Reaction null-space filter: extracting reactionless synergies for optimal postural balance from motion capture data

This paper introduces the notion of a reactionless synergy: a postural variation for a specific motion pattern/strategy, whereby the movements of the segments do not alter the force/moment balance at the feet. Given an optimal initial posture in terms of stability, a reactionless synergy can ensure optimality throughout the entire movement. Reactionless synergies are derived via a dynamical model wherein the feet are regarded to be unfixed. Though in contrast with the conventional fixed-feet models, this approach has the advantage of exhibiting the reactions at the feet explicitly. The dynamical model also facilitates a joint-space decomposition scheme yielding two motion components: the reactionless synergy and an orthogonal complement responsible for the dynamical coupling between the feet and the support. Since the reactionless synergy provides the basis (a feedforward control component) for optimal balance control, it may play an important role when evaluating balance abnormalities or when assessing optimality in balance control. We show how to apply the proposed method for analysis of motion capture data obtained from three voluntary movement patterns in the sagittal plane: squat, sway, and forward bend.     

Analysis of an optimal control model of multi-joint arm movements

 In this paper, we propose a model of biological motor control for generation of goal-directed multi-joint arm movements, and study the formation of muscle control inputs and invariant kinematic features of movements. The model has a hierarchical structure that can determine the control inputs for a set of redundant muscles without any inverse computation. Calculation of motor commands is divided into two stages, each of which performs a transformation of motor commands from one coordinate system to another. At the first level, a central controller in the brain accepts instructions from higher centers, which represent the motor goal in the Cartesian space. The controller computes joint equilibrium trajectories and excitation signals according to a minimum effort criterion. At the second level, a neural network in the spinal cord translates the excitation signals and equilibrium trajectories into control commands to three pairs of antagonist muscles which are redundant for a two-joint arm. No inverse computation is required in the determination of individual muscle commands. The minimum effort controller can produce arm movements whose dynamic and kinematic features are similar to those of voluntary arm movements. For fast movements, the hand approaches a target position along a near-straight path with a smooth bell-shaped velocity. The equilibrium trajectories in X and Y show an ‘N’ shape, but the end-point equilibrium path zigzags around the hand path. Joint movements are not always smooth. Joint reversal is found in movements in some directions. The excitation signals have a triphasic (or biphasic) pulse pattern, which leads to stereotyped triphasic (or biphasic) bursts in muscle control inputs, and a dynamically modulated joint stiffness. There is a fixed sequence of muscle activation from proximal muscles to distal muscles. The order is preserved in all movements. For slow movements, it is shown that a constant joint stiffness is necessary to produce a smooth movement with a bell-shaped velocity. Scaled movements can be reproduced by varying the constraints on the maximal level of excitation signals according to the speed of movement. When the inertial parameters of the arm are altered, movement trajectories can be kept invariant by adjusting the pulse height values, showing the ability to adapt to load changes. These results agree with a wide range of experimental observations on human voluntary movements. Received: 4 December 1995 / Accepted in revised form: 17 September 1996     

How does microgravity affect the muscular and kinematic synergies in a complex movement?

The planning and the execution of voluntary movement relies on sensorimotor transformations in which representations of the external environment are integrated into motor programs. We studied executions of Whole Body Pointing movements, in normal and in transient microgravity (parabolic flights) conditions. Three processes could lead to adaptation to the new environmental condition: a radical change of terrestrial synergies, their partial modification or preservation. By applying a multivariate analysis on kinematic and electromyographic (EMG) data and by comparing the 1g and 0g conditions, our findings hint the hypothesis the descending information from vestibular system may be directed to change the synergies' modulation. An analogous analysis was performed on the kinematics: the invariance of intersegmental coordination among the segments' elevation angles suggests that these kinematic waveforms are used as reference signals to determine the appropriate muscle synergies in a subordinate and flexible manner in order to adapt to the novel mechanical constraints.     

