Biomechanical capabilities influence postural control strategies in the cat hindlimb

Comparison of strength profile representations using musculoskeletal models and their applications in robotics

Musculoskeletal models provide an approach towards simulating the ability of the human body in a variety of human-robot applications. A promising use for musculoskeletal models is to model the physical capabilities of the human body, for example, estimating the strength at the hand. Several methods of modelling and representing human strength with musculoskeletal models have been used in ergonomic analysis, human-robot interaction and robotic assistance. However, it is currently unclear which methods best suit modelling and representing limb strength. This paper compares existing methods for calculating and representing the strength of the upper limb using musculoskeletal models. It then details the differences and relative advantages of the existing methods, enabling the discussion on the appropriateness of each method for particular applications.

Modern three-dimensional digital methods for studying locomotor biomechanics in tetrapods

Here, we review the modern interface of three-dimensional (3D) empirical (e.g. motion capture) and theoretical (e.g. modelling and simulation) approaches to the study of terrestrial locomotion using appendages in tetrapod vertebrates. These tools span a spectrum from more empirical approaches such as XROMM, to potentially more intermediate approaches such as finite element analysis, to more theoretical approaches such as dynamic musculoskeletal simulations or conceptual models. These methods have much in common beyond the importance of 3D digital technologies, and are powerfully synergistic when integrated, opening a wide range of hypotheses that can be tested. We discuss the pitfalls and challenges of these 3D methods, leading to consideration of the problems and potential in their current and future usage. The tools (hardware and software) and approaches (e.g. methods for using hardware and software) in the 3D analysis of tetrapod locomotion have matured to the point where now we can use this integration to answer questions we could never have tackled 20 years ago, and apply insights gleaned from them to other fields.

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.

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.

Neuromuscular organisation and robustness of postural control in the presence of perturbations

Perturbation-based exercise interventions challenge balance and improve reactive motor control. Our purpose was to investigate the modular organisation during a standing balance task in both stable and unstable conditions to provide new insights into the neuromuscular control mechanisms needed to cope with perturbations. Fifteen participants performed 54 cycles of a specific task (i.e. pass from a double- to a single-leg standing) on stable ground and an unstable oscillating platform (Posturomed). Muscle synergies were extracted from the electromyographic activity of thirteen lower limb muscles. The maximum Lyapunov exponents of different body segments were calculated using kinematic data. We found two synergies functionally associated with the single- and double-leg stance in both stable and unstable conditions. Nonetheless, in the unstable condition participants needed an extra muscle synergy also functionally related to the single stance. Although a simple organisation of the neuromuscular system was sufficient to maintain the postural control in both conditions, the increased challenge in the oscillating platform was solved by adding one extra synergy. The addition of a new synergy with complementary function highlighted an increased motor output's robustness (i.e. ability to cope with errors) in the presence of perturbations.

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.

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.

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.

The mechanical actions of muscles predict the direction of muscle activation during postural perturbations in the cat hindlimb

Humans and cats respond to balance challenges, delivered via horizontal support surface perturbations, with directionally selective muscle recruitment and constrained ground reaction forces. It has been suggested that this postural strategy arises from an interaction of limb biomechanics and proprioceptive networks in the spinal cord. A critical experimental validation of this hypothesis is to test the prediction that the principal directions of muscular activation oppose the directions responding muscles exert their forces on the environment. Therefore, our objective was to quantify the endpoint forces of a diverse set of cat hindlimb muscles and compare them with the directionally sensitive muscle activation patterns generated in the intact and decerebrate cat. We hypothesized that muscles are activated based on their mechanical advantage. Our primary expectation was that the principal direction of muscle activation during postural perturbations will be directed oppositely (180°) from the muscle endpoint ground reaction force. We found that muscle activation during postural perturbations was indeed directed oppositely to the endpoint reaction forces of that muscle. These observations indicate that muscle recruitment during balance challenges is driven, at least in part, by limb architecture. This suggests that sensory sources that provide feedback about the mechanical environment of the limb are likely important to appropriate and effective responses during balance challenges. Finally, we extended the analysis to three dimensions and different stance widths, laying the groundwork for a more comprehensive study of postural regulation than was possible with measurements confined to the horizontal plane and a single stance configuration.

