Faculty Bibliography

A coordinate system is composed of an encoding, defining the dimensions of the space, and an origin. We examine the coordinate encoding used to update motor plans during sensory-motor adaptation to center-out reaches. Adaptation is induced using a novel paradigm in which feedback of reach endpoints is perturbed following a sinewave pattern over trials; the perturbed dimensions of the feedback were the axes of a Cartesian coordinate system in one session and a polar coordinate system in another session. For center-out reaches to randomly chosen target locations, reach errors observed at one target will require different corrections at other targets within Cartesian- and polar-coded systems. The sinewave adaptation technique allowed us to simultaneously adapt both dimensions of each coordinate system (x-y, or reach gain and angle), and identify the contributions of each perturbed dimension by adapting each at a distinct temporal frequency. The efficiency of this technique further allowed us to employ perturbations that were a fraction the size normally used, which avoids confounding automatic adaptive processes with deliberate adjustments made in response to obvious experimental manipulations. Subjects independently corrected errors in each coordinate in both sessions, suggesting that the nervous system encodes both a Cartesian- and polar-coordinate-based internal representation for motor adaptation. The gains and phase lags of the adaptive responses are not readily explained by current theories of sensory-motor adaptation.

This paper proposes a parametric model for saccadic waveforms. The model has a small number of parameters, yet it effectively simulates a variety of physiologic saccade properties. In particular, the model reproduces the established relationship between peak saccadic angular velocity and saccadic amplitude (i.e., the saccadic main sequence). The proposed saccadic waveform model can be used in the evaluation and validation of methods for quantitative saccade analysis. For example, we use the proposed saccade model to evaluate four well-known saccade detection algorithms. The comparison indicates the most reliable algorithm is one by Nystrom et al. We further use the proposed saccade model to evaluate the standard technique used for the estimation of peak saccadic angular velocity. The evaluation shows the occurrence of systematic errors. We thus suggest that saccadic angular velocity values determined by the standard technique (low-pass differentiation) should be interpreted and used with caution.

Healthy individuals appear to use both vector-coded reach plans that encode movements in terms of their desired direction and extent, and target-coded reach plans that encode the desired endpoint position of the effector. We examined whether these vector and target reach-planning codes are differentially affected after stroke. Participants with stroke and healthy controls made blocks of reaches that were grouped by target location (providing target-specific practice) and by movement vector (providing vector-specific practice). Reach accuracy was impaired in the more affected arm after stroke, but not distinguishable for target- versus vector-grouped reaches. Reach velocity and acceleration were not only impaired in both the less and more affected arms poststroke, but also not distinguishable for target- versus vector-grouped reaches. As previously reported in controls, target-grouped reaches yielded isotropic (circular) error distributions and vector-grouped reaches yielded error distributions elongated in the direction of the reach. In stroke, the pattern of variability was similar. However, the more affected arm showed less elongated error ellipses for vector-grouped reaches compared to the less affected arm, particularly in individuals with right-hemispheric stroke. The results suggest greater impairment to the vector-coded movement-planning system after stroke, and have implications for the development of personalized approaches to poststroke rehabilitation: Motor learning may be enhanced by practice that uses the preserved code or, conversely, by retraining the more impaired code to restore function.

Coordinate systems for movement planning are comprised of an anchor point (e.g., retinocentric coordinates) and a representation (encoding) of the desired movement. One of two representations is often assumed: a final-position code describing desired limb endpoint position and a vector code describing movement direction and extent. The existence of movement-planning systems using both representations is controversial. In our experiments, participants completed reaches grouped by target location (providing practice for a final-position code) and the same reaches grouped by movement vector (providing vector-code practice). Target-grouped reaches resulted in the isotropic (circular) distribution of errors predicted for position-coded reaches. The identical reaches grouped by vector resulted in error ellipses aligned with the reach direction, as predicted for vector-coded reaches. Manipulating only recent movement history to provide better learning for one or the other movement code, we provide definitive evidence that both movement representations are used in the identical task.

We examine the possibility that sensory and motor adaptation may be induced via a sinusoidally incremented perturbation. This sinewave adaptation method provides superior data for fitting a parametric model than when using the standard step-function method of perturbation, due to the relative difficulty of fitting a decaying exponential vs. a sinusoid. Using both experimental data and simulations, we demonstrate the difficulty of detecting the presence of motor adaptation using a step-function perturbation, compared to detecting motor adaptation using our sinewave perturbation method.

