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WIREs Cogn Sci
Impact Factor: 3.175

Space and time in the context of equilibrium‐point theory

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Abstract Advances to the equilibrium‐point (EP) theory and solutions to several classical problems of action and perception are suggested and discussed. Among them are (1) the posture–movement problem of how movements away from a stable posture can be made without evoking resistance of posture‐stabilizing mechanisms resulting from intrinsic muscle and reflex properties; (2) the problem of kinesthesia or why our sense of limb position is fairly accurate despite ambiguous positional information delivered by proprioceptive and cutaneous signals; (3) the redundancy problems in the control of multiple muscles and degrees of freedom. Central to the EP hypothesis is the notion that there are specific neural structures that represent spatial frames of reference (FRs) selected by the brain in a task‐specific way from a set of available FRs. The brain is also able to translate or/and rotate the selected FRs by modifying their major attributes—the origin, metrics, and orientation—and thus substantially influence, in a feed‐forward manner, action and perception. The brain does not directly solve redundancy problems: it only limits the amount of redundancy by predetermining where, in spatial coordinates, a task‐specific action should emerge and allows all motor elements, including the environment, to interact to deliver a unique action, thus solving the redundancy problem (natural selection of action). The EP theory predicts the existence of specific neurons associated with the control of different attributes of FRs and explains the role of mirror neurons in the inferior frontal gyrus and place cells in the hippocampus. WIREs Cogni Sci 2011 2 287–304 DOI: 10.1002/wcs.108 This article is categorized under: Neuroscience > Behavior

Threshold position control of single‐joint actions. By changing the threshold joint angle (ΔR) from its initial value (R), the system shifts the torque‐angle characteristic of the joint in the flexion direction. The final characteristic (thick curve in each panel) represents a set of possible equilibrium points (EPs) that the system can reach. Each EP is the combination of the position and torque that can be established in the process of the interaction of the joint segment with the external forces (loads). A specific final EP (a, b, or c) of the redundant set of potential EPs is established depending on external condition (isotonic in A, isometric in B and intermediate in C, respectively). In D, shift in R can be combined with co‐facilitation of flexors and extensors, resulting in a range (C) in which muscles are coactive. This process does not affect the final EP, a, but elicits additional torque (ΔT) at the initial position (Q) that helps to speed up the movement. Note that in all panels, the initial torque‐angle characteristic (thin curve) determines the resistance of the posture‐stabilizing mechanisms to deviations from the initial position (Q). Following the shift in the threshold position (in A), muscle activity and torque at the initial position begin to increase (vertical arrow), resulting in movement acceleration toward the final referent position in A, C, and D. In this way, the nervous system converts the posture‐stabilizing to movement‐producing mechanisms, thus solving the posture–movement problem. In B, movement is prevented and the shift in R results in an increase in isometric muscle torque (Reprinted with permission from Ref 22. Copyright 2010 John Wiley & Sons).

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Different forms of threshold position control. The specific form of threshold position control is chosen depending on the desired action. (A) In motor tasks involving a single joint, the system changes the referent joint angle R and the activity of muscles is generated depending on the difference between the actual joint angle (Q) and angle R. (B) In tasks involving the whole arm, the system changes the referent arm configuration (Ra) that defines a common threshold position for all arm muscles, except that the system may set thresholds for agonist and antagonist muscle groups differently such that these groups will be coactive at the R configuration and in the range, C, of adjacent configurations—referent range for muscle coactivation. (C) In precision grip force control, the system changes the referent hand opening (aperture), Ro, that defines a virtual distance between the index finger and the thumb. In the presence of the object, the actual hand aperture (Qo) is constrained by the size of the object held between the fingers whereas, in the referent position, the fingers virtually penetrate the object. Deviated by the object from their thresholds of activation, hand muscles generate activity and grip forces in proportion to the gap between the Qo and Ro. (D) In tasks involving skeletal muscles of the whole body, the system changes the referent body configuration (Rc). During the gymnastic exercise, the athlete presumably specifies an Rc configuration at which the net joint torques are zero and cannot compensate the weight torques of body segments. The body will move until the difference between Qc and Rc become sufficient to elicit muscle activation and torques that balance the weight torques. (E) A single step or continuous walking is produced by a discrete or, respectively, continuous shifts in the referent location (Rl) of the whole body in space (Reprinted with permission from Ref 28,29. Copyright 2007 Elsevier).

