Adaptation

As shown in Fig. 3.3A and B (blue lines), during field A the x component of adaptation remained close to baseline throughout the phase in both conditions (N_B= 16 and 32). This indicates an appropriate lack of adaptive response, as during field A no perturbation was applied in the x dimension. However, we earlier observed that the x component of MPE showed an increase in the beginning of this phase without any perturbations involved (Fig.

3.2, blue line). To assess whether this induced MPE had any effects on the x component of adaptation, we looked at the average adaptation across the first 10 channel trials of field A in the x dimension. The values were obtained as 0.056 ± 0.024 for condition 1 (t-test:

t(11) = 2.41, p = 0.04), and 0.019 ± 0.020 for condition 2 (t(11) = 0.844, p = 0.416), indicating minimal effects by the x-component of MPE on the adaptation behaviour. This implied that the MPE in the x dimension was irrelevant to the task and thus resulted in minimal adaptive response. Previous studies have also shown that the nervous system estimates the relevance of observed errors, and only adapts to the errors that are relevant to the goal of the task (Wei and Körding, 2009).

During field B, the force field was in the x dimension, resulting in a rapid increase in the x component of adaptation up to ∼ 55% for both conditions. This rapid adaptation was then followed by a rapid decay in the subsequent error-clamp phase (Fig. 3.3C and D, right panels: Early vs Late trials of error-clamp phase), indicating a fragile memory formed for the learning of field B.

Examining the z component of adaptation in Fig. 3.3A and B (red line), we observed a progressive increase in the adaptation level over the course of field A, reaching up to ∼ 80%

by the end of the field for both conditions. At the beginning of field B, the force field was turned off in the z dimension, resembling a washout period for the z component of adaptation.

As a result, subjects deadapted to the force field (Fig. 3.3C and D, left panels), and by the end of field B, the adaptation dropped to a lower, yet still significantly positive level.

This suggested an incomplete deadaptation process before the onset of error-clamp phase (Fig. 3.3C and D, left panels, Late B: t-test: t(11) = 3.16, p = 0.009 for condition 1, and t(11) = 2.60, p = 0.024 for condition 2). Finally during the error-clamp phase, the adaptation

3.3 Results 61

Late ALate BEarly C Late ALate BEarly CLate C

Adaptation

Fig. 3.3 The time course of adaptation decomposed to its x (blue) and z (red) components, and shown for condition 1 (A) and condition 2 (B). The bar plots in C and D show the summary of adaptive behaviour for the z (left) and x (right) components and for each condition. Each bar plot represents the mean adaptation in the final 10 channel trials of field A (Late A), the last 2 trials of field B (Late B), the first 10 trials, and the last 10 trials of error-clamp phase (Early C and Late C).

(paired t-test:^∗p< 0.05,^∗∗∗p< 0.001, ns: not significant).

62 Spontaneous Recovery

level remained almost flat, with no significant difference between the early and late trials in this phase (paired t-test: t(11) = −0.592, p = 0.565 for condition 1, and t(11) = 0.673, p= 0.515 for condition 2; Fig. 3.3C and D, left panels).

Comparing the adaptive behaviour in z dimension with what is normally observed in conventional spontaneous recovery paradigms (Criscimagna-Hemminger and Shadmehr, 2008; Pekny et al., 2011; Smith et al., 2006), it can be seen that in previous paradigms the memory of field A was seemingly fully washed out by an opposing field (B), but was reactivated (in the form of adaptation rebound) early in the following error-clamp phase.

In our paradigm, however, we did not observe such behaviour in the memory of field A (z component of adaptation). As shown, the adaptation to field A was never totally washed out before the error-clamp phase, and more importantly, preserved some learning in a low yet consistent level throughout channel trials (i.e., no significant rebound was observed).

We further examined the adaptation behaviour from a different perspective, by looking at the magnitude and angle of the adaptation vector in the xz plane. Fig. 3.4A and C show the angle of adaptation (measured from the x axis) averaged across subjects (circular mean) for each condition. As shown, the adaptation angle remained close to optimal (i.e., 90^◦) during field A, consistent with the angle of perturbation in this field. When the force field was switched to field B (x dimension), the vector of adaptation also rotated towards 0^◦, inline with the direction of the second force field. Interestingly, during this rotation the magnitude of adaptation remained unchanged (no significant difference was observed in the magnitude of adaptation between field B and the final trials of field A; Fig. 3.4B and D). This indicated that when the field direction switched, subjects did not reduce the strength of their compensatory forces, but just rotated the force direction in order to compensate for the perturbations in the new direction (field B). The amount of rotation was slightly larger in the second condition (due to longer exposure in field B), but the effect was not significant (last two trials of field B: 65.0^◦± 7.2^◦ for condition 1, and 67.7^◦± 9.5^◦ for condition 2; Watson-Williams test:

F_1,22= 0.05, p = 0.82).

During the error-clamp phase, we observed that the adaptation vector spontaneously rotated back towards the initially learned force field direction (i.e., 90^◦) while also decaying

3.3 Results 63

Fig. 3.4 A and C show the time course of adaptation angle averaged across subjects (circular mean ± circular standard error) for condition 1 and condition 2, respectively. B and D also illustrate the adaptation magnitude for each condition. The p-values are shown for the paired t-test between the adaptation levels in field B and the final trials of field A.

progressively in strength (Fig. 3.4). This behaviour was mainly attributed to the x component of adaptation (that is, the memory of field B) during the error-clamp phase. As shown earlier in Fig. 3.3A and B, the adaptation in x dimension showed a fast decay over the error-clamp trials, while the z component of adaptation preserved a somewhat constant level throughout.

This led to an effect on the adaptation angle, whereby the direction of adaptation showed a rebound (spontaneous recovery) towards the direction of the initially learned force field (field A). This behaviour suggested a more general form of spontaneous recovery that could not be recognised in conventional paradigms, in which fields A and B were in opposite directions.

In the following, we test whether a dual-rate model can account for this observation.