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., & Defrin, R. (2009). Characteristics of the nociceptive withdrawal response elicited under aware and unaware conditions. J Electromyogr Kinesiol, 19(2), e114–22.
Abstract: BACKGROUND: Nociceptive withdrawal reflexes (NWR) are subject to supraspinal modulation. Therefore, awareness about a noxious stimulation may affect its characteristics. The goal of this study was to investigate the effect of different degrees of awareness on the NWR. METHOD: Eight subjects performed back and forth hand movements from a common starting point towards four visual targets during which NWR was evoked when subjects were either unaware or aware of a noxious stimulation (unaware-NWR and aware-NWR). For the comparison between the NWR under both conditions, onset latencies and kinematic variables were computed respectively from the recorded Biceps Brachii EMG and from the spatial coordinates of hand reflective markers. RESULTS: The onset latency of unaware-NWR (mean+/-SD 73.9+/-13 ms) was significantly shorter than that of the aware-NWR (91.1+/-27 ms, p<0.05). The total duration of the muscular activation was shorter in unaware-NWR than in aware-NWR. The slopes of the tangential velocity-time curves were steeper for unaware-NWR than for aware-NWR (p=0.057). CONCLUSIONS: The results suggest that supraspinal regulation of NWR under different degrees of awareness involves the re-parameterization of selected spatiotemporal aspects of a pre-structured motor response.
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Liebermann, D. G., & Goodman, D. (2007). Pre-landing muscle timing and post-landing effects of falling with continuous vision and in blindfold conditions. J Electromyogr Kinesiol, 17(2), 212–227.
Abstract: The present study examined the effect of continuous vision and its occlusion in timing of pre-landing actions during free falls. When vision is occluded, muscle activation is hypothesized to start relative to onset of the fall. However, when continuous vision is available onset of action is hypothesized to be relative to the moment of touchdown. Six subjects performed 6 randomized sets of 6 trials after becoming familiar with the task. The 36 trials were divided in 2 visual conditions (vision and blindfold) and 3 heights of fall (15, 45 and 75 cm). EMG activity was recorded from the gastrocnemius and rectus femoris muscles during the falls. The latency of onset (L(o)) and the lapse from EMG onset to touchdown (T(c)) were obtained from these muscles. Vertical forces were recorded to assess the effects of pre-landing activity on the impacts at collision with and without continuous vision. Peak amplitude (F(max)), time to peak (T(max)) and peak impulse normalized to momentum (I(norm)) were used as outcome measures. Within flight time ranges of approximately 50-400 ms, the results showed that L(o) and T(c) follow a similar linear trend whether continuous vision was available or occluded. However, the variability of T(c) for each of the muscles was larger in the vision occluded condition. Analyses of variance showed that the rectus femoris muscle started consistently earlier in no vision trials. Finally, impact forces were not different in vision or blindfold conditions, and thus, they were not affected by minor differences in the timing of muscles prior to landing. Thus, it appears that knowing the surroundings before falling may help to reduce the need for a continuous visual input. The relevance of such input cannot be ruled out for falls from high landing heights, but cognitive factors (e.g., attention to specific cues and anticipation of a fall) may play a dominant role in timing actions during short duration falls encountered daily.
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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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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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