Subjects

Experiments were approved by the Northwestern University Institutional Review Board. Methods were carried out in accordance with IRB approval. All subjects provided informed consent before beginning each study. Eight subjects participated in the first and second experiments. Based on a power analysis of simulations using these data, four subjects from the second experiment also participated in the third experiment30.

Setup

All protocol and data collection were executed using MATLAB R2017b. Subjects sat in front of a 15.5-inch 1920 × 1080 resolution computer monitor at a distance of 24–36 inches. The screen displayed a black two-link system over a uniform white background (Figs 1 and 2). The arm had link lengths of 5 cm, widths of 5 points (1.8 mm), and endcap diameters of 6 points (2.1 mm).

Figure 1 Experiment 1 Setup and Conditions. Assessed component is highlighted green, while all other components are displayed black. Fixture markings in grey are shown here for clarity but were not displayed during experiments. (a) Absolute speed condition. Subjects assessed highlighted proximal link speed in three speed conditions: 30, 60, or 120 °/s. Distal link rotated at 60 °/s. (b) Joint speed condition. Subjects assessed highlighted distal link speed in three speed conditions: 30, 60, or 120 °/s. Proximal link rotated at 60 °/s. (c) Linear speed condition. Subjects assessed highlighted endpoint speed in three speed conditions: 2, 4, or 8 cm/s. Proximal and distal links were driven by endpoint position. Full size image

Figure 2 Experiment 2 Setup and Conditions. For each shift condition, subjects assessed highlighted joint speed in three speed conditions: 30, 60, or 120 °/s. Fixture markings in grey are shown here for clarity but were not displayed during experiments. (a) No shift condition. Reference frame rotated at 60 °/s. (b) Small shift condition. Reference frame rotated at 60 °/s in one stimulus, and 85 °/s in the other stimulus (c) Large shift condition. Reference frame rotated at 60 °/s in one stimulus, and 120 °/s in the other stimulus. Full size image

Each visual stimulus was presented for 2 seconds, with a 1 second pause between stimuli during which only the white background was shown. Animations were presented at 30 frames per second. Subjects were asked to indicate which stimulus moved faster in the dictated reference frame via a pop-up window prompt. Subjects had unimpaired or corrected vision.

Experiments

Three two-alternative forced choice experiments investigated different aspects of visual speed discrimination. During each experiment, two examples of the two-link arm were displayed to subjects in random order. One stimulus always moved at a nominal speed, whereas the other stimulus differed from the nominal speed by a magnitude determined by an adaptive staircase. The adaptive staircase was defined as:

$$x(n+1)=x(n)-\frac{C}{{n}_{shift}+1}[z(n)-\varphi ]$$ (1)

where x was the difference in movement speeds between stimuli, C was the starting speed difference, n shift was the number of decision reversals, ϕ was the target JND probability (84%), and z was a Boolean indicator for the subject’s decision (z = 1 when correct and z = 0 when incorrect)31. Thus, when subjects correctly identified the faster stimulus, the speed difference between stimuli decreased for the next trial. Likewise, if subjects incorrectly selected the slower stimulus, the speed difference between stimuli increased for the next trial.

The JND for each condition was calculated as the final stimulus difference x tested in the adaptive staircase, which converged after 25 decision reversals. The 84% JND has a unique property32 in that it is linearly variable with the uncertainty (i.e. standard deviation) of the underlying estimator:

$$SD=\frac{JN{D}_{84 \% }}{\sqrt{2}}$$ (2)

Thus, the 84% JND was converted to uncertainty, normalized, and used as the outcome metric for statistical analyses.

Experiment 1: Effect of Speed Type

To determine how discrimination differs between categories of movements, three speed types were tested: absolute speed, joint speed, and linear speed (Fig. 1). These speed types correspond with different types of proprioceptive feedback that could be provided for prosthetic limbs: speed of a prosthetic joint relative to the torso (absolute) or residual limb (joint), or speed of the prosthetic end effector (linear).

Absolute speed refers to rotational movement relative to a global, static reference frame. In this condition, the proximal link moved at a nominal speed of either 30, 60, or 120 °/s counter-clockwise (CCW) for one stimulus, and a speed determined by the adaptive staircase in Equation (1) for the other stimulus, starting at C = 50%. The distal link moved at a nominal speed of 60 °/s CCW and accelerated and decelerated randomly but equally for both stimuli; thus, the movement profile was not constant, but was identical for both stimuli (Fig. 1a).

Joint speed refers to rotational movement relative to a dynamic reference frame, in this case the proximal link. In this condition, the proximal link moved at a nominal speed of 60 °/s CCW and accelerated and decelerated randomly but equally for both stimuli; thus, the movement profile was not constant, but was identical for both stimuli. The distal link moved at a nominal speed of either 30, 60, or 120 °/s CCW for one stimulus, and a speed determined by the adaptive staircase in Equation (1) for the other stimulus, starting at C = 50% (Fig. 1b).

The random acceleration and deceleration on the proximal link during the joint speed condition was implemented to prevent subjects observing absolute speed to estimate joint speed of the distal link by varying the speed of the reference frame. The random acceleration and deceleration on the distal link during the absolute speed condition was implemented to match the joint speed condition, even though it likely had no effect on estimates.

Linear speed refers to movement in a straight line relative to a static Cartesian reference frame. In this condition, the linkage endpoint moved along a straight path at a constant speed of either 2, 4, or 8 cm/s for one stimulus, and a speed determined by the adaptive staircase in Equation (1) for the other stimulus, starting at C = 50%. The links were driven by inverse kinematics to follow the endpoint (Fig. 1c).

