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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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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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Roijezon, U., Djupsjobacka, M., Bjorklund, M., Hager-Ross, C., Grip, H., & Liebermann, D. G. (2010). Kinematics of fast cervical rotations in persons with chronic neck pain: a cross-sectional and reliability study. BMC Musculoskelet Disord, 11, 222.
Abstract: BACKGROUND: Assessment of sensorimotor function is useful for classification and treatment evaluation of neck pain disorders. Several studies have investigated various aspects of cervical motor functions. Most of these have involved slow or self-paced movements, while few have investigated fast cervical movements. Moreover, the reliability of assessment of fast cervical axial rotation has, to our knowledge, not been evaluated before. METHODS: Cervical kinematics was assessed during fast axial head rotations in 118 women with chronic nonspecific neck pain (NS) and compared to 49 healthy controls (CON). The relationship between cervical kinematics and symptoms, self-rated functioning and fear of movement was evaluated in the NS group. A sub-sample of 16 NS and 16 CON was re-tested after one week to assess the reliability of kinematic variables. Six cervical kinematic variables were calculated: peak speed, range of movement, conjunct movements and three variables related to the shape of the speed profile. RESULTS: Together, peak speed and conjunct movements had a sensitivity of 76% and a specificity of 78% in discriminating between NS and CON, of which the major part could be attributed to peak speed (NS: 226 +/- 88 degrees /s and CON: 348 +/- 92 degrees /s, p < 0.01). Peak speed was slower in NS compared to healthy controls and even slower in NS with comorbidity of low-back pain. Associations were found between reduced peak speed and self-rated difficulties with running, performing head movements, car driving, sleeping and pain. Peak speed showed reasonably high reliability, while the reliability for conjunct movements was poor. CONCLUSIONS: Peak speed of fast cervical axial rotations is reduced in people with chronic neck pain, and even further reduced in subjects with concomitant low back pain. Fast cervical rotation test seems to be a reliable and valid tool for assessment of neck pain disorders on group level, while a rather large between subject variation and overlap between groups calls for caution in the interpretation of individual assessments.
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Markstrom, J. L., Liebermann, D. G., Schelin, L., & Hager, C. K. (2022). Atypical Lower Limb Mechanics During Weight Acceptance of Stair Descent at Different Time Frames After Anterior Cruciate Ligament Reconstruction. Am J Sports Med, , 1–9.
Abstract: BACKGROUND: An anterior cruciate ligament (ACL) rupture may result in poor sensorimotor knee control and, consequentially, adapted movement strategies to help maintain knee stability. Whether patients display atypical lower limb mechanics during weight acceptance of stair descent at different time frames after ACL reconstruction (ACLR) is unknown. PURPOSE: To compare the presence of atypical lower limb mechanics during the weight acceptance phase of stair descent among athletes at early, middle, and late time frames after unilateral ACLR. STUDY DESIGN: Controlled laboratory study. METHODS: A total of 49 athletes with ACLR were classified into 3 groups according to time after ACLR-early (<6 months; n = 17), middle (6-18 months; n = 16), and late (>18 months; n = 16)-and compared with asymptomatic athletes (control; n = 18). Sagittal plane hip, knee, and ankle angles; angular velocities; moments; and powers were compared between the ACLR groups' injured and noninjured legs and the control group as well as between legs within groups using functional data analysis methods. RESULTS: All 3 ACLR groups showed greater knee flexion angles and moments than the control group for injured and noninjured legs. For the other outcomes, the early group had, compared with the control group, less hip power absorption, more knee power absorption, lower ankle plantarflexion angle, lower ankle dorsiflexion moment, and less ankle power absorption for the injured leg and more knee power absorption and higher vertical ground reaction force for the noninjured leg. In addition, the late group showed differences from the control group for the injured leg revealing more knee power absorption and lower ankle plantarflexion angle. Only the early group took a longer time than the control group to complete weight acceptance and demonstrated asymmetry for multiple outcomes. CONCLUSION: Athletes with different time frames after ACLR revealed atypically large knee angles and moments during weight acceptance of stair descent for both the injured and the noninjured legs. These findings may express a chronically adapted strategy to increase knee control. In contrast, atypical hip and ankle mechanics seem restricted to an early time frame after ACLR. CLINICAL RELEVANCE: Rehabilitation after ACLR should include early training in controlling weight acceptance. Including a control group is essential when evaluating movement patterns after ACLR because both legs may be affected.
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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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