Investigating reduction of dimensionality during single-joint elbow movements: a case study on muscle synergies

Dissecting muscle synergies in the task space

The muscle synergy is a guiding concept in motor control research that relies on the general notion of muscles 'working together' towards task performance. However, although the synergy concept has provided valuable insights into motor coordination, muscle interactions have not been fully characterised with respect to task performance. Here, we address this research gap by proposing a novel perspective to the muscle synergy that assigns specific functional roles to muscle couplings by characterising their task-relevance. Our novel perspective provides nuance to the muscle synergy concept, demonstrating how muscular interactions can 'work together' in different ways: (1) irrespective of the task at hand but also (2) redundantly or (3) complementarily towards common task-goals. To establish this perspective, we leverage information- and network-theory and dimensionality reduction methods to include discrete and continuous task parameters directly during muscle synergy extraction. Specifically, we introduce co-information as a measure of the task-relevance of muscle interactions and use it to categorise such interactions as task-irrelevant (present across tasks), redundant (shared task information), or synergistic (different task information). To demonstrate these types of interactions in real data, we firstly apply the framework in a simple way, revealing its added functional and physiological relevance with respect to current approaches. We then apply the framework to large-scale datasets and extract generalizable and scale-invariant representations consisting of subnetworks of synchronised muscle couplings and distinct temporal patterns. The representations effectively capture the functional interplay between task end-goals and biomechanical affordances and the concurrent processing of functionally similar and complementary task information. The proposed framework unifies the capabilities of current approaches in capturing distinct motor features while providing novel insights and research opportunities through a nuanced perspective to the muscle synergy.

Toward a unifying framework for the modeling and identification of motor primitives

A large body of evidence suggests that human and animal movements, despite their apparent complexity and flexibility, are remarkably structured. Quantitative analyses of various classes of motor behaviors consistently identify spatial and temporal features that are invariant across movements. Such invariant features have been observed at different levels of organization in the motor system, including the electromyographic, kinematic, and kinetic levels, and are thought to reflect fixed modules-named motor primitives-that the brain uses to simplify the construction of movement. However, motor primitives across space, time, and organization levels are often described with ad-hoc mathematical models that tend to be domain-specific. This, in turn, generates the need to use model-specific algorithms for the identification of both the motor primitives and additional model parameters. The lack of a comprehensive framework complicates the comparison and interpretation of the results obtained across different domains and studies. In this work, we take the first steps toward addressing these issues, by introducing a unifying framework for the modeling and identification of qualitatively different classes of motor primitives. Specifically, we show that a single model, the anechoic mixture model, subsumes many popular classes of motor primitive models. Moreover, we exploit the flexibility of the anechoic mixture model to develop a new class of identification algorithms based on the Fourier-based Anechoic Demixing Algorithm (FADA). We validate our framework by identifying eight qualitatively different classes of motor primitives from both simulated and experimental data. We show that, compared to established model-specific algorithms for the identification of motor primitives, our flexible framework reaches overall comparable and sometimes superior reconstruction performance. The identification framework is publicly released as a MATLAB toolbox (FADA-T, https://tinyurl.com/compsens) to facilitate the identification and comparison of different motor primitive models.

Motor synergy generalization framework for new targets in multi-planar and multi-directional reaching task

Humans can rapidly adapt to new situations, even though they have redundant degrees of freedom (d.f.). Previous studies in neuroscience revealed that human movements could be accounted for by low-dimensional control signals, known as motor synergies. Many studies have suggested that humans use the same repertories of motor synergies among similar tasks. However, it has not yet been confirmed whether the combinations of motor synergy repertories can be re-used for new targets in a systematic way. Here we show that the combination of motor synergies can be generalized to new targets that each repertory cannot handle. We use the multi-directional reaching task as an example. We first trained multiple policies with limited ranges of targets by reinforcement learning and extracted sets of motor synergies. Finally, we optimized the activation patterns of sets of motor synergies and demonstrated that combined motor synergy repertories were able to reach new targets that were not achieved with either original policies or single repertories of motor synergies. We believe this is the first study that has succeeded in motor synergy generalization for new targets in new planes, using a full 7-d.f. arm model, which is a realistic mechanical environment for general reaching tasks.

