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.

Abstract: Surface-constrained motion, i.e., motion constraint by a rigid surface, is commonly found in daily activities. The current work investigates the choice of hand paths constrained to a concave hemispherical surface. To gain insight regarding the paths and their relationship with task dynamics, we simulated various control policies. The simulations demonstrated that following a geodesic path is advantageous not only in terms of path length, but also in terms of motor planning and sensitivity to motor command errors. These stem from the fact that the applied forces lie in a single plane (that of the geodesic path itself). To test whether human subjects indeed follow the geodesic, and to see how such motion compares to other paths, we recorded movements in a virtual haptic-visual environment from eleven healthy subjects. The task was comprised of point-to-point motion between targets at two elevations (30 degrees and 60 degrees ). Three typical choices of paths were observed from a frontal plane projection of the paths: circular arcs, straight lines, and arcs close to the geodesic path for each elevation. Based on the measured hand paths, we applied k-means blind separation to divide the subjects into three groups and compared performance indicators. The analysis confirmed that subjects who followed paths closest to the geodesic produced faster and smoother movements, compared to the others. The 'better' performance reflects the dynamical advantages of following the geodesic path, as shown by the simulations, and may also reflect invariant features of the control policies used to produce such a surface-constrained motion.

Abstract: BACKGROUND: Recovery of voluntary movement is a main rehabilitation goal. Efforts to identify effective upper limb (UL) interventions after stroke have been unsatisfactory. This study includes personalized impairment-based UL reaching training in virtual reality (VR) combined with non-invasive brain stimulation to enhance motor learning. The approach is guided by limiting reaching training to the angular zone in which active control is preserved (“active control zone”) after identification of a “spasticity zone”. Anodal transcranial direct current stimulation (a-tDCS) is used to facilitate activation of the affected hemisphere and enhance inter-hemispheric balance. The purpose of the study is to investigate the effectiveness of personalized reaching training, with and without a-tDCS, to increase the range of active elbow control and improve UL function. METHODS: This single-blind randomized controlled trial will take place at four academic rehabilitation centers in Canada, India and Israel. The intervention involves 10 days of personalized VR reaching training with both groups receiving the same intensity of treatment. Participants with sub-acute stroke aged 25 to 80 years with elbow spasticity will be randomized to one of three groups: personalized training (reaching within individually determined active control zones) with a-tDCS (group 1) or sham-tDCS (group 2), or non-personalized training (reaching regardless of active control zones) with a-tDCS (group 3). A baseline assessment will be performed at randomization and two follow-up assessments will occur at the end of the intervention and at 1 month post intervention. Main outcomes are elbow-flexor spatial threshold and ratio of spasticity zone to full elbow-extension range. Secondary outcomes include the Modified Ashworth Scale, Fugl-Meyer Assessment, Streamlined Wolf Motor Function Test and UL kinematics during a standardized reach-to-grasp task. DISCUSSION: This study will provide evidence on the effectiveness of personalized treatment on spasticity and UL motor ability and feasibility of using low-cost interventions in low-to-middle-income countries. TRIAL REGISTRATION: ClinicalTrials.gov, ID: NCT02725853 . Initially registered on 12 January 2016.