Defining feasible bounds on muscle activation in a redundant biomechanical task: practical implications of redundancy

The role of the deep cervical extensor muscles in multi-directional isometric neck strength

Clinical management of whiplash-associated disorders is challenging and often unsuccessful, with over a third of whiplash injuries progressing to chronic neck pain. Previous imaging studies have identified muscle fat infiltration, indicative of muscle weakness, in the deep cervical extensor muscles (multifidus and semispinalis cervicis). Yet, kinematic and muscle redundancy prevent the direct assessment of individual neck muscle strength, making it difficult to determine the role of these muscles in motor dysfunction. The purpose of this study was to determine the effects of deep cervical extensor muscle weakness on multi-directional neck strength and muscle activation patterns. Maximum isometric forces and associated muscle activation patterns were computed in 25 test directions using a 3-joint, 24-muscle musculoskeletal model of the head and neck. The computational approach accounts for differential torques about the upper and lower cervical spine. To facilitate clinical translation, the test directions were selected based on locations where resistance could realistically be applied to the head during clinical strength assessments. Simulation results reveal that the deep cervical extensor muscles are active and contribute to neck strength in directions with an extension component. Weakness of this muscle group leads to complex compensatory muscle activation patterns characterized primarily by increased activation of the superficial extensors and deep upper cervical flexors, and decreased activation of the deep upper cervical extensors. These results provide a biomechanistic explanation for movement dysfunction that can be used to develop targeted diagnostics and treatments for chronic neck pain in whiplash-associated disorders.

Muscle redundancy is greatly reduced by the spatiotemporal nature of neuromuscular control

Animals must control numerous muscles to produce forces and movements with their limbs. Current theories of motor optimization and synergistic control are predicated on the assumption that there are multiple highly diverse feasible activations for any motor task ("muscle redundancy"). Here, we demonstrate that the dimensionality of the neuromuscular control problem is greatly reduced when adding the temporal constraints inherent to any sequence of motor commands: the physiological time constants for muscle activation-contraction dynamics. We used a seven-muscle model of a human finger to fully characterize the seven-dimensional polytope of all possible motor commands that can produce fingertip force vector in any direction in 3D, in alignment with the core models of Feasibility Theory. For a given sequence of seven force vectors lasting 300 ms, a novel single-step extended linear program finds the 49-dimensional polytope of all possible motor commands that can produce the sequence of forces. We find that muscle redundancy is severely reduced when the temporal limits on muscle activation-contraction dynamics are added. For example, allowing a generous ± 12% change in muscle activation within 50 ms allows visiting only ∼ 7% of the feasible activation space in the next time step. By considering that every motor command conditions future commands, we find that the motor-control landscape is much more highly structured and spatially constrained than previously recognized. We discuss how this challenges traditional computational and conceptual theories of motor control and neurorehabilitation for which muscle redundancy is a foundational assumption.

Neuromuscular control: from a biomechanist's perspective

Understanding neural control of movement necessitates a collaborative approach between many disciplines, including biomechanics, neuroscience, and motor control. Biomechanics grounds us to the laws of physics that our musculoskeletal system must obey. Neuroscience reveals the inner workings of our nervous system that functions to control our body. Motor control investigates the coordinated motor behaviours we display when interacting with our environment. The combined efforts across the many disciplines aimed at understanding human movement has resulted in a rich and rapidly growing body of literature overflowing with theories, models, and experimental paradigms. As a result, gathering knowledge and drawing connections between the overlapping but seemingly disparate fields can be an overwhelming endeavour. This review paper evolved as a need for us to learn of the diverse perspectives underlying current understanding of neuromuscular control. The purpose of our review paper is to integrate ideas from biomechanics, neuroscience, and motor control to better understand how we voluntarily control our muscles. As biomechanists, we approach this paper starting from a biomechanical modelling framework. We first define the theoretical solutions (i.e., muscle activity patterns) that an individual could feasibly use to complete a motor task. The theoretical solutions will be compared to experimental findings and reveal that individuals display structured muscle activity patterns that do not span the entire theoretical solution space. Prevalent neuromuscular control theories will be discussed in length, highlighting optimality, probabilistic principles, and neuromechanical constraints, that may guide individuals to families of muscle activity solutions within what is theoretically possible. Our intention is for this paper to serve as a primer for the neuromuscular control scientific community by introducing and integrating many of the ideas common across disciplines today, as well as inspire future work to improve the representation of neural control in biomechanical models.