Temporal Synergies Detection in Gait Cyclograms Using Wearable Technology

The human gait can be described as the synergistic activity of all individual components of the sensory–motor system. The central nervous system (CNS) develops synergies to execute endpoint motion by coordinating muscle activity to reflect the global goals of the endpoint trajectory. This paper proposes a new method for assessing temporal dynamic synergies. Principal component analysis (PCA) has been applied on the signals acquired by wearable sensors (inertial measurement units, IMU and ground reaction force sensors, GRF mounted on feet) to detect temporal synergies in the space of two-dimensional PCA cyclograms. The temporal synergy results for different gait speeds in healthy subjects and stroke patients before and after the therapy were compared. The hypothesis of invariant temporal synergies at different gait velocities was statistically confirmed, without the need to record and analyze muscle activity. A significant difference in temporal synergies was noticed in hemiplegic gait compared to healthy gait. Finally, the proposed PCA-based cyclogram method provided the therapy follow-up information about paretic leg gait in stroke patients that was not available by observing conventional parameters, such as temporal and symmetry gait measures.

A network information theoretic framework to characterise muscle synergies in space and time

Objective Current approaches to muscle synergy extraction rely on linear dimensionality reduction algorithms that make specific assumptions on the underlying signals. However, to capture nonlinear time varying, large-scale but also muscle-specific interactions, a more generalised approach is required. Approach Here we developed a novel framework for muscle synergy extraction that relaxes model assumptions by using a combination of information- and network theory and dimensionality reduction. We first quantify informational dynamics between muscles, time-samples or muscle-time pairings using a novel mutual information formulation. We then model these pairwise interactions as multiplex networks and identify modules representing the network architecture. We employ this modularity criterion as the input parameter for dimensionality reduction, which verifiably extracts the identified modules, and also to characterise salient structures within each module. Main results This novel framework captures spatial, temporal and spatiotemporal interactions across two benchmark datasets of reaching movements, producing distinct spatial groupings and both tonic and phasic temporal patterns. Readily interpretable muscle synergies spanning multiple spatial and temporal scales were identified, demonstrating significant task dependence, ability to capture trial-to-trial fluctuations and concordance across participants. Furthermore, our framework identifies submodular structures that represent the distributed networks of co-occurring signal interactions across scales. Significance The capabilities of this framework are illustrated through the concomitant continuity with previous research and novelty of the insights gained. Several previous limitations are circumvented including the extraction of functionally meaningful and multiplexed pairwise muscle couplings under relaxed model assumptions. The extracted synergies provide a holistic view of the movement while important details of task performance are readily interpretable. The identified muscle groupings transcend biomechanical constraints and the temporal patterns reveal characteristics of fundamental motor control mechanisms. We conclude that this framework opens new opportunities for muscle synergy research and can constitute a bridge between existing models and recent network-theoretic endeavours.

Human Weight Compensation With a Backdrivable Upper-Limb Exoskeleton: Identification and Control

Active exoskeletons are promising devices for improving rehabilitation procedures in patients and preventing musculoskeletal disorders in workers. In particular, exoskeletons implementing human limb’s weight support are interesting to restore some mobility in patients with muscle weakness and help in occupational load carrying tasks. The present study aims at improving weight support of the upper limb by providing a weight model considering joint misalignments and a control law including feedforward terms learned from a prior population-based analysis. Three experiments, for design and validation purposes, are conducted on a total of 65 participants who performed posture maintenance and elbow flexion/extension movements. The introduction of joint misalignments in the weight support model significantly reduced the model errors, in terms of weight estimation, and enhanced the estimation reliability. The introduced control architecture reduced model tracking errors regardless of the condition. Weight support significantly decreased the activity of antigravity muscles, as expected, but increased the activity of elbow extensors because gravity is usually exploited by humans to accelerate a limb downwards. These findings suggest that an adaptive weight support controller could be envisioned to further minimize human effort in certain applications.

