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.

Understanding and Synergy: A Single Concept at Different Levels of Analysis?

Biological systems differ from the inanimate world in their behaviors ranging from simple movements to coordinated purposeful actions by large groups of muscles, to perception of the world based on signals of different modalities, to cognitive acts, and to the role of self-imposed constraints such as laws of ethics. Respectively, depending on the behavior of interest, studies of biological objects based on laws of nature (physics) have to deal with different salient sets of variables and parameters. Understanding is a high-level concept, and its analysis has been linked to other high-level concepts such as “mental model” and “meaning”. Attempts to analyze understanding based on laws of nature are an example of the top-down approach. Studies of the neural control of movements represent an opposite, bottom-up approach, which starts at the interface with classical physics of the inanimate world and operates with traditional concepts such as forces, coordinates, etc. There are common features shared by the two approaches. In particular, both assume organizations of large groups of elements into task-specific groups, which can be described with only a handful of salient variables. Both assume optimality criteria that allow the emergence of families of solutions to typical tasks. Both assume predictive processes reflected in anticipatory adjustments to actions (motor and non-motor). Both recognize the importance of generating dynamically stable solutions. The recent progress in studies of the neural control of movements has led to a theory of hierarchical control with spatial referent coordinates for the effectors. This theory, in combination with the uncontrolled manifold hypothesis, allows quantifying the stability of actions with respect to salient variables. This approach has been used in the analysis of motor learning, changes in movements with typical and atypical development and with aging, and impaired actions by patients with various neurological disorders. It has been developed to address issues of kinesthetic perception. There seems to be hope that the two counter-directional approaches will meet and result in a single theoretical scheme encompassing biological phenomena from figuring out the best next move in a chess position to activating motor units appropriate for implementing that move on the chessboard.

Visual feedback improves bimanual force control performances at planning and execution levels

The purpose of this study was to determine the effect of different visual conditions and targeted force levels on bilateral motor synergies and bimanual force control performances. Fourteen healthy young participants performed bimanual isometric force control tasks by extending their wrists and fingers under two visual feedback conditions (i.e., vision and no-vision) and three targeted force levels (i.e., 5%, 25%, and 50% of maximum voluntary contraction: MVC). To estimate bilateral motor synergies across multiple trials, we calculated the proportion of good variability relative to bad variability using an uncontrolled manifold analysis. To assess bimanual force control performances within a trial, we used the accuracy, variability, and regularity of total forces produced by two hands. Further, analysis included correlation coefficients between forces from the left and right hands. In addition, we examined the correlations between altered bilateral motor synergies and force control performances from no-vision to vision conditions for each targeted force level. Importantly, our findings revealed that the presence of visual feedback increased bilateral motor synergies across multiple trials significantly with a reduction of bad variability as well as improved bimanual force control performances within a trial based on higher force accuracy, lower force variability, less force regularity, and decreased correlation coefficients between hands. Further, we found two significant correlations in (a) increased bilateral motor synergy versus higher force accuracy at 5% of MVC and (b) increased bilateral motor synergy versus lower force variability at 50% of MVC. Together, these results suggested that visual feedback effectively improved both synergetic coordination behaviors across multiple trials and stability of task performance within a trial across various submaximal force levels.

Frequency-Dependent Effects on Coordination and Prefrontal Hemodynamics During Finger Force Production Tasks

Behavioral stability partially depends on the variability of net outcomes by means of the co-varied adjustment of individual elements such as multi-finger forces. The properties of cyclic actions affect stability and variability of the performance as well as the activation of the prefrontal cortex that is an origin of subcortical structure for the coordinative actions. Little research has been done on the issue of the relationship between stability and neuronal response. The purpose of the study was to investigate the changes in the neural response, particularly at the prefrontal cortex, to the frequencies of isometric cyclic finger force production. The main experimental task was to produce finger forces while matching the produced force to sine-wave templates as accurately as possible. Also, the hemodynamics responses of the prefrontal cortex, including oxy-hemoglobin concentration (ΔHbO) and the functional connectivity, were measured using functional near-infrared spectroscopy. The frequency conditions comprised 0.1, 1, and 2 Hz. The uncontrolled manifold (UCM) approach was applied to compute synergy indices in time-series. The relative phase (RP), the coefficient of variation (CV) of the peak and trough force values were computed as the indices of performance accuracy. The statistical parametric mapping (SPM) was implemented to compare the synergy indices of three frequency conditions in time-series. A less accurate performance in the high-frequency condition was caused not by the RP, but mainly by the inconsistent peak force values (CV; p < 0.01, ηp2 = 0.90). The SPM analysis revealed that the synergy indices were larger in the low-frequency than in high-frequency conditions. Further, the ΔHbO remained unchanged under all frequency conditions, while the functional connectivity decreased with an increase in the frequency of cyclic force production. The current results suggested that the concurrent activation of the prefrontal region mainly depends on the frequency of cyclic force production, which was associated with the strength of stability indices and performance errors. The current study is the first work to uncover the effect of frequency on the multi-finger synergies as to the hemodynamic response in the prefrontal cortex, which possibly provides a clue of the neural mechanism of synergy formation and its changes.