Voluntary muscle coactivation in quiet standing elicits reciprocal rather than coactive agonist-antagonist control of reactive balance

Muscle coactivation increases in challenging balance conditions as well as with advanced age and mobility impairments. Increased muscle coactivation can occur both in anticipation of (feedforward) and in reaction to (feedback) perturbations, however, the causal relationship between feedforward and feedback muscle coactivation remains elusive. Here, we hypothesized that feedforward muscle coactivation would increase both the body's initial mechanical resistance due to muscle intrinsic properties and the later feedback-mediated muscle coactivation in response to postural perturbations. Young adults voluntarily increased leg muscle coactivation using visual biofeedback before support-surface perturbations. In contrast to our hypothesis, feedforward muscle coactivation did not increase the body's initial intrinsic resistance to perturbations, nor did it increase feedback muscle coactivation. Rather, perturbations with feedforward muscle coactivation elicited a medium- to long-latency increase of feedback-mediated agonist activity but a decrease of feedback-mediated antagonist activity. This reciprocal rather than coactivation effect on ankle agonist and antagonist muscles enabled faster reactive ankle torque generation, reduced ankle dorsiflexion, and reduced center of mass (CoM) motion. We conclude that in young adults, voluntary feedforward muscle coactivation can be independently modulated with respect to feedback-mediated muscle coactivation. Furthermore, our findings suggest feedforward muscle coactivation may be useful for enabling quicker joint torque generation through reciprocal, rather than coactivated, agonist-antagonist feedback muscle activity. As such our results suggest that behavioral context is critical to whether muscle coactivation functions to increase agility versus stability.NEW & NOTEWORTHY Feedforward and feedback muscle coactivation are commonly observed in older and mobility impaired adults and are considered strategies to improve stability by increasing body stiffness prior to and in response to perturbations. In young adults, voluntary feedforward coactivation does not necessarily increase feedback coactivation in response to perturbations. Instead, feedforward coactivation enabled faster ankle torques through reciprocal agonist-antagonist muscle activity. As such, coactivation may promote either agility or stability depending on the behavioral context.

Brain-spinal cord interaction in long-term motor sequence learning in human: An fMRI study

The spinal cord is important for sensory guidance and execution of skilled movements. Yet its role in human motor learning is not well understood. Despite evidence revealing an active involvement of spinal circuits in the early phase of motor learning, whether long-term learning engages similar changes in spinal cord activation and functional connectivity remains unknown. Here, we investigated spinal-cerebral functional plasticity associated with learning of a specific sequence of visually-guided joystick movements (sequence task) over six days of training. On the first and last training days, we acquired high-resolution functional images of the brain and cervical cord simultaneously, while participants practiced the sequence or a random task while electromyography was recorded from wrist muscles. After six days of training, the subjects' motor performance improved in the sequence compared to the control condition. These behavioral changes were associated with decreased co-contractions and increased reciprocal activations between antagonist wrist muscles. Importantly, early learning was characterized by activation in the C8 level, whereas a more rostral activation in the C6-C7 was found during the later learning phase. Motor sequence learning was also supported by increased spinal cord functional connectivity with distinct brain networks, including the motor cortex, superior parietal lobule, and the cerebellum at the early stage, and the angular gyrus and cerebellum at a later stage of learning. Our results suggest that the early vs. late shift in spinal activation from caudal to rostral cervical segments synchronized with distinct brain networks, including parietal and cerebellar regions, is related to progressive changes reflecting the increasing fine control of wrist muscles during motor sequence learning.

