Table 1.
Demographics and clinical assessments.
Fig 1.
Experimental setup and protocol.
(A) Schematic of the experimental setup. (B) The virtual environment. (C) Model of the lower extremities. Participants viewed the model from a first-person perspective. (D) Experimental protocol. MDS-UPDRS: Movement Disorder Society – Unified Parkinson’s Disease Rating Scale. (E) An example of foot trajectories and a definition of foot clearance (FC) for the LOW obstacle. Also, prescribed success ranges are shown in the shaded dotted box for both LOW and HIGH obstacles. (F) Schematic of state-space model variables for a LOW obstacle. Foot trajectories during skill acquisition are shown. FCEst represents the motor output (estimated foot clearance) of the state-space model; represents the estimated threshold of the success range for the LOW obstacle. In this example, as
is higher than the success range,
represents the estimated upper threshold; and e represents a motor error between the success range threshold and FCEst.
Table 2.
Participant-dependent parameters and population-based hyper-priors in the best model.
Fig 2.
Example foot clearance data for (A) a control participant and (B) a participant with PD.
Each data point represents foot clearance on a different obstacle. Empty circles correspond to LOW obstacles, and gray circles correspond to HIGH obstacles. The light and dark gray shaded areas represent the target range for the LOW and HIGH obstacles, respectively.
Fig 3.
Observed foot clearance data during skill acquisition and model fit.
Example participants (A) in the control group and (B) in the PD group. Data points represent the observed foot clearance as a function of obstacle number (Empty circle: LOW and Gray circle: HIGH). The solid black lines represent the model fit. The shaded areas represent 95% credible intervals, but these areas are frequently difficult to visualize as they are quite narrow.
Fig 4.
Posterior probabilities from the Bayesian estimation.
Population () and individual parameter posterior probabilities for (A-D) learning rate and (E-H) interference. (A and E) The population parameter posterior probabilities are transformed using a sigmoid function for visualization. (B and F) BGroup and qGroup represent the difference in population parameters between the control and PD groups. The difference was calculated after transforming the posterior probabilities using a sigmoid function. P(group difference < 0) indicates the proportion of the group difference probability below zero. (C and G) BEffect size and qEffect size represent the effect size of the difference in population parameters between the control and PD groups. The effect size was calculated using untransformed posterior probabilities. P(|effect size| > 0.1) indicates the proportion of the probability outside the ROPE using the posterior probability effect sizes. The black rectangle represents the “dead zone” where the effect is negligible or too small to be of any practical relevance. (D and H) Individual learning rate and interference posterior probabilities were sorted according to the median learning rate for visualization purposes. For all panels, the black dots represent the median of the posterior probability, and the bars represent the 95% credible intervals.
Fig 5.
Performance error during baseline and no feedback trials.
Performance error for each group (A) for LOW obstacles, (B) HIGH obstacles, and (C) ∆ performance error (no feedback – baseline) for LOW and HIGH obstacles. The dots represent participants, and the connecting lines represent changes in performance error. Solid black lines represent means for each group. The dotted lines represent zero. Asterisks indicate statistical significance: *: p < 0.05, ***: p < 0.001.
Fig 6.
Performance error during the end of practice on Day 1 and retention on Day 2.
Performance error for each group (A) for LOW obstacles, (B) HIGH obstacles, and (C) ∆ performance error (retention – end of practice) for LOW and HIGH obstacles. The dots represent participants, and connecting lines represent changes in performance error. Solid black lines represent medians for each group. The dotted lines represent zero. Asterisks indicate statistical significance: **: p < 0.01, ***: p < 0.001.
Fig 7.
Associations between skill acquisition on Day 1 and learning performance. (A) Relationship between ∆ performance error for online performance improvement (no feedback – baseline) on Day 1 and learning rate estimated by the Hierarchical Bayesian estimation. (B) Relationship between ∆ performance error for overnight retention (retention – end of practice) on Day 2 and interference estimated by the Hierarchical Bayesian estimation. (C) Relationship between performance error during retention on Day 2 and model-based performance error at the end of skill acquisition estimated by the Hierarchical Bayesian estimation. For panels A and B, the black dots and lines represent the PD group data and regression fits, while the gray dots and lines represent the control data and regression fits. The dotted black line in (C) represents a regression fit for the full dataset.