Clarifying the Biomechanical Concept of Coordination Through Comparison With Coordination in Motor Control

Coordination is a multidisciplinary concept in human movement science, particularly in the field of biomechanics and motor control. However, the term is not used synonymously by researchers and has substantially different meanings depending on the studies. Therefore, it is necessary to clarify the meaning of coordination to avoid confusion. The meaning of coordination in motor control from computational and ecological perspectives has been clarified, and the meanings differed between them. However, in biomechanics, each study has defined the meaning of the term and the meanings are diverse, and no study has attempted to bring together the diversity of the meanings of the term. Therefore, the purpose of this study is to provide a summary of the different meanings of coordination across the theoretical landscape and clarify the meaning of coordination in biomechanics. We showed that in biomechanics, coordination generally means the relation between elements that act toward the achievement of a motor task, which we call biomechanical coordination. We also showed that the term coordination used in computational and ecological perspectives has two different meanings, respectively. Each one had some similarities with biomechanical coordination. The findings of this study lead to an accurate understanding of the concept of coordination, which would help researchers formulate their empirical arguments for coordination in a more transparent manner. It would allow for accurate interpretation of data and theory development. By comprehensively providing multiple perspectives on coordination, this study intends to promote coordination studies in biomechanics.

Upper-Limb Muscle Synergy Features in Human-Robot Interaction with Circle-Drawing Movements

The upper-limb rehabilitation robots can be developed as an efficient tool for motor function assessments. Circle-drawing has been used as a specific task for robot-based motor function measurement. The upper-limb movement-related kinematic and kinetic parameters measured by motion and force sensors embedded in the rehabilitation robots have been widely studied. However, the muscle synergies characterized by multiple surface electromyographic (sEMG) signals in upper limbs during human-robot interaction (HRI) with circle-drawing movements are rarely investigated. In this research, the robot-assisted and constrained circle-drawing movements for upper limb were used to increase the consistency of muscle synergy features. Both clockwise and counterclockwise circle-drawing tasks were implemented by all healthy subjects using right hands. The sEMG signals were recorded from six muscles in upper limb, and nonnegative matrix factorization (NMF) analysis was utilized to obtain muscle synergy information. Both synergy pattern and activation coefficient were calculated to represent the spatial and temporal features of muscle synergies, respectively. The results obtained from the experimental study confirmed that high structural similarity of muscle synergies was found among the subjects during HRI with circle-drawing movement by healthy subjects, which indicates healthy people may share a common underlying muscle control mechanism during constrained upper-limb circle-drawing movement. This study indicates the muscle synergy analysis during the HRI with constrained circle-drawing movement could be considered as a task for upper-limb motor function assessment.

Temporal Dynamics of Corticomuscular Coherence Reflects Alteration of the Central Mechanisms of Neural Motor Control in Post-Stroke Patients

The neural control of muscular activity during a voluntary movement implies a continuous updating of a mix of afferent and efferent information. Corticomuscular coherence (CMC) is a powerful tool to explore the interactions between the motor cortex and the muscles involved in movement realization. The comparison of the temporal dynamics of CMC between healthy subjects and post-stroke patients could provide new insights into the question of how agonist and antagonist muscles are controlled related to motor performance during active voluntary movements. We recorded scalp electroencephalography activity, electromyography signals from agonist and antagonist muscles, and upper limb kinematics in eight healthy subjects and seventeen chronic post-stroke patients during twenty repeated voluntary elbow extensions and explored whether the modulation of the temporal dynamics of CMC could contribute to motor function impairment. Concomitantly with the alteration of elbow extension kinematics in post-stroke patients, dynamic CMC analysis showed a continuous CMC in both agonist and antagonist muscles during movement and highlighted that instantaneous CMC in antagonist muscles was higher for post-stroke patients compared to controls during the acceleration phase of elbow extension movement. In relation to motor control theories, our findings suggest that CMC could be involved in the online control of voluntary movement through the continuous integration of sensorimotor information. Moreover, specific alterations of CMC in antagonist muscles could reflect central command alterations of the selectivity in post-stroke patients.

A Novel Muscle Synergy Extraction Method Used for Motor Function Evaluation of Stroke Patients: A Pilot Study

In this paper, we present a novel muscle synergy extraction method based on multivariate curve resolution–alternating least squares (MCR-ALS) to overcome the limitation of the nonnegative matrix factorization (NMF) method for extracting non-sparse muscle synergy, and we study its potential application for evaluating motor function of stroke survivors. Nonnegative matrix factorization (NMF) is the most widely used method for muscle synergy extraction. However, NMF is susceptible to components’ sparseness and usually provides inferior reliability, which significantly limits the promotion of muscle synergy. In this study, MCR-ALS was employed to extract muscle synergy from electromyography (EMG) data. Its performance was compared with two other matrix factorization algorithms, NMF and self-modeling mixture analysis (SMMA). Simulated data sets were utilized to explore the influences of the sparseness and noise on the extracted synergies. As a result, the synergies estimated by MCR-ALS were the most similar to true synergies as compared with SMMA and NMF. MCR-ALS was used to analyze the muscle synergy characteristics of upper limb movements performed by healthy (n = 11) and stroke (n = 5) subjects. The repeatability and intra-subject consistency were used to evaluate the performance of MCR-ALS. As a result, MCR-ALS provided much higher repeatability and intra-subject consistency as compared with NMF, which were important for the reliability of the motor function evaluation. The stroke subjects had lower intra-subject consistency and seemingly had more synergies as compared with the healthy subjects. Thus, MCR-ALS is a promising muscle synergy analysis method for motor function evaluation of stroke patients.

