Liebermann, D. G., Berman, S., Weingarden H., Levin, M. F., & Weiss, P. L. (2009). Kinematic features of arm and trunk movements in stroke patients and age-matched healthy controls during reaching in virtual and physical environments. In Virtual Rehabilitation International Conference (pp. 179–184).
Abstract: Motor performance of stroke patients and healthy individuals was compared in terms of selected kinematic features of arm and trunk movements while subjects reached for visual targets in virtual (VR) and physical (PH) environments. In PH, the targets were placed at an extended arm distance, while in VR comparably placed virtual targets were presented via GestureTek's IREX system. Our goal was to obtain further insights into research methods related to VR-based rehabilitation. Eight right-hemiparetic stroke patients (age =46-87 years) and 8 healthy adults (age =51-73 years) completed 84 reaching movements in VR and PH environments while seated. The results showed that arm and trunk movements differed in the two environments in patients and to a lesser extent in healthy individuals. Arm motion of patients became jerkier in VR, with larger paths and longer movement durations, and presented greater arm torsion (i.e., larger elbow rotations around the hand-shoulder axis). Interestingly, patients also showed a significant reduction of compensatory trunk movements during VR reaching. The findings indicate that when targets were perceived to be beyond hand reach, stroke patients may be less able to estimate 3D virtual target locations obtained from the 2D TV planar displays. This was not the case for healthy participants.
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Liebermann, D. G., Krasovsky, T., & Berman, S. (2008). Planning maximally smooth hand movements constrained to nonplanar workspaces. J Mot Behav, 40(6), 516–531.
Abstract: The article characterizes hand paths and speed profiles for movements performed in a nonplanar, 2-dimensional workspace (a hemisphere of constant curvature). The authors assessed endpoint kinematics (i.e., paths and speeds) under the minimum-jerk model assumptions and calculated minimal amplitude paths (geodesics) and the corresponding speed profiles. The authors also calculated hand speeds using the 2/3 power law. They then compared modeled results with the empirical observations. In all, 10 participants moved their hands forward and backward from a common starting position toward 3 targets located within a hemispheric workspace of small or large curvature. Comparisons of modeled observed differences using 2-way RM-ANOVAs showed that movement direction had no clear influence on hand kinetics (p < .05). Workspace curvature affected the hand paths, which seldom followed geodesic lines. Constraining the paths to different curvatures did not affect the hand speed profiles. Minimum-jerk speed profiles closely matched the observations and were superior to those predicted by 2/3 power law (p < .001). The authors conclude that speed and path cannot be unambiguously linked under the minimum-jerk assumption when individuals move the hand in a nonplanar 2-dimensional workspace. In such a case, the hands do not follow geodesic paths, but they preserve the speed profile, regardless of the geometric features of the workspace.
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Liebermann, D. G. (2008). Biomechanical aspects of motor control in human landing. In R. Bartlett, & Y. Hong (Eds.), Routledge Handbook of Biomechanics and Human Movement Science. Routledge Ltd.
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Liebermann, D. G., & Franks I.M. (2008). Video-feedback and information technologies. In I.M. Franks, & M. Hughes (Eds.), Essentials of notational analysis. E & FN Spon Pub.
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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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