In the study of visual-motor control, perhaps the most familiar findings involve adaptation to externally imposed movement errors. Theories of visual-motor adaptation based on optimal information processing suppose that the nervous system identifies the sources of errors to effect the most efficient adaptive response. We report two experiments using a novel perturbation based on stimulating a visually induced reflex in the reaching arm. Unlike adaptation to an external force, our method induces a perturbing reflex within the motor system itself, i.e., perturbing forces are self-generated. This novel method allows a test of the theory that error source information is used to generate an optimal adaptive response. If the self-generated source of the visually induced reflex perturbation is identified, the optimal response will be via reflex gain control. If the source is not identified, a compensatory force should be generated to counteract the reflex. Gain control is the optimal response to reflex perturbation, both because energy cost and movement errors are minimized. Energy is conserved because neither reflex-induced nor compensatory forces are generated. Precision is maximized because endpoint variance is proportional to force production. We find evidence against source-identified adaptation in both experiments, suggesting that sensory-motor information processing is not always optimal.

We analyze the problem of obstacle avoidance from a Bayesian decision-theoretic perspective using an experimental task in which reaches around a virtual obstacle were made toward targets on an upright monitor. Subjects received monetary rewards for touching the target and incurred losses for accidentally touching the intervening obstacle. The locations of target-obstacle pairs within the workspace were varied from trial to trial. We compared human performance to that of a Bayesian ideal movement planner (who chooses motor strategies maximizing expected gain) using the Dominance Test employed in Hudson et al. (2007). The ideal movement planner suffers from the same sources of noise as the human, but selects movement plans that maximize expected gain in the presence of that noise. We find good agreement between the predictions of the model and actual performance in most but not all experimental conditions.

When movement outcome differs consistently from the intended movement, errors are used to correct subsequent movements (e.g., adaptation to displacing prisms or force fields) by updating an internal model of motor and/or sensory systems. Here, we examine changes to an internal model of the motor system under changes in the variance structure of movement errors lacking an overall bias. We introduced a horizontal visuomotor perturbation to change the statistical distribution of movement errors anisotropically, while monetary gains/losses were awarded based on movement outcomes. We derive predictions for simulated movement planners, each differing in its internal model of the motor system. We find that humans optimally respond to the overall change in error magnitude, but ignore the anisotropy of the error distribution. Through comparison with simulated movement planners, we found that aimpoints corresponded quantitatively to an ideal movement planner that updates a strictly isotropic (circular) internal model of the error distribution. Aimpoints were planned in a manner that ignored the direction-dependence of error magnitudes, despite the continuous availability of unambiguous information regarding the anisotropic distribution of actual motor errors.

Although horizontal binocular retinal disparity between images in the two eyes resulting from their different views of the world has long been the centerpiece for understanding the unique characteristics of stereovision, it does not suffice to explain many binocular phenomena. Binocular depth contrast (BDC), the induction of an appearance of visual pitch in a centrally located line by pitched-from-vertical flanking lines, has particularly been the subject of a good deal of attention in this regard. In the present article, we show that BDC does not cross the median plane but is restricted to the side of the visual field containing a unilateral inducer. These results cannot be explained by the use of retinal disparity alone or in combination with any additional factors or processes previously suggested to account for stereovision. We present a two-channel three-stage neuromathematical model that accounts quantitatively for present and previous BDC results and also accounts for a large number of the most prominent features of binocular pitch perception: Stage 1 of the differencing channel obtains the difference between the retinal orientations of the images in the two eyes separately for the inducer and the test line; stage 1 of the summing channel obtains the corresponding sums. Signals from inducer and test stimuli are combined linearly in each channel in stage 2, and in stage 3 the outputs from the two channels are combined along with a bias signal from the body-referenced mechanism to yield ', the model's prediction for the perception of pitch.

Motor control requires the generation of a precise temporal sequence of control signals sent to the skeletal musculature. We describe an experiment that, for good performance, requires human subjects to plan movements taking into account uncertainty in their movement duration and the increase in that uncertainty with increasing movement duration. We do this by rewarding movements performed within a specified time window, and penalizing slower movements in some conditions and faster movements in others. Our results indicate that subjects compensated for their natural duration-dependent temporal uncertainty as well as an overall increase in temporal uncertainty that was imposed experimentally. Their compensation for temporal uncertainty, both the natural duration-dependent and imposed overall components, was nearly optimal in the sense of maximizing expected gain in the task. The motor system is able to model its temporal uncertainty and compensate for that uncertainty so as to optimize the consequences of movement.