How does the CNS control arm reaching movements? Introducing a hierarchical nonlinear predictive control organization based on the idea of muscle synergies

In this study, we introduce a hierarchical and modular computational model to explain how the CNS (Central Nervous System) controls arm reaching movement (ARM) in the frontal plane and under different conditions. The proposed hierarchical organization was established at three levels: 1) motor planning, 2) command production, and 3) motor execution. Since in this work we are not discussing motion learning, no learning procedure was considered in the model. Previous models mainly assume that the motor planning level produces the desired trajectories of the joints and feeds it to the next level to be tracked. In the proposed model, the motion control is described based on a regulatory control policy, that is, the output of the motor planning level is a step function defining the initial and final desired position of the hand. For the command production level, a nonlinear predictive model was developed to explain how the time-invariant muscle synergies (MSs) are recruited. We used the same computational model to explain the arm reaching motion for a combined ARM task. The combined ARM is defined as two successive ARM such that it starts from point A and reaches to point C via point B. To develop the model, kinematic and kinetic data from six subjects were recorded and analyzed during ARM task performance. The subjects used a robotic manipulator while moving their hand in the frontal plane. The EMG data of 15 muscles were also recorded. The MSs used in the model were extracted from the recorded EMG data. The proposed model explains two aspects of the motor control system by a novel computational approach: 1) the CNS reduces the dimension of the control space using the notion of MSs and thereby, avoids immense computational loads; 2) at the level of motor planning, the CNS generates the desired position of the hand at the starting, via and the final points, and this amounts to a regulatory and non-tracking structure.

Motor Control System for Adaptation of Healthy Individuals and Recovery of Poststroke Patients: A Case Study on Muscle Synergies

Understanding the complex neuromuscular strategies underlying behavioral adaptation in healthy individuals and motor recovery after brain damage is essential for gaining fundamental knowledge on the motor control system. Relying on the concept of muscle synergy, which indicates the number of coordinated muscles needed to accomplish specific movements, we investigated behavioral adaptation in nine healthy participants who were introduced to a familiar environment and unfamiliar environment. We then compared the resulting computed muscle synergies with those observed in 10 moderate-stroke survivors throughout an 11-week motor recovery period. Our results revealed that computed muscle synergy characteristics changed after healthy participants were introduced to the unfamiliar environment, compared with those initially observed in the familiar environment, and exhibited an increased neural response to unpredictable inputs. The altered neural activities dramatically adjusted through behavior training to suit the unfamiliar environment requirements. Interestingly, we observed similar neuromuscular behaviors in patients with moderate stroke during the follow-up period of their motor recovery. This similarity suggests that the underlying neuromuscular strategies for adapting to an unfamiliar environment are comparable to those used for the recovery of motor function after stroke. Both mechanisms can be considered as a recall of neural pathways derived from preexisting muscle synergies, already encoded by the brain's internal model. Our results provide further insight on the fundamental principles of motor control and thus can guide the future development of poststroke therapies.

Space-by-Time Modular Decomposition Effectively Describes Whole-Body Muscle Activity During Upright Reaching in Various Directions

The modular control hypothesis suggests that motor commands are built from precoded modules whose specific combined recruitment can allow the performance of virtually any motor task. Despite considerable experimental support, this hypothesis remains tentative as classical findings of reduced dimensionality in muscle activity may also result from other constraints (biomechanical couplings, data averaging or low dimensionality of motor tasks). Here we assessed the effectiveness of modularity in describing muscle activity in a comprehensive experiment comprising 72 distinct point-to-point whole-body movements during which the activity of 30 muscles was recorded. To identify invariant modules of a temporal and spatial nature, we used a space-by-time decomposition of muscle activity that has been shown to encompass classical modularity models. To examine the decompositions, we focused not only on the amount of variance they explained but also on whether the task performed on each trial could be decoded from the single-trial activations of modules. For the sake of comparison, we confronted these scores to the scores obtained from alternative non-modular descriptions of the muscle data. We found that the space-by-time decomposition was effective in terms of data approximation and task discrimination at comparable reduction of dimensionality. These findings show that few spatial and temporal modules give a compact yet approximate representation of muscle patterns carrying nearly all task-relevant information for a variety of whole-body reaching movements.

