reduction of impacts during landings |
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Journal Article |
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Year |
1991 |
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Ergonomics |
Abbreviated Journal |
Ergonomics |
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34 |
Issue |
11 |
Pages |
1399-1406 |
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Adult; Analysis of Variance; Biomechanics; *Cues; Humans; Male; Motor Activity/*physiology; Psychomotor Performance/physiology; Vision, Ocular/*physiology |
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While a common view is that vision is essential to motor performance, some recent studies have shown that continuous visual guidance may not always be required within certain time constraints. This study investigated a landing-related task (self-released falls) to assess the extent to which visual information enhances the ability to reduce the impacts at touchdown. Six individuals performed six blocked trials from four height categories in semi-counterbalanced order (5-10, 20-25, 60-65, and 90-95 cm) in vision and no-vision conditions randomly assigned. A series of two-way ANOVA with repeated measures were carried out separately on each dependent variable collapsed over six trials. The results indicated that vision during the flight did not produce softer landings. Indeed, in analysing the first peak (PFP) a main effect for visual condition was revealed in that the mean amplitude was slightly higher when vision was available (F(1,5) = 6.57; p less than 0.05), thus implicating higher forces at impact. The results obtained when the time to the first peak (TFP) was applied showed no significant differences between conditions (F(1,5) less than 1). As expected, in all cases, the analyses yielded significant main effects for the height categories factor. It appears that during self-initiated falls in which the environmental cues are known before the event, visual guidance is not necessary in order to adopt a softer landing strategy. |
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Research Department, Wingate Institute, Israel |
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0014-0139 |
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PMID:1800107 |
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55 |
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