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.
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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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Melzer, I., Krasovsky, T., Oddsson, L. I. E., & Liebermann, D. G. (2010). Age-related differences in lower-limb force-time relation during the push-off in rapid voluntary stepping. Clin Biomech (Bristol, Avon), 25(10), 989–994.
Abstract: BACKGROUND: This study investigated the force-time relationship during the push-off stage of a rapid voluntary step in young and older healthy adults, to study the assumption that when balance is lost a quick step may preserve stability. The ability to achieve peak propulsive force within a short time is critical for the performance of such a quick powerful step. We hypothesized that older adults would achieve peak force and power in significantly longer times compared to young people, particularly during the push-off preparatory phase. METHODS: Fifteen young and 15 older volunteers performed rapid forward steps while standing on a force platform. Absolute anteroposterior and body weight normalized vertical forces during the push-off in the preparation and swing phases were used to determine time to peak and peak force, and step power. Two-way analyses of variance ('Group' [young-older] by 'Phase' [preparation-swing]) were used to assess our hypothesis (P </= 0.05). FINDINGS: Older people exerted lower peak forces (anteroposterior and vertical) than young adults, but not necessarily lower peak power. More significantly, they showed a longer time to peak force, particularly in the vertical direction during the preparation phase. INTERPRETATIONS: Older adults generate propulsive forces slowly and reach lower magnitudes, mainly during step preparation. The time to achieve a peak force and power, rather than its actual magnitude, may account for failures in quickly performing a preventive action. Such delay may be associated with the inability to react and recruit muscles quickly. Thus, training elderly to step fast in response to relevant cues may be beneficial in the prevention of falls.
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Levin, M. F., Liebermann, D. G., Parmet, Y., & Berman, S. (2015). Compensatory Versus Noncompensatory Shoulder Movements Used for Reaching in Stroke. Neurorehabil Neural Repair, .
Abstract: BACKGROUND: The extent to which the upper-limb flexor synergy constrains or compensates for arm motor impairment during reaching is controversial. This synergy can be quantified with a minimal marker set describing movements of the arm-plane. OBJECTIVES: To determine whether and how (a) upper-limb flexor synergy in patients with chronic stroke contributes to reaching movements to different arm workspace locations and (b) reaching deficits can be characterized by arm-plane motion. METHODS: Sixteen post-stroke and 8 healthy control subjects made unrestrained reaching movements to targets located in ipsilateral, central, and contralateral arm workspaces. Arm-plane, arm, and trunk motion, and their temporal and spatial linkages were analyzed. RESULTS: Individuals with moderate/severe stroke used greater arm-plane movement and compensatory trunk movement compared to those with mild stroke and control subjects. Arm-plane and trunk movements were more temporally coupled in stroke compared with controls. Reaching accuracy was related to different segment and joint combinations for each target and group: arm-plane movement in controls and mild stroke subjects, and trunk and elbow movements in moderate/severe stroke subjects. Arm-plane movement increased with time since stroke and when combined with trunk rotation, discriminated between different subject groups for reaching the central and contralateral targets. Trunk movement and arm-plane angle during target reaches predicted the subject group. CONCLUSIONS: The upper-limb flexor synergy was used adaptively for reaching accuracy by patients with mild, but not moderate/severe stroke. The flexor synergy, as parameterized by the amount of arm-plane motion, can be used by clinicians to identify levels of motor recovery in patients with stroke.
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Davidowitz, I., Parmet, Y., Frenkel-Toledo, S., Banina, M. C., Soroker, N., Solomon, J. M., et al. (2019). Relationship Between Spasticity and Upper-Limb Movement Disorders in Individuals With Subacute Stroke Using Stochastic Spatiotemporal Modeling. Neurorehabil Neural Repair, 33(2), 141–152.
Abstract: BACKGROUND: Spasticity is common in patients with stroke, yet current quantification methods are insufficient for determining the relationship between spasticity and voluntary movement deficits. This is partly a result of the effects of spasticity on spatiotemporal characteristics of movement and the variability of voluntary movement. These can be captured by Gaussian mixture models (GMMs). OBJECTIVES: To determine the influence of spasticity on upper-limb voluntary motion, as assessed by the bidirectional Kullback-Liebler divergence (BKLD) between motion GMMs. METHODS: A total of 16 individuals with subacute stroke and 13 healthy aged-equivalent controls reached to grasp 4 targets (near-center, contralateral, far-center, and ipsilateral). Two-dimensional GMMs (angle and time) were estimated for elbow extension motion. BKLD was computed for each individual and target, within the control group and between the control and stroke groups. Movement time, final elbow angle, average elbow velocity, and velocity smoothness were computed. RESULTS: Between-group BKLDs were much larger than within control-group BKLDs. Between-group BKLDs for the near-center target were lower than those for the far-center and contralateral targets, but similar to that for the ipsilateral target. For those with stroke, the final angle was lower for the near-center target, and the average velocity was higher. Velocity smoothness was lower for the near-center than for the ipsilateral target. Elbow flexor and extensor passive muscle resistance (Modified Ashworth Scale) strongly explained BKLD values. CONCLUSIONS: Results support the view that individuals with poststroke spasticity have a velocity-dependent reduction in active elbow joint range and that BKLD can be used as an objective measure of the effects of spasticity on reaching kinematics.
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