A Vexing Question in Motor Control: The Degrees of Freedom Problem

The human “marionette” is extremely complex and multi-articulated: anatomical redundancy (in terms of Degrees of Freedom: DoFs), kinematic redundancy (movements can have different trajectories, velocities, and accelerations and yet achieve the same goal, according to the principle of Motor Equivalence), and neurophysiological redundancy (many more muscles than DoFs and multiple motor units for each muscle). Although it is quite obvious that such abundance is not noxious at all because, in contrast, it is instrumental for motor learning, allowing the nervous system to “explore” the space of feasible actions before settling on an elegant and possibly optimal solution, the crucial question then boils down to figure out how the nervous system “chooses/selects/recruits/modulates” task-dependent subsets of countless assemblies of DoFs as functional motor synergies. Despite this daunting conceptual riddle, human purposive behavior in daily life activities is a proof of concept that solutions can be found easily and quickly by the embodied brain of the human cognitive agent. The point of view suggested in this essay is to frame the question above in the old-fashioned but still seminal observation by Marr and Poggio that cognitive agents should be regarded as Generalized Information Processing Systems (GIPS) and should be investigated according to three nearly independent but complementary levels of analysis: 1) the computational level, 2) the algorithmic level, and 3) the implementation level. In this framework, we attempt to discriminate as well as aggregate the different hypotheses and solutions proposed so far: the optimal control hypothesis, the muscle synergy hypothesis, the equilibrium point hypothesis, or the uncontrolled manifold hypothesis, to mention the most popular ones. The proposed GIPS follows the strategy of factoring out shaping and timing by adopting a force-field based approach (the Passive Motion Paradigm) that is inspired by the Equilibrium Point Hypothesis, extended in such a way to represent covert as well overt actions. In particular, it is shown how this approach can explain spatio-temporal invariances and, at the same time, solve the Degrees of Freedom Problem.

Case Studies in Neuroscience: The central and somatosensory contributions to finger interdependence and coordination: lessons from a study of a “deafferented person”

We tested finger force interdependence and multifinger force-stabilizing synergies in a patient with large-fiber peripheral neuropathy (“deafferented person”). The subject performed a range of tasks involving accurate force production with one finger and with four fingers. In one-finger tasks, nontask fingers showed unintentional force production (enslaving) with an atypical pattern: very large indices for the lateral (index and little) fingers and relatively small indices for the central (middle and ring) fingers. Indices of multifinger synergies stabilizing total force and of anticipatory synergy adjustments in preparation to quick force pulses were similar to those in age-matched control females. During constant force production, removing visual feedback led to a slow force drift to lower values (by ~25% over 15 s). The results support the idea of a neural origin of enslaving and suggest that the patterns observed in the deafferented person were reorganized based on everyday manipulation tasks. The lack of significant changes in the synergy index shows that synergic control can be organized in the absence of somatosensory feedback. We discuss the control of the hand in deafferented persons within the α-model of the equilibrium-point hypothesis and suggest that force drift results from an unintentional drift of the control variables to muscles toward zero values. NEW & NOTEWORTHY We demonstrate atypical patterns of finger enslaving and unchanged force-stabilizing synergies in a person with large-fiber peripheral neuropathy. The results speak strongly in favor of central origin of enslaving and its reorganization based on everyday manipulation tasks. The data show that synergic control can be implemented in the absence of somatosensory feedback. We discuss the control of the hand in deafferented persons within the α-model of the equilibrium-point hypothesis.

Hip retraction enhances walking stability on a ramp: an equilibrium point hypothesis-based study

Hip retraction is a phenomenon observed in human walking. The swing leg rotates backward at the end of the motion. Its positive effect on motion stability was reported in the literature based on some simple models for running or walking. In this study, it is shown that hip retraction angle increases in humans during their ascending and descending walk on a stair. In previous studies, hip retraction was modeled by defining a proper motion for the swing leg. According to the equilibrium point hypothesis, the central nervous system (CNS) defines only the equilibrium point(s) and stiffness(es) for body joint(s) to control the human motion. Human body motion emerges as its natural response as a result of the external forces and the defined equilibrium points of joints. Considering the hip torque as a spring-like model with an equilibrium point and stiffness, this study revealed that the hip retraction can be generated by the natural response of the swing leg. Besides, the stabilizing effect of hip retraction was demonstrated by a model for human’s ascending and descending walking on a ramp with a range of positive and negative angles, respectively. The findings suggest that the CNS needs to define equilibrium point just ahead of the stance leg to take advantage of the hip retraction effect on ascending and descending walks on a ramp.

Should the Equilibrium Point Hypothesis (EPH) Be Considered a Scientific Theory?

The purpose of this commentary is to discuss factors that limit consideration of the equilibrium point hypothesis as a scientific theory. The EPH describes control of motor neuron threshold through the variable lambda, which corresponds to a unique referent configuration for a muscle, joint, or combination of joints. One of the most compelling features of the equilibrium point hypothesis is the integration of posture and movement control into a single mechanism. While the essential core of the hypothesis is based upon spinal circuitry interacting with peripheral mechanics, the proponents have extended the theory to include the higher-level processes that generate lambda, and in doing so, imposed an injunction against the supraspinal nervous system modeling, computing, or predicting dynamics. This limitation contradicts evidence that humans take account of body and environmental dynamics in motor selection, motor control, and motor adaptation processes. A number of unresolved limitations to the EPH have been debated in the literature for many years, including whether muscle resistance to displacement, measured during movement, is adequate to support this form of control, violations in equifinality predictions, spinal circuits that alter the proposed invariant characteristic for muscles, and limitations in the description of how the complexity of spinal circuitry might be integrated to yield a unique and stable equilibrium position for a given motor neuron threshold. In addition, an important empirical limitation of EPH is the measurement of the invariant characteristic, which needs to be done under a constant central state. While there is no question that the EPH is an elegant and generative hypothesis for motor control research, the claim that this hypothesis has reached the status of a scientific theory is premature.