# Consistent visuomotor adaptations and generalizations can be achieved through different rotations of robust motor modules

## Abstract

Humans can adapt their motor commands in response to alterations in the movement environment. This is achieved by tuning different motor primitives, generating adaptations that can be generalized also to relevant untrained scenarios. A theory of motor primitives has shown that natural movements can be described as combinations of muscle synergies. Previous studies have shown that motor adaptations are achieved by tuning the recruitment of robust synergy modules. Here we tested if: 1) different synergistic tunings can be achieved in response to the same perturbations applied with different orders of exposure; 2) different synergistic tunings can explain different patterns of generalization of adaptation. We found that exposing healthy individuals to two visuomotor rotation perturbations covering different parts of the same workspace in a different order resulted in different tunings of the activation of the same set of synergies. Nevertheless, these tunings resulted in the same net biomechanical adaptation patterns. We also show that the characteristics of the different tunings correlate with the presence and extent of generalization of adaptation to untrained portions of the workspace. Our results confirm synergies as invariant motor primitives whose recruitment is dynamically tuned during motor adaptations.

## Introduction

Complex movements can be easily adapted in response to discrepancies between the expected and actual sensorimotor outputs. This is achieved through the recalibration of the neural representation of the body and the environmental interaction dynamics that are thought to be stored in internal models that characterize both the forward and inverse dynamics of movement1,2,3,4,5,6. Internal models can be adapted as a response to changes in the mapping between movement and its associated feedback or in response to perturbations modifying the dynamic characteristics of the movement in a relevant way7.

Several seminal studies have suggested that internal models are constituted by combinations of motor primitives8,9,10,11,12, an observation that is corroborated by the fact that adaptation to specific perturbations can be generalized to untrained compatible contexts9,10,11,13,14,15,16. These motor primitives are thought to explain the mapping between state variables such as limb position and movement velocities, into motor commands12.

A conceptually correlated theory of motor primitives and movement modularity has been proposed and widely demonstrated in both animal models and humans, that is, the muscle synergies hypothesis17,18,19,20. Muscle synergies are thought to be the functional building blocks of force production during natural movements. Studies employing stimulation21,22,23,24 and optogenetics25,26 techniques have individuated the presence of such modules in the spinal cord of rodents, frogs and primates. In humans, on top of the fertile literature describing muscle synergies during natural behaviors27,28,29,30,31,32, studies on impaired individuals have demonstrated the solidity of this hypothesis in describing neurological conditions such as stroke33,34.

As motor adaptations have been mainly studied, in humans, using computational models derived from metrics of biomechanical error, there is small evidence connecting the re-organization of the internal models that happens during adaptation with the supposed functional constituents of movement.

Previous studies have suggested muscle synergies as potential physiological blocks of computationally-derived primitive-based models12, but only in recent years muscle synergies analysis has been used to describe adaptive behaviors, including visuomotor adaptations during isometric reaching movements35,36,37. In this latter scenario, studies have shown that muscle synergies are robust with respect to changes in the motor plan36, and that adaptation to specific perturbations depends on how the perturbations map on the synergistic structure35,37. As a case in point, it has been demonstrated that adaptation to a 45° visuomotor rotation is achieved by similarly rotating the activation maps of a set of fixed muscle synergies36.

Nevertheless, if adaptation to visuomotor rotations is achieved by rotating the activation patterns of synergies of specific shape and workspace, either the synergies are rotated solidly and invariantly in response to consistent perturbations or, more likely, the patterns of rotation of each synergy depend on the spatial and temporal characteristics of the training. In such modular model, a visuomotor rotation that only affects a portion of the movement space is supposed to induce the rotation of only the subset of synergies active in that subspace, to an extent that depends on the effect of the perturbation on the synergistic workspace.

A dynamic synergistic model of adaptation like the one just described could explain adaptation-related phenomena such as generalization. Generalization of visuomotor rotations has been observed to depend on both the distance between the pre-adapted targets and the newly experienced ones38 and the amount of angular rotation of the perturbation that needs to be generalized39. In a muscle synergy-based representation, both phenomena could depend on which specific synergies have been rotated and how they have been rotated during the initial adaptation.