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

Measured muscle activation patterns often vary significantly from musculoskeletal model predictions that use optimization to resolve redundancy. Although experimental muscle activity exhibits both inter- and intra-subject variability we lack adequate tools to quantify the biomechanical latitude that the nervous system has when selecting muscle activation patterns. Here, we identified feasible ranges of individual muscle activity during force production in a musculoskeletal model to quantify the degree to which biomechanical redundancy allows for variability in muscle activation patterns. In a detailed cat hindlimb model matched to the posture of three cats, we identified the lower and upper bounds on muscle activity in each of 31 muscles during static endpoint force production across different force directions and magnitudes. Feasible ranges of muscle activation were relatively unconstrained across force magnitudes such that only a few (0-13%) muscles were found to be truly "necessary" (e.g. exhibited non-zero lower bounds) at physiological force ranges. Most of the muscles were "optional", having zero lower bounds, and frequently had "maximal" upper bounds as well. Moreover, "optional" muscles were never selected by optimization methods that either minimized muscle stress, or that scaled the pattern required for maximum force generation. Therefore, biomechanical constraints were generally insufficient to restrict or specify muscle activation levels for producing a force in a given direction, and many muscle patterns exist that could deviate substantially from one another but still achieve the task. Our approach could be extended to identify the feasible limits of variability in muscle activation patterns in dynamic tasks such as walking.

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.

How the brain and spinal cord control the body is a fundamental question of critical scientific and clinical importance. The preferred experimental approach to answer this question has been to infer the neural control strategy by analyzing recordings of muscle activity and limb mechanics collected while animals and people use their limbs. This has led to a popular, but not yet proven, hypothesis that the brain and spinal cord simplify the control of the numerous muscles by grouping them into few functional units called neural synergies. Our detailed experiments and simulations challenge the utility of this approach and the validity of its interpretation. We point out that mechanical constraints can also explain those experimental recordings. In particular, the anatomy of the limb combined with the type of tasks studied and analysis used, suffice to give the appearance of neural synergies. To be clear, we do not disprove the neural synergy hypothesis. Rather, in the tradition of scientific debate, by showing an alternative explanation to the available data we challenge the community and ourselves to design novel experiments and analyses to conclusively test that hypothesis by ruling out the confounds we point out.

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.

Estimation of musculoskeletal models from in situ measurements of muscle action in the rat hindlimb

Musculoskeletal models are often created by making detailed anatomical measurements of muscle properties. These measurements can then be used to determine the parameters of canonical models of muscle action. We describe here a complementary approach for developing and validating muscle models, using in situ measurements of muscle actions. We characterized the actions of two rat hindlimb muscles: the gracilis posticus (GRp) and the posterior head of biceps femoris (BFp; excluding the anterior head with vertebral origin). The GRp is a relatively simple muscle, with a circumscribed origin and insertion. The BFp is more complex, with an insertion distributed along the tibia. We measured the six-dimensional isometric forces and moments at the ankle evoked from stimulating each muscle at a range of limb configurations. The variation of forces and moments across the workspace provides a succinct characterization of muscle action. We then used this data to create a simple muscle model with a single point insertion and origin. The model parameters were optimized to best explain the observed force-moment data. This model explained the relatively simple muscle, GRp, very well (R(2)>0.85). Surprisingly, this simple model was also able to explain the action of the BFp, despite its greater complexity (R(2)>0.84). We then compared the actions observed here with those predicted using recently published anatomical measurements. Although the forces and moments predicted for the GRp were very similar to those observed here, the predictions for the BFp differed. These results show the potential utility of the approach described here for the development and refinement of musculoskeletal models based on in situ measurements of muscle actions.

