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.

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.