Thus, a total of 9 conditions were tested: 3 speed types, with 3 tested speeds each. Starting positions were randomized for all trials. For absolute and joint speed trials, the distal link was prevented from crossing the proximal link during movement; invalid starting positions were resampled until conditions were met. Proximal and distal link speeds were bounded between 0 and 180 °/s, preventing clockwise movement and invalid starting positions due to resampling. For linear speed trials, the starting position and movement direction were resampled if the endpoint trajectory exceeded the range of the linkage, or if the endpoint didn’t move CCW relative to the origin. The proximal link, distal link, or endpoint were highlighted according to the tested condition.

Statistical analyses performed in RStudio (RStudio, Inc., version 1.1.447) quantified main and interaction effects of the speed type and the observed nominal speed. A Shapiro-Wilk test confirmed normality of the data. A general linear model took the form:

$$SD\sim {\beta }_{0}+speed+type+speed\times type$$

where speed was coded as a continuous independent variable in units of octaves (0 at slowest speed, 2 at fastest), and type was coded as a categorical independent variable. Because the interaction term was found to be significant, a simple main effects analysis was performed for speed33. Corrections for 6 comparisons were made via a Bonferroni correction factor.

Experiment 2: Effect of Reference Frame Speed Shift

While the first experiment provided an estimate of joint speed perception, it only did so at one reference frame speed. Although results showed a higher uncertainty for joint speed observations than for absolute or linear speed observations, it did not shed any light on possible interaction between changes to the reference frame speed and visual uncertainty. Further, one concern from the first experiment was that during joint speed conditions, subjects could conceivably identify the faster joint speed of two stimuli by observing either the joint speed or the absolute rotational speed of the distal link. This ambiguity left open the possibility that the higher uncertainty was due to observing a faster absolute speed, rather than due to the joint speed nature of the observation itself. We therefore developed a second experiment to determine how joint speed discrimination differs due to changes in reference frame speed. This experiment investigates visual perception of a prosthetic limb while the residual limb is moving non-uniformly. In this experiment, three reference frame conditions were tested. The proximal link rotated at 60 °/s CCW for one stimulus, and a shifted speed of 60, 85, or 120 °/s CCW for the other stimulus; these speeds correspond with an increase of 0, ½, or 1 octave above 60 °/s, respectively. The distal link rotated at 30, 60, or 120 °/s CCW for one stimulus, and a speed determined by the adaptive staircase in Equation (1) for the other stimulus, starting at C = 50%. Thus, a total of 9 conditions were tested: 3 reference frame speed shifts, with 3 distal link speeds each (Fig. 2). Each link was highlighted green at the joint, with a highlight length of 2 cm.

Statistical analyses were performed to quantify how reference frame speed shift magnitude affects uncertainty. A Shapiro-Wilk test confirmed normality of the data. A multiple linear regression model took the form:

$$SD\sim {\beta }_{0}+speed+shift+speed\times shift$$

where speed and shift were coded as continuous independent variables. The interaction term was used to determine if shift magnitude impacts uncertainty differently at different speeds. The interaction term was not found to be significant (B = 0.0002, t(68) = 0.304, p = 0.762), thus the term was removed and the reduced model was reanalyzed33.

After inspecting the data, post-hoc analyses tested the pairs of stimuli subjects chose incorrectly. There were two possible stimulus pairs: one where the speed shift of the reference frame aligned with the faster of the two stimuli, and one where the speed shift occurred with the slower of the two stimuli. The former pair might be considered an easier choice – the correct answer with the faster distal link happens to be the stimulus with the faster proximal link – while the latter pair might be considered a more difficult choice – the correct answer with the faster distal link is the stimulus with the slower proximal link. Therefore, we wanted to determine if speed or shift impacted the rate of errors due to unaligned stimulus changes (the difficult choice). If there was no impact, subjects should make roughly the same number of errors during aligned pairs and unaligned pairs.

Post-hoc statistical analyses were performed using a multiple linear regression model taking the form:

$$Rate\sim {\beta }_{0}+speed+shift+speed\times shift$$

where speed and shift were coded as continuous independent variables. A Shapiro-Wilk test confirmed normality of the data. The interaction term was not found to be significant (B = 0.280, t(44) = 1.098, p = 0.278), thus the term was removed and the reduced model was reanalyzed33.

Experiment 3: Effect of Audio Feedback

To determine if joint speed estimates could be improved with supplementary feedback, the no shift conditions from the second experiment were repeated. Subjects were provided frequency-modulated audio feedback matching the joint speed of stimuli according to the following equation:

$$f(\omega )={f}_{min}\cdot {2}^{\frac{\omega }{{V}_{step}}}$$ (3)

where f min was the minimum frequency which was provided when joint speed was zero, and V step was the speed increase required to increase the audio feedback pitch by one octave. For this study, f min was set to 220 Hz (A 3 ), and V step was set to 60 °/s. Audio signals were generated and output with a sampling frequency of 48 kHz. Subjects wore noise-cancelling headphones, and audio was played at a moderate volume. Based on pilot studies, the starting difference C between joint speeds was set at 10% to allow the adaptive staircase to converge more smoothly.

Statistical analyses were performed using a general linear model taking the form:

$$SD\sim {\beta }_{0}+speed+feedback+speed\times feedback$$

where speed was coded as a continuous independent variable and feedback was coded as a categorical independent variable. A Shapiro-Wilk test confirmed normality of the data. The purpose of this model was to determine if vision + audio improved joint speed discrimination beyond vision. The interaction term determined if the benefit of audio feedback was partially dependent on distal link speed, or if benefit was global. A main effects analysis compared vision and vision + audio. Because the interaction term was significant, and a simple main effects analysis was performed for speed33. Corrections for 3 comparisons were made via a Bonferroni correction factor.