Directional constraint of endpoint force emerges from hindlimb anatomy

Postural control requires the coordination of force production at the limb endpoints to apply an appropriate force to the body. Subjected to horizontal plane perturbations, quadruped limbs stereotypically produce force constrained along a line that passes near the center of mass. This phenomenon, referred to as the force constraint strategy, may reflect mechanical constraints on the limb or body, a specific neural control strategy or an interaction among neural controls and mechanical constraints. We used a neuromuscular model of the cat hindlimb to test the hypothesis that the anatomical constraints restrict the mechanical action of individual muscles during stance and constrain the response to perturbations to a line independent of perturbation direction. In a linearized neuromuscular model of the cat hindlimb, muscle lengthening directions were highly conserved across 10,000 different muscle activation patterns, each of which produced an identical, stance-like endpoint force. These lengthening directions were closely aligned with the sagittal plane and reveal an anatomical structure for directionally constrained force responses. Each of the 10,000 activation patterns was predicted to produce stable stance based on Lyapunov stability analysis. In forward simulations of the nonlinear, seven degree of freedom model under the action of 200 random muscle activation patterns, displacement of the endpoint from its equilibrium position produced restoring forces, which were also biased toward the sagittal plane. The single exception was an activation pattern based on minimum muscle stress optimization, which produced destabilizing force responses in some perturbation directions. The sagittal force constraint increased during simulations as the system shifted from an inertial response during the acceleration phase to a viscoelastic response as peak velocity was obtained. These results qualitatively match similar experimental observations and suggest that the force constraint phenomenon may result from the anatomical arrangement of the limb.

Muscle mass in musculoskeletal models

Most current models of musculoskeletal dynamics lump a muscle's mass with its body segment, and then simulate the dynamics of these body segments connected by joints. As shown here, this popular approach leads to errors in the system's inertia matrix and hence in all aspects of the dynamics. Two simplified mathematical models were created to capture the relevant features of monoarticular and biarticular muscles, and the errors were analyzed. The models were also applied to two physiological examples: the triceps surae muscles that plantar flex the human ankle and the biceps femoris posterior muscle of the rat hind limb. The analysis of errors due to lumping showed that these errors can be large. Although the errors can be reduced in some postures, they cannot be easily eliminated in models that use segment lumping. Some options for addressing these errors are discussed.

Subject-specific muscle synergies in human balance control are consistent across different biomechanical contexts

The musculoskeletal redundancy of the body provides multiple solutions for performing motor tasks. We have proposed that the nervous system solves this unconstrained problem through the recruitment of motor modules or functional muscle synergies that map motor intention to action. Consistent with this hypothesis, we showed that trial-by-trial variations in muscle activation for multidirectional balance control in humans were constrained by a small set of muscle synergies. However, apparent muscle synergy structures could arise from characteristic patterns of sensory input resulting from perturbations or from low-dimensional optimal motor solutions. Here we studied electromyographic (EMG) responses for balance control across a range of biomechanical contexts, which alter not only the sensory inflow generated by postural perturbations, but also the muscle activation patterns used to restore balance. Support-surface translations in 12 directions were delivered to subjects standing in six different postural configurations: one-leg, narrow, wide, very wide, crouched, and normal stance. Muscle synergies were extracted from each condition using nonnegative matrix factorization. In addition, muscle synergies from the normal stance condition were used to reconstruct muscle activation patterns across all stance conditions. A consistent set of muscle synergies were recruited by each subject across conditions. When balance demands were extremely different from the normal stance (e.g., one-legged or crouched stance), task-specific muscle synergies were recruited in addition to the preexisting ones, rather generating de novo muscle synergies. Taken together, our results suggest that muscle synergies represent consistent motor modules that map intention to action, regardless of the biomechanical context of the task.

Force transmission between synergistic skeletal muscles through connective tissue linkages

The classic view of skeletal muscle is that force is generated within its muscle fibers and then directly transmitted in-series, usually via tendon, onto the skeleton. In contrast, recent results suggest that muscles are mechanically connected to surrounding structures and cannot be considered as independent actuators. This article will review experiments on mechanical interactions between muscles mediated by such epimuscular myofascial force transmission in physiological and pathological muscle conditions. In a reduced preparation, involving supraphysiological muscle conditions, it is shown that connective tissues surrounding muscles are capable of transmitting substantial force. In more physiologically relevant conditions of intact muscles, however, it appears that the role of this myofascial pathway is small. In addition, it is hypothesized that connective tissues can serve as a safety net for traumatic events in muscle or tendon. Future studies are needed to investigate the importance of intermuscular force transmission during movement in health and disease.