Analysis of muscle synergy for evaluation of task-specific performance in stroke patients

Muscle synergy represents a central neural module that organizes and activates a group of muscles when performing a certain task. However, whether muscle synergy is a good physiological indicator of motor ability in task performance for patients suffering stroke is not clear. The purpose of this study is to understand how information of task-specific muscle synergy in healthy subjects and patients post stroke can be used to evaluate their motor ability, and further to assist motor rehabilitation for stroke patients. Electromyography (EMG) signals and movement kinematics in reaching tasks were recorded in 5 healthy subjects and 4 stroke patients. Muscle synergies were extracted from EMGs and compared cross healthy and stroke subjects. Normal synergies displayed a characteristic pattern common in healthy subjects. But pathological synergies in stroke subjects lacked the characteristics of normal synergy without a common component, implicating varying extent of damage to the motor module due to lesion in cerebral circuits. Further analysis in stroke subjects showed that pathological patterns of synergy in stroke subjects corresponded to the abnormality in their movement control compared with healthy subjects. Data showed that task-specific muscle synergy did reveal a positive correlation to the ability of neural control of tasks. It was further observed that task-specific synergy was changed towards the normal pattern after intervention with functional electrical stimulation in patients post stroke.

A Longitudinal Electromyography Study of Complex Movements in Poststroke Therapy. 2: Changes in Coordinated Muscle Activation

Fine motor control is achieved through the coordinated activation of groups of muscles, or "muscle synergies." Muscle synergies change after stroke as a consequence of the motor deficit. We investigated the pattern and longitudinal changes in upper limb muscle synergies during therapy in a largely unconstrained movement in patients with a broad spectrum of poststroke residual voluntary motor capacity. Electromyography (EMG) was recorded using wireless telemetry from 6 muscles acting on the more-affected upper body in 24 stroke patients at early and late therapy during formal Wii-based Movement Therapy (WMT) sessions, and in a subset of 13 patients at 6-month follow-up. Patients were classified with low, moderate, or high motor-function. The Wii-baseball swing was analyzed using a non-negative matrix factorization (NMF) algorithm to extract muscle synergies from EMG recordings based on the temporal activation of each synergy and the contribution of each muscle to a synergy. Motor-function was clinically assessed immediately pre- and post-therapy and at 6-month follow-up using the Wolf Motor Function Test, upper limb motor Fugl-Meyer Assessment, and Motor Activity Log Quality of Movement scale. Clinical assessments and game performance demonstrated improved motor-function for all patients at post-therapy (p < 0.01), and these improvements were sustained at 6-month follow-up (p > 0.05). NMF analysis revealed fewer muscle synergies (mean ± SE) for patients with low motor-function (3.38 ± 0.2) than those with high motor-function (4.00 ± 0.3) at early therapy (p = 0.036) with an association trend between the number of synergies and the level of motor-function. By late therapy, there was no significant change between groups, although there was a pattern of increase for those with low motor-function over time. The variability accounted for demonstrated differences with motor-function level (p < 0.05) but not time. Cluster analysis of the pooled synergies highlighted the therapy-induced change in muscle activation. Muscle synergies could be identified for all patients during therapy activities. These results show less complexity and more co-activation in the muscle activation for patients with low motor-function as a higher number of muscle synergies reflects greater movement complexity and task-related phasic muscle activation. The increased number of synergies and changes within synergies by late-therapy suggests improved motor control and movement quality with more distinct phases of movement.