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Basic rules describing threshold position control, EMG, and force regulation for a single muscle. Symbol λ* is the composite (net) threshold; λ is its central component; µ is a temporal parameter related to the dynamic sensitivity of muscle spindle afferents; v is the velocity of change in the muscle length (v = dx/dt); ρ is the shift in the threshold resulting from the intermuscular interaction, in particular, reciprocal inhibition, and cutaneous stimuli (e.g., from pressure‐sensitive receptors in the finger pads during grasping); ε(t) represents temporal changes in the threshold resulting, in particular, from intrinsic properties of motoneurons; [u]+ = u if u ≥ 0 and 0 otherwise. Note that muscle activation is a strongly nonlinear function of x − λ*, implying that contrary to the servo‐assistance hypothesis, muscle activation cannot be decomposed into two additive components, one resulting from central and the other from reflex influences on motoneurons.

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Physiological origin of threshold position control. (A): Minimal integrative unit that produces threshold position control at the level of a single motoneuron (MN). The MN receives afferent influences that depend on the muscle length as well as central control influences that are independent of muscle length. The MN is recruited when the membrane potential exceeds the electrical threshold (V+). (B) When the muscle innervated by the MN is stretched quasi‐statically from the biomechanically minimal length (x) in the absence of independent control input, the motoneuronal membrane potential increases from its initial value (Vi) according to length‐dependent feedback from the muscle (lower diagonal line). The electrical threshold (V+) is reached at length λ+ that is higher than the biomechanically maximal muscle length (x+). When independent control facilitation is added (vertical arrow), the same stretch elicits motoneuronal recruitment at a shorter threshold length (λ). (C) Shifts in the spatial threshold (horizontal arrow) can also result from changes in the electrical threshold (vertical arrow). In both cases (B or C), shifts in the membrane potentials and respective changes in the threshold position are initiated prior to the onset of EMG activity and force generation (a feed‐forward process). Thereby, the activity of motoneurons and muscle force emerge depending on the difference between the actual (x) and the threshold (λ) muscle length (Reprinted with permission from Ref 13. Copyright 2007 Springer).

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Threshold position control underlies voluntary motor actions. A family of static torque‐angle characteristics (solid curves) was obtained in unloading experiments. Each of the filled circles a–d shows the respective mean initial equilibrium point (EP), i.e., the combination of the elbow angle and torque established by the subject before unloading. Open circles show the final EPs established after different amounts of unloading. For each characteristic, the tonic EMG activity (vertical segments) decreased with the decreasing load. The dashed curve shows the passive torque‐angle characteristic measured in a separate experiment by rotating the manipulandum with the forearm on it when the subject was instructed to completely relax his arm muscles. Note that each solid curve merges with the characteristic of passive muscles at a specific position—threshold joint angle (R). This threshold was different (ΔR) for different characteristics (Δλ show the difference in terms of threshold muscle length). Thus the voluntary motor action responsible for the transition from one torque‐angle characteristic to another was associated with a change in the threshold joint angle (Reprinted with permission from Ref 6. Copyright 1986 Heldref Publications).

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Basic rules in solving the redundancy problems in the control of multiple muscles and degrees of freedom. First, the brain reduces the amount of redundancy by constraining neuromuscular elements to function in task‐specific spatial frames of reference (FRs). Second, neuromuscular elements within each and in different FRs interact to minimize the gaps between the actual and referent values of variables at any level of control hierarchy. Sensory signals from subordinated levels are delivered to higher levels to make, if necessary, corrections of referent variables. Asterisk (*) implies that the respective variable might depend on velocity..

