Sensitivity analyses of probabilistic and deterministic DTI tractography methodologies for studying arm muscle architecture.

PURPOSE: To determine the sensitivity profiles of probabilistic and deterministic DTI tractography methods in estimating geometric properties in arm muscle anatomy. METHODS: Spin-echo diffusion-weighted MR images were acquired in the dominant arm of 10 participants. Both deterministic and probabilistic tractography were performed in two different muscle architectures of the parallel-structured biceps brachii (and the pennate-structured flexor carpi ulnaris. Muscle fascicle geometry estimates and number of fascicles were evaluated with respect to tractography turning angle, polynomial fitting order, and SNR. The DTI tractography estimated fascicle lengths were compared with measurements obtained from conventional cadaveric dissection and ultrasound modalities. RESULTS: The probabilistic method generally estimated fascicle lengths closer to ranges reported by conventional methods than the deterministic method, most evident in the biceps brachii (p > 0.05), consisting of longer, arc-like fascicles. For both methods, a wide turning angle (50º-90°) generated fascicle lengths that were in close agreement with conventional methods, most evident in the flexor carpi ulnaris (p > 0.05), consisting of shorter, feather-like fascicles. The probabilistic approach produced at least two times more fascicles than the deterministic approach. For both approaches, second-order fitting yielded about double the complete tracts as third-order fitting. In both muscles, as SNR decreased, deterministic tractography produced less fascicles but consistent geometry (p > 0.05), whereas probabilistic tractography produced a consistent number but altered geometry of fascicles (p < 0.001). CONCLUSION: Findings from this study provide best practice recommendations for implementing DTI tractography in skeletal muscle and will inform future in vivo studies of healthy and pathological muscle structure.

Stretch reflex gain scaling at the shoulder varies with synergistic muscle activity.

The unique anatomy of the shoulder allows for expansive mobility but also sometimes precarious stability. It has long been suggested that stretch-sensitive reflexes contribute to maintaining joint stability through feedback control, but little is known about how stretch-sensitive reflexes are coordinated between the muscles of the shoulder. The purpose of this study was to investigate the coordination of stretch reflexes in shoulder muscles elicited by rotations of the glenohumeral joint. We hypothesized that stretch reflexes are sensitive to not only a given muscle's background activity but also the aggregate activity of all muscles crossing the shoulder based on the different groupings of muscles required to actuate the shoulder in three rotational degrees of freedom. We examined the relationship between a muscle's background activity and its reflex response in eight shoulder muscles by applying rotational perturbations while participants produced voluntary isometric torques. We found that this relationship, defined as gain scaling, differed at both short and long latencies based on the direction of voluntary torque generated by the participant. Therefore, gain scaling differed based on the aggregate of muscles that were active, not just the background activity in the muscle within which the reflex was measured. Across all muscles, the consideration of torque-dependent gain scaling improved model fits (ΔR2) by 0.17 ± 0.12. Modulation was most evident when volitional torques and perturbation directions were aligned along the same measurement axis, suggesting a functional role in resisting perturbations among synergists while maintaining task performance.NEW & NOTEWORTHY Careful coordination of muscles crossing the shoulder is needed to maintain the delicate balance between the joint's mobility and stability. We provide experimental evidence that stretch reflexes within shoulder muscles are modulated based on the aggregate activity of muscles crossing the joint, not just the activity of the muscle in which the reflex is elicited. Our results reflect coordination through neural coupling that may help maintain shoulder stability during encounters with environmental perturbations.

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.

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.

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.

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.

Neuromechanic: a computational platform for simulation and analysis of the neural control of movement.

Neuromusculoskeletal models solve the basic problem of determining how the body moves under the influence of external and internal forces. Existing biomechanical modeling programs often emphasize dynamics with the goal of finding a feed-forward neural program to replicate experimental data or of estimating force contributions or individual muscles. The computation of rigid-body dynamics, muscle forces, and activation of the muscles are often performed separately. We have developed an intrinsically forward computational platform (Neuromechanic, www.neuromechanic.com) that explicitly represents the interdependencies among rigid body dynamics, frictional contact, muscle mechanics, and neural control modules. This formulation has significant advantages for optimization and forward simulation, particularly with application to neural controllers with feedback or regulatory features. Explicit inclusion of all state dependencies allows calculation of system derivatives with respect to kinematic states and muscle and neural control states, thus affording a wealth of analytical tools, including linearization, stability analyses and calculation of initial conditions for forward simulations. In this review, we describe our algorithm for generating state equations and explain how they may be used in integration, linearization, and stability analysis tools to provide structural insights into the neural control of movement.