Directional constraint of endpoint force emerges from hindlimb anatomy

Late acquisition of erect hindlimb posture and function in the forerunners of therian mammals

The evolutionary transition from early synapsids to therian mammals involved profound reorganization in locomotor anatomy and function, centered around a shift from "sprawled" to "erect" limb postures. When and how this functional shift was accomplished has remained difficult to decipher from the fossil record alone. Through biomechanical modeling of hindlimb force-generating performance in eight exemplar fossil synapsids, we demonstrate that the erect locomotor regime typifying modern therians did not evolve until just before crown Theria. Modeling also identifies a transient phase of increased performance in therapsids and early cynodonts, before crown mammals. Further, quantifying the global actions of major hip muscle groups indicates a protracted juxtaposition of functional redeployment and conservatism, highlighting the intricate interplay between anatomical reorganization and function across postural transitions. We infer a complex history of synapsid locomotor evolution and suggest that major evolutionary transitions between contrasting locomotor behaviors may follow highly nonlinear trajectories.

ROLE OF FORELIMB MORPHOLOGY IN MUSCLE SENSORIMOTOR FUNCTIONS DURING LOCOMOTION IN THE CAT

Previous studies established strong links between morphological characteristics of mammalian hindlimb muscles and their sensorimotor functions during locomotion. Less is known about the role of forelimb morphology in motor outputs and generation of sensory signals. Here, we measured morphological characteristics of 46 forelimb muscles from 6 cats. These characteristics included muscle attachments, physiological cross-sectional area (PCSA), fascicle length, etc. We also recorded full-body mechanics and EMG activity of forelimb muscles during level overground and treadmill locomotion in 7 and 16 adult cats of either sex, respectively. We computed forelimb muscle forces along with force- and length-dependent sensory signals mapped onto corresponding cervical spinal segments. We found that patterns of computed muscle forces and afferent activities were strongly affected by the muscle's moment arm, PCSA, and fascicle length. Morphology of the shoulder muscles suggests distinct roles of the forelimbs in lateral force production and movements. Patterns of length-dependent sensory activity of muscles with long fibers (brachioradialis, extensor carpi radialis) closely matched patterns of overall forelimb length, whereas the activity pattern of biceps brachii matched forelimb orientation. We conclude that cat forelimb muscle morphology contributes substantially to locomotor function, particularly to control lateral stability and turning, rather than propulsion.

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.

Movement goals encoded within the cortex and muscle synergies to reduce redundancy pre and post-stroke. The relevance for gait rehabilitation and the prescription of walking-aids. A literature review and scholarly discussion

Current knowledge of neural and neuromuscular processes controlling gait and movement as well as an understanding of how these mechanisms change following stroke is an important basis for the development of effective rehabilitation interventions. To support the translation of findings from basic research into useful treatments in clinical practice, up-to-date neuroscience should be presented in forms accessible to all members of the multidisciplinary team. In this review we discuss aspects of cortical control of gait and movement, muscle synergies as a way of translating cortical commands into specific muscle activity and as an efficient means of reducing neural and musculoskeletal redundancy. We discuss how these mechanisms change following stroke, potential consequences for gait rehabilitation, and the prescription and use of walking-aids as well as areas requiring further research.

Musculoskeletal geometry accounts for apparent extrinsic representation of paw position in dorsal spinocerebellar tract

Proprioception, the sense of limb position and motion, arises from individual muscle receptors. An important question is how and where in the neuroaxis our high level "extrinsic" sense of limb movement originates. In the 1990s, a series of papers detailed the properties of neurons in the dorsal spinocerebellar tract (DSCT) of the cat. Despite their direct projections from sensory receptors, it appeared that half of these neurons had consistent, high-level tuning to paw position rather than to joint angles (or muscle lengths). These results suggested that many DSCT neurons compute paw position from lower level sensory information. We examined the contribution of musculoskeletal geometry to this apparent extrinsic representation by simulating a three-joint hindlimb with mono- and biarticular muscles, each providing a muscle spindlelike signal, modulated by the muscle length. We simulated neurons driven by randomly weighted combinations of these signals and moved the paw to different positions under two joint-covariance conditions similar to the original experiments. Our results paralleled those experiments in a number of respects: 1) Many neurons were tuned to paw position relative to the hip under both conditions. 2) The distribution of tuning was strongly bimodal, with most neurons driven by whole-leg flexion or extension. 3) The change in tuning between conditions clustered around zero (median absolute change ~20°). These results indicate that, at least for these constraint conditions, extrinsic-like representation can be achieved simply through musculoskeletal geometry and convergent muscle length inputs. Consequently, they suggest a reinterpretation of the earlier results may be required.NEW & NOTEWORTHY A classic experiment concluding that many dorsal spinocerebellar tract neurons encode paw position rather than joint angles has been cited by many studies as evidence for high-level computation occurring within a single synapse of the sensors. However, our study provides evidence that such a computation is not required to explain the results. Using simulation, we replicated many of the original results with purely random connectivity, suggesting that a reinterpretation of the classic experiment is needed.