Experimentally quantifying the feasible torque space of the human shoulder

Daily tasks rely on our ability to generate multi-dimensional shoulder torques. When function is limited, strength assessments are used to identify impairments and guide treatment. However, these assessments are often one-dimensional and limited in their sensitivity to diagnose shoulder pathology. To address these limitations, we have proposed novel metrics to quantify shoulder torque capacity in all directions. To quantify the feasible torque space of the shoulder, we measured maximal volitional shoulder torques in 32 unique directions and fit an ellipsoid model to these data. This ellipsoid model was used to quantify overall strength magnitude, strength balance, and the directions in which participants were strongest and weakest. We used these metrics to characterize three-dimensional shoulder strength in healthy adults and demonstrated their repeatability across days. Finally, using musculoskeletal simulations, we showed that our proposed metrics can distinguish between changes in muscle strength associated with aging or rotator cuff tears and quantified the influence of altered experimental conditions on this diagnostic capacity. Our results demonstrate that the proposed metrics can robustly quantify the feasible torque space of the shoulder and may provide a clinically useful description of the functional capacity of the shoulder in health and disease.

Electroplating of HAp-brushite coating on metallic bioimplants with advanced hemocompatibility and osteocompatibility properties

In cases of severe bone tissue injuries, the use of metallic bioimplants is quite widespread due to their high strength, high fracture toughness, hardness, and corrosion resistance. However, they lack adequate biocompatibility and show poor metal-tissue integration during the post-operative phase. To mitigate this drawback, it is beneficial to add a biocompatible polymer layer to ensure a quick growth of cell or tissue over the surface of metallic bioimplant material. Furthermore, this additional layer should possess good adherence with the underlying material and also accompany a rapid bonding between the tissue and the implant material, in order to reduce the recovery time for the patient. Therefore, in this work, we report a novel green electroplating route for growing porous hydroxyapatite-brushite coatings on a stainless steel surface. The malic acid used for the production of hydroxyapatite-brushite coatings has been obtained from an extract of locally available apple fruit (Malus domestica). We demonstrate the effect of electroplating parameters on the structural morphology of the electroplated composite layer via XRD, SEM with EDS, and FTIR characterization techniques and report an optimized set of electroplating parameters that will yield the best composite coating in terms of thickness, adherence to substrate and speed. The hemocompatibility and osteocompatibility studies on the electroplated composites coating show this technology's effectiveness and potential applicability in biomedical applications. Compared to other routes reported in the literature, this electroplating route is quicker and yields better composite coatings with faster bone tissue growth potential.

Coupling of shoulder joint torques in individuals with chronic stroke mirrors controls, with additional non-load-dependent negative effects in a combined-torque task

BACKGROUND

After stroke, motor control is often negatively affected, leaving survivors with less muscle strength and coordination, increased tone, and abnormal synergies (coupled joint movements) in their affected upper extremity. Humeral internal and external rotation have been included in definitions of abnormal synergy but have yet to be studied in-depth.

OBJECTIVE

Determine the ability to generate internal and external rotation torque under different shoulder abduction and adduction loads in persons with chronic stroke (paretic and non-paretic arm) and uninjured controls.

METHODS

24 participants, 12 with impairments after stroke and 12 controls, completed this study. A robotic device controlled abduction and adduction loading to 0, 25, and 50% of maximum strength in each direction. Once established against the vertical load, each participant generated maximum internal and external rotation torque in a dual-task paradigm. Four linear mixed-effects models tested the effect of group (control, non-paretic, and paretic), load (0, 25, 50% adduction or abduction), and their interaction on task performance; one model was created for each combination of dual-task directions (external or internal rotation during abduction or adduction). The protocol was then modeled using OpenSim to understand and explain the role of biomechanical (muscle action) constraints on task performance.

RESULTS

Group was significant in all task combinations. Paretic arms were less able to generate internal and external rotation during abduction and adduction, respectively. There was a significant effect of load in three of four load/task combinations for all groups. Load-level and group interactions were not significant, indicating that abduction and adduction loading affected each group in a similar manner. OpenSim musculoskeletal modeling mirrored the experimental results of control and non-paretic arms and also, when adjusted for weakness, paretic arm performance. Simulations incorporating increased co-activation mirrored the drop in performance observed across all dual-tasks in paretic arms.

