Distortions of the Efferent Copy during Force Perception: A Study of Force Drifts and Effects of Muscle Vibration

Highlights

• Force matching leads to consistent overshoots, which do not depend on force level.

• Vibration of flexor or extensor hand/finger muscles leads to similar force matching errors.

• Vibration affects referent coordinate and apparent stiffness in the match-hand only.

• The results suggest that efferent signals may be distorted before they contribute to perception.

Abstract

We used a finger force matching task to explore the role of efferent signals in force perception. Healthy, young participants performed accurate force production tasks at different force levels with the index and middle fingers of one hand (task-hand). They received visual feedback during an early part of each trial only. After the feedback was turned off, the force drifted toward lower magnitudes. After 5 s of the drift, the participants matched the force with the same finger pair of the other hand (match-hand). The match-hand consistently overshot the task-hand force by a magnitude invariant over the initial force levels. During force matching, both hands were lifted and lowered smoothly to estimate their referent coordinate (RC) and apparent stiffness values. These trials were performed without muscle vibration and under vibration applied to the finger/hand flexors or extensors of the task-hand or match-hand. Effects of vibration were seen in the match-hand only; they were the same during vibration of flexors and extensors. We interpret the vibration-induced effects as consequences of using distorted copies of the central commands to the task-hand during force matching. In particular, using distorted copies of the RC for the antagonist muscle group could account for the differences between the task-hand and match-hand. We conclude that efferent signals may be distorted before their participation in the perceptual process. Such distortions emerge spontaneously and may be amplified by the response of sensory endings to muscle vibration combined over both agonist and antagonist muscle groups.

Introduction

Despite the general agreement that afferent and efferent neural signals interact to produce coordinated movements (reviewed in Latash, 1993, Feldman, 2015), the extent to which these two processes contribute to stable kinesthetic percepts is largely unknown. Von Holst and Mittelstaedt, 1950, Sperry, 1950, suggested that the central nervous system (CNS) used a copy of motor commands – efferent copy (EC), a.k.a. efference copy, a.k.a. corollary discharge – to estimate afferent information based on the expected sensory outcome from ongoing motor processes. Von Holst and Mittelstaedt associated EC with a copy of the signals from alpha-motoneuronal pools, which was assumed to predict changes in sensory signals from proprioceptors expected from the planned action (reafference). If the prediction happened to be wrong, an error signal was sent to the alpha-motoneurons correcting the action. Reafference affected perception only if it differed from the prediction based on EC. This scheme has been criticized recently by Feldman, 2009, Feldman, 2016 because of its inability to explain how animals can relax after moving an effector to a different position. Indeed, if the muscles in both positions are relaxed, the output of all alpha-motoneurons is zero, and EC is also zero. Position-sensitive sensory endings, including those in muscle spindles, are expected to show a change in their firing frequency, which cannot be predicted based on the unchanged EC. Hence, this reafference has to induce changes in muscle activation and produce motion of the effector in clear contradiction to the everyday experience that animals, including humans, can relax muscles in various positions. Note that this criticisms applies to the original formulation of the EC concept only.

Many recent studies have assumed that neural structures within the animal’s body perform computational operations with neural signals, including EC, with the help of so-called “internal models” (Houde and Chang, 2015, Shadmehr, 2017, Brooks and Cullen, 2019), hypothetical computational networks predicting both action mechanics and its sensory consequences. This assumption is not trivial. In particular, Nikolai Bernstein, 1947, Bernstein, 1967 emphasized that the brain could not in principle predict mechanical consequences of efferent signals it generated because of the unpredictable time-varying external forces and mechanical coupling among body segments. If mechanical consequences cannot be predicted, the brain is also unable to predict sensory consequences of efferent signals, in particular signals from proprioceptors sensitive to forces and displacements. In this paper, we try to define EC within a theoretical approach based on the concept of parametric control of movement with time-varying referent coordinates (RCs) for effectors (reviewed in Latash, 2010, Latash, 2019, Feldman, 2015). Within this approach, a stable kinesthetic percept is equivalent to a stable manifold – the iso-perceptual manifold (IPM, Latash, 2018) – in the multi-dimensional space of afferent and efferent signals at the selected level of analysis. Within this general concept, efferent process defines a value of RC for the effector, and sensory signals inform the CNS on deviations of the effector from the RC.

Any kinematic degree-of-freedom (e.g., axis of joint rotation or fingertip coordinate) can be viewed as being controlled by opposing agonist–antagonist groups of muscles (Fig. 1A). The force-coordinate, F(X), characteristic of such an effector represents the algebraic sum of the F(X) characteristics for the two muscle groups. The neural control of the effector illustrated in Fig. 1A may be viewed as setting values of RC_AG and RC_ANT for the muscle groups. Alternatively, two other variables can be used corresponding to the coordinate where the net force is zero (the white circle in Fig. 1A), the reciprocal command or R-command, and to the spatial range where both muscle groups are active, the co-activation command or C-command (Feldman, 1980). At the level of mechanics, a change in the R-command (ΔR in Fig. 1A) produces a change in RC for the effector while a change in the C-command (ΔC in Fig. 1A) produces a change in the slope of the F(X) characteristic, its apparent stiffness, k (Latash and Zatsiorsky, 1993).

