Automatic learning mechanisms for flexible human locomotion
- Department of Neuroscience, The Johns Hopkins University School of Medicine, United States
- Center for Movement Studies, Kennedy Krieger Institute, United States
- Division of Biokinesiology and Physical Therapy, University of Southern California, United States
- Neuroscience Graduate Program, University of Southern California, United States
- Department of Physical Medicine and Rehabilitation, The Johns Hopkins University School of Medicine, United States
Figures
Box 1—figure 1
Standard paradigm and measures.
(A) Treadmill belt speeds for the standard split-belt paradigm. (B) Schematic time course of standard motor measures of walking adaptation: step length asymmetry – a measure of error (solid purple), Δ motor output – a measure of compensatory spatial and temporal asymmetries (dotted blue), and perturbation – the effect of the speed asymmetry on the walking pattern (dashed red). In baseline, the belts are tied, and perturbation, Δ motor output, and step length asymmetry are all ~0. In adaptation, the right leg is faster than the left such that the perturbation is positive. The Δ motor output is still ~0 in early adaptation, causing step length asymmetry errors (negative purple line). By late adaptation, the Δ motor output is adapted to match the perturbation, and step length asymmetry returns to ~0. Changes to Δ motor output persist in tied belts post-adaptation, but the perturbation is ~0, causing step length asymmetry aftereffects (positive purple line).
Box 2—figure 1
Relevant results from Leech et al., 2018a.
(A) Treadmill belt speeds and step length asymmetry time course, similar to that described in Box 1—figure 1. Vertical dashed gray lines indicate iterations of the speed match task, where participants adjust the speed of the right belt with a keypad to match it to the left. (B) Time courses of the belt speeds (top; orange = right, black = left) and step length asymmetry (bottom) in selected iterations of the speed match task. Left, ‘before adapt’: last baseline task. Right, ‘after adapt’: first post-adaptation task. Dotted horizontal lines depict the right speed (orange, top) and step length asymmetry magnitude (purple, bottom) at adaptation plateau (average over the last 30 strides). (C) Belt speed (top; right relative to left) and step length asymmetry (bottom) magnitudes at the end of the tasks shown in B. All curves show group mean ± SE, and all data is collected in the Leech et al. study (Leech et al., 2018a).
Figure 1 with 1 supplement
Experiment 1, hypotheses and predictions.
(A) Conceptual schematic of our paradigm with the Ramp Down task: after adaptation, the right belt speed is gradually ramped down to match the left. (B–C) Predictions for the Ramp Down motor measures made by two competing hypotheses. (B) Recalibration only: recalibration can only change movement gradually. The Δ motor output (dotted blue line) changes slowly and does not track the rapidly decreasing perturbation (dashed red line), so that step length asymmetry aftereffects emerge immediately (solid purple line, magnitude is positive). (C) Recalibration + mapping: mapping can change movement immediately. In the first part of the task (highlighted in green), the mapping contribution to Δ motor output (dark blue shade) is scaled down immediately as the perturbation decreases. Hence, the Δ motor output (dotted blue line) changes rapidly and tracks the perturbation (dashed red line), so that there are no step length asymmetry aftereffects (solid purple line, magnitude is ~zero). In the second part of the task, the mapping contribution to Δ motor output is zero, and the recalibration contribution to Δ motor output (light blue shade) does not change significantly. Hence, the Δ motor output (dotted blue line) does not track the perturbation (red dashed line), and step length asymmetry aftereffects emerge (solid purple line, magnitude is positive). Right column inset: conceptual explanation of how both hypotheses may account for the speed match results from Leech et al. (Leech et al., 2018a). In the first post-adaptation speed match task, participants increase the speed of the right belt from zero to a value that is smaller than adaptation but larger than the left belt (top panel). The perturbation increases until a value that is positive but smaller than adaptation (dashed red line, middle and bottom panels). Leech et al. observed symmetric step lengths at the end of the task, indicating that the Δ motor output (dotted blue line) is smaller than it was in adaptation and matches the perturbation. The decrease in Δ motor output can be explained by the recalibration only hypothesis as forgetting/unlearning (middle panel), or by the recalibration + mapping hypothesis as flexible scaling of the mapping contribution (bottom panel).
Figure 1—figure supplement 1
Experiment 1, conceptual schematic of the learning mechanisms.
