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Flash, T., Richardson, M. E., Handzel, A. A., & Liebermann, D. G. (2003). Computational Models and Geometric Approaches in Arm Trajectory Control Studies. In M. L. Latash, & M. F. Levin (Eds.), Progress in Motor Control III: From Basic Science to Applications. Champaign, Il: Human Kinetics.
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Falk, B., Eliakim, A., Dotan, R., Liebermann, D. G., Regev, R., & Bar-Or, O. (1997). Birth weight and physical ability in 5- to 8-yr-old healthy children born prematurely. Med Sci Sports Exerc, 29(9), 1124–1130.
Abstract: Recent advances in perinatal care have resulted in increased survival rates of extremely small and immature newborns. This has resulted in some neurodevelopmental impairment. The purpose of this study was to quantitatively evaluate and compare neuromuscular performance in children born prematurely at various levels of subnormal birth weight (BW). Subjects were 5- to 8-yr-old children born prematurely at different levels of subnormal BW (535-1760 g, N = 22, PM), and age-matched controls born at full term (> 2500 g, N = 15, CON). None of the subjects had any clinically defined neuromuscular disabilities. Body mass (BM) of PM was lower than that of CON (18.3 +/- 2.7 vs 21.7 +/- 3.8 kg) with no difference in height or sum of 4 skinfolds. Peak mechanical power output determined with a 15-s modified Wingate Anaerobic Test and corrected for BM was lower (P = 0.07) in PM than in CON (5.11 +/- 1.07 vs 5.94 +/- 1.00 W.kg-1). This was especially noticeable in children born at extremely low BW (ELBW, < 1000 g, 4.49 +/- 1.04 W.kg-1, P < 0.01). Peak power, determined in a force-plate vertical jump, corrected for BM was lower in PM vs CON (25.5 +/- 5.4 vs 30.8 +/- 5.2 W.kg-1, respectively P = 0.01), especially in the ELBW group (20.0 +/- 5.5 W.kg-1). Similarly, the elapsed time between peak velocity and actual jump take-off was longer in PM than in CON (41.2 +/- 9.4 vs 35.8 +/- 5.8 ms, respectively, P = 0.04). No differences were observed in peak force. The results suggest that performance deficiencies of prematurely-born children may be a result of inferior inter-muscular coordination. The precise neuromotor factors responsible for this should be identified by future research.
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Davidowitz, I., Parmet, Y., Frenkel-Toledo, S., Banina, M. C., Soroker, N., Solomon, J. M., et al. (2019). Relationship Between Spasticity and Upper-Limb Movement Disorders in Individuals With Subacute Stroke Using Stochastic Spatiotemporal Modeling. Neurorehabil Neural Repair, 33(2), 141–152.
Abstract: BACKGROUND: Spasticity is common in patients with stroke, yet current quantification methods are insufficient for determining the relationship between spasticity and voluntary movement deficits. This is partly a result of the effects of spasticity on spatiotemporal characteristics of movement and the variability of voluntary movement. These can be captured by Gaussian mixture models (GMMs). OBJECTIVES: To determine the influence of spasticity on upper-limb voluntary motion, as assessed by the bidirectional Kullback-Liebler divergence (BKLD) between motion GMMs. METHODS: A total of 16 individuals with subacute stroke and 13 healthy aged-equivalent controls reached to grasp 4 targets (near-center, contralateral, far-center, and ipsilateral). Two-dimensional GMMs (angle and time) were estimated for elbow extension motion. BKLD was computed for each individual and target, within the control group and between the control and stroke groups. Movement time, final elbow angle, average elbow velocity, and velocity smoothness were computed. RESULTS: Between-group BKLDs were much larger than within control-group BKLDs. Between-group BKLDs for the near-center target were lower than those for the far-center and contralateral targets, but similar to that for the ipsilateral target. For those with stroke, the final angle was lower for the near-center target, and the average velocity was higher. Velocity smoothness was lower for the near-center than for the ipsilateral target. Elbow flexor and extensor passive muscle resistance (Modified Ashworth Scale) strongly explained BKLD values. CONCLUSIONS: Results support the view that individuals with poststroke spasticity have a velocity-dependent reduction in active elbow joint range and that BKLD can be used as an objective measure of the effects of spasticity on reaching kinematics.
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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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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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