Short-Term Effects of the Repeated Exposure to Trip-like Perturbations on Inter-Segment Coordination during Walking: An UCM Analysis

The minimum toe clearance (MTC) results from the coordination of all bilateral lower limb body segments, i.e., a redundant kinematic chain. We tested the hypothesis that repeated exposure to trip-like perturbations induces a more effective covariation of limb segments during steady walking, in accordance with the uncontrolled manifold (UCM) theory, to minimize the MTC across strides. Twelve healthy young adults (mean age 26.2 ± 3.3 years) were enrolled. The experimental protocol consisted of three identical trials, each involving three phases carried outin succession: steady walking (baseline), managing trip-like perturbations, and steady walking (post-perturbation). Lower limb kinematics collected during both steady walking phases wereanalyzed in the framework of the UCM theory to test the hypothesis that the reduced MTC variability following the perturbation can occur, in conjunction with more effective organization of the redundant lower limb segments. Results revealed that, after the perturbation, the synergy underlying lower limb coordination becomes stronger. Accordingly, the short-term effects of the repeated exposure to perturbations modify the organization of the redundant lower limb-related movements. In addition, results confirm that the UCM theory is a promising tool for exploring the effectiveness of interventions aimed at purposely modifying motor behaviors.

Computational Modeling: Human Dynamic Model

Improvements in quantitative measurements of human physical activity are proving extraordinarily useful for studying the underlying musculoskeletal system. Dynamic models of human movement support clinical efforts to analyze, rehabilitate injuries. They are also used in biomechanics to understand and diagnose motor pathologies, find new motor strategies that decrease the risk of injury, and predict potential problems from a particular procedure. In addition, they provide valuable constraints for understanding neural circuits. This paper describes a physics-based movement analysis method for analyzing and simulating bipedal humanoid movements. The model includes the major body segments and joints to report human movements' energetic components. Its 48 degrees of freedom strike a balance between very detailed models that include muscle models and straightforward two-dimensional models. It has sufficient accuracy to analyze and synthesize movements captured in real-time interactive applications, such as psychophysics experiments using virtual reality or human-in-the-loop teleoperation of a simulated robotic system. The dynamic model is fast and robust while still providing results sufficiently accurate to be used to animate a humanoid character. It can also estimate internal joint forces used during a movement to create effort-contingent stimuli and support controlled experiments to measure the dynamics generating human behaviors systematically. The paper describes the innovative features that allow the model to integrate its dynamic equations accurately and illustrates its performance and accuracy with demonstrations. The model has a two-foot stance ability, capable of generating results comparable with an experiment done with subjects, and illustrates the uncontrolled manifold concept. Additionally, the model's facility to capture large energetic databases opens new possibilities for theorizing as to human movement function. The model is freely available.

Visual Feedback Improves Bimanual Force Control Performances at Planning and Execution Levels

The purpose of this study was to determine whether altered interlimb coordination patterns across trials improved bimanual force control capabilities within a trial. Fourteen healthy young participants completed bimanual force control tasks at 5%, 25%, and 50% of maximum voluntary contraction with and without visual feedback. To estimate synergetic coordination patterns between hands across multiple trials, we analyzed our primary outcome measure by performing an uncontrolled manifold analysis. In addition, we calculated force accuracy, variability, and regularity within a trial to quantify task stabilization. Using Pearson’s correlation analyses, we determined the relation between the changes in bilateral motor synergies (i.e., a proportion of good variability relative to bad variability) and bimanual force control performance from no-vision to vision conditions. The findings revealed that the presence of visual feedback significantly increased bilateral motor synergies with a reduction of bad variability components across multiple trials, and decreased force error, variability, and regularity within a trial. Further, we observed significant positive correlations between higher bilateral motor synergies and increased improvements in force control capabilities. These findings suggested that bimanual synergetic coordination behaviors at the planning level modulated by external sensory feedback may be related to advanced task stabilization patterns at the execution level.