Functional muscle synergies constrain force production during postural tasks

We recently demonstrated that a set of five functional muscle synergies were sufficient to characterize both hindlimb muscle activity and active forces during automatic postural responses in cats standing at multiple postural configurations. This characterization depended critically upon the assumption that the endpoint force vector (synergy force vector) produced by the activation of each muscle synergy rotated with the limb axis as the hindlimb posture varied in the sagittal plane. Here, we used a detailed, 3D static model of the hindlimb to confirm that this assumption is biomechanically plausible: as we varied the model posture, simulated synergy force vectors rotated monotonically with the limb axis in the parasagittal plane (r2=0.94+/-0.08). We then tested whether a neural strategy of using these five functional muscle synergies provides the same force-generating capability as controlling each of the 31 muscles individually. We compared feasible force sets (FFSs) from the model with and without a muscle synergy organization. FFS volumes were significantly reduced with the muscle synergy organization (F=1556.01, p<0.01), and as posture varied, the synergy-limited FFSs changed in shape, consistent with changes in experimentally measured active forces. In contrast, nominal FFS shapes were invariant with posture, reinforcing prior findings that postural forces cannot be predicted by hindlimb biomechanics alone. We propose that an internal model for postural force generation may coordinate functional muscle synergies that are invariant in intrinsic limb coordinates, and this reduced-dimension control scheme reduces the set of forces available for postural control.     

Challenges and new approaches to proving the existence of muscle synergies of neural origin

Muscle coordination studies repeatedly show low-dimensionality of muscle activations for a wide variety of motor tasks. The basis vectors of this low-dimensional subspace, termed muscle synergies, are hypothesized to reflect neurally-established functional muscle groupings that simplify body control. However, the muscle synergy hypothesis has been notoriously difficult to prove or falsify. We use cadaveric experiments and computational models to perform a crucial thought experiment and develop an alternative explanation of how muscle synergies could be observed without the nervous system having controlled muscles in groups. We first show that the biomechanics of the limb constrains musculotendon length changes to a low-dimensional subspace across all possible movement directions. We then show that a modest assumption--that each muscle is independently instructed to resist length change--leads to the result that electromyographic (EMG) synergies will arise without the need to conclude that they are a product of neural coupling among muscles. Finally, we show that there are dimensionality-reducing constraints in the isometric production of force in a variety of directions, but that these constraints are more easily controlled for, suggesting new experimental directions. These counter-examples to current thinking clearly show how experimenters could adequately control for the constraints described here when designing experiments to test for muscle synergies--but, to the best of our knowledge, this has not yet been done.     

Three-dimensional model to predict muscle forces and their relation to motor variances in reaching arm movements

A three-dimensional (3-D) arm movement model is presented to simulate kinematic properties and muscle forces in reaching arm movements. Healthy subjects performed reaching movements repetitively either with or without a load in the hand. Joint coordinates were measured. Muscle moment arms, 3-D angular acceleration, and moment of inertias of arm segments were calculated to determine 3-D joint torques. Variances of hand position, arm configuration, and muscle activities were calculated. Ratios of movement variances observed in the two conditions (load versus without load) showed no differences for hand position and arm configuration variances. Virtual muscle force variances for all muscles except deltoid posterior and EMG variances for four muscles increased significantly by moving with the load. The greatly increased variances in muscle activity did not imply equally high increments in kinematic variances. We conclude that enhanced muscle cooperation through synergies helps to stabilize movement at the kinematic level when a load is added.     