(A) Forward model recalibration. By the end of adaptation, the forward model is recalibrated to account for the full split perturbation. The recalibration mechanism can only access the last learned Δ motor output and uses it regardless of the perturbation (the Δ motor output usplit, light blue, is used for all perturbations ptied, p2, p3,..., psplit, red), leading to step length asymmetry aftereffects throughout the Ramp Down. (B) Stimulus-response mapping. Mapping can access all Δ motor outputs learned in adaptation and can select the one matching the perturbation (the appropriate Δ motor output utied, u2, u3,..., or usplit, dark blue, is used in response to perturbations ptied, p2, p3,..., or psplit, red), leading to no step length asymmetry aftereffect. (C) Recalibration + mapping. The Δ motor output can match perturbations accounted for by mapping (the appropriate Δ motor output in the range of ur, ur+1,..., usplit, dark blue, is used in response to perturbations in the range pr, pr+1,..., psplit), such that step length asymmetry remains zero in the first part of the Ramp Down. For smaller perturbations, the Δ motor output is fixed to the last learned calibration (the Δ motor output ur, light blue, is used for all smaller perturbations ptied,..., pr), such that step length asymmetry aftereffects begin to emerge. Note that these are simplified illustrations of concepts and not realistic predictions.
Figure 2 with 2 supplements
Experiment 1, step length asymmetry.
(A) Top: Experimental protocol. The Ramp Down task (purple) is used to test the predictions illustrated in Figure 1. Bottom: Step length asymmetry time course. Background shading darkness increases with belt speed difference (color bar). Phases (except Ramp tasks) are truncated to the participant with fewest strides. (B) Zoomed-in baseline ramp and post-adaptation Ramp Down tasks. Speed differences for which step length asymmetry is not significantly different from zero are indicated by the green shade. Inset depicts predictions made by the competing hypotheses as in Figure 1. All curves show group mean ± SE.
Figure 2—figure supplement 1
Experiment 1, analysis of step length asymmetry aftereffects in ramp tasks.
Step length asymmetry (pre-averaged within participant for strides taken at the same speed) as a function of speed. Purple line and dots show group mean. Lighter pink shade shows 95% CI, and darker purple shade shows CI for alpha level corrected for multiple comparisons (depicted for all points but used for significance testing only when 95% CI excludes zero). Green shaded background represents speeds for which step length asymmetry is not significantly different than zero.
Figure 2—figure supplement 2
Experiment 1, variability in adaptation.
(A) Within-participant variance in step length asymmetry in the first and last 30 strides of adaptation. (B) Decay in variance between these time points. Bars and error bars: group mean ± CI, circles: individual participants.
Figure 3 with 2 supplements
Experiment 1, perturbation and Δ motor output.
(A) Perturbation (red) and Δ motor output (blue) data for the Ramp Down task. (B–C) Perturbation data (red) and model fit for the Δ motor output (blue) for the recalibration + mapping model and three recalibration only models. Timeseries curves show group mean ± SE, and green shade corresponds to speeds with symmetric step lengths as in Figure 2. Bar insets in (C): BIC difference between recalibration + mapping and each recalibration only model (bar ± error bar shows group mean ± CI, circles show individual participants’ data).
Figure 3—figure supplement 1
Experiment 1, individual participants’ recalibration + mapping fits and perceptual results.
Perturbation (red circles), Δ motor output (blue circles), and recalibration + mapping model fitted to the Δ motor output (black line), for the Ramp Down task. Green shaded area represents strides between button presses of the perceptual task. The insets show step length asymmetry, Δ motor output, and perturbation at adaptation plateau (mean of the last 30 strides; circles are individual participants and error bars depict group mean ± SE).
Figure 3—figure supplement 2
Experiment 1, individual participants’ dual state fits.
Perturbation (red circles), Δ motor output (blue circles), and dual state model fitted to the Δ motor output (black line), for the Ramp Down task.
Figure 4 with 1 supplement
Experiment 1, perceptual results.
(A) Top: perturbation data (red) and recalibration + mapping fit (blue); this is the same as Figure 3B. Bottom: perceptual task button presses (green, group mean ± SE of button press stride depicted as a function of belt speed difference). Right: measures of motor recalibration (‘’) and total motor adaptation (‘’). (B) Perturbation compensation (normalized perceptual and motor measures of adaptation): bounds (green - labeled ‘total’ to clarify it is the total realignment), (dark blue), and (light blue). (C–D) Individual participants’ versus (first or second button press). Solid black: least squares line. Dashed gray: unity line.
