Motor synergies and the equilibrium-point hypothesis

Abstract

The article offers a way to unite three recent developments in the field of motor control and coordination: (1) The notion of synergies is introduced based on the principle of motor abundance; (2) The uncontrolled manifold hypothesis is described as offering a computational framework to identify and quantify synergies; and (3) The equilibrium-point hypothesis is described for a single muscle, single joint, and multijoint systems. Merging these concepts into a single coherent scheme requires focusing on control variables rather than performance variables. The principle of minimal final action is formulated as the guiding principle within the referent configuration hypothesis. Motor actions are associated with setting two types of variables by a controller, those that ultimately define average performance patterns and those that define associated synergies. Predictions of the suggested scheme are reviewed, such as the phenomenon of anticipatory synergy adjustments, quick actions without changes in synergies, atypical synergies, and changes in synergies with practice. A few models are briefly reviewed.

Figure 1

A scheme of a control hierarchy. At each level, a few-to-many mapping takes place (the input is low-dimensional as compared to the output). Output signals serve as the inputs into a hierarchically lower level. Feedback loops are not shown not to overload the scheme but they are assumed both within each level and across levels.

Figure 2

An illustration of the idea of “good” and “bad” components of variance (V_GOOD and V_BAD). The task is to produce a constant force level (F_TASK) using two effectors that generate forces F₁ and F₂. The dashed line corresponding to the equation F_TASK = F₁ + F₂ defines the uncontrolled manifold (UCM) for this performance variable. Three ellipses illustrate possible data point distributions. The circular distribution (A) implies no co-variation between F₁ and F₂, a non-synergy. The ellipse elongated along the dashed line (B) corresponds to V_GOOD > V_BAD - a synergy stabilizing F_TASK. The ellipse elongated orthogonal to the UCM corresponds to V_BAD > V_GOOD, which may be interpreted as a co-variation destabilizing F_TASK.

Figure 3

An illustration of the EP-hypothesis for a single muscle. Setting a value of λ defines a dependence of active muscle force on muscle length (IC). Muscle force, level of activation, and length all change along IC. The point of intersection between the load characteristic (L, isotonic load, isometric load, and elastic load are illustrated with the solid, dashed, and dotted lines respectively) is the equilibrium point (EP) of the system corresponding to a combination of muscle length (L_EP) and muscle force (F_EP).

Figure 4

Within the EP-hypothesis, movement can emerge following a change in the external load (L) or a shift in the central control variable λ. A shift from λ₁ to λ₂ may lead to a change in muscle force (isometric conditions, EP₀ – EP₁), muscle length (isotonic conditions, EP₀ – EP₂), or both (EP₀ – EP₃).

Figure 5

A hypothetical hierarchy of conrol variables within the referent configuration hypothesis illustrated with the task of placing the endpoint of a redundant kinematic chain into a target. At the higher level, based on the task, a referent configuration {R,C} is selected. At the next level, these signals project on n {r,c} pairs for individual joints. At the next level, each {r,c} pair serves as the input into a synergy that defines m λ values for the participating muscles.

Figure 6

Setting a value of referent aperture (AP_REF) leads to active force production against the walls of the hand-held object because of the difference between the actual aperture (AP_ACT) and AP_REF (upper panels). This mode of control would always leads to equality of the two opposing forces (F₁ + F₂ = 0; lower panels) that may be achieved at different spatial locations if AP_REF is located off-center (as in panel B).

Figure 7

A hypothetical control scheme with two types of control variables, CV1 related to a desired value of a performance variable, and CV2 related to synergies that do or do not stabilize that variable.

Figure 8

Top: The subject placed the upper arm on the table and performed quick elbow flexion movements. Bottom: Equilibrium trajectories reconstructed for the wrist and elbow joints when only the elbow joint was instructed to perform a fast movement. Note the large peak-to-peak amplitude of the wrist equilibrium trajectory and the similar timing of the trajectory peaks. The purpose of the control of the wrist is to prevent its motion under the action of interaction torques. ET – equilibrium trajectory. Modified by permission from Latash ML, Aruin AS, Zatsiorsky VM (1999) The basis of a simple synergy: Reconstruction of joint equilibrium trajectories during unrestrained arm movements. Human Movement Science 18: 3–30.

Figure 9

The subject lifted an instrumented handle quickly in the vertical direction towards a target. The handle could be pre-loaded to introduce a non-zero moment of force in a static condition. Two typical trials are illustrated. In one trial (perturbed trial), the handle was fixed to the table, the digits slipped off the sensors, and the hand moved without the handle. Panel A shows the time profiles of the thumb and index finger coordinates under the two conditions. Panel B shows the time changes in the hand aperture in the two trials. Note the transient closure of the index finger and the thumb and the smaller aperture in the final state.

Figure 10

Changes in the index of multi-finger synergy stabilizing total force (ΔΔV) prior to a quick force pulse production at a self-selected time and “as quickly as possible” following an auditory signal. Note the early drop in ΔV in the self-paced trials (solid lines), but not in the reaction-time trials (dashed lines). Average time profiles are shown with standard deviation (thin lines). Reproduced by permission from Olafsdottir H, Yoshida N, Zatsiorsky VM, Latash ML (2005) Anticipatory covariation of finger forces during self-paced and reaction time force production. Neuroscience Letters 381: 92–96.

Figure 11

Three possible scenarios of synergy changes during force production with two index fingers. Before practice a synergy existed stabilizing the total force across repetitive trials (V_GOOD > V_BAD in panel A). With practice, V_BAD drops. If V_GOOD stays unchanged, decreases less that V_BAD, or increases, this may be interpreted as the synergy becoming stronger (panel B). If V_GOOD decreases in proportion to V_BAD, more accurate performance is accompanied by the unchanged synergy (panel C). V_GOOD can also drop more than V_BAD leading to a more spherical data distribution (panel D), a weaker synergy.