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A verification of the concept of the referent body configuration: the occurrence of global EMG minima during vertical jumps. EMG minima in 21 muscles across the body occur during the flight phase in each jump (at time a and c) and during transition from body flexion to extension (at time b) in preparation to jumps (in about 80% of jumps). Surface EMG activity of 16–21 functionally diverse muscles of the legs, trunk, and arms was recorded, typically, from the pectoralis major (PM), deltoid anterior (DA), upper trapezius (UT), middle trapezius (MT), lattissimus dorsi (LD), erector spinae (ES), thoracic back extensors (TBE), lumbar back extensors (LBE), lateral abdominus (LA), rectus abdominus (RA), external oblique (EO), extensor carpi radialis (ECR), flexor carpi radialis (FCR), bicepsbrachii (BB), triceps brachii (TB), brachioradialis (BR), gluteus medius (Gm), tensor fascia latae (TFL), rectus femoris (RF), semitendinosus (ST), vastus medialis (VM), biceps femoris (BF), lateral gastrocnemius (LG), and tibialis anterior (TA) (Reprinted with permission from 31. Copyright 2004 Springer)..

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Central and afferent components of position sense. (A) When muscles compensate an external load, the segment arrives at position Q deviated from the threshold position R by P. Position Q can be sensed adequately by combining the control signal responsible for setting the threshold position, R, with deviation from it, P, delivered by proprioceptive signals. (B) An isotonic movement is produced by changing the threshold position (ΔR). The resulting change in the joint angle (ΔQ) can be perceived based on the central component (ΔR) of position sense even if its afferent component remains constant (ΔP = 0). (C) When movement is prevented (isometric condition), changes in the threshold position (ΔR) results in an increase in proprioceptive feedback (by ΔP) and isometric torque. In this case, the central and afferent components of position sense are equal but opposite (ΔP = − ΔR) and, taken together, elicit no sensation of motion (ΔQ = 0) (Reprinted with permission from Ref 2. Copyright 2009 Springer).

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Human step as an emergent response to changes in the gap between the actual location (Ql) of the body and its centrally specified referent location (Rl) in the environment. During standing, body posture Qc (solid figure) is stabilized such that the center of the body mass is within the area of body support. Externally elicited deviations from posture Qc evoke position‐ and velocity‐dependent muscle resistance. The area from which the center of body mass should move at some speed to reach the foot support area without a fall of the body is called the dynamic stability area. Posture‐stabilizing mechanisms would generate resistance in response to an intentional step if it were made without any concerns with these mechanisms (classical posture–movement problem). To make a step, the nervous system shifts the referent location of the body (upper horizontal arrow and dashed figure) until it virtually reaches a final position, Rl, located at some distance from the initial position of the body. The virtual relocation of the body elicits (vertical arrow) step‐like changes in the referent body configuration, Rc. Following an increase in the gap between Qc and Rc, muscles are activated, and produce a real step. Although the center of body mass initially appears outside the initial body support area resulting from the referent shifts, it moves toward and eventually reaches the new body support area, thus excluding the risk of body fall. Multiple steps (gait) result from continuous shifts in the referent body location in the environment. Since the posture‐stabilizing mechanisms are shifted with the virtual body displacement, they do not resist but rather produce the step or gait.

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Resetting of threshold arm configuration in point‐to‐point arm movements in frontal (x) and sagittal (y) directions. Note that the activity of seven muscles at the initial arm position is practically zero (background noise level) and, after transient EMG bursts, returns to zero at the final positions (A, B). Muscles are activated in response to perturbations of the arm at the initial (C) and final (D, E) positions. The results imply that motoneurons of arm muscles were near their activation threshold and that the threshold arm position was reset when movement was made. On the top of each panel, the hand trajectories as well as the initial and final arm configurations are shown; x and y are major components of trajectories for the motion to the frontal and sagittal targets, respectively. Muscles that remained active at the final position could be deactivated in response to perturbation in appropriate direction (e.g., DP in E) (Reprinted with permission from Ref 7. Copyright 2006 Springer).

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In fast point‐to‐point arm movements, shifts in the arm equilibrium position are ceased substantially before the end of movements. An example of fast arm movements in temporal (A) and spatial coordinates (B). Point i is the initial hand position. Point h is the hand position at the time when the shifts of the hand to the final equilibrium position, a, has been completed. Thus, the equilibrium position substantially leads the actual hand position. Because of this discrepancy, muscles generate forces sufficient for a high‐speed movement. Curves and points i, a and h were experimentally measured (Reprinted with permission from Ref 42. Copyright 2001 Springer).

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