Herein we tested the hypotheses that the tuning of synergies recruitment that happens during adaptation to visuomotor rotations is not invariant but depends dynamically on the way in which the perturbations are experienced. We also tested the hypothesis that the characteristics of the tuning achieved through adaptation correlate with the presence and extent of generalization. To do so we investigated (1) if synergies always rotate in the same way when adapting to the same visuomotor rotations experienced in different parts of the workspace in different temporal orders and (2) if the way in which synergies are rotated during an adaptation exercise performed on a specific subspace correlates with generalizing behaviors observed in a subsequent adaptation exercise performed on a different subspace.

## Results

### Adaptation and generalization in the biomechanics

The analysis of the force trajectories recorded during the experiments showed that: a) subjects were able to fully adapt to both target-sets regardless of whether they were presented during adaptation or generalization; b) the marked patterns of generalization that can be observed across the different targets are generally dependent on the distance between the generalized targets and the previously adapted ones. These results are presented in Fig. 2.

### Adaptation is achieved through the rotation of fixed motor modules

Gentner and colleagues36 have shown that adaptation to visuomotor rotations is fully explained by a rotation (or tuning) of the activation patterns of a fixed set of muscle synergies. Here we demonstrate that the motor module themselves do not change during this kind of adaptation, thus the synergies recorded at baseline can be used to reconstruct the muscular activity recorded during the whole experiment. Similarly to previous works36,40, we found that four muscle synergies, extracted using the non-negative matrix factorization algorithm (NMF)41 could satisfactorily reconstruct the EMG activity of all subjects during baseline, adaptation and washout (average Variance Accounted For (VAF) across subjects >90%, see Fig. S1 in Supplementary material). This result is consistent with what observed in similar works in literature35,36,42. The synergies extracted from the different subjects were observed to be remarkably similar, with an average normalized dot product at B3 across subjects equal to 0.72 ± 0.08 (Fig. S2).

These four synergies (W1-4) were shown to have distinct functional characteristics and span specific sections of the experimental workspace (Fig. 3a,b). W1 is constituted by the elbow flexors and acts mainly in the lower-left quadrant of the workspace. W2 is constituted by the elbow and shoulder extensors and acts mainly in the upper-right quadrant. W3 is constituted by the muscles commanding shoulder extension and act mainly in the lower-right quadrant. W4 is constituted by muscles involved in shoulder flexion and act mainly in the upper-left quadrant. In our synergistic model of adaptation, we described the adaptive behavior as the modification of the activation patterns (APs) of a fixed set of reference muscle synergies. The reference synergies were selected as the synergies extracted in the last block of baseline (B3), chosen as the block where subjects were fully habituated to both the task and the movement environment. The choice of fixing the synergy modules as the baseline ones is justified by the high degree of similarity observed, for each subject, between the (unrestricted) synergies extracted at baseline and those extracted at the end of adaptation (dot product equal 0.91 ± 0.06) and washout (dot product equal 0.86 ± 0.10, Fig. S2).

We then reconstructed the APs relative to the fixed synergies for each block using a modified version of the NMF algorithm40. The product between the reference synergies and the block-specific APs yielded average values of VAF > 80% across all subjects and were shown to be significantly higher (p < 0.01 for each block, using Mann-Whitney U test and Bonferroni’s correction) than VAF values obtained using random reference synergies (Fig. 3c).

In Fig. 4 we also notice that the adapted APs differ, for some targets, between the group that trained that target during adaptation and the group that did it during generalization. This behavior can be observed clearly in the APs of W1 for target SW, W3 for targets NE, E and SE and W4 for targets E and SE. This qualitative observation suggests that the synergies APs rotate differently between the two groups.

We then analyzed the path to full adaptation for both groups from baseline to washout (Fig. 6). Group1 was able to tune all four synergies by rotating them CW during the exposure to TS1 (Ad1-Ad3), with an emphasis on the synergies mostly spanning the workspace (W2, W3 and W4). During generalization, only small adjustments to the adapted state were sought and regarded exclusively target SW that is the only target that, in our results, did not present a clear generalization behavior. Group2 only tuned three (W1, W2 and W4) of the four synergies during the exposure to TS2, while subsequent adaptation to TS1 was achieved by rotating the previously non-tuned synergy (W3) and only slightly adjusting the rotation of the other ones. Taken all together, these results suggest a dependency of final adaptation on the way in which the synergies are tuned during the initial adaptation period.