Figure 4—figure supplement 1
Experiment 1, baseline ramp perceptual results.
Baseline perceptual task button presses (green vertical lines, group mean ± SE), overlaid on step length asymmetry data (purple line and shade, group mean ± SE).
Figure 5
Experiment 1, perceptual models.
(A–C) Perturbation data (red) and model fits for the Δ motor output (dark blue) for the proprioceptive re-alignment model (PReMo), Perceptual Error Adaptation model (PEA), and perceptuomotor recalibration + mapping model (PM-ReMap). Dark blue bar insets: BIC difference between recalibration + mapping and each perceptual model (bar ± error bar shows group mean ± CI, circles show individual participants’ data). Light blue arrows: model predictions for the perception of belt speed difference. Bottom bar in (C): group mean ± SE of the stride at which belts are predicted to feel equal, with reflecting the perturbation at this stride. (D) Individual participants’ versus (upper or lower bound). Solid black: least squares line. Dashed gray: unity line.
Figure 6
Control experiments, protocols.
(A) General protocol for all Control experiments (tied belts = at the same speed, split belts = right faster than left). (B) Sample participants performing the ascend and descend versions of the speed match task (first iteration after adaptation). Participants respectively increased or decreased the speed of the right belt (dashed orange) using up/down buttons with the goal of matching it to the reference speed of the left belt (solid black). Vision and sound were occluded as shown. The PSE is the belt speed difference at the end of the task (green). (C) Adaptation belt speeds and post-adaptation speed match task version for all Control experiments. All groups except for Small Gradual experienced a catch trial (tied belts) after two-thirds of the adaptation phase.
Figure 7
Control experiments, validation of Experiment 1.
(A) (filled bars) and (open bars) at the end of adaptation for all groups (group mean ± SE). (B) Step length asymmetry as a function of belt speed difference during the first post-adaptation speed match task (interpolated, group mean ± SE). Error bars depict step length asymmetry during the first (depicted to the right or left) and last (depicted in inset) strides in the task (actual data, group mean ± CI). Asterisks represent significant differences.
Figure 8
Control experiments, effect of paradigm manipulation and repetition on relative recalibration contribution.
(A) Comparison of the relative contribution of recalibration to motor adaptation across groups that vary in adaptation duration (left panel, Short, Medium, and Long Ascend), perturbation magnitude (middle panel, Medium Descend and Small Abrupt), or schedule (right panel, Small Abrupt and Gradual). Bars depict the ratio (group mean ± SE); asterisks represent significant differences. (B) Post-adaptation time course of motor (solid lines) and perceptual (dashed lines) aftereffects for Short, Medium, and Long Ascend groups (group mean ± SE). Aftereffects are computed as the tied-belt step length asymmetry (motor) or the final speed difference (perceptual) in each post-adaptation speed match task, normalized to the adaptation perturbation. Gray shades indicate time points for which motor aftereffects are significantly smaller than perceptual aftereffects.
Figure 9 with 4 supplements
Experiment 2, step length asymmetry.
(A) Experimental protocol, equivalent to that of Experiment 1 except for the Ramp Up & Down part shaded in teal, where the right speed was faster than in adaptation (ramped up to 2 m/s and back down to 1.5 m/s). (B) Step length asymmetry time course (entire group mean ± SE). Background shade represents belt speed difference. Phases (except ramp tasks) are truncated to the participant with fewest strides. Inset: Predictions for the step length asymmetry during the teal portion of the Ramp Up & Down task, for the memory-based (top) or structure-based (bottom) mapping hypotheses. (C) Zoomed-in Ramp Up & Down task (entire group mean ± SE). Step length asymmetry for strides taken at right speeds larger than adaptation is shown in teal. (D–E) Separate plots of the step length asymmetry in the Ramp Up & Down task for the subgroups of participants that walked asymmetrically (D, ‘memory-based’) versus symmetrically (E, ‘structure-based’) in the teal portion of the task (subgroups mean ± SE). Insets: circles represent individual participants’ number of strides, in the teal portion of the task, with step length asymmetry below their own baseline CI. Error bars depict subgroup mean ± SE. Subgroup assignment was performed by clustering on this measure.
Figure 9—figure supplement 1
Experiment 2, individual participants’ step length asymmetry in the first portion of the Ramp Up & Down (speed differences larger than adaptation, teal).
The red horizontal line depicts participants’ baseline 95% CI (lower bound). Red shaded area represents the difference between task and baseline asymmetry for strides that had a more negative step length asymmetry than baseline.