CONCLUSION

Common biomechanical constraints (muscle actions) explain limitations in external and internal rotation strength during adduction and abduction dual-tasks, respectively. Additional non-load-dependent effects such as increased antagonist co-activation (hypertonia) may cause the observed decreased performance in individuals with stroke. The inclusion of external rotation in flexion synergy and of internal rotation in extension synergy may be over-simplifications.

Abnormal center of mass feedback responses during balance: A potential biomarker of falls in Parkinson's disease

Although Parkinson disease (PD) causes profound balance impairments, we know very little about how PD impacts the sensorimotor networks we rely on for automatically maintaining balance control. In young healthy people and animals, muscles are activated in a precise temporal and spatial organization when the center of body mass (CoM) is unexpectedly moved that is largely automatic and determined by feedback of CoM motion. Here, we show that PD alters the sensitivity of the sensorimotor feedback transformation. Importantly, sensorimotor feedback transformations for balance in PD remain temporally precise, but become spatially diffuse by recruiting additional muscle activity in antagonist muscles during balance responses. The abnormal antagonist muscle activity remains precisely time-locked to sensorimotor feedback signals encoding undesirable motion of the body in space. Further, among people with PD, the sensitivity of abnormal antagonist muscle activity to CoM motion varies directly with the number of recent falls. Our work shows that in people with PD, sensorimotor feedback transformations for balance are intact but disinhibited in antagonist muscles, likely contributing to balance deficits and falls.

Approaches to revealing the neural basis of muscle synergies: a review and a critique

The central nervous system (CNS) may produce coordinated motor outputs via the combination of motor modules representable as muscle synergies. Identification of muscle synergies has hitherto relied on applying factorization algorithms to multimuscle electromyographic data (EMGs) recorded during motor behaviors. Recent studies have attempted to validate the neural basis of the muscle synergies identified by independently retrieving the muscle synergies through CNS manipulations and analytic techniques such as spike-triggered averaging of EMGs. Experimental data have demonstrated the pivotal role of the spinal premotor interneurons in the synergies' organization and the presence of motor cortical loci whose stimulations offer access to the synergies, but whether the motor cortex is also involved in organizing the synergies has remained unsettled. We argue that one difficulty inherent in current approaches to probing the synergies' neural basis is that the EMG generative model based on linear combination of synergies and the decomposition algorithms used for synergy identification are not grounded on enough prior knowledge from neurophysiology. Progress may be facilitated by constraining or updating the model and algorithms with knowledge derived directly from CNS manipulations or recordings. An investigative framework based on evaluating the relevance of neurophysiologically constrained models of muscle synergies to natural motor behaviors will allow a more sophisticated understanding of motor modularity, which will help the community move forward from the current debate on the neural versus nonneural origin of muscle synergies.

Reorganization of motor modules for standing reactive balance recovery following pyridoxine-induced large-fiber peripheral sensory neuropathy in cats

Task-level goals such as maintaining standing balance are achieved through coordinated muscle activity. Consistent and individualized groupings of synchronously activated muscles can be estimated from muscle recordings in terms of motor modules or muscle synergies, independent of their temporal activation. The structure of motor modules can change with motor training, neurological disorders, and rehabilitation, but the central and peripheral mechanisms underlying motor module structure remain unclear. To assess the role of peripheral somatosensory input on motor module structure, we evaluated changes in the structure of motor modules for reactive balance recovery following pyridoxine-induced large-fiber peripheral somatosensory neuropathy in previously collected data in four adult cats. Somatosensory fiber loss, quantified by postmortem histology, varied from mild to severe across cats. Reactive balance recovery was assessed using multidirectional translational support-surface perturbations over days to weeks throughout initial impairment and subsequent recovery of balance ability. Motor modules within each cat were quantified by non-negative matrix factorization and compared in structure over time. All cats exhibited changes in the structure of motor modules for reactive balance recovery after somatosensory loss, providing evidence that somatosensory inputs influence motor module structure. The impact of the somatosensory disturbance on the structure of motor modules in well-trained adult cats indicates that somatosensory mechanisms contribute to motor module structure, and therefore may contribute to some of the pathological changes in motor module structure in neurological disorders. These results further suggest that somatosensory nerves could be targeted during rehabilitation to influence pathological motor modules for rehabilitation.NEW & NOTEWORTHY Stable motor modules for reactive balance recovery in well-trained adult cats were disrupted following pyridoxine-induced peripheral somatosensory neuropathy, suggesting somatosensory inputs contribute to motor module structure. Furthermore, the motor module structure continued to change as the animals regained the ability to maintain standing balance, but the modules generally did not recover pre-pyridoxine patterns. These results suggest changes in somatosensory input and subsequent learning may contribute to changes in motor module structure in pathological conditions.