The decerebrate cat generates the essential features of the force constraint strategy

Cats actively respond to horizontal perturbations of the supporting surface according to the force constraint strategy. In this strategy, the force responses fall into two groups oriented in either rostral and medial directions or caudal and lateral directions, rather than in strict opposition to the direction of perturbation. When the distance between forelimbs and hindlimbs is decreased, the responses are less constrained and directed more in line with the perturbation. We have recently shown that electromyographic responses from limb muscles of the decerebrate cat resemble those obtained in the intact animal. Our objectives here were to determine whether the decerebrate cat preparation would also exhibit the force constraint strategy and whether that strategy would exhibit the characteristic dependence on limb position on the strategy. Horizontal support surface perturbations were delivered and three-dimensional exerted forces were recorded from all four limbs. Clustered force responses were generated by all four limbs and were found to be statistically indistinguishable between animals decerebrated using two different levels of transection. The directionality of the force responses was preserved throughout successive time epochs during the perturbations. In addition, the clustering of force responses increased with distance between forelimbs and hindlimbs. These results indicate that the force constraint strategy used by terrestrial animals to maintain stability can be generated without the assistance of the cerebral cortices and without prior training. This suggests an important role for the lower brain stem and spinal cord in generating an appropriate strategy to maintain stability.

The brain in its body: motor control and sensing in a biomechanical context

Although it is widely recognized that adaptive behavior emerges from the ongoing interactions among the nervous system, the body, and the environment, it has only become possible in recent years to experimentally study and to simulate these interacting systems. We briefly review work on molluscan feeding, maintenance of postural control in cats and humans, simulations of locomotion in lamprey, insect, cat and salamander, and active vibrissal sensing in rats to illustrate the insights that can be derived from studies of neural control and sensing within a biomechanical context. These studies illustrate that control may be shared between the nervous system and the periphery, that neural activity organizes degrees of freedom into biomechanically meaningful subsets, that mechanics alone may play crucial roles in enforcing gait patterns, and that mechanics of sensors is crucial for their function.

Neuromechanical tuning of nonlinear postural control dynamics

Postural control may be an ideal physiological motor task for elucidating general questions about the organization, diversity, flexibility, and variability of biological motor behaviors using nonlinear dynamical analysis techniques. Rather than presenting "problems" to the nervous system, the redundancy of biological systems and variability in their behaviors may actually be exploited to allow for the flexible achievement of multiple and concurrent task-level goals associated with movement. Such variability may reflect the constant "tuning" of neuromechanical elements and their interactions for movement control. The problem faced by researchers is that there is no one-to-one mapping between the task goal and the coordination of the underlying elements. We review recent and ongoing research in postural control with the goal of identifying common mechanisms underlying variability in postural control, coordination of multiple postural strategies, and transitions between them. We present a delayed-feedback model used to characterize the variability observed in muscle coordination patterns during postural responses to perturbation. We emphasize the significance of delays in physiological postural systems, requiring the modulation and coordination of both the instantaneous, "passive" response to perturbations as well as the delayed, "active" responses to perturbations. The challenge for future research lies in understanding the mechanisms and principles underlying neuromechanical tuning of and transitions between the diversity of postural behaviors. Here we describe some of our recent and ongoing studies aimed at understanding variability in postural control using physical robotic systems, human experiments, dimensional analysis, and computational models that could be enhanced from a nonlinear dynamics approach.

Reaching to multiple targets when standing: the spatial organization of feedforward postural adjustments

We examined the spatial organization of feedforward postural adjustments produced prior to and during voluntary arm reaching movements executed while standing. We sought to investigate whether the activity of postural muscles before and during reaching was directionally tuned and whether a strategy of horizontal force constraint could be observed. To this end, eight human subjects executed self-paced reach-to-point movements on the random illumination of one of 13 light targets placed within a 180 degrees array centered along the midline of the body. Analysis was divided into two periods: a first corresponding to the 250 ms preceding the onset of the reaching movements (termed pPA period) and a second 250-ms period immediately preceding target attainment (the aPA period). For both periods, electromyographic activity of the lower limb muscles revealed a clear directional tuning, with groups of muscles being activated for similar directions of reach. Analysis of horizontal ground reaction forces supported the existence of a force constraint strategy only for the pPA period, however, with those in the aPA period being more widely dispersed. We suggest that the strategy adopted for feedforward pPAs is one where the tuned muscle synergies constrain the forces diagonally away from the center of mass (CoM) to move it within the support base. However, the need to control for final finger and body position for each target during the aPA phase resulted in a distribution of vectors across reaching directions. Overall, our results would support the idea that endpoint limb force during postural tasks depends on the use of functional muscle synergies, which are used to displace the CoM or decelerate the body at the end of the reach.

