Altered Perceptual Sensitivity to Kinematic Invariants in Parkinson's Disease

Ample evidence exists for coupling between action and perception in neurologically healthy individuals, yet the precise nature of the internal representations shared between these domains remains unclear. One experimentally derived view is that the invariant properties and constraints characterizing movement generation are also manifested during motion perception. One prominent motor invariant is the “two-third power law,” describing the strong relation between the kinematics of motion and the geometrical features of the path followed by the hand during planar drawing movements. The two-thirds power law not only characterizes various movement generation tasks but also seems to constrain visual perception of motion. The present study aimed to assess whether motor invariants, such as the two thirds power law also constrain motion perception in patients with Parkinson's disease (PD). Patients with PD and age-matched controls were asked to observe the movement of a light spot rotating on an elliptical path and to modify its velocity until it appeared to move most uniformly. As in previous reports controls tended to choose those movements close to obeying the two-thirds power law as most uniform. Patients with PD displayed a more variable behavior, choosing on average, movements closer but not equal to a constant velocity. Our results thus demonstrate impairments in how the two-thirds power law constrains motion perception in patients with PD, where this relationship between velocity and curvature appears to be preserved but scaled down. Recent hypotheses on the role of the basal ganglia in motor timing may explain these irregularities. Alternatively, these impairments in perception of movement may reflect similar deficits in motor production

Affine differential geometry analysis of human arm movements

Humans interact with their environment through sensory information and motor actions. These interactions may be understood via the underlying geometry of both perception and action. While the motor space is typically considered by default to be Euclidean, persistent behavioral observations point to a different underlying geometric structure. These observed regularities include the “two-thirds power law” which connects path curvature with velocity, and “local isochrony” which prescribes the relation between movement time and its extent. Starting with these empirical observations, we have developed a mathematical framework based on differential geometry, Lie group theory and Cartan’s moving frame method for the analysis of human hand trajectories. We also use this method to identify possible motion primitives, i.e., elementary building blocks from which more complicated movements are constructed. We show that a natural geometric description of continuous repetitive hand trajectories is not Euclidean but equi-affine. Specifically, equi-affine velocity is piecewise constant along movement segments, and movement execution time for a given segment is proportional to its equi-affine arc-length. Using this mathematical framework, we then analyze experimentally recorded drawing movements. To examine movement segmentation and classification, the two fundamental equi-affine differential invariants—equi-affine arc-length and curvature are calculated for the recorded movements. We also discuss the possible role of conic sections, i.e., curves with constant equi-affine curvature, as motor primitives and focus in more detail on parabolas, the equi-affine geodesics. Finally, we explore possible schemes for the internal neural coding of motor commands by showing that the equi-affine framework is compatible with the common model of population coding of the hand velocity vector when combined with a simple assumption on its dynamics. We then discuss several alternative explanations for the role that the equi-affine metric may play in internal representations of motion perception and production

A computational framework for estimating statistical power and planning hypothesis-driven experiments involving one-dimensional biomechanical continua.

Statistical power assessment is an important component of hypothesis-driven research but until relatively recently (mid-1990s) no methods were available for assessing power in experiments involving continuum data and in particular those involving one-dimensional (1D) time series. The purpose of this study was to describe how continuum-level power analyses can be used to plan hypothesis-driven biomechanics experiments involving 1D data. In particular, we demonstrate how theory- and pilot-driven 1D effect modeling can be used for sample-size calculations for both single- and multi-subject experiments. For theory-driven power analysis we use the minimum jerk hypothesis and single-subject experiments involving straight-line, planar reaching. For pilot-driven power analysis we use a previously published knee kinematics dataset. Results show that powers on the order of 0.8 can be achieved with relatively small sample sizes, five and ten for within-subject minimum jerk analysis and between-subject knee kinematics, respectively. However, the appropriate sample size depends on a priori justifications of biomechanical meaning and effect size. The main advantage of the proposed technique is that it encourages a priori justification regarding the clinical and/or scientific meaning of particular 1D effects, thereby robustly structuring subsequent experimental inquiry. In short, it shifts focus from a search for significance to a search for non-rejectable hypotheses

A pilot study evaluating use of a computer-assisted neurorehabilitation platform for upper-extremity stroke assessment

