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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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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.
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Liebermann, D. G., Biess, A., Friedman, J., Gielen, C. C. A. M., & Flash, T. (2006). Intrinsic joint kinematic planning. I: reassessing the Listing's law constraint in the control of three-dimensional arm movements. Exp Brain Res, 171(2), 139–154.
Abstract: This study tested the validity of the assumption that intrinsic kinematic constraints, such as Listing's law, can account for the geometric features of three-dimensional arm movements. In principle, if the arm joints follow a Listing's constraint, the hand paths may be predicted. Four individuals performed 'extended arm', 'radial', 'frontal plane', and 'random mixed' movements to visual targets to test Listing's law assumption. Three-dimensional rotation vectors of the upper arm and forearm were calculated from three-dimensional marker data. Data fitting techniques were used to test Donders' and Listing's laws. The coefficient values obtained from fitting rotation vectors to the surfaces described by a second-order equation were analyzed. The results showed that the coefficients that represent curvature and twist of the surfaces were often not significantly different from zero, particularly not during randomly mixed and extended arm movements. These coefficients for forearm rotations were larger compared to those for the upper arm segment rotations. The mean thickness of the rotation surfaces ranged between approximately 1.7 degrees and 4.7 degrees for the rotation vectors of the upper arm segment and approximately 2.6 degrees and 7.5 degrees for those of the forearm. During frontal plane movements, forearm rotations showed large twist scores while upper arm segment rotations showed large curvatures, although the thickness of the surfaces remained low. The curvatures, but not the thicknesses of the surfaces, were larger for large versus small amplitude radial movements. In conclusion, when examining the surfaces obtained for the different movement types, the rotation vectors may lie within manifolds that are anywhere between curved or twisted manifolds. However, a two-dimensional thick surface may roughly represent a global arm constraint. Our findings suggest that Listing's law is implemented for some types of arm movement, such as pointing to targets with the extended arm and during radial reaching movements.
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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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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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