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Schweitzer, N., Apter, Y., Ben-David, J., Liebermann, D. G., & Parush, A. (1995). A field study of braking reactions during driving II: Minimum driver braking times. Ergonomics, 38(9), 1903–1910.
Abstract: The minimum total braking time (i.e. the braking reaction time plus the accelerator-to-brake movement time) plays an important role in defining a minimum following gap (MFG). This study was designed to obtain a lower limit for this gap. Total braking times (TBT) of a group of 51 male and female young athletes were monitored during real driving conditions. Sudden braking applied by a leading private passenger vehicle initiated the trials. A within-subject design was used to study the effects of different factors on braking time. Individuals performed a series of semi-counterbalanced trials at two following distances (6 and 12 m), two speeds (60 and 80 km/h) and three expectancy stages (naïve driving, partial knowledge, and full knowledge of the forthcoming manoeuvre). A three-way repeated measures ANOVA showed no major effects of ‘speed’, but major effects of the ‘expectancy’ and the ‘distance’ factors. The experiment yielded a mean TBT of 0·678 s (SD = 0·144 s) for trials averaged over distances and speeds in the naïve condition only. The data emphasize the role played by pre-cues in the braking response prior to emergency stops. Both the level of awareness of the forthcoming manoeuvre and the distance between vehicles appear to determine the response time. The descriptive statistics presented may also provide the basis for an objective, acceptable and legally valid minimum time gap for prosecution of ‘careless’ drivers.
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Liebermann, D. G., Levin, M. F., McIntyre, J., Weiss, P. L., & Berman, S. (2010). Arm path fragmentation and spatiotemporal features of hand reaching in healthy subjects and stroke patients. Conf Proc IEEE Eng Med Biol Soc, 2010, 5242–5245.
Abstract: Arm motion in healthy humans is characterized by smooth and relatively short paths. The current study focused on 3D reaching in stroke patients. Sixteen right-hemiparetic stroke patients and 8 healthy adults performed 42 reaching movements towards 3 visual targets located at an extended arm distance. Performance was assessed in terms of spatial and temporal features of the movement; i.e., hand path, arm posture and smoothness. Differences between groups and within subjects were hypothesized for spatial and temporal aspects of reaching under the assumption that both are independent. As expected, upper limb motion of patients was characterized by longer and jerkier hand paths and slower speeds. Assessment of the number of sub-movements within each movement did not clearly discriminate between groups. Principal component analyses revealed specific clusters of either spatial or temporal measures, which accounted for a large proportion of the variance in patients but not in healthy controls. These findings support the notion of a separation between spatial and temporal features of movement. Stroke patients may fail to integrate the two aspects when executing reaching movements towards visual targets.
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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.
Keywords: Analysis of Variance; Arm/physiology; Biomechanics; *Computer Simulation; Humans; *Models, Biological; Movement/*physiology; *Nonlinear Dynamics; Posture/physiology; Psychomotor Performance/*physiology; Range of Motion, Articular/physiology; Reaction Time/physiology; Space Perception/*physiology; Time Factors; Torque
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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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Grip, H., Tengman, E., Liebermann, D. G., & Hager, C. K. (2019). Kinematic analyses including finite helical axes of drop jump landings demonstrate decreased knee control long after anterior cruciate ligament injury. PLoS One, 14(10), e0224261.
Abstract: The purpose was to evaluate the dynamic knee control during a drop jump test following injury of the anterior cruciate ligament injury (ACL) using finite helical axes. Persons injured 17-28 years ago, treated with either physiotherapy (ACLPT, n = 23) or reconstruction and physiotherapy (ACLR, n = 28) and asymptomatic controls (CTRL, n = 22) performed a drop jump test, while kinematics were registered by motion capture. We analysed the Preparation phase (from maximal knee extension during flight until 50 ms post-touchdown) followed by an Action phase (until maximal knee flexion post-touchdown). Range of knee motion (RoM), and the length of each phase (Duration) were computed. The finite knee helical axis was analysed for momentary intervals of ~15 degrees of knee motion by its intersection (DeltaAP position) and inclination (DeltaAP Inclination) with the knee's Anterior-Posterior (AP) axis. Static knee laxity (KT100) and self-reported knee function (Lysholm score) were also assessed. The results showed that both phases were shorter for the ACL groups compared to controls (CTRL-ACLR: Duration 35+/-8 ms, p = 0.000, CTRL-ACLPT: 33+/-9 ms, p = 0.000) and involved less knee flexion (CTRL-ACLR: RoM 6.6+/-1.9 degrees , p = 0.002, CTRL-ACLR: 7.5 +/-2.0 degrees , p = 0.001). Low RoM and Duration correlated significantly with worse knee function according to Lysholm and higher knee laxity according to KT-1000. Three finite helical axes were analysed. The DeltaAP position for the first axis was most anterior in ACLPT compared to ACLR (DeltaAP position -1, ACLPT-ACLR: 13+/-3 mm, p = 0.004), with correlations to KT-1000 (rho 0.316, p = 0.008), while the DeltaAP inclination for the third axis was smaller in the ACLPT group compared to controls (DeltaAP inclination -3 ACLPT-CTRL: -13+/-5 degrees , p = 0.004) and showed a significant side difference in ACL injured groups during Action (Injured-Non-injured: 8+/-2.7 degrees , p = 0.006). Small DeltaAP inclination -3 correlated with low Lysholm (rho 0.391, p = 0.002) and high KT-1000 (rho -0.450, p = 0.001). Conclusions Compensatory movement strategies seem to be used to protect the injured knee during landing. A decreased DeltaAP inclination in injured knees during Action suggests that the dynamic knee control may remain compromised even long after injury.
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