Inverse dynamic investigation of voluntary leg lateral movements in weightlessness: a new microgravity-specific strategy

This study deals with the quantitative assessment of exchanged forces and torques at the restraint point during whole body posture perturbation movements in long-term microgravity. The work was based on the results of a previous study focused on trunk bending protocol, which suggested that the minimization of the torques exchanged at the restraint point could be a strategy for movement planning in microgravity (J. Biomech. 36(11) (2003) 1691). Torques minimization would lead to the optimization of muscles activity, to the minimization of energy expenditure and, ultimately, to higher movement control capabilities. Here, we focus on leg lateral abduction from anchored stance. The analysis was based on inverse dynamic modelling, leading to the estimation of the total angular momentum at the supporting ankle joint. Results agree with those obtained for trunk bending movements and point out a consistent minimization of the torques exchanged at the restraint point in weightlessness. Given the kinematic features of the examined motor task, this strategy was interpreted as a way to master the rotational dynamic effects on the frontal plane produced by leg lateral abduction. This postural stabilizing effects was the result of a multi-segmental compensation strategy, consisting of the counter rotation of the supporting limb and trunk accompanying the leg raising. The observed consistency of movement-posture co-ordination patterns among lateral leg raising and trunk bending is put forward as a novel interpretative issue of the adaptation mechanisms of the motor system to sustained microgravity, especially if one considers the completely different kinematics of the centre of mass, which was observed in weightlessness for these two motor tasks.     

Understanding muscle coordination of the human leg with dynamical simulations

Muscles coordinate multijoint motion by generating forces that cause reaction forces throughout the body. Thus, a muscle can redistribute existing segmental energy by accelerating some segments and decelerating others. In the process, a muscle may also produce or absorb energy, in which case its summed energetic effect on the segments is positive or negative, respectively. This Borelli Lecture shows how dynamical simulations derived from musculoskeletal models reveal muscle-induced segmental energy redistribution and muscle co-functions and synergies. Synergy occurs when co-excited muscles distribute segmental energy differently to execute the motor task. In maximum height jumping, high vertical velocity at lift-off occurs desirably at full body extension because biarticular leg muscles redistribute the energy produced by the uniarticular leg muscles. In pedaling, synergistic ankle plantarflexor force generation during leg extension allows the high energy produced by the uniarticular hip and knee extensors to be delivered to the crank. An analogous less-powerful flexor synergy exists during leg flexion. Hamstrings reduce crank deceleration during the leg extension-to-flexion transition by not only producing energy but delivering it to the crank through its contribution to the tangential (accelerating) crank force, though this hamstrings function occurs at the opposite (flexion-extension) transition when pedaling backwards. In walking, the eccentric quadriceps activity in early stance not only decelerates the leg but also accelerates the trunk. In mid-stance, the uni- and biarticular plantarflexors, by having opposite segmental energetic effects, act in synergy to support the whole body, so segmental potential and kinetic energy exchange can occur. To conclude, the extraction of unmeasurable variables from dynamical simulations emulating task kinematics, kinetics, and EMGs shows how the production of force and energy by individual muscles contribute to the energy flow among the individual segments during task execution.     

Altered flexion-relaxation responses exist during asymmetric trunk flexion movements among persons with unilateral lower-limb amputation

Repetitive exposures to altered gait and movement following lower-limb amputation (LLA) have been suggested to contribute to observed alterations in passive tissue properties and neuromuscular control in/surrounding the lumbar spine. These alterations, in turn, may affect the synergy between passive and active tissues during trunk movements. Eight males with unilateral LLA and eight non-amputation controls completed quasi-static trunk flexion–extension movements in seven distinct conditions of rotation in the transverse plane: 0° (sagittally-symmetric), ±15°, ±30°, and ±45° (sagittally-asymmetric). Electromyographic (EMG) activity of the bilateral lumbar erector spinae and lumbar kinematics were simultaneously recorded. Peak lumbar flexion and EMG-off angles were determined, along with the difference (“DIFF”) between these two angles and the magnitude of peak normalized EMG activities. Persons with unilateral LLA exhibited altered and asymmetric synergies between active and passive trunk tissues during both sagittally-symmetric and -asymmetric trunk flexion movements. Specifically, decreased and asymmetric passive contributions to trunk movements were compensated with increases in the magnitude and duration of active trunk muscle responses. Such alterations in trunk passive and active neuromuscular responses may result from repetitive exposures to abnormal gait and movement subsequent to LLA, and may increase the risk for LBP in this population.     

