Abstract: Few computational models have addressed the spatiotemporal features of unconstrained three-dimensional (3D) arm motion. Empirical observations made on hand paths, speed profiles, and arm postures during point-to-point movements led to the assumption that hand path and arm posture are independent of movement speed, suggesting that the geometric and temporal properties of movements are decoupled. In this study, we present a computational model of 3D movements for an arm with four degrees of freedom based on the assumption that optimization principles are separately applied at the geometric and temporal levels of control. Geometric properties (path and posture) are defined in terms of geodesic paths with respect to the kinetic energy metric in the Riemannian configuration space. Accordingly, a geodesic path can be generated with less muscular effort than on any other, nongeodesic path, because the sum of all configuration-speed-dependent torques vanishes. The temporal properties of the movement (speed) are determined in task space by minimizing the squared jerk along the selected end-effector path. The integration of both planning levels into a single spatiotemporal representation simplifies the control of arm dynamics along geodesic paths and results in movements with near minimal torque change and minimal peak value of kinetic energy. Thus, the application of Riemannian geometry allows for a reconciliation of computational models previously proposed for the description of arm movements. We suggest that geodesics are an emergent property of the motor system through the exploration of dynamical space. Our data validated the predictions for joint trajectories, hand paths, final postures, speed profiles, and driving torques.

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: PURPOSE: Skeletal muscle echogenicity intensity (EI) is considered a measure of muscle quality, being associated with old age and pathologies. Whether EI variations can be identified in healthy adults, due to habitual shortened or elongated muscle position is unknown. Thus, this study aimed to assess the relationship between thoracic kyphosis angulation and EI scores of muscles spanning this region ((Lower Trapezius (LT), Rhomboid Major (RM), Erector Spine (ES)) in healthy young people and in addition to examine the relationship between the change in thoracic kyphosis angle from relaxed to upright position (� degrees ) and the EI of these muscles. METHODS: Thoracic kyphosis in relaxed and erect standing was measured using a digital inclinometer in 29 healthy adults (16 women, 13 men), aged 25-35 years. The thoracic kyphosis angles including the difference between relaxed and erect postures (� degrees ) were correlated to the EI scores of right and left LT, RM and ES. RESULTS: No significant differences in EI were found between the 3 muscles EI or between sides, hence they were pooled together to a total thoracic EI score (TTEI). Although the TTEI did not correlate with relaxed or erect thoracic kyphosis, it was significantly but negatively correlated with � degrees in the entire group: Pearson's correlation coefficient of r = -0.544; p = .01 and in men; r = -0.732; p = .01, failing to reach significance in women; r = -0.457. CONCLUSION: The negative association between the EI of the explored muscles and � degrees could imply a possible relationship between these muscles range of movement excursions and their composition.