Figure 9—figure supplement 2
Experiment 2, individual participants’ strides to plateau computation.
Step length asymmetry in adaptation (blue circles), and plateau range (red rectangle; y-axis: plateau mean ± SD, x-axis: strides at plateau).
Figure 9—figure supplement 3
Experiment 2, comparison between subgroups of strides to plateau measure.
Individual (black circles) and group mean ± SE (bars and error bars) strides to plateau measure divided by subgroup.
Figure 9—figure supplement 4
Experiment 2, variability in adaptation.
(A) Within-participant variance in step length asymmetry in the first and last 30 strides of adaptation, for participants in each subgroup. (B) Decay in variance between these time points. Bars and error bars: subgroup mean ± CI, circles: individual participants.
Figure 10
Summary of self-reported deliberate changes to the walking pattern in adaptation.
Only one participant accurately described changes to the walking pattern that related to adaptation, while other responses were negative (i.e. no deliberate changes, three participants), irrelevant (seven participants), or inaccurate (five participants).
Figure 11
Schematic model of adaptation.
Body movement depends on environment perturbations (red) and Δ motor output (blue). The Δ motor output is adjusted by recalibration (light blue) and mapping (dark blue) mechanisms, which perform different operations and are arranged in tandem. We propose the following architecture and flow: (1. Recalibration) The recalibration mechanism produces adjustment that is fixed regardless of perturbation size (light blue box, is constant for varying ). The same recalibration adjustment serves as an input to both areas responsible for conscious perception (green box) and Δ motor output (blue box). (2. Perception) Conscious perception is computed by cancelling out the recalibration adjustment from the actual sensory feedback (green box, perception of the belt speed difference perturbation is the difference between the actual speed difference and recalibration ). The perceived perturbation serves as an input to the mapping mechanism (dark blue box). (3. Mapping) The mapping mechanism produces adjustment that can vary in magnitude to appropriately account for the perceived perturbation (dark blue box, scales with and matches its magnitude). (4. Δ Motor output) The overall adjustment to Δ motor output is computed by adding the mapping adjustment and recalibration adjustment . The corner in the Δ motor output versus perturbation profile arises because mapping is computed based on the perceived perturbation (not the actual perturbation ) and is only learnt for positive (the experienced direction). When the perturbation is perceived to be opposite to adaptation, even if it is not, mapping is zero and the Δ motor output is constant, reflecting recalibration adjustments only (blue box, when and the mapping adjustment is zero and ).
Appendix 2—figure 1 with 1 supplement
Experiment 1, perceptual models simulations.
Top: original proprioceptive re-alignment model (PReMo). Middle: expanded version of PReMo that accounts for perceptual realignment. Bottom: perceptuomotor recalibration + mapping model (PM-ReMap). (A) Simulations for adaptation by recalibration only. Only PM-ReMap can account for perceptual realignment (belts feel equal halfway through the Ramp Down). (B) Simulations for adaptation by both recalibration and mapping. Only PM-ReMap can account for the pattern of motor aftereffects (emerging halfway through the Ramp Down).
Appendix 2—figure 1—figure supplement 1
Experiment 1, evaluation of ‘ηV’ and ‘Glearnt’ parameters of perceptual models.
(A) Effect of varying ηV on the point of subjective equality. ηV only affects PM-ReMap, with accurate predictions for ηV = 0. (PReMo original, top: no PSE in task – right feels faster throughout – regardless of ηV; PReMo expaned realignment, middle: PSE is at the end of the task – when speeds are actually equal – regardless of ηV; PM-ReMap, bottom: PSE is when ∆ motor output = perturbation for ηV = 0 only). (B) Evaluation of why only PM-ReMap can accurately model mapping in the Ramp Down. Right column: only PM-ReMap predicts separable value ranges for the ideal G* in the first versus second halves of the Ramp Down (dark blue, goal G = value in Glearnt range that is closest to ideal G*. Glearnt = [-1,1] covers all biologically plausible values, allowing G≈G* and ~no aftereffects for all models, but only PM-ReMap has different Gs in first vs second halves). Left column for PM-ReMap: Glearnt covers only values learnt in adaptation, and this leads to accurate aftereffects predictions (first-half: G* = learned values of Δ motor output, resulting in G=G* and no aftereffects; second-half: G* = non-learned values, resulting in G=0 and aftereffects).
