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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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Steinhart, S., Weiss, P. L., & Friedman, J. (2021). Proximal and distal movement patterns during a graphomotor task in typically developing children and children with handwriting problems. J Neuroeng Rehabil, 18(1), 178.
Abstract: BACKGROUND: Therapists specializing in handwriting difficulties in children often address motor problems including both proximal and distal movements in the upper extremity. Kinematic measures can be used to investigate various aspects of handwriting. This study examined differences in movement patterns in proximal and distal joints of the upper extremity during graphomotor tasks between typically developing children with and without handwriting problems. Additionally, it explored relationships between movement patterns, speed, and legibility of writing. METHODS: Forty-one children, aged 7-11 years, were assessed with the Aleph Aleph Ktav Yad Hebrew Handwriting assessment and the Beery Test of Visual Motor Integration and, based on their scores, were divided into a research group (with handwriting difficulties) and a control group (without handwriting difficulties). Upper extremity joint movement patterns were analyzed with a motion capture system. Differences in the quality of shapes traced and copied on a graphics tablet positioned horizontally and vertically were compared. Between-group differences and relationships with speed and legibility were analyzed. RESULTS: In both groups, there was greater movement in the distal compared to the proximal joints, greater movement when performing the task in a horizontal compared to a vertical plane, and greater movement when tracing than copying. Joint movements in the arm executed scaled-down versions of the shapes being drawn. While the amount of joint displacement was similar between groups, children in the research group showed greater dissimilarity between the drawn shape and the shape produced by the proximal joints. Finally, the drawing measure on the tablet was a significant predictor of legibility, speed of writing, visual motor integration and motor coordination, whereas the dissimilarity measure of joint movement was a significant predictor of speed of writing and motor coordination. CONCLUSIONS: This study provides support for the role of the distal upper extremity joints in the writing process and some guidance to assist clinicians in devising treatment strategies for movement-related handwriting problems. While we observed differences in proximal joint movements between the children with and without handwriting difficulties, the extent to which they are responsible for the differences in drawing quality remains to be determined. Further studies should use a similar methodology to examine additional tasks such as drawing shapes of varying sizes.
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Friedman, J., Brown, S., & Finkbeiner, M. (2013). Linking cognitive and reaching trajectories via intermittent movement control. Journal of Mathematical Psychology, 57(3-4), 140–151.
Abstract: Theories of decision-making have traditionally been constrained by reaction time data. A limitation of reaction time data, particularly for studying the temporal dynamics of cognitive processing, is that they index only the endpoint of the decision making process. Recently, physical reaching trajectories have been used as proxies for underlying mental trajectories through decision space. We suggest that this approach has been oversimplified: while it is possible for the motor control system to access the current state of the evidence accumulation process, this access is intermittent. Instead, we demonstrate how a model of arm movements that assumes intermittent, not continuous, access to the decision process is sufficient to describe the effects of stimulus quality and viewing time in curved reaching movements.
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Lowenthal-Raz, J., Liebermann, D. G., Friedman, J., & Soroker, N. (2024). Kinematic descriptors of arm reaching movement are sensitive to hemisphere-specific immediate neuromodulatory effects of transcranial direct current stimulation post stroke. Sci Rep, 14(1), 11971.
Abstract: Transcranial direct current stimulation (tDCS) exerts beneficial effects on motor recovery after stroke, presumably by enhancement of adaptive neural plasticity. However, patients with extensive damage may experience null or deleterious effects with the predominant application mode of anodal (excitatory) stimulation of the damaged hemisphere. In such cases, excitatory stimulation of the non-damaged hemisphere might be considered. Here we asked whether tDCS exerts a measurable effect on movement quality of the hemiparetic upper limb, following just a single treatment session. Such effect may inform on the hemisphere that should be excited. Using a single-blinded crossover experimental design, stroke patients and healthy control subjects were assessed before and after anodal, cathodal and sham tDCS, each provided during a single session of reaching training (repeated point-to-point hand movement on an electronic tablet). Group comparisons of endpoint kinematics at baseline-number of peaks in the speed profile (NoP; smoothness), hand-path deviations from the straight line (SLD; accuracy) and movement time (MT; speed)-disclosed greater NoP, larger SLD and longer MT in the stroke group. NoP and MT revealed an advantage for anodal compared to sham stimulation of the lesioned hemisphere. NoP and MT improvements under anodal stimulation of the non-lesioned hemisphere correlated positively with the severity of hemiparesis. Damage to specific cortical regions and white-matter tracts was associated with lower kinematic gains from tDCS. The study shows that simple descriptors of movement kinematics of the hemiparetic upper limb are sensitive enough to demonstrate gain from neuromodulation by tDCS, following just a single session of reaching training. Moreover, the results show that tDCS-related gain is affected by the severity of baseline motor impairment, and by lesion topography.
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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.
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