Research ArticlePerceptual and Motor Effects of Muscle Co-activation in a Force Production Task
Introduction
According to the physical approach to the neural control of movement, voluntary actions are performed by changes in parameters of corresponding laws of nature (reviewed in Latash, 2016, Latash, 2019). The classical equilibrium-point hypothesis (Feldman, 1966, Feldman, 1986) and its development for multi-muscle systems (reviewed in Latash, 2010, Feldman, 2015) associate time-varying control parameters with spatial referent coordinates (RCs) for the effectors. RCs are reflection of changes in neurophysiological parameters that exert effects on muscle activations and biomechanical variables but remain independent of those variables (Feldman, 2019). At the single-muscle level, RC is associated with subthreshold depolarization of the corresponding alpha-motoneuronal pool translated into threshold of the stretch reflex. Assuming an action, movement or force production, along a single coordinate, the neural control may be associated with setting RCs for the agonist and antagonist muscle groups, RCAG and RCANT.
Two basic commands have been introduced within this approach to describe the control of a single joint, the reciprocal and co-activation commands (r-command and c-command, Feldman, 1980). The idea of two commands have been generalized to any effector controlled by two opposing muscle groups, the R-command and C-command (reviewed in Latash, 2019). Both commands are expressed in spatial units. The R-command defines the coordinate where the forces by the agonist and antagonist muscles balance each other. The C-command defines the spatial range where both agonist and antagonist muscles are active if the external load is zero. This spatial range is centered about the coordinate defined by the R-command. During typical movements at moderate speeds, a change in the effector spatial location defined by the R-command is commonly associated with relatively invariant coactivation zone, defined by the C-command, which is readdressed to the new effector location. This feature of movements has been interpreted as pointing at a control hierarchy with the C-command being subordinate to the R-command (reviewed in Feldman, 2015).
Fig. 1A illustrates the two commands assuming, for simplicity, agonist and antagonist muscles with symmetrical properties. Note that this assumption is not crucial; it is useful, however, to explain our main hypotheses. Specifying RC for a muscle group leads to a non-linear dependence of muscle force on coordinate, FX(X). The net force by the effector is equal to the algebraic sum of the force by the agonist (positive values) and antagonist (negative values) groups, and the effector FX(X) characteristic is the sum of the two opposing muscle group characteristics.
In the traditional language of biomechanics, a change in the R-commands leads to shifts of a coordinate (RC) for the effector where the net muscle force, FX, along a coordinate X is zero. A change in the C-command leads to rotation of the FX(X) characteristic, i.e., to a change in its slope (k – apparent stiffness, Latash and Zatsiorsky, 1993). This is illustrated in Fig. 1B, which shows effects of changes in the R- and C-commands (ΔR and ΔC) on the FX(X) characteristic.
Mechanical effects of changes in the two basic commands depend on the external force field (reviewed in Feldman, 2015). Fig. 1C illustrates the control of an effector producing force in isometric conditions along a coordinate X with its location at X = 0. For simplicity, we assume a planar case and active force production against an infinitely rigid object (gravity force is assumed constant).
Note that this mechanically non-redundant task is abundant at the control level: An infinite number of combinations {RCAG; RCANT} can be used to produce a desired force level corresponding to an infinite number of the effector FX(X) characteristics (three are illustrated in Fig. 1C). In the language of biomechanics, this fact is reflected in an infinite number of {RC; k} pairs that are equally able to solve the task. Indeed, recent experiments have shown that humans use highly variable pairs {RC; k} across trials when trying to produce the same force magnitude in isometric conditions under continuous visual control on the force magnitude (Ambike et al., 2016a, Reschechtko and Latash, 2017).
It is easy to co-contract limb muscles without moving the limb in the absence of an external stop (the reader can try this himself or herself). This observation suggests that the C-command can be changed naturally without a change in the R-command. In isometric conditions, however, a change in the C-command without a change in the R-command is expected to lead to a change in the effector force. This is illustrated by Fig. 1D, which shows two FX(X) characteristics corresponding to two magnitudes of the C-command, C1 and C2, that define different coactivation zones shown with the two double-ended arrows. Given the aforementioned hierarchy with the C-command being subordinate to the R-command (Feldman, 2015), one could expect that a change in the C-command does not necessarily lead to an adjustment in the R-command. This leads to a prediction that co-activating muscles in isometric conditions could produce an unintentional increase in the net force (FΔC in Fig. 1D) even if the subject tries his or her best to follow the instruction to keep the net force constant in the absence of visual feedback on the force magnitude. This was our Hypothesis-1, and the first goal of the study was to test this hypothesis.
The second goal of our study was to explore effects of changes in the C-command on force perception. The idea that kinesthetic perception is affected by the motor (efferent) process is rather old; it dates back at least to the notions of efferent copy and corollary discharge (Von Holst and Mittelstaedt, 1950, Sperry, 1950). Recently, this idea has been developed within the theory of control with RCs (Feldman and Latash, 1982; reviewed in Feldman, 2015, Latash, 2016, Latash, 2019): The efferent process is associated with setting a system of coordinates for estimating signals from relevant peripheral receptors. When an effector produces force in isometric conditions, both R-command and C-command are needed for the estimation of sensory signals and generation of veridical force percepts. On the other hand, if changes in the C-command are indeed associated with motor errors (as in Fig. 1D), it is reasonable to expect them to lead also to perceptual errors. In other words, if the central nervous system does not adjust the R-command as required to keep the net force constant, in a sense it ignores the self-generated changes in the C-command. Then, it may also be expected to ignore these changes in the perceptual domain. So, our Hypothesis-2 was that the subjects would not perceive an increase in force predicted by Hypothesis-1 as reflected by both verbal reports and matching the force with the contralateral hand.
As an exploratory manipulation, we also estimated the R- and C-commands, as reflected in the RC and k values, in the initial state and at the end of the trial (after the co-contraction and force matching episodes, see Methods) using the “inverse piano” device (Martin et al., 2011). This device allows the application of positional perturbation to fingers and the estimation of their RC and k magnitudes (Ambike et al., 2016a). We avoided making predictions, primarily because of the documented strong drifts in RC and k in the absence of visual feedback (Ambike et al., 2016b, Reschechtko and Latash, 2017) and likely strong effects of contralateral force production on the force of the task hand during the force matching episodes (cf. Li et al., 2002).
Section snippets
Subjects
Eleven subjects (6 males and 5 females, 27–65 years old, mass 75 ± 8.0 kg, height 1.67 ± 0.08 m) participated in this study. All subjects self-identified as right-handed according to the preferred hand used during writing and eating. None of the subjects identified themselves as ambidextrous or cross-dominant. The subjects were healthy, had no history of hand injury or neuromotor disorder. They provided written informed consent in accordance with procedures approved by the Office of Research
Results
Although the subjects perceived the experiment as challenging, they all performed consistently across repetitive trials. Averaged across all subjects forces with standard error shades are illustrated in Fig. 3. This figure also illustrates the times when forces were quantified. The task-hand matched the required force level (FIM = 10 NU) accurately. Both episodes of the inverse piano (IP1 and IP2) led to a transient increase in the task-hand FIM and its drop close to the initial level. Muscle
Discussion
The results of the experiment have confirmed Hypothesis-1. Indeed, when instructed to co-contract muscles without a change in the net force, the subjects showed a consistent force increase as predicted from the idea that changes in the C-command are not automatically accompanied by adjustments in the hierarchically higher R-command (Feldman, 2015; see also Fig. 1D). As far as Hypothesis-2 is concerned, the results were ambiguous. The counter-intuitive prediction that the subjects would not
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