Hip and ankle responses for reactive balance emerge from varying priorities to reduce effort and kinematic excursion: A simulation study

Although standing balance is important in many daily activities, there has been little effort in developing detailed musculoskeletal models and simulations of balance control compared to other whole-body motor activities. Our objective was to develop a musculoskeletal model of human balance that can be used to predict movement patterns in reactive balance control. Similar to prior studies using torque-driven models, we investigated how movement patterns during a reactive balance response are affected by high-level task goals (e.g., reducing center-of-mass movement, maintaining vertical trunk orientation, and minimizing effort). We generated 23 forward dynamics simulations where optimal muscle excitations were found using cost functions with different weights on minimizing these high-level goals. Variations in hip and ankle angles observed experimentally (peak hip flexion=7.9-53.1°, peak dorsiflexion=0.5-4.7°) could be predicted by varying the priority of these high-level goals. More specifically, minimizing center-of-mass motion produced a hip strategy (peak hip flexion and ankle dorsiflexion angles of 45.5° and 2.3°, respectively) and the response shifted towards an ankle strategy as the priority to keep the trunk vertical was increased (peak hip and ankle angles of 13.7° and 8.5°, respectively). We also found that increasing the priority to minimize muscle stress always favors a hip strategy. These results are similar to those from sagittal-plane torque-driven models. Our muscle-actuated model facilitates the investigation of neuromechanical interactions governing reactive balance control to predict muscle activity and movement patterns based on interactions between neuromechanical elements such as spinal reflexes, muscle short-range stiffness, and task-level sensorimotor feedback.

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.

Accurate stepping on a narrow path: mechanics, EMG, and motor cortex activity in the cat

How do cats manage to walk so graciously on top of narrow fences or windowsills high above the ground while apparently exerting little effort? In this study we investigated cat full-body mechanics and the activity of limb muscles and motor cortex during walking along a narrow 5-cm path on the ground. We tested the hypotheses that during narrow walking 1) lateral stability would be lower because of the decreased base-of-support area and 2) the motor cortex activity would increase stride-related modulation because of imposed demands on lateral stability and paw placement accuracy. We measured medio-lateral and rostro-caudal dynamic stability derived from the extrapolated center of mass position with respect to the boundaries of the support area. We found that cats were statically stable in the frontal plane during both unconstrained and narrow-path walking. During narrow-path walking, cats walked slightly slower with more adducted limbs, produced smaller lateral forces by hindlimbs, and had elevated muscle activities. Of 174 neurons recorded in cortical layer V, 87% of forelimb-related neurons (from 114) and 90% of hindlimb-related neurons (from 60) had activities during narrow-path walking distinct from unconstrained walking: more often they had a higher mean discharge rate, lower depth of stride-related modulation, and/or longer period of activation during the stride. These activity changes appeared to contribute to control of accurate paw placement in the medio-lateral direction, the width of the stride, rather than to lateral stability control, as the stability demands on narrow-path and unconstrained walking were similar.

Body stability and muscle and motor cortex activity during walking with wide stance

