Spatial generalization from learning dynamics of reaching movements

Abstract

When subjects practice reaching movements in a force field, they learn a new sensorimotor map that associates desired trajectories to motor commands. The map is formed in the brain with elements that allow for generalization beyond the region of training. We quantified spatial generalization properties of these elements by training in one extreme of the reachable space and testing near another. Training resulted in rotations in the preferred direction (PD) of activation of some arm muscles. We designed force fields that maintained a constant rotation in muscle PDs as the shoulder joint rotated in the horizontal plane. In such fields, training in a small region resulted in generalization to near and far work spaces (80 cm). In one such field, the forces on the hand reversed directions for a given hand velocity with respect to the location of original training. Despite this, there was generalization. However, if the field was such that the change in the muscle PDs reversed as the work spaces changed, then performance was worse than performance of naive subjects. We suggest that the sensorimotor map of arm dynamics is represented in the brain by elements that globally encode the position of the arm but locally encode its velocity. The elements have preferred directions of movement but are modulated globally by the position of the shoulder joint. We suggest that tuning properties of cells in the motor system influence behavior and that this influence is reflected in the way that we learn dynamics of reaching movements.

Fig. 1.

Experimental setup. A, Subjects reached to visual targets while holding the handle of a manipulandum. The location of their hand was displayed directly above their hand via a video projector on a horizontal screen that was mounted at <1 cm above the handle. B, Performance was measured in three small work spaces, each a semicircle of radius 10 cm. When the hand was in a given work space, it was initially positioned at the center target. For odd-numbered movements, targets were chosen randomly from the marked locations on the circumference of the work space. Targets for even-numbered targets were always at the center of the work space. The typical joint angle vector at the left work space (Left) was q_l = (104°,71°), that at the center work space (Center) was q_c = (63°,90°), and that at the right work space (Right) wasq_r = (13°,65°). A typical arm link length for the upper arm was l₁ = 33 cm, and that for the forearm wasl₂ = 34 cm.

Fig. 2.

EMG and kinematic data from a typical subject who trained for three sets (each set, 192 movements) at Left in fieldB₃ and was then tested at Right in joint space translation of that field, named B₄.A, EMG data from biceps during movements in the null field (solid line) and in the force fieldB₃ (dashed line). Data are aligned to the initiation of movement. The arm is in the Left work space. Each subfigure indicates EMG activity for a movement toward a target at one of the eight directions. Thesolid line is for the null field, and the dashed line is for the last set of training in fieldB₃. The center figure is the spatial tuning function for this muscle in the null and force fields. The EMG from time −50 to 100 msec for each movement is averaged, and the mean ± SD over all movements toward each of eight directions is shown. The preferred direction vector is the sum of the eight vectors. The means ± SD of the vector's angle and the length are noted by the gray region. Training in the field is coincident with a −38° rotation in the preferred direction vector.B, Magnitude of the hand velocity vector perpendicular to the direction of the target, averaged for each target set. Theblack lines are for training inB₃ at Left (3 target sets). The gray line is for the test of generalization at Right inB₄ (1 target set). Movementnumbers are indicated. C, Magnitude of the parallel velocity vector toward targets. Little change is observed.D, Maximum displacement perpendicular (Perp.) to the direction of the target. The bin size is 16 movements. Connected lines indicate a target set (192 movements). E, Spatial EMG function for biceps in the Right work space. Field B₄ at Right required a rotation of −31° in the biceps' preferred direction, similar to the rotation that field B₃ required at Left. Coincident with this, performance measures indicated generalization.L, Left; R, Right.

Fig. 3.

Generalization from Left or Right to Center. The fields are translation invariant in both hand and joint coordinates.A, Subjects practiced in the null field, then learned field B₁ at Right, and were then tested at Center (C) in field B₁(bin size = 64 movements; mean ± SEM). Performance at Center was significantly better than that of naive controls. B, Subjects learned field B₂ at Left and were tested at Center on B₂. Performance at Center was significantly better than that of naive controls.

Fig. 4.

Generalization across the work space. The fields are translation invariant in both hand and joint coordinates.A, Subjects trained at Left inB₁ and were then tested at Right inB₁ (bin size = 64 movements). Performance at Right was significantly better than that in controls.B, Subjects trained at Right inB₂ and were tested at Left inB₂. Performance at Left was significantly better than that in controls. C, Rotations with respect to the null field in the preferred direction of EMG tuning functions during learning of field B₁ at Left (mean ± SE; bin size = 192 movements) and testing in fieldB₁ at Right are shown. At Right, the rotation of EMG was similar to the rotation that was recorded at Left. The field was nearly translation invariant in terms of muscle rotations (as well as hand forces), coincident with generalization of performance measures.

Fig. 5.

Generalization across the work space. The field is translation invariant in joint coordinates but not hand coordinates.A, Subjects trained at Left inB₃ and were then tested at Right inB₄ (bin size = 64 movements). Performance at Right was significantly better than that in controls.B, Rotations with respect to the null field in the preferred direction of EMG tuning functions during learning of fieldB₃ at Left (bin size = 192 movements) and testing in field B₄ at Right are shown. EMG rotations remained invariant to changes in arm configuration. Such invariance is sufficient for generalization of training.

Fig. 6.

Generalization does not occur when the EMG rotations at one arm configuration do not match the rotations that are required for movements in another arm configuration. A, Performance of subjects that trained in B₃at Left and were tested in B₃ at Right (mean ± SE; bin size = 64 movements) is shown. The field was configuration independent in hand-centered coordinates but not joint coordinates. Subjects performed significantly worse than did naive controls. B, Rotations with respect to the null field in the preferred direction of EMG tuning functions during learning of B₃at Left and testing in field B₃ at Right are shown. The rotations at Left are opposite the rotations required to move in the same hand-centered field at Right. When the relative change in EMG PD angles rotates with arm configuration, training does not generalize. C, Subjects that learned fieldB₃ at Right were also significantly worse than control subjects in their test of generalization at Left.Disp., Displacement.