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Biess, A., Liebermann, D. G., & Flash, T. (2007). A computational model for redundant human three-dimensional pointing movements: integration of independent spatial and temporal motor plans simplifies movement dynamics. J Neurosci, 27(48), 13045–13064.
Abstract: 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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Liebermann, D. G., & Goodman, D. (1991). Effects of visual guidance on the reduction of impacts during landings. Ergonomics, 34(11), 1399–1406.
Abstract: 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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Liebermann, D. G., & Goodman, D. (2007). Pre-landing muscle timing and post-landing effects of falling with continuous vision and in blindfold conditions. J Electromyogr Kinesiol, 17(2), 212–227.
Abstract: The present study examined the effect of continuous vision and its occlusion in timing of pre-landing actions during free falls. When vision is occluded, muscle activation is hypothesized to start relative to onset of the fall. However, when continuous vision is available onset of action is hypothesized to be relative to the moment of touchdown. Six subjects performed 6 randomized sets of 6 trials after becoming familiar with the task. The 36 trials were divided in 2 visual conditions (vision and blindfold) and 3 heights of fall (15, 45 and 75 cm). EMG activity was recorded from the gastrocnemius and rectus femoris muscles during the falls. The latency of onset (L(o)) and the lapse from EMG onset to touchdown (T(c)) were obtained from these muscles. Vertical forces were recorded to assess the effects of pre-landing activity on the impacts at collision with and without continuous vision. Peak amplitude (F(max)), time to peak (T(max)) and peak impulse normalized to momentum (I(norm)) were used as outcome measures. Within flight time ranges of approximately 50-400 ms, the results showed that L(o) and T(c) follow a similar linear trend whether continuous vision was available or occluded. However, the variability of T(c) for each of the muscles was larger in the vision occluded condition. Analyses of variance showed that the rectus femoris muscle started consistently earlier in no vision trials. Finally, impact forces were not different in vision or blindfold conditions, and thus, they were not affected by minor differences in the timing of muscles prior to landing. Thus, it appears that knowing the surroundings before falling may help to reduce the need for a continuous visual input. The relevance of such input cannot be ruled out for falls from high landing heights, but cognitive factors (e.g., attention to specific cues and anticipation of a fall) may play a dominant role in timing actions during short duration falls encountered daily.
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Liebermann, D. G., Biess, A., Friedman, J., Gielen, C. C. A. M., & Flash, T. (2006). Intrinsic joint kinematic planning. I: reassessing the Listing's law constraint in the control of three-dimensional arm movements. Exp Brain Res, 171(2), 139–154.
Abstract: This study tested the validity of the assumption that intrinsic kinematic constraints, such as Listing's law, can account for the geometric features of three-dimensional arm movements. In principle, if the arm joints follow a Listing's constraint, the hand paths may be predicted. Four individuals performed 'extended arm', 'radial', 'frontal plane', and 'random mixed' movements to visual targets to test Listing's law assumption. Three-dimensional rotation vectors of the upper arm and forearm were calculated from three-dimensional marker data. Data fitting techniques were used to test Donders' and Listing's laws. The coefficient values obtained from fitting rotation vectors to the surfaces described by a second-order equation were analyzed. The results showed that the coefficients that represent curvature and twist of the surfaces were often not significantly different from zero, particularly not during randomly mixed and extended arm movements. These coefficients for forearm rotations were larger compared to those for the upper arm segment rotations. The mean thickness of the rotation surfaces ranged between approximately 1.7 degrees and 4.7 degrees for the rotation vectors of the upper arm segment and approximately 2.6 degrees and 7.5 degrees for those of the forearm. During frontal plane movements, forearm rotations showed large twist scores while upper arm segment rotations showed large curvatures, although the thickness of the surfaces remained low. The curvatures, but not the thicknesses of the surfaces, were larger for large versus small amplitude radial movements. In conclusion, when examining the surfaces obtained for the different movement types, the rotation vectors may lie within manifolds that are anywhere between curved or twisted manifolds. However, a two-dimensional thick surface may roughly represent a global arm constraint. Our findings suggest that Listing's law is implemented for some types of arm movement, such as pointing to targets with the extended arm and during radial reaching movements.
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Liebermann, D. G., Levin, M. F., McIntyre, J., Weiss, P. L., & Berman, S. (2010). Arm path fragmentation and spatiotemporal features of hand reaching in healthy subjects and stroke patients. Conf Proc IEEE Eng Med Biol Soc, 2010, 5242–5245.
Abstract: Arm motion in healthy humans is characterized by smooth and relatively short paths. The current study focused on 3D reaching in stroke patients. Sixteen right-hemiparetic stroke patients and 8 healthy adults performed 42 reaching movements towards 3 visual targets located at an extended arm distance. Performance was assessed in terms of spatial and temporal features of the movement; i.e., hand path, arm posture and smoothness. Differences between groups and within subjects were hypothesized for spatial and temporal aspects of reaching under the assumption that both are independent. As expected, upper limb motion of patients was characterized by longer and jerkier hand paths and slower speeds. Assessment of the number of sub-movements within each movement did not clearly discriminate between groups. Principal component analyses revealed specific clusters of either spatial or temporal measures, which accounted for a large proportion of the variance in patients but not in healthy controls. These findings support the notion of a separation between spatial and temporal features of movement. Stroke patients may fail to integrate the two aspects when executing reaching movements towards visual targets.
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