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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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Noy, L., Alon, U., & Friedman, J. (2015). Corrective jitter motion shows similar individual frequencies for the arm and the finger. Exp Brain Res, 233(4), 1307–1320.
Abstract: A characteristic of visuomotor tracking of non-regular oscillating stimuli are high-frequency jittery corrective motions, oscillating around the tracked stimuli. However, the properties of these corrective jitter responses are not well understood. For example, does the jitter response show an idiosyncratic signature? What is the relationship between stimuli properties and jitter properties? Is the jitter response similar across effectors with different inertial properties? To answer these questions, we measured participants' jitter frequencies in two tracking tasks in the arm and the finger. Thirty participants tracked the same set of eleven non-regular oscillating stimuli, vertically moving on a screen, once with forward-backward arm movements (holding a tablet stylus) and once with upward-downward index finger movements (with a motion tracker attached). Participants' jitter frequencies and tracking errors varied systematically as a function of stimuli frequency and amplitude. Additionally, there were clear individual differences in average jitter frequencies between participants, ranging from 0.7 to 1.15 Hz, similar to values reported previously. A comparison of individual jitter frequencies in the two tasks showed a strong correlation between participants' jitter frequencies in the finger and the arm, despite the very different inertial properties of the two effectors. This result suggests that the corrective jitter response stems from common neural processes.
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