Neuromuscular independence of abdominal wall muscles as demonstrated by middle-eastern style dancers.

Previous studies analyzing neuromuscular independence of the abdominal wall have involved a participant population with no specific training in separating individual muscle segments. We chose to study nine women trained in the art of middle-eastern dance, anticipating they may have unique skills in motor control. Specifically, we were searching for evidence of separation of upper rectus abdominis (URA) from lower rectus abdominis (LRA), as well as understanding what role the oblique muscles play in abdominal wall synergies. EMG analysis was done on eight trunk muscles bilaterally as the dancers participated in 30 dance, planar, and curl-up activities. The filtered data were then cross-correlated to determine the time lag between pairs of signals. Only three dance movements demonstrated consistent evidence of an ability to separate URA/LRA activation timing. The external and internal oblique muscles tend to align themselves temporally with the LRA. However, these findings were only evident in these three specific "belly-roll" conditions, all with low levels of muscle activation, and no external torque. Evidence of significantly different activation levels (% MVC) between URA/LRA was demonstrated in eight conditions, all of which required various pelvis movements with minimal thorax motion.     

Head position during various locomotor executions after prolonged microgravity exposure

Head orientation in the sagittal plane was assessed before and the second and sixth days after a prolonged microgravity exposure (6 months) in 7 astronauts, which were instructed to execute various locomotor movements (stair ascent, jump down and level walk). Crewmembers systematically flexed down the head when they executed the locomotion the second day post-flight compared to the pre-flight walk. Cephalic orientation was normally positioned when movements was performed the sixth day after Earth re-entry. This head flexion may reflect a strategy used by cosmonauts to increase the vestibular sensibility, and then improve the control of the dynamic equilibrium during locomotor movements. The high rate of re-adaptation indicated that cosmonauts rapidly recovered their normal walking capacities despite the prolonged microgravity exposure.     

Comparison of Trunk Activity during Gait Initiation and Walking in Humans

To understand the role of trunk muscles in maintenance of dynamic postural equilibrium we investigate trunk movements during gait initiation and walking, performing trunk kinematics analysis, Erector spinae muscle (ES) recordings and dynamic analysis. ES muscle expressed a metachronal descending pattern of activity during walking and gait initiation. In the frontal and horizontal planes, lateroflexion and rotation occur before in the upper trunk and after in the lower trunk. Comparison of ES muscle EMGs and trunk kinematics showed that trunk muscle activity precedes corresponding kinematics activity, indicating that the ES drive trunk movement during locomotion and thereby allowing a better pelvis mobilization. EMG data showed that ES activity anticipates propulsive phases in walking with a repetitive pattern, suggesting a programmed control by a central pattern generator. Our findings also suggest that the programs for gait initiation and walking overlap with the latter beginning before the first has ended.     

Optimization of muscle activity for task-level goals predicts complex changes in limb forces across biomechanical contexts

Optimality principles have been proposed as a general framework for understanding motor control in animals and humans largely based on their ability to predict general features movement in idealized motor tasks. However, generalizing these concepts past proof-of-principle to understand the neuromechanical transformation from task-level control to detailed execution-level muscle activity and forces during behaviorally-relevant motor tasks has proved difficult. In an unrestrained balance task in cats, we demonstrate that achieving task-level constraints center of mass forces and moments while minimizing control effort predicts detailed patterns of muscle activity and ground reaction forces in an anatomically-realistic musculoskeletal model. Whereas optimization is typically used to resolve redundancy at a single level of the motor hierarchy, we simultaneously resolved redundancy across both muscles and limbs and directly compared predictions to experimental measures across multiple perturbation directions that elicit different intra- and interlimb coordination patterns. Further, although some candidate task-level variables and cost functions generated indistinguishable predictions in a single biomechanical context, we identified a common optimization framework that could predict up to 48 experimental conditions per animal (n = 3) across both perturbation directions and different biomechanical contexts created by altering animals' postural configuration. Predictions were further improved by imposing experimentally-derived muscle synergy constraints, suggesting additional task variables or costs that may be relevant to the neural control of balance. These results suggested that reduced-dimension neural control mechanisms such as muscle synergies can achieve similar kinetics to the optimal solution, but with increased control effort (≈2×) compared to individual muscle control. Our results are consistent with the idea that hierarchical, task-level neural control mechanisms previously associated with voluntary tasks may also be used in automatic brainstem-mediated pathways for balance.     

