Differences in adaptation rates after virtual surgeries provide direct evidence for modularity

Abstract

Whether the nervous system relies on modularity to simplify acquisition and control of complex motor skills remains controversial. To date, evidence for modularity has been indirect, based on statistical regularities in the motor commands captured by muscle synergies. Here we provide direct evidence by testing the prediction that in a truly modular controller it must be harder to adapt to perturbations that are incompatible with the modules. We investigated a reaching task in which human subjects used myoelectric control to move a mass in a virtual environment. In this environment we could perturb the normal muscle-to-force mapping, as in a complex surgical rearrangement of the tendons, by altering the mapping between recorded muscle activity and simulated force applied on the mass. After identifying muscle synergies, we performed two types of virtual surgeries. After compatible virtual surgeries, a full range of movements could still be achieved recombining the synergies, whereas after incompatible virtual surgeries, new or modified synergies would be required. Adaptation rates after the two types of surgery were compared. If synergies were only a parsimonious description of the regularities in the muscle patterns generated by a nonmodular controller, we would expect adaptation rates to be similar, as both types of surgeries could be compensated with similar changes in the muscle patterns. In contrast, as predicted by modularity, we found strikingly faster adaptation after compatible surgeries than after incompatible ones. These results indicate that muscle synergies are key elements of a modular architecture underlying motor control and adaptation.

Figure 1.

Concept of incompatible surgery. Illustration of a tendon transfer surgery that makes a putative muscle synergy unable to generate any force. A, An idealized arm with two pairs of antagonist muscles at two joints (m₁ to m₄), each generating a force in a specific direction at the end point (f₁ to f₄), is controlled by a muscle synergy recruiting two muscles simultaneously (m₁ and m₂). The activation of the synergy generates a force that is the sum of the forces generated by each constituent muscle (f_syn = f₁ + f₂). B, A tendon transfer surgery affecting the force generated by two muscles. C, After the surgery, one of the muscles participating to the synergy (m₁′) generates a force in a direction that cancels the force of the other synergistic muscle (m₂). The synergy no longer generates any force (f′_syn = f′₁ + f′₂ = 0).

Figure 2.

Experimental setup and protocol. A, Subjects sat in front of a desktop and applied forces on a transducer attached to a forearm, wrist, and hand splint. A flat monitor occluded the subject's hand and displayed a virtual scene colocated with the real desktop. B, Transparent spheres positioned on a horizontal plane with centers at the same height as the center of the palm indicated force targets that the subjects were instructed to reach with a smaller spherical cursor moving on the same plane according to the force applied (force control) or estimated from EMGs recorded from 13 arm and shoulder muscles (EMG control; see Materials and Methods). C, Subjects were instructed to perform a center-out reaching task in which they had to maintain the cursor in a central start location for 1 s, reach a target as soon as it appeared at one of eight peripheral locations, and maintain the cursor at the target for 0.2 s. D, Each subject performed a single experimental session consisting of 16 trials of maximum voluntary force generation in eight directions, 72 trials of reaching to targets in eight directions at three force magnitudes (10, 20, and 30% MVF) in force control, and the following blocks of 24 trials each in EMG control: one block of familiarization (FAM), two series of 24 blocks for each surgery type (6 baseline blocks, 12 surgery blocks, 6 washout blocks), and 6 additional baseline blocks.

Figure 3.

Examples of EMG-to-force matrix, synergies, and virtual surgeries. A, EMG-to-force matrix H estimated for Subject 2 from EMG and force data recorded during the generation of planar isometric forces. Each column of H, representing the planar force generated by one muscle, is illustrated by a colored arrow (1, brachioradialis; 2, biceps brachii short head; 3, biceps brachii long head; 4, triceps brachii lateral head; 5, triceps brachii long head; 6, infraspinatus; 7, anterior deltoid; 8, middle deltoid; 9, posterior deltoid; 10, pectoralis major; 11, teres major; 12, latissimus dorsi; 13, middle trapezius). B, Muscle synergies (matrix W) are identified by nonnegative matrix factorization from the EMG data. Each column of W, a vector specifying a specific pattern of relative level of muscle activation, is illustrated by color-coded horizontal bars. C, Forces associated with each muscle synergy (i.e., columns of the matrix product H W) span the entire force space. D, Forces generated by muscles after a compatible virtual surgery obtained by recombination of the original forces as after a complex rearrangement of the tendons (T_c). E, Synergy forces after the compatible surgery still span the force space. F, Muscle forces after an incompatible surgery generated by a rotation matrix (T_i) that maps a vector in the column space of W into a vector in the null space of H. G, Such rotation aligns the forces associated with all synergies in the same direction; thus synergy forces after the incompatible surgery do not span the entire force space.