Appendix 3—figure 1 with 1 supplement
Experiment 2, evaluation of Ramp Up & Down step length asymmetry differences from Experiment 1.
(A) Step length asymmetry time course during the Ramp Down task of Experiment 1 (group mean ± SE). Magenta arrow: range of speeds for which step length asymmetry is not significantly different from zero (no aftereffect). (B) Step length asymmetry time course during the Ramp Up & Down task of Experiment 2 (entire group mean ± SE). Teal: portion of the task that differs from Exp. 1 because the speed difference is larger than adaptation (>1 m/s). Magenta: portion of the task with speeds equal to Exp. 1. The magenta arrow matches that of panel A (speeds with no aftereffect in Exp. 1). Dotted gray line: predicted asymmetry if no additional learning occurred (negative peak magnitude is estimated based on initial adaptation asymmetry). (C) Experiment 2 individual participants’ additional aftereffect versus additional learning (mean SLA over speed ranges marked by magenta versus teal arrows in panel B). Black line: least square line between the measures. Gray lines: confidence interval for participants in Exp. 1 (CI for the mean SLA over ‘no aftereffect’ range).
Appendix 3—figure 1—figure supplement 1
Experiment 2, modeling analysis of the second portion of the Ramp Up & Down.
(A) Step length asymmetry data and (B) model fits by the flexible recalibration + mapping model (left) and recalibration only model (right), for the second portion of the Ramp Up & Down (strides 60–123, speed differences 1 m/s to 0 m/s). Purple line and shade depict group mean ± SE. Speed configurations to the left of the dashed black vertical line had no aftereffects in E1. (C) BIC difference between the recalibration only and flexible recalibration + mapping models. The error bar depicts group mean and confidence interval, purple dots depict individual participant data. Positive BIC difference indicates that the flexible recalibration + mapping model fits the data better than the recalibration only model.
Appendix 4—figure 1 with 1 supplement
Primary clustering analysis for Experiment 1 (A&B) and 2 (C&D).
(A&C) Cluster assignment (color of square) for each participant (y axis) computed with each ‘k’ iteration of the algorithm (x axis). The MinPts and Epsilon parameters computed and used for each ‘k’ iteration are reported on top of the graph. Different colors represent different clusters, and white spaces represent outliers. The algorithm selected the final cluster to be that for k=9 for both experiments; of note, results were identical for all ‘k’ iterations from 9 to 20 (A) or 9–19 (C). (B&D) Measure used for clustering (y-axis, # strides in ramp below/above baseline, see Methods) for each participant (x-axis), color-coded by cluster assignment.
Appendix 4—figure 1—figure supplement 1
Secondary clustering analysis for Experiment 1.
Participants clusters (after selection of the best k iteration) computed using different measures (reported above graph). Red boxes indicate participants assigned to cluster 1, and white spaces indicate outliers. For all measures, only one cluster was detected.
Author response image 1
Tables
Author response table 1
| BIC Difference | |||
|---|---|---|---|
| New Model BIC - "recalibration+mapping BIC" | |||
| New Model | Mean | CI Lower Bound | CI Upper Bound |
| 'DualStateRelaxed' | 8.64 | 3.82 | 13.75 |
| 'DualStateRelaxedV2' | 61.13 | 40.82 | 81.16 |
| 'PremoOriginalRelaxed' | 26.00 | 18.48 | 32.99 |
| 'PremoOriginalRelaxedV2' | 28.73 | 20.93 | 35.93 |
Additional files
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Supplementary file 1
Supplementary tables with statistical results for Experiment 1 and control experiments.
- https://cdn.elifesciences.org/articles/101671/elife-101671-supp1-v1.docx
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Supplementary file 2
Supplementary tables with statistical results for Experiment 2 and clustering analysis.
- https://cdn.elifesciences.org/articles/101671/elife-101671-supp2-v1.docx
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Supplementary file 3
Questionnaire responses for Experiment 2.
- https://cdn.elifesciences.org/articles/101671/elife-101671-supp3-v1.docx
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Supplementary file 4
Pseudocode for the clustering analysis.
- https://cdn.elifesciences.org/articles/101671/elife-101671-supp4-v1.docx
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MDAR checklist
- https://cdn.elifesciences.org/articles/101671/elife-101671-mdarchecklist1-v1.pdf
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Automatic learning mechanisms for flexible human locomotion
eLife 13:RP101671.
https://doi.org/10.7554/eLife.101671.3