### Generalization in the synergistic representation of movement

We hypothesized that, if the movement space and thus the adaptation behavior are bound to the workspace spanned by the existing muscle synergies35,36,37, generalization behaviors will also depend on how the synergies are pre-trained. In our experiment we observed patterns of generalization consistent with this hypothesis. The target presenting the highest degree of generalization is target N, which is the only target that, during generalization, had both adjacent targets already pre-adapted. Group1, which is the group that experienced target N during generalization (Fig. 7a), presents shapes of APs during the first 5 movements of generalization that are remarkably similar to those observed in the baseline CCW-rotated target. We observed a significant (p < 0.01, rho = −0.34) linear correlation between the values of NC and the similarity between the APs at Ad1/Ad4 and the baseline CCW-rotated target (Fig. 7b). We also observed that similarity during generalization is significantly higher than during adaptation (Fig. 7c, p = 0.03). These results taken together further confirm that adaptation and generalization to a CW visuomotor rotation depend on a CW tuning of the synergies.

To better understand the reasons behind the different levels of generalization that we observed across the different targets, we analyzed the patterns of generalization with respect to the way in which the synergies are tuned for each target in both groups (Fig. 7d). Target SW, that is the only target that does not present generalization, is adapted by tuning W1 and W3 that are the two synergies presenting the biggest differences in rotation after adaptation between the two groups (Fig. 5d). Target N, on the other hand, is the only target whose adaptation depends on the tuning of synergies W2 and W4, which are the two synergies showing the closest preferred angles between the two groups after adaptation. In Fig. 7e is shown the link between the average APs similarity with the baseline CCW-rotated targets and the difference in preferred angles calculated between the two groups; it is possible to appreciate a trend where targets associated with synergies showing higher differences in the preferred angle after tuning present lower overall similarity. Plotting the average APs similarity with the baseline CCW-rotated targets over the difference in preferred angles calculated between the two groups, it is possible to appreciate a trend where targets associated with synergies showing higher differences in the preferred angle after tuning present lower overall similarity (Fig. 7e). Nevertheless, the differences across the four groups presented in Fig. 7e were not significant (p = 0.09 based on Kruskal-Wallis test). These results, although qualitative, suggest that generalization is synergy-dependent and correlates with how similarly the APs tune, during the first adaptation period, towards the optimally tuned preferred angles.

## Discussion

Here we have shown that adaptation to visuomotor rotations can be achieved through different rotations of the same set of muscle synergies. The two different final tunings that we observed depend primarily on the initial rotation achieved when adapting to a first sub-set of targets, while subsequent exposures to untrained targets appear to lead only to small adjustments that happen mostly in un-trained or less-trained parts of the workspace. We have also shown that there is an influence of previous synergies tuning on the presence and extent of generalization after pre-adaptation to targets in a shared workspace.

Rotational tunings in muscular and M1 activities have been observed to happen during motor adaptations to visual rotations and force-fields43,44,45. Those results have been so far extended also to muscle synergies35,36, by demonstrating that simple visuomotor rotations, compatible with the existing synergies workspace, are achieved rapidly through tuning of synergies APs, while more complex adaptations non-describable using the already present synergistic structures may require a slower rewiring of the synergies themselves12,35. The fast rates of adaptation observed in our results suggest that only the former component of adaptation is at play in our experiment.

We observed, as initially hypothesized, differential paths of APs tuning for the two groups, characterized by under-rotations (W1 for Group1, W3 for Group2), over-rotations (W2 and W3, Group1) and theoretically-optimal rotations (W4 for Group1, W1, W2 and W4 for Group2). Interestingly, most examples of optimally tuned synergies have been observed in Group2, where three of the four synergies appear rotated close to the expected 45°. It is possible that this result is correlated with the fact that Group2 first trains on the target-set (TS2) that spans all the workspace. On the other side, Group1, which was initially trained on a smaller sub-space, presents non-optimal tuning in three of the four synergies. These results, taken together, suggest that optimal synergies tuning is obtained through optimal sampling of the movement space.

