Article Figures & Data
Figures
- 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 ql = (104°,71°), that at the center work space (Center) was qc = (63°,90°), and that at the right work space (Right) wasqr = (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.
