Referent control and motor equivalence of reaching from standing

Abstract

Motor actions may result from central changes in the referent body configuration, defined as the body posture at which muscles begin to be activated or deactivated. The actual body configuration deviates from the referent configuration, particularly because of body inertia and environmental forces. Within these constraints, the system tends to minimize the difference between these configurations. For pointing movement, this strategy can be expressed as the tendency to minimize the difference between the referent trajectory (R_T) and actual trajectory (Q_T) of the effector (hand). This process may underlie motor equivalent behavior that maintains the pointing trajectory regardless of the number of body segments involved. We tested the hypothesis that the minimization process is used to produce pointing in standing subjects. With eyes closed, 10 subjects reached from a standing position to a remembered target located beyond arm length. In randomly chosen trials, hip flexion was unexpectedly prevented, forcing subjects to take a step during pointing to prevent falling. The task was repeated when subjects were instructed to intentionally take a step during pointing. In most cases, reaching accuracy and trajectory curvature were preserved due to adaptive condition-specific changes in interjoint coordination. Results suggest that referent control and the minimization process associated with it may underlie motor equivalence in pointing.

New & noteworthy: Motor actions may result from minimization of the deflection of the actual body configuration from the centrally specified referent body configuration, in the limits of neuromuscular and environmental constraints. The minimization process may maintain reaching trajectory and accuracy regardless of the number of body segments involved (motor equivalence), as confirmed in this study of reaching from standing in young healthy individuals. Results suggest that the referent control process may underlie motor equivalence in reaching.

Keywords: adaptation; arm movement; compensation; interjoint coordination; motor control; redundancy; synergy.

Fig. 1.

Referent and actual body configurations during pointing from standing. Muscles are activated depending on the difference between the referent (R) and actual (Q) body configurations. The shift in R results in a change in the referent trajectory of the endpoint (R_T), where subscript T refers to the endpoint trajectory. Under the influence of gravity (vertical arrow), the final actual body configuration and the final endpoint position of the trajectory (Q_T) are below their respective referent values. Muscles are activated to minimize the gap between the actual and referent states for both the body configuration and the endpoint position. Muscle activation proceeds until a balance is achieved between muscle and external forces (e.g., gravity).

Fig. 2.

Experimental conditions. In the initial position, participants reached a remembered target (open circle) placed beyond the arm's reach with the eyes closed before the arm movement onset. In most of the trials, no perturbation was applied because the board that could prevent hip flexion was moved away (free-hip condition). In 30% of randomly chosen trials, hip flexion was unexpectedly prevented by an electromagnetic device (blocked-hip condition), forcing subjects to take a step to prevent falling. In yet another experiment, subjects made an intentional step during reaching in the absence of perturbation (intentional-step condition).

Fig. 3.

Spatiotemporal profiles of motion of body segments in different conditions in a representative subject (S1). The endpoint trajectories (A) and velocity profiles (B) remained similar, regardless of substantial motion of the trunk (shoulder marker) and foot. In A, circles indicate the final endpoint position and the instantaneous trunk position at that moment. In B, the circle and the vertical line indicate velocities of different body segments at the time of the endpoint movement offset. B shows that trunk motion exceeded the minimum (horizontal line) required for reaching the target; trunk position at the endpoint movement offset was more anterior in the blocked-hip and intentional-step conditions than the in free-hip condition. In B, the trunk continued to move after the endpoint movement offset, especially in the blocked-hip and intentional-step conditions.

Fig. 4.

Spatiotemporal profiles of motion of body segments in different conditions in another subject (S2). Like in S1 (Fig. 3), endpoint trajectories and velocity profiles in S2 were preserved across conditions (A). The velocity profile was symmetrical in S1. In contrast to S1, deceleration phases in S2 were prolonged in all conditions, resulting in an asymmetrical velocity profile (B). Trunk displacement after the endpoint movement offset (vertical line) in S2 was smaller than in S1.

Fig. 5.

An example of violations of trajectory invariance. The endpoint trajectories in the free-hip and blocked-hip conditions were similar but different from those in the intentional-step condition, although the endpoint movement accuracy was preserved in all conditions (subject S3).

Fig. 6.

Timing of movement events (the onset, peak velocity, and offset) for different body segments during pointing (group data). For the endpoint, the timing (mean ± SD) remained similar across conditions. The trunk and endpoint movement onsets were not always synchronized, but in all cases the trunk continued to move after the endpoint movement offset, especially in the blocked-hip and intentional-step conditions. Foot movement was initiated earlier in the intentional-step condition compared with the blocked-hip condition.

Fig. 7.

Condition-dependent interjoint coordination (A) and individual changes in the joint angles (B) during pointing (subject S1). In A, for better comparison, the initial points in the angular trajectories were adjusted to be matched. In B, each solid line indicates the mean and dotted lines the 95% confidence interval for changes in elbow, shoulder, and hip joint angles. In the free-hip and blocked-hip conditions, the interjoint coordinations began to diverge some time after the motion onset (A). In A, the interjoint coordination during the intentional-step condition began to diverge from the very beginning from coordinations during the other conditions. Interjoint coordinations at the endpoint movement offset (circles) were substantially different for all 3 conditions. In other words, the invariance of endpoint trajectories and movement accuracy were maintained due to condition-dependent changes in the interjoint coordination. Interjoint coordination continued to change after the endpoint movement offset (circles), indicating that the changes in the joint angles during this period neutralized the influence of continuous body motion on the endpoint position. Similarly, the divergence of individual joint displacement occurred before the endpoint movement offset (B).

Fig. 8.

Interjoint coordination during pointing in another subject (S2). Conventions are as described in Fig. 7. Changes in elbow, shoulder, and hip joint angles after the endpoint movement offset (A, circles) were smaller than in S1. The influence of trunk displacement on endpoint was not completely neutralized by changing interjoint coordination, resulting in prolonged deceleration time of the endpoint (B).

Fig. 9.

With referent control, the system can reach the desired goal even if external force characteristics are not known. Regardless of load characteristic (a, increasing; b, nonmonotonic; c, decreasing), changes in the equilibrium joint angle (ΔQ) are monotonically related to shifts of the referent angle (ΔR) at which active muscle torque (thick curves) begin to be generated. Filled circles are equilibrium points at which muscle and load forces are balanced. The nervous system can thus monotonically shift the referent position until the desired final torque and/or position are reached.