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Biess, A., Flash, T., & Liebermann, D. G. (2011). Riemannian geometric approach to human arm dynamics, movement optimization, and invariance. Phys Rev E Stat Nonlin Soft Matter Phys, 83(3 Pt 1), 031927.
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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Frenkel-Toledoa, S., Bentin, S., Perry, A., Liebermann, D. G., & Soroker, N. (2014). Mirror-neuron system recruitment by action observation: Effects of focal brain damage on mu suppression. NeuroImage, 87, 127–137.
Abstract: Mu suppression is the attenuation of EEG power in the alpha frequency range (8-12 Hz), recorded over the sensorimotor cortex during execution and observation of motor actions. Based on this dual characteristic it is thought to signalize activation of a human analogue of the mirror neuron system (MNS) found in macaque monkeys, though much uncertainty remains concerning its specificity and full significance. To further explore the hypothesized relationship between mu suppression and MNS activation, we investigated how it is affected by damage to cortical regions, including areas where the MNS is thought to reside. EEG was recorded in 33 first-event stroke patients during observation of video-clips showing reaching and grasping hand movements. We examined the modulation of EEG oscillations at central and occipital sites, and analyzed separately the lower (8-10 Hz) and higher (10-12 Hz) segments of the alpha/mu range. Suppression was determined relative to observation of a non-biological movement. Normalized lesion data were used to investigate how damage to regions of the fronto-parietal cortex affects the pattern of suppression. The magnitude of mu suppression during action observation was significantly reduced in the affected hemisphere compared to the unaffected hemisphere. Differences between the hemispheres were significant at central (sensorimotor) sites but not at occipital (visual) sites. Total hemispheric volume loss did not correlate with mu suppression. Suppression in the lower mu range in the unaffected hemisphere (C3) correlated with lesion extent within the right inferior parietal cortex. Our lesion study supports the role of mu suppression as a marker of MNS activation, as suggested by findings gathered in previous studies in normal subjects.
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Berman, S., Liebermann, D. G., & McIntyre, J. (2014). Constrained Motion Control on a Hemispherical Surface – Path Planning. J Neurophysiol, 111(5), 954–968.
Abstract: 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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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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Frenkel-Toledo, S., Bentin, S., Perry, A., Liebermann, D. G., & Soroker, N. (2013). Dynamics of the EEG Power in the Frequency and Spatial Domains During Observation and Execution of Manual Movements. Brain Res, 1509, 43–57.
Abstract: Mu suppression is the attenuation of EEG power in the alpha frequency range (8-12Hz) while executing or observing a motor action. Whereas typically observed at central scalp sites, there are diverging reports about the extent of the attenuation over the cortical mantle, its exact frequency range and the specificity of this phenomenon. We investigated the modulation of EEG oscillations in frequency-bands from 4 to 12Hz at frontal, central, parietal and occipital sites during the execution of manual movements and during observation of similar actions from allocentric (i.e., facing the actor) and egocentric (i.e., seeing the actor from behind) viewpoints. Suppression was determined relative to observation of a non-biological movement. Action observation elicited greater suppression in the lower (8-10Hz) compared to the higher mu range (10-12Hz), and greater suppression in the entire 4-12Hz range at frontal and central sites compared to parietal and occipital sites. In addition, suppression tended to be greater during observation of a motor action from allocentric compared to egocentric viewpoints. During execution of movement, suppression of the EEG occurred primarily in the higher alpha range and was absent at occipital sites. In the theta range (4-8Hz), the EEG amplitude was suppressed during action observation and execution. The results suggest a functional distinction between modulation of mu and alpha rhythms, and between the higher and lower ranges of the mu rhythms. The activity of the presumed human mirror neuron system seems primarily evident in the lower mu range and in the theta range.
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