Closed-loop and open-loop control of posture and movement during human trunk bending

Closed-loop (CL) and open-loop (OL) types of motor control during human forward upper trunk bending are investigated. A two-joint (hip and ankle) biomechanical model of the human body is used. The analysis is performed in terms of the movements along eigenvectors of the motion equation (“eigenmovements” or “natural synergies”). Two analyzed natural synergies are called “H-synergy” (Hip) and “A-synergy” (Ankle) according to the dominant joint in each of these synergies. Parameters of CL control were estimated using a sudden support platform displacement applied during the movement execution. The CL gain in the H-synergy increased and in the A-synergy decreased during the movement as compared with the quiet standing. The analysis of the time course of OL control signal suggests that the H-synergy (responsible for the prime movement, i.e. bending per se) is controlled according to the EP theory whereas for the associated A-synergy (responsible for posture adjustment, i.e. equilibrium maintenance) muscle forces and gravity forces are balanced for any its final amplitude and therefore the EP theory is not applicable to its control.     

Three-dimensional spine kinematics during multidirectional,target-directed trunk movement in sitting

The current study provides a quantitative assessment of three-dimensional spine motion during target-directed trunk movements in sitting. Subjects sat on an elevated surface, without foot support, and targets were placed in five directions, at three subject-specific distances (based on trunk height). Subjects were asked to lean toward the target, touch it with their head, and return to upright sitting. A retro-reflective motion analysis system was used to measure spine motion, using three kinematic trunk models (1, 3 and 7 segments). Significant differences were noted in the total trunk motion measured between the models, as well as between target distances and directions. In the most segmented model, inter-segmental trunk motion was also found to differ between trunk levels, with complex interaction effects involving target distance and direction. These findings suggest that inter-segmental spine motion is complex, task dependent, and often unevenly distributed between spine levels, with motion patterns differing between subjects, even in the absence of pathology. Use of a multi-segmental model provides the most interpretable findings, allowing for differentiation of individual motion patterns of the spine. Such an approach may be beneficial to the understanding of movement-related spine pathologies.     

Functional muscle synergies to support the knee against moment specific loads while weight bearing

ObjectiveExternally applied abduction and rotational loads are major contributors to the knee joint injury mechanism; yet, how muscles work together to stabilize the knee against these loads remains unclear. Our study sought to evaluate lower limb functional muscle synergies in healthy young adults such that muscle activation can be directly related to internal knee joint moments.MethodsConcatenated non-negative matrix factorization extracted muscle and moment synergies of 22 participants from electromyographic signals and joint moments elicited during a weight-bearing force matching protocol.ResultsTwo synergy sets were extracted: Set 1 included four synergies, each corresponding to a general anterior, posterior, medial, or lateral force direction. Frontal and transverse moments were coupled during medial and lateral force directions. Set 2 included six synergies, each corresponding to a moment type (extension/flexion, ab/adduction, internal/external rotation). Hamstrings and quadriceps dominated synergies associated with respective flexion and extension moments while quadriceps-hamstring co-activation was associated with knee abduction. Rotation moments were associated with notable contributions from hamstrings, quadriceps, gastrocnemius, and hip ab/adductors, corresponding to a general co-activation muscle synergy.ConclusionOur results highlight the importance of muscular co-activation of all muscles crossing the knee to support it during injury-inducing loading conditions such as externally applied knee abduction and rotation. Functional muscle synergies can provide new insight into the relationship between neuromuscular control and knee joint stability by directly associating biomechanical variables to muscle activation.     