Evaluation of Functional Correlation of Task-Specific Muscle Synergies with Motor Performance in Patients Poststroke

The central nervous system produces movements by activating specifically programmed muscle synergies that are also altered with injuries in the brain, such as stroke. In this study, we hypothesize that there exists a positive correlation between task-specific muscle synergy and motor functions at joint and task levels in patients following stroke. The purpose here is to define and evaluate neurophysiological metrics based on task-specific muscle synergy for assessing motor functions in patients. A patient group of 10 subjects suffering from stroke and a control group of nine age-matched healthy subjects were recruited to participate in this study. Electromyography (EMG) signals and movement kinematics were recorded in patients and control subjects while performing arm reaching tasks. Muscle synergies of individual patients were extracted off-line from EMG records of each patient, and a baseline pattern of muscle synergy was obtained from the pooled EMG data of all nine control subjects. Peak velocities and movement durations of each reaching movement were computed from measured kinematics. Similarity indices of matching components to those of the baseline synergy were defined by synergy vectors and time profiles, respectively, as well as by a combined similarity of vector and time profile. Results showed that pathological synergies of patients were altered from the characteristics of baseline synergy with missing components, or varied vector patterns and time profiles. The kinematic performance measured by peak velocities and movement durations was significantly poorer for the patient group than the control group. In patients, all three similarity indices were found to correlate significantly to the kinematics of movements for the reaching tasks. The correlation to the Fugl-Meyer score of arm was the highest with the vector index, the lowest with the time profile index, and in between with the combined index. These findings illustrate that the analysis of task-specific muscle synergy can provide valuable insights into motor deficits for patients following stroke, and the task-specific similarity indices are useful neurophysiological metrics to predict the function of neuromuscular control at the joint and task levels for patients.

Biofeedback Signals for Robotic Rehabilitation: Assessment of Wrist Muscle Activation Patterns in Healthy Humans

Electrophysiological recordings from human muscles can serve as control signals for robotic rehabilitation devices. Given that many diseases affecting the human sensorimotor system are associated with abnormal patterns of muscle activation, such biofeedback can optimize human-robot interaction and ultimately enhance motor recovery. To understand how mechanical constraints and forces imposed by a robot affect muscle synergies, we mapped the muscle activity of seven major arm muscles in healthy individuals performing goal-directed discrete wrist movements constrained by a wrist robot. We tested six movement directions and four force conditions typically experienced during robotic rehabilitation. We analyzed electromyographic (EMG) signals using a space-by-time decomposition and we identified a set of spatial and temporal modules that compactly described the EMG activity and were robust across subjects. For each trial, coefficients expressing the strength of each combination of modules and representing the underlying muscle recruitment, allowed for a highly reliable decoding of all experimental conditions. The decomposition provides compact representations of the observable muscle activation constrained by a robotic device. Results indicate that a low-dimensional control scheme incorporating EMG biofeedback could be an effective add-on for robotic rehabilitative protocols seeking to improve impaired motor function in humans.

Functional connectivity changes during a working memory task in rat via NMF analysis

Working memory (WM) is necessary in higher cognition. The brain as a complex network is formed by interconnections among neurons. Connectivity results in neural dynamics to support cognition. The first aim is to investigate connectivity dynamics in medial prefrontal cortex (mPFC) networks during WM. As brain neural activity is sparse, the second aim is to find the intrinsic connectivity property in a feature space. Using multi-channel electrode recording techniques, spikes were simultaneously obtained from mPFC of rats that performed a Y-maze WM task. Continuous time series converted from spikes were embedded in a low-dimensional space by non-negative matrix factorization (NMF). mPFC network in original space was constructed by measuring connections among neurons. And the same network in NMF space was constructed by computing connectivity values between the extracted NMF components. Causal density (Cd) and global efficiency (E) were estimated to present the network property. The results showed that Cd and E significantly peaked in the interval right before the maze choice point in correct trials. However, the increase did not emerge in error trials. Additionally, Cd and E in two spaces displayed similar trends in correct trials. The difference was that the measures in NMF space were significantly greater than those in original space. Our findings indicated that the anticipatory changes in mPFC networks may have an effect on future WM behavioral choices. Moreover, the NMF analysis achieves a better characterization for a brain network.

Do muscle synergies reduce the dimensionality of behavior?