Stride-to-Stride Variability of the Center of Mass in Male Trained Runners After an Exhaustive Run: A Three Dimensional Movement Variability Analysis With a Subject-Specific Anthropometric Model

The motion of the human body can be described by the motion of its center of mass (CoM). Since the trajectory of the CoM is a crucial variable during running, one can assume that trained runners would try to keep their CoM trajectory constant from stride to stride. However, when exposed to fatigue, runners might have to adapt certain biomechanical parameters. The Uncontrolled Manifold approach (UCM) and the Tolerance, Noise, and Covariation (TNC) approach are used to analyze changes in movement variability while considering the overall task of keeping a certain task relevant variable constant. The purpose of this study was to investigate if and how runners adjust their CoM trajectory during a run to fatigue at a constant speed on a treadmill and how fatigue affects the variability of the CoM trajectory. Additionally, the results obtained with the TNC approach were compared to the results obtained with the UCM analysis in an earlier study on the same dataset. Therefore, two TNC analyses were conducted to assess effects of fatigue on the CoM trajectory from two viewpoints: one analyzing the CoM with respect to a lab coordinate system (PVlab) and another one analyzing the CoM with respect to the right foot (PVfoot). Full body kinematics of 13 healthy young athletes were captured in a rested and in a fatigued state and an anthropometric model was used to calculate the CoM based on the joint angles. Variability was quantified by the coefficient of variation of the length of the position vector of the CoM and by the components Tolerance, Noise, and Covariation which were analyzed both in 3D and the projections in the vertical, anterior-posterior and medio-lateral coordinate axes. Concerning PVlab we found that runners increased their stride-to-stride variability in medio-lateral direction (1%). Concerning PVfoot we found that runners lowered their CoM (4 mm) and increased their stride-to-stride variability in the absorption phase in both 3D and in the vertical direction. Although we identified statistically relevant differences between the two running states, we have to point out that the effects were small (CV ≤ 1%) and must be interpreted cautiously.

The relation between kinematic synergy to stabilize the center of mass during walking and future fall risks: a 1-year longitudinal study

Background Incorrect body weight shifting is a frequent cause of falls, and the control of the whole-body center of mass (CoM) by segmental coordination is essential during walking. Uncontrolled manifold (UCM) analysis is a method of examining the relation between variance in segmental coordination and CoM stability. However, no prospective cohort study has thoroughly investigated how variance in segmental configurations to stabilize the CoM relates to future falls. This study explored whether variance to stabilize the CoM was related to future falls. Methods At the baseline visit, 30 community-dwelling older adults walked 20 times on a 6-m walkway. Using kinematic data collected during walking by a three-dimensional motion capture system, UCM analysis was performed to investigate how segmental configuration contributes to CoM stability in the frontal plane. One year after the baseline visit, we evaluated whether the subjects experienced falls. Twelve subjects had experienced falls, and 16 had not. Comparisons of variance between older adults with and without falls were conducted by covariate analysis. Results No significant differences in variance were found in the mediolateral direction, whereas in the vertical direction, older adults with fall experiences had a greater variance, reflecting an unstable CoM, than those with no fall experiences. Conclusions We verified that the high variance in segmental configurations that destabilize the CoM in the vertical direction was related to future falls. The variables of UCM analysis can be useful for evaluating fall risk.

Inter-joint coordination between the ankle and hip joints during quiet standing in individuals with motor incomplete spinal cord injury

Individuals with motor incomplete spinal cord injuries (iSCI) often have impaired abilities to maintain upright balance. For able-bodied (AB) individuals, the ankle and hip joint accelerations are in anti-phase to minimize the postural sway during quiet standing. Here we investigated how inter-joint coordination between the ankle and hip joints was affected in individuals with iSCI leading to their larger postural sway during quiet standing. Data from sixteen individuals with iSCI, fourteen age- and sex-matched AB individuals and thirteen young AB individuals were analyzed. The participants performed quiet standing during which kinematic and kinetic data were recorded. Postural sway was quantified using center-of-pressure velocity and center-of-mass acceleration. Individual ankle and hip joint kinematics were quantified, and the inter-joint coordination was assessed using the cancellation index (CI), goal-equivalent variance (GEV), non-goal-equivalent variance (NGEV) and uncontrolled manifold (UCM) ratio. Individuals with iSCI displayed greater postural sway compared to AB individuals. The contribution of ankle angular acceleration towards one's sway was significantly greater for those with iSCI compared to AB groups. CI and the UCM ratio were not statistically different between the groups, while GEV and NGEV were significantly greater for the iSCI group compared to the AB groups. We demonstrated that individuals with iSCI show larger postural sway compared to the AB individuals during quiet standing, primarily due to larger ankle joint acceleration. We also demonstrated that the inter-joint coordination between ankle and hip joint is not affected in individuals with iSCI, which is not successfully able to reduce the large COM acceleration.