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Carmeli E., & Liebermann, D. G. (2007). The Function of the Aging Hand. In T. L. Kauffman, M. Moran, & J. Barr (Eds.), The Geriatric Rehabilitation Manual. NY: Elsevier.
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Cantergi, D., Awasthi, B., & Friedman, J. (2021). Moving objects by imagination? Amount of finger movement and pendulum length determine success in the Chevreul pendulum illusion. Human Movement Science, 80, 102879.
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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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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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Bezalel, G., Nachoum Arad, G., Plotnik, M., & Friedman, J. (2021). Voluntary step execution in patients with knee osteoarthritis: Symptomatic vs. non-symptomatic legs. Gait Posture, 83, 60–66.
Abstract: BACKGROUND: Individuals with osteoarthritis fall at a greater rate than the general population, likely as a result of weakness, pain, movement limitations, and a decline in balance. Due to the high prevalence of osteoarthritis in the population, understanding the mechanisms leading to greater fall risk is an important issue to better understand. RESEARCH QUESTION: What is the influence of unilateral knee osteoarthritis on the characteristics of performing a voluntary step (i.e., similar to that performed to avoid a fall after a perturbation), compared to healthy age-matched controls? METHODS: Case-control study performed in a Health maintenance organization physical therapy clinic. The research group consisted of a referred sample of 21 patients with unilateral knee osteoarthritis. The control group consisted of 22 age-matched healthy individuals. All participants were over 65 years of age. Participants were excluded if they had a surgical procedure to back or lower limb within one year before testing, oncological or neurological disease or a deficit in tactile sense. Movements were performed with and without dual tasking. MEASUREMENTS: Duration of the initiation phase (cue to step initiation), preparatory phase (step initiation to foot off) and swing phase (foot off to foot contact). RESULTS: In the preparatory phase and swing phase, the osteoarthritis group moved more slowly than the control group, and these differences were larger for forward compared to backward movements. Dual-tasking slowed responses in the pre-movement initiation stage across groups. SIGNIFICANCE: The differences in basic parameters, and the slower movements in the osteoarthritis group, are consistent with known features of osteoarthritis, being a disease commonly regarded as primarily “mechanical”, and are likely to increase fall risk. These response deficits suggest we should take advantage of advanced rehabilitation techniques, including cognitive loading, to help prevent falls in older adults with osteoarthritis.
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