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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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Issurin, V. B., Liebermann, D. G., & Tenenbaum, G. (1994). Effect of vibratory stimulation training on maximal force and flexibility (Vol. 12).
Abstract: In this study, we investigated a new method of training for maximal strength and flexibility, which included exertion with superimposed vibration (vibratory stimulation, VS) on target muscles. Twenty-eight male athletes were divided into three groups, and trained three times a week for 3 weeks in one of the following conditions: (A) conventional exercises for strength of the arms and VS stretching exercises for the legs; (B) VS strength exercises for the arms and conventional stretching exercises for the legs; (C) irrelevant training (control group). The vibration was applied at 44 Hz while its amplitude was 3 mm. The effect of training was evaluated by means of isotonic maximal force, heel-to-heel length in the two-leg split across, and flex-and-reach test for body flexion. The VS strength training yielded an average increase in isotonic maximal strength of 49.8%, compared with an average gain of 16% with conventional training, while no gain was observed for the control group. The VS flexibility training resulted in an average gain in the legs split of 14.5 cm compared with 4.1 cm for the conventional training and 2 cm for the control groups, respectively. The ANOVA revealed significant pre-post training effects and an interaction between pre-post training and 'treatment' effects (P < 0.001) for the isotonic maximal force and both flexibility tests. It was concluded that superimposed vibrations applied for short periods allow for increased gains in maximal strength and flexibility.
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Hoffman, J. R., Liebermann, D., & Gusis, A. (1997). Relationship of leg strength and power to ground reaction forces in both experienced and novice jump trained personnel. Aviat Space Environ Med, 68(8), 710–714.
Abstract: METHODS: There were 14 male soldiers who participated in this study examining the relationship of leg strength and power on landing performance. Subjects were separated into two groups. The first group (E, n = 7) were parachute training instructors and highly experienced in parachute jumping. The second group of subjects (N, n = 7) had no prior parachute training experience and were considered novice jumpers. All subjects were tested for one-repetition maximum (1 RM) squat strength and maximal jump power. Ground reaction forces (GRF) and the time to peak force (TPF) at landing were measured from jumps at four different heights (95 cm, 120 cm, 145 cm, and 170 cm). All jumps were performed from a customized jump platform onto a force plate. RESULTS: No differences were seen between E and N in either IRM squat strength or in MJP. In addition, no differences were seen between the groups for time to peak force at any jump height. However, significantly greater GRF were observed in E compared to N. Moderate to high correlations between maximal jump power and GRF (r values ranging from 0.62-0.93) were observed in E. Although maximal jump power and the TPF was significantly correlated (r = -0.89) at only 120 cm for E, it was interesting to note that the correlations between MJP and the time to peak force in E were all negative and that the correlations between these variables in N were all positive. CONCLUSIONS: These results suggest that experienced parachutists may use a different landing strategy than novice jumpers. This difference may be reflected by differences in GRF generated during impact and a more efficient utilization of muscle power during the impact phase of the landing.
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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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