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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., 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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Liebermann, D. G., & Hoffman, J. R. (2005). Timing of preparatory landing responses as a function of availability of optic flow information. J Electromyogr Kinesiol, 15(1), 120–130.
Abstract: This study investigated temporal patterns of EMG activity during self-initiated falls with different optic flow information ('gaze directions'). Onsets of EMG during the flight phase were monitored from five experienced volunteers that completed 72 landings in three gaze directions (downward, mid-range and horizontal) and six heights of fall (10-130 cm). EMG recordings were obtained from the right gastrocnemius, tibialis anterior, biceps femoris and rectus femoris muscles, and used to determine the latency of onset (L(o)) and the perceived time to contact (T(c)). Impacts at touchdown were also monitored using as estimates the major peak of the vertical ground reaction forces (F(max)) normalized to body mass, time to peak (T(max)), peak impulse (I(norm)) normalized to momentum, and rate of change of force (dF(max)/dt). Results showed that L(o) was longer as heights of fall increased, but remained within a narrow time-window at >50 cm landings. No significant differences in L(o) were observed when gaze direction was changed. The relationship between T(c) and flight time followed a linear trend regardless of gaze direction. Gaze direction did not significantly affect the landing impacts. In conclusion, availability of optic flow during landing does not play a major role in triggering the preparatory muscle actions in self-initiated falls. Once a structured landing plan has been acquired, the relevant muscles respond relative to the start of the fall.
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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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Liebermann, D. G., Buchman, A. S., & Franks, I. M. (2006). Enhancement of motor rehabilitation through the use of information technologies. Clin Biomech (Bristol, Avon), 21(1), 8–20.
Abstract: The recent development of information technologies has dramatically increased the tools available for facilitating motor rehabilitation. This review focuses on technologies which can be used to augment movement-related information both to patients as well as to their therapists. A brief outline of the motor system emphasizes the role of spinal motor neurons in the control of voluntary movement and rehabilitative efforts. Technologies which induce passive motion to stimulate spinal motor output as well as technologies that stimulate active voluntary movements are discussed. Finally, we review technologies and notational methods that can be used to quantify and assess the quality of movement for evaluating the efficacy of motor rehabilitation efforts. We conclude that stronger evidence is necessary to determine the applicability of the wide range of technologies now available to clinical rehabilitation efforts.
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