Effects of kinematic complexity and number of muscles on musculoskeletal model robustness to muscle dysfunction

The robustness of motor outputs to muscle dysfunction has been investigated using musculoskeletal modeling, but with conflicting results owing to differences in model complexity and motor tasks. Our objective was to systematically study how the number of kinematic degrees of freedom, and the number of independent muscle actuators alter the robustness of motor output to muscle dysfunction. We took a detailed musculoskeletal model of the human leg and systematically varied the model complexity to create six models with either 3 or 7 kinematic degrees of freedom and either 14, 26, or 43 muscle actuators. We tested the redundancy of each model by quantifying the reduction in sagittal plane feasible force set area when a single muscle was removed. The robustness of feasible force set area to the loss of any single muscle, i.e. general single muscle loss increased with the number of independent muscles and decreased with the number of kinematic degrees of freedom, with the robust area varying from 1% and 52% of the intact feasible force set area. The maximum sensitivity of the feasible force set to the loss of any single muscle varied from 75% to 26% of the intact feasible force set area as the number of muscles increased. Additionally, the ranges of feasible muscle activation for maximum force production were largely unconstrained in many cases, indicating ample musculoskeletal redundancy even for maximal forces. We propose that ratio of muscles to kinematic degrees of freedom can be used as a rule of thumb for estimating musculoskeletal redundancy in both simulated and real biomechanical systems.

Feasibility Theory Reconciles and Informs Alternative Approaches to Neuromuscular Control

We present Feasibility Theory, a conceptual and computational framework to unify today's theories of neuromuscular control. We begin by describing how the musculoskeletal anatomy of the limb, the need to control individual tendons, and the physics of a motor task uniquely specify the family of all valid muscle activations that accomplish it (its ‘feasible activation space’). For our example of producing static force with a finger driven by seven muscles, computational geometry characterizes—in a complete way—the structure of feasible activation spaces as 3-dimensional polytopes embedded in 7-D. The feasible activation space for a given task is the landscape where all neuromuscular learning, control, and performance must occur. This approach unifies current theories of neuromuscular control because the structure of feasible activation spaces can be separately approximated as either low-dimensional basis functions (synergies), high-dimensional joint probability distributions (Bayesian priors), or fitness landscapes (to optimize cost functions).

Effect of Kinetic Degrees of Freedom on Multi-Finger Synergies and Task Performance during Force Production and Release Tasks

Complex structures present in a human body has relatively large degrees-of-freedom (DOFs) as compared to the requirement of a particular task. This phenomenon called motor redundancy initially deemed as a computational problem rather can be understood as having the flexibility to perform the certain task successfully. Hence, the purpose of our study was to examine the positive impact of extra DOFs (redundant DOFs) during force production tasks. For this purpose, an experimental setup was designed to simulate archery-like shooting, and purposeful organization of a redundant set of finger forces determined the stability of important performance variables as well as accurate and precise performance. DOFs were adjusted by changing the number of fingers explicitly involved in the task. The concept of motor synergy and computational framework of uncontrolled manifold (UCM) approach was used to quantify stability indices during finger force production. As a result, accuracy and precision of the task improved with an increase in DOFs. Also, the stability indices of net finger forces and moment increased with active DOFs of fingers. We concluded that the controller actively utilizes extra DOFs to increase the stability of the performance, which is associated with the improved accuracy and precision of the task.