Figure 4.

Construction of compatible and incompatible virtual surgeries. A, Venn diagram illustrating the different subspaces of the muscle space used for the construction of the virtual surgeries: the column space of the synergies R(W) (cyan set), the null space of the EMG-to-force matrix N(H) (orange set), and the common subspace of N(H) and R(W) (magenta set). w and w′ represent generic vectors in the column space of the synergies, and n represents a vector in N(H) that is not in R(W). B, A compatible rotation in muscle space maps a vector w in R(W) (cyan plane) that is not in N(H) (orange arrow) into a second vector w′ in R(W). C, An incompatible rotation in muscle space, in contrast, maps a vector w in R(W) that is not in N(H) (orange plane) into a vector n in N(H) that in not in R(W) (cyan plane).

Figure 5.

Example of cursor trajectories. Trajectories of the cursor on the horizontal plane during individual trials of Subject 2 are shown for different targets (color coded) before undergoing a virtual surgery (baseline; first column), immediately after a virtual surgery (second column), at the end of the exposure to the virtual surgery (third column), and after undoing the virtual surgery (washout; last column), for compatible (first row) and incompatible (second row) virtual surgeries. The motion of the cursor was simulated in real time as that of a mass attached by a damped spring to the center of the real handle under the force applied to the handle estimated from the recorded EMGs (see Materials and Methods). Trajectories are shown from the target “go” signal until the end of the trial.

Figure 6.

Comparison of task performance changes during virtual surgery and control experiments. A, Angular error of the initial movement direction with respect to the target direction, averaged across subjects and blocks of 24 trials (solid lines; shaded areas indicate SEM) for compatible virtual surgery (green), incompatible virtual surgery (red), compatible control (cyan), and incompatible control (magenta) experiments. B, Fraction of trials in which the cursor did not reach and hold on the target, averaged across subjects and blocks of 24 trials. Differences between compatible and incompatible conditions in both performance measures were significant at the end of the exposure to the perturbation (surgery block 12) in the virtual surgery experiments, but not in the control experiments.

Figure 7.

Examples of muscle pattern reconstruction by baseline synergies and synergies extracted from the last block after the incompatible surgery. A, Muscle patterns recorded in Subject 2 for different trials (different columns) to one target (direction 225°; gray areas) throughout an experimental session and their reconstruction by the synergies extracted from the initial baseline block (solid lines) and by the synergies extracted from the last block after incompatible surgery (dotted lines). The vertical lines indicate the time of movement onset (1), the time of the first peak of the cursor tangential velocity (2), and the time of target acquisition (3). The corresponding cursor trajectories and events (1–3) are shown for each trial above the muscle activation waveforms. TriLat, Triceps brachii lateral head; InfraSp, infraspinatus; DeltA, anterior deltoid; DeltM, middle deltoid; PectMaj, pectoralis major; TerMaj, teres major; LatDorsi, latissimus dorsi; TrapMid, middle trapezius. B, Synergies extracted from the initial force control block (left, as in Fig. 3B) and extracted from the last block after the incompatible surgery (right) for the same subject and used for the muscle pattern reconstruction in A. Synergy vectors are normalized to their maximum muscle activation.

Figure 8.

Reconstruction quality of muscle patterns by synergy combinations during virtual surgeries. Synergy reconstruction error (R²) averaged across subjects and blocks of 24 trials (solid lines; shaded areas indicate SEM) for compatible surgery (green), incompatible surgery (red), compatible control (cyan), and incompatible control (magenta) experiments. The reconstruction quality was significantly reduced only during the exposure to incompatible surgeries, indicating a reorganization of the muscle patterns.