Neuromotor noise, error tolerance and velocity-dependent costs in skilled performance

Abstract

In motor tasks with redundancy neuromotor noise can lead to variations in execution while achieving relative invariance in the result. The present study examined whether humans find solutions that are tolerant to intrinsic noise. Using a throwing task in a virtual set-up where an infinite set of angle and velocity combinations at ball release yield throwing accuracy, our computational approach permitted quantitative predictions about solution strategies that are tolerant to noise. Based on a mathematical model of the task expected results were computed and provided predictions about error-tolerant strategies (Hypothesis 1). As strategies can take on a large range of velocities, a second hypothesis was that subjects select strategies that minimize velocity at release to avoid costs associated with signal- or velocity-dependent noise or higher energy demands (Hypothesis 2). Two experiments with different target constellations tested these two hypotheses. Results of Experiment 1 showed that subjects chose solutions with high error-tolerance, although these solutions also had relatively low velocity. These two benefits seemed to outweigh that for many subjects these solutions were close to a high-penalty area, i.e. they were risky. Experiment 2 dissociated the two hypotheses. Results showed that individuals were consistent with Hypothesis 1 although their solutions were distributed over a range of velocities. Additional analyses revealed that a velocity-dependent increase in variability was absent, probably due to the presence of a solution manifold that channeled variability in a task-specific manner. Hence, the general acceptance of signal-dependent noise may need some qualification. These findings have significance for the fundamental understanding of how the central nervous system deals with its inherent neuromotor noise.

Figure 1. Workspace, execution space and solution manifold.

A: Workspace with the position of the center post and target skittle in Experiment 1. Two ball trajectories exemplify how different release variables can lead to the same result with zero error (trajectory 1, 2, dashed lines). Trajectory 3 shows a trajectory with non-zero error. B: Workspace with center post and target as used in Experiment 2. Three select trajectories exemplify the redundancy of solutions as in panel A. C: Execution space and solution manifold of target and center post configuration in Experiment 1. White denotes zero-error solutions, increasing error is shown by increasingly darker grey shades, black denotes a post hit. The release variables of trajectory 1 and 2 correspond to points 1 and 2 on the solution manifold, the variables of trajectory 3 correspond to the point 3 in a grey-shaded area (error  = 30cm). D: Corresponding execution space and solution manifold. The three points correspond to the three trajectories of panel B.

Figure 2. Experimental setup.

Participants stand in front of the setup with their forearm resting on the horizontal lever arm. The rotation of the arm is recorded by the potentiometer, when the finger opens the contact switch the ball in the virtual simulation is released. Online recordings of the arm movements are displayed on the projection screen.

Figure 3. Histograms of all data and predictions for Hypotheses 1 and 2 for both experiments.

A, B: Histograms of all subjects' trials plotted onto the execution space of Experiment 1 and 2 (see Figure 1B and D). The data are plotted onto a grid of 36x36 bins on the execution space. C, D: Simulation of Hypothesis 1: The vertical dimension represents the expected result E(R) calculated as the Gaussian weighted averages over a matrix of execution variables transformed by the softmax function. The most error-tolerant solution with maximum E(R), shown by the red circle, is at α = −44 deg and v = 161 deg/s. In Experiment 2 error-tolerant solutions quantified as expected result E(R) are at an angle α = −82 deg, the optimal strategy for E(R) is at the highest velocity v = 1000 deg/s. E, F: Simulation of Hypothesis 2: The expected result E(R) has its optimal value at the minimum velocity α = −29 deg and v = 122 deg/s. In Experiment 2 E(R) shows its maximum value at α = 83 deg and v = 142 deg/s.

Figure 4. Descriptive results of Experiment 1.

A: Time series of errors (median and interquartile range) averaged across 9 participants. The trials were also averaged such that for every non-overlapping series of 15 trials the median was plotted with the corresponding interquartile ranges shown by the error bars. The line represents an exponential fit to highlight the time course. B: Distribution of trials of individual participants in sessions 2 and 3 plotted in execution space. The 360 trials of each of the 9 participants are represented by the 95% confidence ellipses.

Figure 5. Two-dimensional histograms of two representative individuals' data and the corresponding hypothesized distributions for Experiment 1.

The left panel shows the trial frequency, the middle panel shows the expected result E(R) of Hypothesis 1, the right panel shows the predicted distribution of Hypothesis 2. As the units of the three distributions are different they were all normalized to the range between 0 and 1. Note that the black color codes the lowest value and should not be mistaken for the high-penalty regions in Figure 3.

Figure 6. Descriptive results of Experiment 2.

A: Time series of errors over trials (median and interquartile range). The errors were averaged over 9 participants. The trials were also averaged such that for every non-overlapping series of 15 trials the median was plotted with the corresponding interquartile ranges shown by the error bars. The line represents an exponential fit to highlight the time course. B: Distribution of trials of individual participants in sessions 2 to 5 in execution space. The 720 trials of each of the 9 participants are represented by the 95% confidence ellipses.

Figure 7. Two-dimensional histograms of two representative individuals' data and the corresponding hypothesized distributions for Experiment 2.

The left panel shows the trial frequency, the right panel shows the expected result E(R) of Hypothesis 1, the right panel shows the predicted distribution of Hypothesis 2. As the units of the three distributions are different they were all normalized to the range between 0 and 1. Note that the black color codes the lowest value and should not be mistaken for the high-penalty regions in Figure 3.

Figure 8. Standard deviations of velocity and angle plotted against their respective mean velocity.

A: Data of all subjects in Experiment 2 (9 participants in 4 sessions with 3 blocks each). The linear regressions did not show any dependency of variability on the velocity. B: Data of Experiment 3 where subjects performed the same throwing movement but without a target. While standard deviations did not scale with increasing mean velocity in Experiment 2, velocity-dependent variability or noise was observed in this Experiment.