Biomechanical Methods to Quantify Muscle Effort During Resistance Exercise

Chiu, LZF. Biomechanical methods to quantify muscle effort during resistance exercise. J Strength Cond Res 32(2): 502-513, 2018-Muscle hypertrophy and strength adaptations elicited by resistance training are dependent on the force exerted by active muscles. As an exercise may use many muscles, determining force for individual muscles or muscle groupings is important to understand the relation between an exercise and these adaptations. Muscle effort-the amount of force or a surrogate measure related to the amount of force exerted during a task-can be quantified using biomechanical methods. The purpose of this review was to summarize the biomechanical methods used to estimate muscle effort in movements, particularly resistance training exercises. These approaches include the following: (a) inverse dynamics with rigid body models, (b) forward dynamics and EMG-driven models, (c) normalized EMG, and (d) inverse dynamics with point-mass models. Rigid body models quantify muscle effort as net joint moments. Forward dynamics and EMG-driven models estimate muscle force as well as determine the effect of a muscle's action throughout the body. Nonlinear relations between EMG and muscle force and normalization reference action selection affect the usefulness of EMG as a measure of muscle effort. Point-mass models include kinetics calculated from barbell (or other implement) kinematics recorded using electromechanical transducers or measured using force platforms. Point-mass models only allow the net force exerted on the barbell or lifter-barbell system to be determined, so they cannot be used to estimate muscle effort. Data from studies using rigid body models, normalized EMG, and musculoskeletal modeling should be combined to develop hypotheses regarding muscle effort; these hypotheses should be verified by training interventions.

The Impact of Segmental Trunk Support on Posture and Reaching While Sitting in Healthy Adults

The authors investigated postural and arm control in seated reaches while providing trunk support at midribs and pelvic levels in adults. Kinematics and electromyography of the arm and ipsiliateral and contralateral paraspinal muscles were examined before and during reaching. Kinematics remained constant across conditions, but changes were observed in neuromuscular control. With midribs support, the ipsilateral cervical muscle showed either increased anticipatory activity or earlier compensatory muscle responses, suggesting its major role in head stabilization. The baseline activity of bilateral lumbar muscles was enhanced with midribs support, whereas with pelvic support, the activation frequency of paraspinal muscles increased during reaching. The results suggest that segmental trunk support in healthy adults modulates ipsilateral or contralateral paraspinal activity while overall kinematic outputs remain invariant.

Instantaneous Metabolic Cost of Walking: Joint-Space Dynamic Model with Subject-Specific Heat Rate

A subject-specific model of instantaneous cost of transport (ICOT) is introduced from the joint-space formulation of metabolic energy expenditure using the laws of thermodynamics and the principles of multibody system dynamics. Work and heat are formulated in generalized coordinates as functions of joint kinematic and dynamic variables. Generalized heat rates mapped from muscle energetics are estimated from experimental walking metabolic data for the whole body, including upper-body and bilateral data synchronization. Identified subject-specific energetic parameters-mass, height, (estimated) maximum oxygen uptake, and (estimated) maximum joint torques-are incorporated into the heat rate, as opposed to the traditional in vitro and subject-invariant muscle parameters. The total model metabolic energy expenditure values are within 5.7 ± 4.6% error of the measured values with strong (R2 > 0.90) inter- and intra-subject correlations. The model reliably predicts the characteristic convexity and magnitudes (0.326-0.348) of the experimental total COT (0.311-0.358) across different subjects and speeds. The ICOT as a function of time provides insights into gait energetic causes and effects (e.g., normalized comparison and sensitivity with respect to walking speed) and phase-specific COT, which are unavailable from conventional metabolic measurements or muscle models. Using the joint-space variables from commonly measured or simulated data, the models enable real-time and phase-specific evaluations of transient or non-periodic general tasks that use a range of (aerobic) energy pathway similar to that of steady-state walking.

