Characterizing Human Perception of Speed Differences in Walking: Insights From a Drift Diffusion Model

Abstract

Despite its central role in the proper functioning of the motor system, sensation has been less studied than motor outputs in sensorimotor adaptation paradigms. This is likely due to the difficulty of measuring sensation non-invasively: while motor outputs have easily observable consequences, sensation is inherently an internal variable of the motor system. In this study, we investigated how well participants can sense relevant sensory stimuli that induce locomotor adaptation. We addressed this question with a split-belt treadmill, which moves the legs at different speeds. We used a two-alternative forced-choice paradigm with multiple repetitions of various speed differences considering the probabilistic nature of perceptual responses. We found that the participants correctly identified a speed difference of 49.7 mm/s in 75% of the trials when walking at 1.05 m/s (i.e., 4.7% Weber Fraction). To gain insight into the perceptual process in walking, we applied a drift-diffusion model (DDM) relating the participants' identification of speed difference (i.e., stimulus identification) and their response time during walking. The implemented DDM was able to predict participants' stimulus identification for all speed differences by simply using the recorded reaction times (RTs) to fit a single set of model parameters. Taken together, our results indicate that individuals can accurately identify smaller speed differences than previously reported and that participants' stimulus perception follows the evidence accumulation process outlined by drift diffusion models, conventionally used for short-latency, static sensory tasks, rather than long-latency, and motor tasks such as walking.

Keywords: decision-making; human locomotion; motor control; sensorimotor adaptation.

Figure 1.

Protocol and methods for characterizing the perception of belt speed differences. A, Experimental protocol. Participants completed a familiarization block followed by 3 testing blocks. B, In each testing block, participants completed a series of perceptual tasks (indicated by the gray shaded areas). Specifically, Panel B shows one of the four sequences within a testing block. Each testing block includes four presentations of this sequence, either as a mirror image (where the belt speed differences are reversed) or with the presentation order flipped. As a result, each testing block comprises a total of four presentations for each non-zero stimulus magnitude and eight null trials. C, Description of the perceptual task. The task began with an auditory cue (red circle in the task schematic). Upon hearing the cue, participants were instructed to identify the slower moving belt and make a keypress to indicate their response. In this study, we analyzed RTs and the choice made in the task. The task ended when the participant indicated a choice or after 8 strides of walking. D, Schematic of the DDM. The DDM for 2AFC tasks represents the temporal evolution of a decision variable as a random walk (black and gray jagged lines). Decisions are made when one of the two decision barriers is reached (dashed lines: a and b = −a). RT is composed of a non-decision and decision interval. In this study, the non-decision time is defined as the interval between the auditory start cue and the onset of the evidence accumulation process. An example of the evolution of the decision variable is shown as the black jagged line, which has some drift rate (red line) and noisy evidence accumulation until reaching the upper threshold a, indicating that a decision has been made.

Figure 2.

Individual variability in the perception of belt speed differences. The color in the circles and bar plots represent individual participants ordered by the magnitude of the JND. A, Point of subjective equality (PSE) estimates are displayed as colored bars. Error bars illustrate the 95% confidence interval (CI) from the logistic regression models. The height of each bar plot and the error bars indicate the best estimate and approximate confidence intervals propagated from β₀ and β₁ (PSE = −β₀/β₁) presuming fixed β₁ to its maximum likelihood value. Asterisks display significant PSE. The average of the individual PSEs is represented by the black bar height and the horizontal dashed line. B, Just noticeable difference (JND) estimate with 95% CI (errorbars). Values are computed as 1.1/β₁. Confidence intervals are computed by applying the same transformation to the edges of the CI of β₁. This results in skewed CIs. Note that all the individual JNDs are significantly different from zero. The average of the individual JNDs are represented by the height of the black bar and the horizontal dashed line. C, Mean RTs vs. mean overall accuracy across all stimulus magnitudes for each participant (± 1.96*standard error). The color of the dots corresponds to the JND values displayed in the gradient scale in panel B. The group average behavior is shown as the black data point.

Figure 3.

Choice, accuracy, and mean RTs as a function of stimulus magnitude. A, Choice as a function of stimulus magnitude (ΔV, black labels) or stimulus magnitude scaled by mean walking speed ( $\mathrm{\Delta }V/\overline{V}$, gray labels). Here, positive values indicate the left leg is moving slower, and vice versa. Circles indicate group average responses across participants, while the error bars indicate 1.96*standard error of the mean. The thin gray lines represent logistic fits to individual data (see Methods) and the thick black line represents the mean of the individual logistic fits. We used a generalized linear fixed model to fit the data of individual participants or a generalized linear mixed model with random effects. B, Accuracy as a function of stimulus magnitude or stimulus magnitude scaled by mean walking speed. The data shown in the circles (group average ± 1.96*standard error) is equivalent to that shown in the left panel but averaged across positive and negative stimuli. Accuracy score was not calculated for the null trials. C, Mean RT as a function of stimulus magnitude or stimulus magnitude scaled by mean walking speed. Circles indicate the experimental data (group average ± 1.96*standard error). Note that the color gradient in the circles among all panels depend on the absolute stimulus magnitude, which is a measure of task difficulty. Darker shades of gray mean easier tasks.

Figure 4.

Drift-Diffusion model can predict choices based on RTs from the 2AFC task data recorded during walking. In all panels the circles represent the experimental data (group average). The color gradient in the data among all panels depend on the absolute stimulus magnitude, which is a measure of task difficulty. Darker shades of gray mean easier tasks. A, Choices vs. stimulus magnitude (ΔV, black labels) or stimulus magnitude scaled by mean walking speed ( $\mathrm{\Delta }V/\overline{V}$, gray labels). Black line represents the average of the individual fits to the choice data using generalized linear mixed models. This line is equivalent to that shown in Figure 3A. The blue line shows the prediction for the choices from the DDM fit on the reaction time data from panel B. B, Mean RT vs. stimulus magnitude or stimulus magnitude scaled by mean walking speed. The DDM model was fit to each individual participant. The blue line represents the mean curve from fitting the RT data to each individual.