Fig 1.
(A) Experimental setup. Subjects made reaching movements from mid-line in both forward (90°) and backward (270°) directions, using a robotic manipulandum. The location of the hand was represented by a filled yellow circle, while the view of arm was occluded. (B) Trial Types. Null movements (grey arrows) were made in the absence of the any force from the robot. During force-field trial movements, the robot applied forces that were dependent on a single or combination of motion kinematics. During velocity-dependent force-field movements the manipulandum applied lateral forces that scaled with movement velocity (black arrows). For position-dependent movements, the lateral force scaled with hand position with respect to the start position. Lastly, for both unbiased and position biased combination force-field movements the lateral force scaled with both hand position and velocity. During error-clamp movements the manipulandum constrained the movement trajectory between the two targets by countering any lateral motions. (C) Experimental Paradigm. Subjects first completed a baseline period, during which they experienced null movements with sparse instances of error-clamp movements (blue bars). The 1st transition period, contained an initial period of null movements, followed by the abrupt application of the force-field. The adaptation period contained only force-field and error-clamp trials. Finally, the 2nd transition period started with force-field movements followed by only error-clamp trials (thick blue bar). The frequency of error clamp trials increased during the two transition periods.
Fig 2.
Adaptation and subsequent decay for training in position- and velocity -dependent force-fields (A). Comparison of the adaptation coefficients during position (pFF, blue curve) and velocity-dependent force-field training (vFF, red curve). Each point during the adaptation period is the average adaptation coefficient across subjects for windows of 10 or 15 trials. During the decay period, the points are average across all subjects for each trial. The start of the decay period is shown as a vertical dashed line. Shaded areas show standard error. (B) Normalized decay for pFF and vFF training. The adaptation coefficients were scaled with respect to the first coefficient in the decay period, with the first point rescaled to a value of 1.0. Bar graphs show the average adaptation across subjects for early and late epochs of the decay, represented by the shaded areas. Error bars are standard error. (C and D) Temporal force profiles during adaptation and decay for pFF and vFF training. Top panel shows the evolution of the force patterns in the early and late stages of adaptation, while the bottom panel shows the changes in early and late stages of the decay period. The average force across all subjects is shown by a gray trace. The contribution of position and velocity to the force profile is represented by the blue and pink dashed lines. The combination of the position and velocity contribution is shown by a black dashed line, and approximates actual exerted forces. The R2 value from the regression between actual (thick gray trace) and combined position-velocity fit (black dashed trace) is provided in the top left of each panel.
Fig 3.
Gain-space representation of adaptation and decay for training in position- and velocity-dependent force-fields.
(A) Evolution of position- and velocity-dependent gains during adaptation and decay for pFF training. Gain-space trajectories during adaptation and decay periods are shown in blue and gray, respectively, and are averaged across all subjects. The adaptation goal is shown as a blue filled square. Each point in the trajectory has a contribution that is goal-aligned and goal-misaligned, as shown by the two vectors. Three points were selected to compare the gains of the goal-aligned and misaligned components, labeled by the filled ellipses and the numbers 1, 2, and 3. Points 1 and 2 were early and late in the adaptation period, and were the same for both force-field types (training trials 1–15 and 150–160). Point 3 represents the average over a two trial window during the decay period at which the adaptation coefficient for the goal-aligned component was not significantly different from the early learning value (trials 12–14 and 16–18 of the decay period for pFF and vFF, respectively). Ellipses show standard error. (B) Evolution of position- and velocity-dependent gains during adaptation and decay for vFF training. Gain-space trajectories during adaptation and decay are shown in red and gray, respectively. The goal of adaptation is represented as a red filled square. Direction of the goal-aligned and goal-misaligned components are shown as red and cyan vectors, respectively. (C and D) The evolution of the goal-aligned and goal-misaligned components during training and decay are shown for each force-field perturbation. Each point during the adaptation period is the average across subjects for windows of 10 or 15 trials. Shaded regions show the standard error. Bar graphs show the amplitude of the goal-misaligned component during the periods that are highlighted in panels A and B as 1, 2, and 3. The asterisk above the bar graph represents the result of the ANOVA across the goal-misaligned components at points 1, 2, and 3. Error bars show standard error of gains for each point.
Fig 4.
Simulation of symmetric and asymmetric viscoelastic primitive models for adaptation to different force-field types.
Simulation of the gain-space trajectories for the (A) symmetric and (B) asymmetric viscoelastic primitive models fit simultaneously to the vFF and pFF behavioral data (Symmetric model: αK = αB = 0.951, σK = σB = 0.401, η = 1.5 x 10−4, ρ = 0.51. Asymmetric model: αK = 0.942, αB = 0.951, σK = 0.464, σB = 0.379, η = 1.5 x 10−4, ρ = 0.47). Adaptation and decay to pFF and vFF, and predictions of behavior for ucFF, and pcFF force-field training are depicted by the colored and gray traces, respectively. (C) Normalized decay of position- and velocity-dependent gains for the predictions of the symmetric (black trace) and asymmetric (orange trace) primitive models for ucFF and pcFF training.
Fig 5.
Gain-space representation of adaptation and decay for training in combination force-fields.
(A and B) Gain-space trajectories during training in the unbiased combination (ucFF, green trace) and position biased force-field (pcFF, purple trace) are shown. The respective gain-space trajectories during the decay periods are shown in gray. The learning goal of the adaptation in gain space is shown by the filled green and purple squares. The directions of position-aligned and velocity-aligned components are shown by blue and red arrows, respectively. (C and D) Evolution of the applied position- and velocity-dependent gains during adaptation and decay of the combination force-field training. Position-dependent gains are shown in blue and velocity-dependent gains are shown in red. Each point during the adaptation period is the average across subjects for windows of 10 or 15 trials. The bar graphs show the amplitude of each component for the shaded regions numbered in panels A and B. (E and F) The normalized gain-space trajectories during the decay periods were computed by rescaling the gains during decay by their respective values at the start of the decay period. Thus, the first point is rescaled to [1.0, 1.0] in gain space. The gray lines represent the normalized decay in gain space, and the ellipses show standard error at each point. (G and H) Normalized decay of position- and velocity-dependent gains. The bar graph depicts the comparison between the normalized gains in the early (E) and late (L) epochs. Error bars show standard error of gains for each epoch. Insets in panels A, B, E and F show the predictions of the asymmetric primitive model fit simultaneously to the ucFF and pcFF behavioral data (αK = 0.914, αB = 0.958, σK = 0.546, σB = 0.565, η = 1.5 x 10−4, ρ = 0.48).