The patterns of differential adaptation that we observed suggest that the synergies APs are not the parameters that are directly adapted by the CNS, but rather the tools that are differentially tuned to adapt, while high-level adaptation is likely obtained by updating the sensorimotor transformations mapping the visual targets to the force directions36,46. Then, as different muscular activation patterns can produce the same force47, similarly can different combinations of synergies APs, without necessarily invalidating the synergies hypothesis. From our results it appears that muscle synergies constrain the adaptable mapping between the desired motion and the motor commands2. Given the sensory prediction error calculated in the forward representation of movements48, motor commands are then updated in the synergy-space in a parsimonious way, thus leaving preferably un-altered the synergistic structure (unless changes are necessary35) and the APs that are compatible with the desired force output.

We initially hypothesized that, if adaptation patterns are constrained by the synergistic structural components of the workspace (as our experiment appears to confirm), this likely reflects also on how training on an initial set of targets generalizes on a set of newly experienced ones in the same workspace. In accordance with our hypothesis, the results of our experiment show that the patterns of generalization after pre-adaptation depend on pre-tuning of specific synergies. The target presenting the higher level of generalization is target N, which requires the tuning of synergies W2 and W4. As observed in Fig. 6 both groups are able to engage these two synergies at their boundaries (Group1 while training NW, NE and E; Group2 while training N and SE) in two sub-spaces of identical extension (135°) and rotated of only 45° between them. As a result, the final tuning of those two synergies is similar between the two groups and close to the theoretically ideal rotation (45°). The biggest differences in AP tuning between the two groups are observed in W3 and, to a smaller extent, W1. It is then interesting to notice that all the targets showing limited generalization recruits at least one of these two synergies for its adaptation (Fig. 7d), while target SW, that does not show generalization, recruits both.

Our results are in agreement with previous studies showing that generalization of visuomotor rotations depends on the angular distance between the pre-adapted targets and the new ones16,38. In fact, in the synergy-tuning model of adaptation, pre-training on sub-spaces close to the one that needs to be generalized is likely to lead to the adaptation of one or more of the synergies that are involved in the adaptation of the new movement. This conceptual model could also explain the results showed by Abeele and colleagues39, who found that visual rotations up to 120° present a beneficial effect of pre-adaptation to a 45° smaller rotation, but rotations bigger than 120° did not present a beneficial effect of pre-training. These behaviors may depend, at the synergistic level, on the discrepancy in the workspace covered by the original synergies, the pre-tuned ones and the ones that need to be ultimately tuned. Our results suggest that if the synergy sets involved in all three movements (original, pre-adapted and generalized) fully overlap, generalization is maximized, while as different synergies are recruited (as it is likely for big deviations, as in our 4-synergy space most movement are driven by just two APs that usually span about 160°) generalization is reduced or lost.

As an additional remark, in this work we present an analysis based on the extraction of 4 synergies. Although the interpretation of our results is bound to the shapes and functional characteristics of these 4 synergies, the choice is arbitrary, as arbitrary are all criteria used for order selection in muscle synergy analysis. Nevertheless, ours and previous results in literature35,36 suggest that the result we are observing are independent from the number of modules selected during the extraction of muscle synergies.

In conclusion, our results present evidence that the modularity in motor commands as explained by a muscle synergies model influences motor adaptation and its generalization. Considering the rich literature describing visuomotor adaptations, our results present the rationale for considering the functional constraints posed by modular organization of movement in the interpretation of the results of adaptation experiments. The link between muscle synergies, adaptations and, possibly, the mechanisms of motor learning, could have sensible practical validity in the field of neurorehabilitation, where synergistic representation of the impaired and target movements, and of the “modular” path that can be used to translate the former into the latter, could be used to design ad-hoc therapies for patients.