Biomechanical and neural mechanisms of balance control during walking are still poorly understood. In this study, we examined the body dynamic stability, activity of limb muscles, and activity of motor cortex neurons [primarily pyramidal tract neurons (PTNs)] in the cat during unconstrained walking and walking with a wide base of support (wide-stance walking). By recording three-dimensional full-body kinematics we found for the first time that during unconstrained walking the cat is dynamically unstable in the forward direction during stride phases when only two diagonal limbs support the body. In contrast to standing, an increased lateral between-paw distance during walking dramatically decreased the cat's body dynamic stability in double-support phases and prompted the cat to spend more time in three-legged support phases. Muscles contributing to abduction-adduction actions had higher activity during stance, while flexor muscles had higher activity during swing of wide-stance walking. The overwhelming majority of neurons in layer V of the motor cortex, 82% and 83% in the forelimb and hindlimb representation areas, respectively, were active differently during wide-stance walking compared with unconstrained condition, most often by having a different depth of stride-related frequency modulation along with a different mean discharge rate and/or preferred activity phase. Upon transition from unconstrained to wide-stance walking, proximal limb-related neuronal groups subtly but statistically significantly shifted their activity toward the swing phase, the stride phase where most of body instability occurs during this task. The data suggest that the motor cortex participates in maintenance of body dynamic stability during locomotion.

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.

Stability radius as a method for comparing the dynamics of neuromechanical systems

Robust motor behaviors emerge from neuromechanical interactions that are nonlinear, have delays, and contain redundant neural and biomechanical components. For example, in standing balance a subject's muscle activity (neural control) decreases as stance width (biomechanics) increases when responding to a lateral perturbation, yet the center-of-mass motion (behavior) is nearly identical regardless of stance width. We present stability radius, a technique from robust control theory, to overcome the limitations of classical stability analysis tools, such as gain margin, which are insufficient for predicting how concurrent changes in both biomechanics (plant) and neural control (controller) affect system behavior. We first present the theory and then an application to a neuromechanical model of frontal-plane standing balance with delayed feedback. We show that stability radius can quantify differences in the sensitivity of system behavior to parameter changes, and predict that narrowing stance width increases system robustness. We further demonstrate that selecting combinations of stance width (biomechanics) and feedback gains (neural control) that have the same stability radius produce similar center-of-mass behavior in simulation. Therefore, stability radius may provide a useful tool for understanding neuromechanical interactions in movement and could aid in the design of devices and therapies for improving motor function.

Practical limits on muscle synergy identification by non-negative matrix factorization in systems with mechanical constraints

Statistical decomposition, including non-negative matrix factorization (NMF), is a convenient tool for identifying patterns of structured variability within behavioral motor programs, but it is unclear how the resolved factors relate to actual neural structures. Factors can be extracted from a uniformly sampled, low-dimension command space. In practical application, the command space is limited, either to those activations that perform some task(s) successfully or to activations induced in response to specific perturbations. NMF was applied to muscle activation patterns synthesized from low dimensional, synergy-like control modules mimicking simple task performance or feedback activation from proprioceptive signals. In the task-constrained paradigm, the accuracy of control module recovery was highly dependent on the sampled volume of control space, such that sampling even 50% of control space produced a substantial degradation in factor accuracy. In the feedback paradigm, NMF was not capable of extracting more than four control modules, even in a mechanical model with seven internal degrees of freedom. Reduced access to the low-dimensional control space imposed by physical constraints may result in substantial distortion of an existing low dimensional controller, such that neither the dimensionality nor the composition of the recovered/extracted factors match the original controller.

Review and perspective: neuromechanical considerations for predicting muscle activation patterns for movement

Muscle coordination may be difficult or impossible to predict accurately based on biomechanical considerations alone because of redundancy in the musculoskeletal system. Because many solutions exist for any given movement, the role of the nervous system in further constraining muscle coordination patterns for movement must be considered in both healthy and impaired motor control. On the basis of computational neuromechanical analyses of experimental data combined with modeling techniques, we have demonstrated several such neural constraints on the temporal and spatial patterns of muscle activity during both locomotion and postural responses to balance perturbations. We hypothesize that subject-specific and trial-by-trial differences in muscle activation can be parameterized and understood by a hierarchical and low-dimensional framework that reflects the neural control of task-level goals. In postural control, we demonstrate that temporal patterns of muscle activity may be governed by feedback control of task-level variables that represent the overall goal-directed motion of the body. These temporal patterns then recruit spatially-fixed patterns of muscle activity called muscle synergies that produce the desired task-level biomechanical functions that require multijoint coordination. Moreover, these principles apply more generally to movement, and in particular to locomotor tasks in both healthy and impaired individuals. Overall, understanding the goals and organization of the neural control of movement may provide useful reduced dimension parameter sets to address the degrees-of-freedom problem in musculoskeletal movement control. More importantly, however, neuromechanical analyses may lend insight and provide a framework for understanding subject-specific and trial-by-trial differences in movement across both healthy and motor-impaired populations.

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.