Muscle Synergies Heavily Influence the Neural Control of Arm Endpoint Stiffness and Energy Consumption

Much debate has arisen from research on muscle synergies with respect to both limb impedance control and energy consumption. Studies of limb impedance control in the context of reaching movements and postural tasks have produced divergent findings, and this study explores whether the use of synergies by the central nervous system (CNS) can resolve these findings and also provide insights on mechanisms of energy consumption. In this study, we phrase these debates at the conceptual level of interactions between neural degrees of freedom and tasks constraints. This allows us to examine the ability of experimentally-observed synergies—correlated muscle activations—to control both energy consumption and the stiffness component of limb endpoint impedance. In our nominal 6-muscle planar arm model, muscle synergies and the desired size, shape, and orientation of endpoint stiffness ellipses, are expressed as linear constraints that define the set of feasible muscle activation patterns. Quadratic programming allows us to predict whether and how energy consumption can be minimized throughout the workspace of the limb given those linear constraints. We show that the presence of synergies drastically decreases the ability of the CNS to vary the properties of the endpoint stiffness and can even preclude the ability to minimize energy. Furthermore, the capacity to minimize energy consumption—when available—can be greatly affected by arm posture. Our computational approach helps reconcile divergent findings and conclusions about task-specific regulation of endpoint stiffness and energy consumption in the context of synergies. But more generally, these results provide further evidence that the benefits and disadvantages of muscle synergies go hand-in-hand with the structure of feasible muscle activation patterns afforded by the mechanics of the limb and task constraints. These insights will help design experiments to elucidate the interplay between synergies and the mechanisms of learning, plasticity, versatility and pathology in neuromuscular systems.

The manner in which the nervous system coordinates the multiple muscles in the body is complex. It has been studied for decades, but a more full understanding is needed to enable the development of effective evaluation and treatment methods in disorders that cause neuromuscular disability such as cerebral palsy and stroke. In addition, the computational control of robots has and will continue to improve as the brain’s methods of muscular control are progressively reverse-engineered. Here, we study the capacity of arm muscles to regulate the stiffness of the hand for tasks such as using tools, stabilizing hand-held objects, and using doors. Using a simplified but generalizable model, we show that there will be necessary trade-offs in the functional capabilities of the limb if the nervous system chooses to control muscles in functional groups. This adds to our understanding of the consequences of different strategies to control muscles for real-world tasks with multiple and often competing demands. It enables future research and clinical experiments on the learning and execution of the multiple tasks of varying difficulty encountered in real life. It also sheds light on the design of control strategies for robots to operate in human and unstructured environments.

Suboptimal Muscle Synergy Activation Patterns Generalize their Motor Function across Postures

We used a musculoskeletal model to investigate the possible biomechanical and neural bases of using consistent muscle synergy patterns to produce functional motor outputs across different biomechanical conditions, which we define as generalizability. Experimental studies in cats demonstrate that the same muscle synergies are used during reactive postural responses at widely varying configurations, producing similarly-oriented endpoint force vectors with respect to the limb axis. However, whether generalizability across postures arises due to similar biomechanical properties or to neural selection of a particular muscle activation pattern has not been explicitly tested. Here, we used a detailed cat hindlimb model to explore the set of feasible muscle activation patterns that produce experimental synergy force vectors at a target posture, and tested their generalizability by applying them to different test postures. We used three methods to select candidate muscle activation patterns: (1) randomly-selected feasible muscle activation patterns, (2) optimal muscle activation patterns minimizing muscle effort at a given posture, and (3) generalizable muscle activation patterns that explicitly minimized deviations from experimentally-identified synergy force vectors across all postures. Generalizability was measured by the deviation between the simulated force direction of the candidate muscle activation pattern and the experimental synergy force vectors at the test postures. Force angle deviations were the greatest for the randomly selected feasible muscle activation patterns (e.g., >100°), intermediate for effort-wise optimal muscle activation patterns (e.g., ~20°), and smallest for generalizable muscle activation patterns (e.g., <5°). Generalizable muscle activation patterns were suboptimal in terms of effort, often exceeding 50% of the maximum possible effort (cf. ~5% in minimum-effort muscle activation patterns). The feasible muscle activation ranges of individual muscles associated with producing a specific synergy force vector was reduced by ~45% when generalizability requirements were imposed. Muscles recruited in the generalizable muscle activation patterns had less sensitive torque-producing characteristics to changes in postures. We conclude that generalization of function across postures does not arise from limb biomechanics or a single optimality criterion. Muscle synergies may reflect acquired motor solutions globally tuned for generalizability across biomechanical contexts, facilitating rapid motor adaptation.