## Methods

### Experimental setup and Protocol

Fourteen healthy individuals (7 females, age 25.6 ± 1.2) participated in this study. Each individual participated in a single experimental session consisting of a series of isometric reaching tasks performed with their right arm. All the experimental procedures described in the following have been approved by the Ethical Committee of University College Dublin and have been conducted according to the WMA’s declaration of Helsinki. All subjects gave written informed consent before participating in this study. During the exercises the subjects sat in a chair with their back straight. Their right forearm was put on a support plan. The hand was strapped to a fixed manipulandum (consisting of a metal cylinder of 4 cm of diameter) attached to a tri-axial load cell (3A120, Interface, UK), while the wrist and forearm were wrapped to the support plan and immobilized using self-adhesive tape. Data from the load cell were sampled at 50 Hz. During all exercises, subjects kept their elbow flexed at 90° and their shoulder horizontally abducted at about 45° (Fig. 1a), so that the manipulandum would be exactly in front of the center of rotation of their shoulder. The elevation of the chair was controlled so to keep the shoulder abducted at 100°. Subjects sat in front of a screen displaying a virtual scene. The virtual scene consisted of a grey cursor, commanded in real time by the x and y components of the force exerted on the load cell through the manipulandum, a filled circle indicating the center of the exercise space and, depending on the phase of the exercise, a target, represented by a hollow circle. Both the center and target circles had a radius of 1.3 cm. Across all the blocks of the experiment subjects experienced a total of 8 different targets, positioned in a compass-like configuration (Fig. 1b) at a distance of 9.5 centimeters from the center of the screen. The force-to-pixel ratio of the virtual scene was set so that each target was positioned at a distance of 15 N with respect to the center (representing 0 N applied to the load cell) of the scene. The virtual scene and the exercise protocol were controlled using a custom software. The experiment was divided in fourteen different blocks during which subjects were asked to reach for different targets shown on the virtual scene. Subjects were allowed to rest for 1 minute between consecutive blocks.

### Biomechanical analysis

The data recorded from the load cell was processed and analyzed to characterize the biomechanical patterns of adaptation and generalization of the two groups of subjects. Only the x and y components of the load cell were considered. The continuous load cell data recorded during each block were first low-pass filtered at 10 Hz using a 3rd order Butterworth filter. After filtering, the load cell data of each reaching movement were segmented between the instant in which the cursor exited the central circle and the instant in which it reached the target circle. All segments were then time-scale normalized to 100 samples. We evaluated the adaptation and generalization patterns by calculating the Normal Curvilinearity (NC) of their reaching trajectories. NC was calculated for each length-normalized movement as the ratio between the length of each movement trajectory and the length of the straight line connecting the boundaries of the circles representing the center of the space and the target. A statistical analysis was performed to assess for differences in the average NC values calculated at the beginning of adaptation and generalization of all targets pooled together to assess for differences in NC due to generalization. This analysis was based on Mann-Whitney U test with significance level α set to 0.05.

### EMG signal recording and processing

EMG signals were recorded from the following 13 upper limb muscles: Brachiradialis (BRD), Biceps brachii short head (BSH), Biceps brachii long head (BLH), Triceps brachii lateral head (TLT), Triceps brachii long head (TLN), Deltoid Anterior (DANT), Medial (DMED) and Posterior (DPOST) heads, Pectoralis Major (PM), Inferior head of the Trapezius (TRAP), Teres Major (TMAJ) and Latissimus Dorsi (LD). EMG signals were recorded through a Delsys Trigno system (Delsys, US), sampled at 2000 Hz and synchronized with the load cell. All the subsequent analyses were performed in the Matlab environment (2014b, Mathworks, US). EMG signals were filtered in the 20Hz–400Hz band by using a 3rd order digital Butterworth filter. Amplitude envelopes were then obtained by low pass filtering the full wave rectified EMGs with a 3rd order Butterworth filter with a cut-off frequency of 10 Hz. Only the EMG data relative to the center-out phase of the movement, as identified from the biomechanical data, were utilized in the synergies analysis.

Before muscle synergies extraction, all the calculated envelopes underwent an amplitude and time scale normalization procedure. Time scale was normalized by segmenting the EMG data based on the synchronized biomechanical data. Each center-out reaching movement was time-scale normalized by resampling the corresponding envelope on a fixed 100-samples time reference, representative of the percentage of execution of each reaching movement. The EMG envelopes of each subject were amplitude normalized by using the values extracted from the initial normalization block; during the normalization block, each participant reached three times to all the 8 targets, and the peak amplitude of each muscle during each movement was calculated. For each muscle the target yielding its maximal activation was identified. The reference normalization value for each muscle was then established as the average across the three peak values recorded across the repetitions of the target maximizing each muscle’s activity during the normalization block.