<p>Abstract</p> <p>Background</p> <p>There is a need to develop cost-effective, sensitive stroke assessment instruments. One approach is examining kinematic measures derived from goal-directed tasks, which can potentially be sensitive to the subtle changes in the stroke rehabilitation process. This paper presents the findings from a pilot study that uses a computer-assisted neurorehabilitation platform, interfaced with a conventional force-reflecting joystick, to examine the assessment capability of the system by various types of goal-directed tasks.</p> <p>Methods</p> <p>Both stroke subjects with hemiparesis and able-bodied subjects used the force-reflecting joystick to complete a suite of goal-directed tasks under various task settings. Kinematic metrics, developed for specific types of goal-directed tasks, were used to assess various aspects of upper-extremity motor performance across subjects.</p> <p>Results</p> <p>A number of metrics based on kinematic performance were able to differentiate subjects with different impairment levels, with metrics associated with accuracy, steadiness and speed consistency showing the best capability. Significant differences were also shown on these metrics between various force field settings.</p> <p>Conclusion</p> <p>The results support the potential of using UniTherapy software with a conventional joystick system as an upper-extremity assessment instrument. We demonstrated the ability of using various types of goal-directed tasks to distinguish between subjects with different impairment levels. In addition, we were able to show that different force fields have a significant effect on the performance across subjects with different impairment levels in the trajectory tracking task. These results provide motivation for studies with a larger sample size that can more completely span the impairment space, and can use insights presented here to refine considerations of various task settings so as to generalize and extend our conclusions.</p

Movement Timing and Invariance Arise from Several Geometries

Human movements show several prominent features; movement duration is nearly independent of movement size (the isochrony principle), instantaneous speed depends on movement curvature (captured by the 2/3 power law), and complex movements are composed of simpler elements (movement compositionality). No existing theory can successfully account for all of these features, and the nature of the underlying motion primitives is still unknown. Also unknown is how the brain selects movement duration. Here we present a new theory of movement timing based on geometrical invariance. We propose that movement duration and compositionality arise from cooperation among Euclidian, equi-affine and full affine geometries. Each geometry posses a canonical measure of distance along curves, an invariant arc-length parameter. We suggest that for continuous movements, the actual movement duration reflects a particular tensorial mixture of these canonical parameters. Near geometrical singularities, specific combinations are selected to compensate for time expansion or compression in individual parameters. The theory was mathematically formulated using Cartan's moving frame method. Its predictions were tested on three data sets: drawings of elliptical curves, locomotion and drawing trajectories of complex figural forms (cloverleaves, lemniscates and limaçons, with varying ratios between the sizes of the large versus the small loops). Our theory accounted well for the kinematic and temporal features of these movements, in most cases better than the constrained Minimum Jerk model, even when taking into account the number of estimated free parameters. During both drawing and locomotion equi-affine geometry was the most dominant geometry, with affine geometry second most important during drawing; Euclidian geometry was second most important during locomotion. We further discuss the implications of this theory: the origin of the dominance of equi-affine geometry, the possibility that the brain uses different mixtures of these geometries to encode movement duration and speed, and the ontogeny of such representations

Fast and fine-tuned corrections when the target of a hand movement is displaced

To study the strategy in responding to target displacements during fast goal-directed arm movements, we examined how quickly corrections are initiated and how vigorously they are executed. We perturbed the target position at various moments before and after movement initiation. Corrections to perturbations before the movement started were initiated with the same latency as corrections to perturbations during the movement. Subjects also responded as quickly to a second perturbation during the same reach, even if the perturbations were only separated by 60 ms. The magnitude of the correction was minimized with respect to the time remaining until the end of the movement. We conclude that despite being executed after a fixed latency, these fast corrections are not stereotyped responses but are suited to the circumstances

Adaptation to Delayed Force Perturbations in Reaching Movements

Adaptation to deterministic force perturbations during reaching movements was extensively studied in the last few decades. Here, we use this methodology to explore the ability of the brain to adapt to a delayed velocity-dependent force field. Two groups of subjects preformed a standard reaching experiment under a velocity dependent force field. The force was either immediately proportional to the current velocity (Control) or lagged it by 50 ms (Test). The results demonstrate clear adaptation to the delayed force perturbations. Deviations from a straight line during catch trials were shifted in time compared to post-adaptation to a non-delayed velocity dependent field (Control), indicating expectation to the delayed force field. Adaptation to force fields is considered to be a process in which the motor system predicts the forces to be expected based on the state that a limb will assume in response to motor commands. This study demonstrates for the first time that the temporal window of this prediction needs not to be fixed. This is relevant to the ability of the adaptive mechanisms to compensate for variability in the transmission of information across the sensory-motor system