Dynamic stability of superior vs. inferior body segments in individuals with transtibial amputation walking in destabilizing environments

Interestingly, young and highly active people with lower limb amputation appear to maintain a similar trunk and upper body stability during walking as able-bodied individuals. Understanding the mechanisms underlying how this stability is achieved after lower-leg amputation is important to improve training regimens for improving walking function in these patients. This study quantified how superior (i.e., head, trunk, and pelvis) and inferior (i.e., thigh, shank, and feet) segments of the body respond to continuous visual or mechanical perturbations during walking. Nine persons with transtibial amputation (TTA) and 12 able-bodied controls (AB) walked on a 2 m×3 m treadmill in a Computer Assisted Rehabilitation Environment (CAREN). Subjects were perturbed by continuous pseudo-random mediolateral movements of either the treadmill platform or the visual scene. TTA maintained a similar local and orbital stability in their superior body segments as AB throughout both perturbation types. However, for their inferior body segments, TTA subjects exhibited greater dynamic instability during perturbed walking. In TTA subjects, these increases in instability were even more pronounced in their prosthetic limb compared to their intact leg. These findings demonstrate that persons with unilateral lower leg amputation maintain upper body stability in spite of increased dynamic instability in their impaired lower leg. Thus, transtibial amputation does significantly impair sensorimotor function, leading to substantially altered dynamic movements of their lower limb segments. However, otherwise relatively healthy patients with unilateral transtibial amputation appear to retain sufficient remaining sensorimotor function in their proximal and contralateral limbs to adequately compensate for their impairment.     

Muscle synergies underlying sit-to-stand tasks in elderly people and their relationship with kinetic characteristics

BackgroundPhysiological evidence suggests that the nervous system controls motion by using a low-dimensional synergy organization for muscle activation. Because the muscle activation produces joint torques, kinetic changes accompanying aging can be related to changes in muscle synergies.ObjectivesWe explored the effects of aging on muscle synergies underlying sit-to-stand tasks, and examined their relationships with kinetic characteristics.MethodsFour younger and three older adults performed the sit-to-stand task at two speeds. Subsequently, we extracted the muscle synergies used to perform these tasks. Hierarchical cluster analysis was used to classify these synergies. We also calculated kinetic variables to compare the groups.ResultsThree independent muscle synergies generally appeared in each subject. The spatial structure of these synergies was similar across age groups. The change in motion speed affected only the temporal structure of these synergies. However, subject-specific muscle synergies and kinetic variables existed.ConclusionsOur results suggest common muscle synergies underlying the sit-to-stand task in both young and elderly adults. People may actively change only the temporal structure of each muscle synergy. The precise subject-specific structuring of each muscle synergy may incorporate knowledge of the musculoskeletal kinetics.     

The effects of unsupervised movement training with visual feedback on upper limb kinematic in persons with shoulder impingement syndrome

Persons with shoulder impingement syndrome (SIS) present impairments that can be improved following supervised movement training with feedback; however, retention is low. The purpose of this study was to evaluate if kinematic changes observed following supervised training can be maintained using unsupervised training with visual feedback. Thirty-three subjects with SIS participated in two visits, one day apart. Kinematic patterns of the upper limb were evaluated once during the first visit, immediately after supervised training; they were evaluated twice during the second visit, before and immediately after unsupervised training. Kinematic patterns were characterized by total excursion and final position during reaching. Unsupervised training consisted of reaching movements performed in front of a mirror. The day after supervised training, subjects with SIS used significantly larger trunk rotation and finished reaching with the trunk more rotated as compared to immediately after supervised training. Following unsupervised training, kinematics of the trunk was back to the level observed immediately after supervised training. Subjects who presented the largest kinematic deficits also significantly improved their shoulder and clavicular movements. Unsupervised training appears to be a good complement to supervised training in order to normalize the kinematic impairments of persons with SIS as compared to healthy subjects.