### Muscle synergies extraction

In our main analysis muscle synergies were extracted from each participant at block B3. In an additional analysis (see Figs S1, S2 and S3, Supplementary material) synergies were also extracted, for each subject, for the data relative to blocks Ad3 and Ad6 pooled together and for the data relative to blocks Wo2 and Wo4 pooled together. The NMF algorithm with multiplicative update rule41 was applied to the matrix D13×(40×100) of the EMG envelopes, containing the time scale and amplitude normalized EMGs from the 40 reaching movements (8 targets × 5 trials). For each subject, a synergy vectors matrix W13xS and a matrix APSx(40x100) of the synergy activation patterns was obtained; a number of synergies from 1 to 13 was extracted, and S was defined as the lowest number of synergies able to explain an average (across subjects) fraction of variance higher than 90%. Similarity between different synergy weights (either across or within subjects) was calculated using the normalized dot product (see Supplementary material).

### Synergies Activation Patterns reconstruction during motor adaptation using the fixed B3 synergies and statistical validation

For each subject, the EMG envelopes of all the subsequent adaptation blocks Ad1–Ad6 and washout blocks Wo1–Wo4 were reconstructed by using the set of baseline synergies extracted at B3 from the same subject. This was achieved by using a modified version of the NMF algorithm (namely Nonnegative Reconstruction, NNR)40, able to reconstruct the matrix D by letting only the coefficients matrix AP update at every algorithm iteration, while keeping the W matrix fixed. The ability of the B3 synergies to account for the envelopes from all the trials was verified in two separate ways. First, the variance accounted for by the reconstruction (VAFREC) was quantified and statistically compared across trials. In second instance the obtained VAFREC values were statistically compared to those expected from chance. For each subject and each block, 100 random synergy matrixes were obtained by shuffling the muscle components within each synergy, in order to obtain structure-less synergy matrixes WSHUFFLE. These matrixes were then used in NNR algorithm and obtain VAFSHUFFLE values from structure-less modules. We then tested for significant differences between VAF obtained from the reference synergies and those obtained from chance for each block. This analysis was based on Mann-Whitney U test with α = 0.05 and Bonferroni’s correction to take into account the repeated analysis on 11 blocks (from B3 to Wo4), for an effective α of 0.0045.

### Calculation of the preferred angles of the synergies APs

To evaluate the angular tuning of synergies APs, we calculated the preferred angle spanned by each synergy AP in the workspace at both baseline and at full adaptation for all 6 adapted/generalized targets. Preferred angles were calculated from the parameters of a cosine fit28 between the RMS of each synergy and the corresponding target position. Synergies APs were fitted using a linear regression in the form: $$AP(\theta )={\beta }_{0}+{\beta }_{1}\,\cos (\theta )+{\beta }_{2}\,\sin (\theta )$$. The preferred angle of each synergy was then calculated from the fitting parameters as $$\vartheta =\,ta{n}^{-1}({\beta }_{2}/{\beta }_{1})$$. The preferred angles at baseline were calculated from the RMS of the average (across repetitions and subjects) APs at B3. Preferred angles at final adaptation were calculated by pooling together, for each group, the RMS of the average (across the last 5 repetitions of each target and across subjects) APs at the end of Ad3 and Ad6.

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## Acknowledgements

This study was partially funded by the UCD Seed Grant #SF1303.

## Author information

Authors

### Contributions

G.S. conceived the study; G.S., C.D.M., J.D.S. and S.C. designed the study protocol; G.S., J.D.S. and M.Z. set up and executed the experiments; G.S., C.D.M. and J.D.S. analyzed the data; G.S. and C.D.M. drafted the manuscript; J.D.S., M.Z. and S.C. reviewed the draft.

### Corresponding author

Correspondence to Giacomo Severini.

## Ethics declarations

### Competing Interests

The authors declare no competing interests.

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Reprints and Permissions

De Marchis, C., Di Somma, J., Zych, M. et al. Consistent visuomotor adaptations and generalizations can be achieved through different rotations of robust motor modules. Sci Rep 8, 12657 (2018). https://doi.org/10.1038/s41598-018-31174-2

• Accepted:

• Published:

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