Structure of the set of feasible neural commands for complex motor tasks

The brain must select its control strategies among an infinite set of possibilities; researchers believe that it must be solving an optimization problem. While this set of feasible solutions is infinite and lies in high dimensions, it is bounded by kinematic, neuromuscular, and anatomical constraints, within which the brain must select optimal solutions. That is, the set of feasible activations is well structured. However, to date there is no method to describe and quantify the structure of these high-dimensional solution spaces. Bounding boxes or dimensionality reduction algorithms do not capture their detailed structure. We present a novel approach based on the well-known Hit-and-Run algorithm in computational geometry to extract the structure of the feasible activations capable of producing 50% of maximal fingertip force in a specific direction. We use a realistic model of a human index finger with 7 muscles, and 4 DOFs. For a given static force vector at the endpoint, the feasible activation space is a 3D convex polytope, embedded in the 7D unit cube. It is known that explicitly computing the volume of this polytope can become too computationally complex in many instances. However, our algorithm was able to sample 1,000,000 uniform at random points from the feasible activation space. The computed distribution of activation across muscles sheds light onto the structure of these solution spaces-rather than simply exploring their maximal and minimal values. Although this paper presents a 7 dimensional case of the index finger, our methods extend to systems with at least 40 muscles. This will allow our motor control community to understand the distributions of feasible muscle activations, providing important contextual information into learning, optimization and adaptation of motor patterns in future research.

Exploring the high-dimensional structure of muscle redundancy via subject-specific and generic musculoskeletal models

Subject-specific and generic musculoskeletal models are the computational instantiation of hypotheses, and stochastic techniques help explore their validity. We present two such examples to explore the hypothesis of muscle redundancy. The first addresses the effect of anatomical variability on static force capabilities for three individual cat hindlimbs, each with seven kinematic degrees of freedom (DoFs) and 31 muscles. We present novel methods to characterize the structure of the 31-dimensional set of feasible muscle activations for static force production in every 3-D direction. We find that task requirements strongly define the set of feasible muscle activations and limb forces, with few differences comparing individual vs. species-average results. Moreover, muscle activity is not smoothly distributed across 3-D directions. The second example explores parameter uncertainty during a flying disc throwing motion by using a generic human arm with five DoFs and 17 muscles to predict muscle fiber velocities. We show that the measured joint kinematics fully constrain the eccentric and concentric fiber velocities of all muscles via their moment arms. Thus muscle activation for limb movements is likely not redundant: there is little, if any, latitude in synchronizing alpha-gamma motoneuron excitation-inhibition for muscles to adhere to the time-critical fiber velocities dictated by joint kinematics. Importantly, several muscles inevitably exhibit fiber velocities higher than thought tenable, even for conservative throwing speeds. These techniques and results, respectively, enable and compel us to continue to revise the classical notion of muscle redundancy for increasingly more realistic models and tasks.

Feasible muscle activation ranges based on inverse dynamics analyses of human walking

Although it is possible to produce the same movement using an infinite number of different muscle activation patterns owing to musculoskeletal redundancy, the degree to which observed variations in muscle activity can deviate from optimal solutions computed from biomechanical models is not known. Here, we examined the range of biomechanically permitted activation levels in individual muscles during human walking using a detailed musculoskeletal model and experimentally-measured kinetics and kinematics. Feasible muscle activation ranges define the minimum and maximum possible level of each muscle's activation that satisfy inverse dynamics joint torques assuming that all other muscles can vary their activation as needed. During walking, 73% of the muscles had feasible muscle activation ranges that were greater than 95% of the total muscle activation range over more than 95% of the gait cycle, indicating that, individually, most muscles could be fully active or fully inactive while still satisfying inverse dynamics joint torques. Moreover, the shapes of the feasible muscle activation ranges did not resemble previously-reported muscle activation patterns nor optimal solutions, i.e. static optimization and computed muscle control, that are based on the same biomechanical constraints. Our results demonstrate that joint torque requirements from standard inverse dynamics calculations are insufficient to define the activation of individual muscles during walking in healthy individuals. Identifying feasible muscle activation ranges may be an effective way to evaluate the impact of additional biomechanical and/or neural constraints on possible versus actual muscle activity in both normal and impaired movements.