Reduction of neuromuscular redundancy for postural force generation using an intrinsic stability criterion

Postural control requires the coordination of multiple muscles to achieve both endpoint force production and postural stability. Multiple muscle activation patterns can produce the required force for standing, but the mechanical stability associated with any given pattern may vary, and has implications for the degree of delayed neural feedback necessary for postural stability. We hypothesized that muscular redundancy is reduced when muscle activation patterns are chosen with respect to intrinsic musculoskeletal stability as well as endpoint force production. We used a three-dimensional musculoskeletal model of the cat hindlimb with 31 muscles to determine the possible contributions of intrinsic muscle properties to limb stability during isometric force generation. Using dynamic stability analysis we demonstrate that within the large set of activation patterns that satisfy the force requirement for posture, only a reduced subset produce a mechanically stable limb configuration. Greater stability in the frontal-plane suggests that neural control mechanisms are more highly active for sagittal-plane and for ankle joint control. Even when the limb was unstable, the time-constants of instability were sufficiently great to allow long-latency neural feedback mechanisms to intervene, which may be preferential for movements requiring maneuverability versus stability. Local joint stiffness of muscles was determined by the stabilizing or destabilizing effects of moment-arm versus joint angle relationships. By preferentially activating muscles with high local stiffness, muscle activation patterns with feedforward stabilizing properties could be selected. Such a strategy may increase intrinsic postural stability without co-contraction, and may be useful criteria in the force-sharing problem.

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.

Inter-joint coupling effects on muscle contributions to endpoint force and acceleration in a musculoskeletal model of the cat hindlimb

The biomechanical principles underlying the organization of muscle activation patterns during standing balance are poorly understood. The goal of this study was to understand the influence of biomechanical inter-joint coupling on endpoint forces and accelerations induced by the activation of individual muscles during postural tasks. We calculated induced endpoint forces and accelerations of 31 muscles in a 7 degree-of-freedom, three-dimensional model of the cat hindlimb. To test the effects of inter-joint coupling, we systematically immobilized the joints (excluded kinematic degrees of freedom) and evaluated how the endpoint force and acceleration directions changed for each muscle in 7 different conditions. We hypothesized that altered inter-joint coupling due to joint immobilization of remote joints would substantially change the induced directions of endpoint force and acceleration of individual muscles. Our results show that for most muscles crossing the knee or the hip, joint immobilization altered the endpoint force or acceleration direction by more than 90 degrees in the dorsal and sagittal planes. Induced endpoint forces were typically consistent with behaviorally observed forces only when the ankle was immobilized. We then activated a proximal muscle simultaneous with an ankle torque of varying magnitude, which demonstrated that the resulting endpoint force or acceleration direction is modulated by the magnitude of the ankle torque. We argue that this simple manipulation can lend insight into the functional effects of co-activating muscles. We conclude that inter-joint coupling may be an essential biomechanical principle underlying the coordination of proximal and distal muscles to produce functional endpoint actions during motor tasks.

Dimensional reduction in sensorimotor systems: a framework for understanding muscle coordination of posture

The simple act of standing up is an important and essential motor behavior that most humans and animals achieve with ease. Yet, maintaining standing balance involves complex sensorimotor transformations that must continually integrate a large array of sensory inputs and coordinate multiple motor outputs to muscles throughout the body. Multiple, redundant local sensory signals are integrated to form an estimate of a few global, task-level variables important to postural control, such as body center of mass (CoM) position and body orientation with respect to Earth-vertical. Evidence suggests that a limited set of muscle synergies, reflecting preferential sets of muscle activation patterns, are used to move task-variables such as CoM position in a predictable direction following postural perturbations. We propose a hierarchical feedback control system that allows the nervous system the simplicity of performing goal-directed computations in task-variable space, while maintaining the robustness afforded by redundant sensory and motor systems. We predict that modulation of postural actions occurs in task-variable space, and in the associated transformations between the low-dimensional task-space and high-dimensional sensor and muscle spaces. Development of neuromechanical models that reflect these neural transformations between low- and high-dimensional representations will reveal the organizational principles and constraints underlying sensorimotor transformations for balance control, and perhaps motor tasks in general. This framework and accompanying computational models could be used to formulate specific hypotheses about how specific sensory inputs and motor outputs are generated and altered following neural injury, sensory loss, or rehabilitation.