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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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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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Ezrati, O., Friedman, J., & Dar, R. (2019). Attenuation of access to internal states in high obsessive-compulsive individuals might increase susceptibility to false feedback: Evidence from a visuo-motor hand-reaching task. Journal of Behavior Therapy and Experimental Psychiatry, 65, 101445.
Abstract: Background and objectives
The Seeking Proxies for Internal States (SPIS) model of obsessive-compulsive disorder (OCD) posits that obsessive-compulsive (OC) individuals have attenuated access to their internal states. Hence, they seek and rely on proxies, or discernible substitutes for these internal states. In previous studies, participants with high OC tendencies and OCD patients, compared to controls, showed increased reliance on external proxies and were more influenced by false feedback when judging their internal states. This study is the first to examine the effects of false feedback on performance of hand movements in participants with high and low OC tendencies.
Method
Thirty-four participants with high OC tendencies and 34 participants with low OC tendencies were asked to perform accurate hand reaches without visual feedback in two separate sessions of a computerized hand-reaching task: once after valid feedback training of their hand location and once with false-rotated feedback. We assessed the accuracy and directional adaptation of participants' reaches.
Results
As predicted, high OC participants evidenced a larger decrease in their hand positioning accuracy after training with false feedback compared to low OC participants.
Limitations
The generalization of our findings to OCD requires replication with a clinical sample.
Conclusions
These results suggest that in addition to self-perceptions, motor performance of OC individuals is prone to be overly influenced by false feedback, possibly due to attenuated access to proprioceptive cues. These findings may be particularly relevant to understanding the distorted sense of agency in OCD.
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Friedman, J., & Korman, M. (2016). Offline Optimization of the Relative Timing of Movements in a Sequence Is Blocked by Retroactive Behavioral Interference. Front. Hum. Neurosci., 10, 623.
Abstract: Acquisition of motor skills often involves the concatenation of single movements into sequences. Along the course of learning, sequential performance becomes progressively faster and smoother, presumably by optimization of both motor planning and motor execution. Following its encoding during training, “how-to” memory undergoes consolidation, reflecting transformations in performance and its neurobiological underpinnings over time. This offline post-training memory process is characterized by two phenomena: reduced sensitivity to interference and the emergence of delayed, typically overnight, gains in performance. Here, using a training protocol that effectively induces motor sequence memory consolidation, we tested temporal and kinematic parameters of performance within (online) and between (offline) sessions, and their sensitivity to retroactive interference. One group learned a given finger-to-thumb opposition sequence (FOS), and showed robust delayed (consolidation) gains in the number of correct sequences performed at 24 h. A second group learned an additional (interference) FOS shortly after the first and did not show delayed gains. Reduction of touch times and inter-movement intervals significantly contributed to the overall offline improvement of performance overnight. However, only the offline inter-movement interval shortening was selectively blocked by the interference experience. Velocity and amplitude, comprising movement time, also significantly changed across the consolidation period but were interference-insensitive. Moreover, they paradoxically canceled out each other. Current results suggest that shifts in the representation of the trained sequence are subserved by multiple processes: from distinct changes in kinematic characteristics of individual finger movements to high-level, temporal reorganization of the movements as a unit. Each of these processes has a distinct time course and a specific susceptibility to retroactive interference. This multiple-component view may bridge the gap in understanding the link between the behavioral changes, which define online and offline learning, and the biological mechanisms that support those changes.
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Friedman, J., Amiaz, A., & Korman, M. (2022). The online and offline effects of changing movement timing variability during training on a finger-opposition task. Sci Rep, 12(1), 13319.
Abstract: In motor learning tasks, there is mixed evidence for whether increased task-relevant variability in early learning stages leads to improved outcomes. One problem is that there may be a connection between skill level and motor variability, such that participants who initially have more variability may also perform worse on the task, so will have more room to improve. To avoid this confound, we experimentally manipulated the amount of movement timing variability (MTV) during training to test whether it improves performance. Based on previous studies showing that most of the improvement in finger-opposition tasks comes from optimizing the relative onset time of the finger movements, we used auditory cues (beeps) to guide the onset times of sequential movements during a training session, and then assessed motor performance after the intervention. Participants were assigned to three groups that either: (a) followed a prescribed random rhythm for their finger touches (Variable MTV), (b) followed a fixed rhythm (Fixed control MTV), or (c) produced the entire sequence following a single beep (Unsupervised control MTV). While the intervention was successful in increasing MTV during training for the Variable group, it did not lead to improved outcomes post-training compared to either control group, and the use of fixed timing led to significantly worse performance compared to the Unsupervised control group. These results suggest that manipulating MTV through auditory cues does not produce greater learning than unconstrained training in motor sequence tasks.
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