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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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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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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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Harel Arzi, Tal Krasovsky, Moshe Pritsch, & Dario G. Liebermann. (2014). Movement control in patients with shoulder instability: a comparison between patients after open surgery and nonoperated patients. Journal of Shoulder and Elbow Surgery, 23(7), 982–992.
Abstract: Background
Open surgery to correct shoulder instability is deemed to facilitate recovery of static and dynamic motor functions. Postoperative assessments focus primarily on static outcomes (e.g., repositioning accuracy). We introduce kinematic measures of arm smoothness to assess shoulder patients after open surgery and compare them with nonoperated patients. Performance among both groups of patients was hypothesized to differ. Postsurgery patients were expected to match healthy controls. Methods All participants performed pointing movements with the affected/dominant arm fully extended at fast, preferred, and slow speeds (36 trials per subject). Kinematic data were collected (100 Hz, 3 seconds), and mixed-design analyses of variance (group, speed) were performed with movement time, movement amplitude, acceleration time, and model-observed similarities as dependent variables. Nonparametric tests were performed for number of velocity peaks. Results Nonoperated and postsurgery patients showed similarities at preferred and faster movement speeds but not at slower speed. Postsurgery patients were closer to maximally smoothed motion and differed from healthy controls mainly during slow arm movements (closer to maximal smoothness, larger movement amplitude, shorter movement time, and lower number of peaks; i.e., less movement fragmentation). Conclusions Arm kinematic analyses suggest that open surgery stabilizes the shoulder but does not necessarily restore normal movement quality. Patients with recurrent anterior shoulder instability (RASI) seem to implement a “safe” but nonadaptive mode of action whereby preplanned stereotypical movements may be executed without depending on feedback. Rehabilitation of RASI patients should focus on restoring feedback-based movement control. Clinical assessment of RASI patients should include higher order kinematic descriptors. Keywords: Smoothness; kinesthesis; arm kinematics; shoulder instability; open surgery
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Merdler, T., Liebermann, D. G., Levin, M. F., & Berman, S. (2013). Arm-plane representation of shoulder compensation during pointing movements in patients with stroke. J Electromyogr Kinesiol, 23(4), 938–947.
Abstract: Improvements in functional motor activities are often accompanied by motor compensations to overcome persistent motor impairment in the upper limb. Kinematic analysis is used to objectively quantify movement patterns including common motor compensations such as excessive trunk displacement during reaching. However, a common motor compensation to assist reaching, shoulder abduction, is not adequately characterized by current motion analysis approaches. We apply the arm-plane representation that accounts for the co-variation between movements of the whole arm, and investigate its ability to identify and quantify compensatory arm movements in stroke subjects when making forward arm reaches. This method has not been previously applied to the analysis of motion deficits. Sixteen adults with right post-stroke hemiparesis and eight healthy age-matched controls reached in three target directions (14 trials/target; sampling rate: 100Hz). Arm-plane movement was validated against endpoint, joint, and trunk kinematics and compared between groups. In stroke subjects, arm-plane measures were correlated with arm impairment (Fugl-Meyer Assessment) and ability (Box and Blocks) scores and were more sensitive than clinical measures to detect mild motor impairment. Arm-plane motion analysis provides new information about motor compensations involving the co-variation of shoulder and elbow movements that may help to understand the underlying motor deficits in patients with stroke.
Keywords: Kinematics; Arm movement; Rehabilitation
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