Imagine that an effector, e.g., a finger, is producing a magnitude of pressing force in isometric conditions (at X = 0, Fig. 1B). This task can be performed with various combinations of the R– and C–commands resulting in various {RC; k} combinations (three such combinations are shown in Fig. 1B). This means, in particular, that even perfect force matching by another effector can be associated with different {RC; k} combinations (e.g., Abolins et al., 2020a). Within this scheme, a change in force in isometric conditions can result from a change in neural commands leading to a change in R, in k, or in both. Afferent signals reflect deviations of the equilibrium state of the system (open circle in Fig. 1B) from RC. Note that signals from many sensory groups in both agonists and antagonists change with deviation from RC due changes in both muscle force and length. Assuming that there is an estimate of the deviation from RC based on the abundant set of afferent signals (A), force sense (F_S) can be expressed as: F_S = A·ƒ₁(k_S) or, alternatively, as F_S = RC_S·ƒ₂(k_S). The subscript S refers to the fact that efferent signals participating in perceptual processes represent copies, possibly imperfect ones, of efferent signals participating in the motor process. The functions ƒ₁ and ƒ₂ are simple trigonometric functions, sine and tangent, in the cartoon scheme in Fig. 1B and may be more complex functions for non-linear F(X) relations.

The scheme illustrated in Fig. 1 leads to a number of predictions, in particular related to vibration-induced kinesthetic illusions. Illusions may be expected if afferent signals are modified artificially and/or if these signals are interpreted within an inadequate reference frame, i.e. perceptual processes use distorted copies of RC and k (Fig. 1B). It is well-known that high-frequency muscle vibration generates illusions of position (Goodwin et al., 1972, Craske, 1977, Lackner and Levine, 1979, Roll and Vedel, 1982) due to the very high activity of primary muscle spindle endings (Brown et al., 1967, Roll and Vedel, 1982). The scheme in Fig. 1 links perception of coordinate and of force; hence, it predicts vibration-induced force illusions, which have been documented and quantified in a recent study (Reschechtko, et al. 2018; see also Cafarelli and Kostka, 1981) using force matching by the contralateral hand. The pattern of errors during force matching has suggested that vibration led to a change not only in afferent signals but also in the efferent component of kinesthetic perception, i.e. RC_S ≠ RC (suggested earlier by Feldman and Latash, 1982a, Feldman and Latash, 1982b). In particular, in the study by Reschechtko et al. (2018), vibration of the extrinsic finger extensors during finger pressing tasks (note that the vibrator was placed over the antagonist muscle!) led to overestimation of the actual force. An increase in the signals from muscle spindles and Golgi tendon organs from the antagonist muscle was expected to lead to perception of lower pressing force (for more detail see the Discussion in Reschechtko et al., 2018). This implies that the vibration led not only to changes in the afferent component of force perception but also to shifts in the efferent component, i.e. in RC_S. Such changes in RC_S have been postulated but never quantified.

Note that traditional analysis of vibration-induced kinesthetic illusions assumes that such illusions are due to the artificially increased signals from peripheral receptors, primarily from the primary endings in muscle spindles, leading to overestimation of the muscle length and velocity (Goodwin et al., 1972, Lackner and Levine, 1979, Sittig et al., 1985). This interpretation works for a number of observations but it fails to account for inversions of the direction of vibration-induced illusions (Feldman and Latash, 1982c) and for the aforementioned force illusions.

Thus, the first goal of this study was to explore vibration-induced force illusions at the level of forces produced by the instructed hand (task-hand) and by the matching hand (match-hand) and at the level of mechanical variables {RC; k} reflecting the R-command and C-command to both hands. We explored effects of vibration applied to flexors or extensors of either task-hand or match-hand. An earlier study (Reschechtko et al., 2018) suggested, but never quantified, larger absolute values of RC_S (note that RC < 0 in Fig. 1) during the vibration of the finger/hand extensors compared to the RC of the other hand. We expected to confirm this conclusion (Hypothesis-1) with direct measurement of RC in both task- and match-hands using the “inverse piano” device (Martin et al., 2011), which applies positional perturbation to fingers allowing to estimate RC and k (Ambike et al., 2016a; see Methods for details). We expected opposite effects of vibration applied to the external finger/hand flexors, i.e., a shift of RC toward lower absolute magnitudes (Hypothesis-2).

Another recent study (Abolins et al., 2020a) has shown that force matching is associated with smaller k values and larger absolute RC values in the match-hand compared to the task-hand. We expected to confirm this observation and also to observe vibration-induced changes in the difference between the RC magnitudes (ΔRC) and k magnitudes (Δk) in the two hands that would follow the patterns predicted by the aforementioned two specific hypotheses. Specifically, we expected to see larger ΔRC between the task-hand and match-hand during the vibration applied to the extensor muscles and smaller ΔRC during the vibration of the extrinsic flexors.

Applying vibration to both flexor and extensor muscle groups in both hands in different trials allowed disentangling effects of vibration on force production and perception. Indeed, if effects of vibration were seen in the task-hand only, they could originate from processes related to force production in that hand (e.g., due to the tonic vibration reflex, Eklund and Hagbarth, 1966), not expected in the match-hand. Distortions of force perception would be unlikely because such effects are expected in both hands. If the effects were seen in the match-hand only, they would suggest no effects on force production (otherwise, these effects would be seen in both hands), only on force perception. Finally, if effects of vibration were seen in both hands, they would point at contributions from both distorted efferent and afferent processes.

In this study we used only the dominant hand as the task-hand and the non-dominant hand as the match-hand to limit the duration of experimental sessions. Note that previous studies have not shown differences in percepts estimated with force matching between the dominant and non-dominant hand (Cuadra and Latash, 2018, Cuadra and Latash, 2019) that could be expected based on the dynamic dominance hypothesis (Sainburg, 2005).