The muscle synergy hypothesis is an archetype of the notion of Dimensionality Reduction (DR) occurring in the central nervous system due to modular organization. Toward validating this hypothesis, it is important to understand if muscle synergies can reduce the state-space dimensionality while maintaining task control. In this paper we present a scheme for investigating this reduction utilizing the temporal muscle synergy formulation. Our approach is based on the observation that constraining the control input to a weighted combination of temporal muscle synergies also constrains the dynamic behavior of a system in a trajectory-specific manner. We compute this constrained reformulation of system dynamics and then use the method of system balancing for quantifying the DR; we term this approach as Trajectory Specific Dimensionality Analysis (TSDA). We then investigate the consequence of minimization of the dimensionality for a given task. These methods are tested in simulations on a linear (tethered mass) and a non-linear (compliant kinematic chain) system. Dimensionality of various reaching trajectories is compared when using idealized temporal synergies. We show that as a consequence of this Minimum Dimensional Control (MDC) model, smooth straight-line Cartesian trajectories with bell-shaped velocity profiles emerged as the optima for the reaching task. We also investigated the effect on dimensionality due to adding via-points to a trajectory. The results indicate that a trajectory and synergy basis specific DR of behavior results from muscle synergy control. The implications of these results for the synergy hypothesis, optimal motor control, motor development, and robotics are discussed.

Model selection for the extraction of movement primitives

A wide range of blind source separation methods have been used in motor control research for the extraction of movement primitives from EMG and kinematic data. Popular examples are principal component analysis (PCA), independent component analysis (ICA), anechoic demixing, and the time-varying synergy model (d'Avella and Tresch, 2002). However, choosing the parameters of these models, or indeed choosing the type of model, is often done in a heuristic fashion, driven by result expectations as much as by the data. We propose an objective criterion which allows to select the model type, number of primitives and the temporal smoothness prior. Our approach is based on a Laplace approximation to the posterior distribution of the parameters of a given blind source separation model, re-formulated as a Bayesian generative model. We first validate our criterion on ground truth data, showing that it performs at least as good as traditional model selection criteria [Bayesian information criterion, BIC (Schwarz, 1978) and the Akaike Information Criterion (AIC) (Akaike, 1974)]. Then, we analyze human gait data, finding that an anechoic mixture model with a temporal smoothness constraint on the sources can best account for the data.

A unifying model of concurrent spatial and temporal modularity in muscle activity

Modularity in the central nervous system (CNS), i.e., the brain capability to generate a wide repertoire of movements by combining a small number of building blocks ("modules"), is thought to underlie the control of movement. Numerous studies reported evidence for such a modular organization by identifying invariant muscle activation patterns across various tasks. However, previous studies relied on decompositions differing in both the nature and dimensionality of the identified modules. Here, we derive a single framework that encompasses all influential models of muscle activation modularity. We introduce a new model (named space-by-time decomposition) that factorizes muscle activations into concurrent spatial and temporal modules. To infer these modules, we develop an algorithm, referred to as sample-based nonnegative matrix trifactorization (sNM3F). We test the space-by-time decomposition on a comprehensive electromyographic dataset recorded during execution of arm pointing movements and show that it provides a low-dimensional yet accurate, highly flexible and task-relevant representation of muscle patterns. The extracted modules have a well characterized functional meaning and implement an efficient trade-off between replication of the original muscle patterns and task discriminability. Furthermore, they are compatible with the modules extracted from existing models, such as synchronous synergies and temporal primitives, and generalize time-varying synergies. Our results indicate the effectiveness of a simultaneous but separate condensation of spatial and temporal dimensions of muscle patterns. The space-by-time decomposition accommodates a unified view of the hierarchical mapping from task parameters to coordinated muscle activations, which could be employed as a reference framework for studying compositional motor control.

Muscle synergies in neuroscience and robotics: from input-space to task-space perspectives

In this paper we review the works related to muscle synergies that have been carried-out in neuroscience and control engineering. In particular, we refer to the hypothesis that the central nervous system (CNS) generates desired muscle contractions by combining a small number of predefined modules, called muscle synergies. We provide an overview of the methods that have been employed to test the validity of this scheme, and we show how the concept of muscle synergy has been generalized for the control of artificial agents. The comparison between these two lines of research, in particular their different goals and approaches, is instrumental to explain the computational implications of the hypothesized modular organization. Moreover, it clarifies the importance of assessing the functional role of muscle synergies: although these basic modules are defined at the level of muscle activations (input-space), they should result in the effective accomplishment of the desired task. This requirement is not always explicitly considered in experimental neuroscience, as muscle synergies are often estimated solely by analyzing recorded muscle activities. We suggest that synergy extraction methods should explicitly take into account task execution variables, thus moving from a perspective purely based on input-space to one grounded on task-space as well.