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 at 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).

Experiment 1, Step length asymmetry.

(A) Top: Experimental protocol. The Ramp Down task (purple) is used to test the predictions illustrated in Fig. 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 Fig. 1. All curves show group mean ± SE.

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 recalibration only and recalibration + mapping models. All curves show group mean ± SE. Green shade corresponds to speeds with symmetric step lengths as in Fig. 2.

Experiment 1, Perceptual Results.

(A) Top: perturbation data (red) and recalibration + mapping fit (blue); this is the same as Fig. 3C. Bottom: perceptual task button presses (green, group mean ± SE), as a function of belt speed difference. Right: measures of motor recalibration (“r”) and total motor adaptation (“uplateau”). (B) Perturbation compensation (normalized perceptual and motor measures of adaptation): compensationperceptual bounds (green), compensationmotor total (dark blue), and compensationmotor recalibration (light blue). (C-D) Individual participants’ compensationmotor recalibration versus compensationperceptual (first or second button press). Solid black: least squares line. Dashed gray: unity line.

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 2m/s and back down to 1.5m/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.

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, 3 participants), irrelevant (7 participants), or inaccurate (5 participants).

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 xr that is fixed regardless of perturbation size (light blue box, xr is constant for varying p). The same recalibration adjustment xr 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 p and recalibration xr). The perceived perturbation serves as an input to the mapping mechanism (dark blue box). (3. Mapping) The mapping mechanism produces adjustment xm that can vary in magnitude to appropriately account for the perceived perturbation (dark blue box, xm scales with and matches its magnitude). (4. Δ Motor output) The overall adjustment to Δ motor output is computed by adding the mapping adjustment xm and recalibration adjustment xr. The corner in the Δ motor output versus perturbation profile arises because mapping is computed based on the perceived perturbation (not the actual perturbation p) and is only learnt for positive (the experienced direction). When the perturbation is perceived to be opposite than adaptation, even if it is not, mapping is zero and the Δ motor output is constant, reflecting recalibration adjustments only (blue box, when and p ≥ 0 the mapping adjustment xm is zero and u = xr).

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).

Relevant results from Leech et al., 2018.

(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 difference (top) 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 at al. study (Leech et al., 2018a).