Experiment 1

In this study, we examined the interactive properties of sensorimotor learning mechanisms associated with the Out and Return rotations in a reciprocating object manipulation task.

In the first experiment, we tested whether separate representations of object dynamics are formed for Out versus Return rotations of the same object. Subjects performed the experiment in three main phases: the P1 phase (exposure in Out and error-clamp in Return), the Training phase (exposure trials in both Out and Return) and the P2 phase (the same as P1). During P1 and P2 we examined the interaction between Out and Return adaptive processes by measuring how an ongoing adaptation in the Out rotations affected the adaptive behaviour in the Return

136 Adaptation to familiar dynamics

rotations. We also asked whether this interaction was enhanced going from P1 to P2 by the concurrent adaptation during the Training phase.

Fig. 6.3A and B illustrate the overall performance of the subjects in terms of the adaptation ratio and the peak displacement (PD), separated for the Out and Return rotations.

Subjects adapted to the object’s dynamics during the Out rotations of P1 and P2 (Fig. 6.3A;

blue data points) and they showed clear after-effects in the following washout periods (i.e., w.o.1 and w.o.2; Fig. 6.3B; blue data points). We examined how the observed behaviour in the Out rotations affected the adaptive behaviour during the Return rotations, in terms of both the adaptation ratio in P1 and P2, and the PD during w.o.1 and w.o.2.

As shown in Fig. 6.3C, the adaptation ratio for the Return movements shows a slight increase over the trials in both P1 and P2 phases, indicating a transfer of adaptation from the Out rotations to the Return rotations. This is particularly important for P1 phase, where the adaptation ratio increases in the Return movements without ever experiencing the object dynamics in this movement direction. In order to precisely quantify the amount of increase in adaptation ratio and examine its significance, we fit a simple single rate state-space model to the adaptation ratio in P1 and P2:

z⁽ⁿ⁺¹⁾= A · z⁽ⁿ⁾+ B · (1 − z⁽ⁿ⁾) z⁽¹⁾= Z₀

(6.1)

where, z⁽ⁿ⁾ represents the adaptation ratio on trial n, and the free parameters A, B, and Z₀ are, respectively, the decay rate (0 ≤ A ≤ 1), the rate of increase of adaptation, and the initial value of adaptation in the beginning of the phase. The solid lines in Fig. 6.3C show the result of the fit for P1 (orange line) and P2 (green line). We were mainly interested in the rate of increase (B) to see if the increase of adaptation was significant. Fig. 6.3D shows the best fit value of parameter B for P1 and P2 phases, with the confidence intervals shown as error bars (see section 6.2.4 for calculation of confidence intervals). A strictly positive value for B means that the increase in adaptation is significant. As shown in the figure, the confidence intervals of B for both P1 and P2 fall within the positive values (the lower bound of B for

6.3 Results 137

Fig. 6.3 Experiment 1. A and B show the overall performance of the subjects in terms of adaptation ratio and PD, respectively. The data is shown as the mean across subjects (the blue and red dots for Out and Return movements, respectively), with the error bars (shaded areas) as the standard error of the mean. The solid lines represent the best model fit based on model M2. C illustrates the adaptation behaviour during the Return movements of P1 and P2 phases. The solid lines show the single-rate state-space model fit to estimate the rate of change of the adaptation. The adaptation rate is shown in panel D with the 95% confidence intervals. Panel E also shows the after effects in the form of PD following the P1 and P2 phase (i.e., w.o.1 and w.o.2). The solid lines show the single-rate state-space model fit with the PD reduction rate shown in panel F (the error bars show the 95% confidence intervals).

138 Adaptation to familiar dynamics

P1 was close to zero with the value of 1.4 × 10⁻³, but still positive) showing a significant, although small, increase of adaptation over trials.

We further examined the after effects of the induced adaptation during the Return trials of P1 and P2. Fig. 6.3E illustrates the PD profile during the washout periods following P1 and P2 for the Return movements. As shown, there is a clear after effect observed in the form of sudden increase in the PD in the beginning of the washout period, followed by progressive decrease towards the end of the washout. We quantified this behaviour by fitting the single rate state-space model (equation 6.1) to the PD data, in which PD was represented by the term (1 − z⁽ⁿ⁾). In this case, the parameter B represented the rate at which the PD decreased.

For a strictly decreasing PD profile (indicating the after effect), the parameter B should be strictly positive (a negative value or the value of zero for B means no reduction in the PD, and thus no after effects). Fig. 6.3F illustrates the value of B with the confidence intervals for the washout periods following P1 and P2. As shown, the whole interval of the value of B rests in the positive direction, indicating a significant after effect in the Return rotations, both for P1 and P2.

The above results show that there is an interaction, in the form of adaptation transfer, between the adaptive mechanisms of Out and Return rotations. As such, an adaptation process during the Out movements induces an adaptive response in the Return movements.

This is particularly interesting about P1, which shows the interaction exists without any prior experience of object dynamics during the Return trials. Comparing the behaviour between P1 and P2, however, we did not find any significant difference, neither in the adaptation ratio, nor in the after effects. This could imply that the pre-existing interaction observed in P1 is not majorly enhanced by the simultaneous dynamic exposure between Out and Return trials during the Training phase. This can be seen from the perspective of the coupling models introduced previously (Table 5.1). We fitted all 10 variations of the model to the data and presented the goodness of fit for each model in Table (6.1). According to the ∆BIC shown in the table, the models that feature a fixed coupling factor (i.e., M1, M2 and M3) outperform other models with adaptive or mixture coupling (Fig. 6.3A illustrates the model fits based on model M2). Particularly the models with the adaptive coupling (M4, M5 and M6) show

6.3 Results 139 Table 6.1 Experiment 1. The goodness of fit for each model is shown in terms of BIC, the sum of squared error of fitting (SSE) and the coefficient of determination R². For each model, we took the difference between the BIC of that model and the BIC of the model M2, as reported with ∆BIC.

Models Description ∆BIC SSE R²(%)

M1 Fixed coupling: single adaptive mechanism 0.25 2.334 75.54 M2 Fixed coupling: shared between two adaptive mechanisms 0 2.333 75.56 M3 Fixed coupling: separate for each adaptive mechanism 4.33 2.322 75.67 M4 Adaptive coupling: single adaptive mechanism 33.7 2.464 74.20 M5 Adaptive coupling: shared between two adaptive mechanisms 33.4 2.462 74.22 M6 Adaptive coupling: separate for each adaptive mechanism 45.3 2.462 74.22 M7 Mixture coupling: single adaptive mechanism 18.1 2.334 75.55 M8 Mixture coupling: shared between two adaptive mechanisms 17.6 2.330 75.58 M9 Mixture coupling: separate for each adaptive mechanism 29.8 2.295 75.96

M10 No coupling 16.1 2.476 74.18

the poorest performance in explaining the data. This suggests a somewhat settled interaction between the adaptive mechanisms of Out and Return rotations, that is not further enhanced by concurrent training. In the following sections, we conduct a more extensive experiment to better quantify the coupling effects in an object manipulation task with familiar dynamics.