Approximating complex musculoskeletal biomechanics using multidimensional autogenerating polynomials.

Computational models of the musculoskeletal system are scientific tools used to study human movement, quantify the effects of injury and disease, plan surgical interventions, or control realistic high-dimensional articulated prosthetic limbs. If the models are sufficiently accurate, they may embed complex relationships within the sensorimotor system. These potential benefits are limited by the challenge of implementing fast and accurate musculoskeletal computations. A typical hand muscle spans over 3 degrees of freedom (DOF), wrapping over complex geometrical constraints that change its moment arms and lead to complex posture-dependent variation in torque generation. Here, we report a method to accurately and efficiently calculate musculotendon length and moment arms across all physiological postures of the forearm muscles that actuate the hand and wrist. Then, we use this model to test the hypothesis that the functional similarities of muscle actions are embedded in muscle structure. The posture dependent muscle geometry, moment arms and lengths of modeled muscles were captured using autogenerating polynomials that expanded their optimal selection of terms using information measurements. The iterative process approximated 33 musculotendon actuators, each spanning up to 6 DOFs in an 18 DOF model of the human arm and hand, defined over the full physiological range of motion. Using these polynomials, the entire forearm anatomy could be computed in <10 µs, which is far better than what is required for real-time performance, and with low errors in moment arms (below 5%) and lengths (below 0.4%). Moreover, we demonstrate that the number of elements in these autogenerating polynomials does not increase exponentially with increasing muscle complexity; complexity increases linearly instead. Dimensionality reduction using the polynomial terms alone resulted in clusters comprised of muscles with similar functions, indicating the high accuracy of approximating models. We propose that this novel method of describing musculoskeletal biomechanics might further improve the applications of detailed and scalable models to describe human movement.

Model of a bilateral Brown-type central pattern generator for symmetric and asymmetric locomotion.

The coordinated activity of muscles is produced in part by spinal rhythmogenic neural circuits, termed central pattern generators (CPGs). A classical CPG model is a system of coupled oscillators that transform locomotor drive into coordinated and gait-specific patterns of muscle recruitment. The network properties of this conceptual model can be simulated by a system of ordinary differential equations with a physiologically inspired coupling locus of interactions capturing the timing relationship for bilateral coordination of limbs in locomotion. Whereas most similar models are solved numerically, it is intriguing to have a full analytical description of this plausible CPG architecture to illuminate the functionality within this structure and to expand it to include steering control. Here, we provided a closed-form analytical solution contrasted against the previous numerical method. The evaluation time of the analytical solution was decreased by an order of magnitude when compared with the numerical approach (relative errors, <0.01%). The analytical solution tested and supported the previous finding that the input to the model can be expressed in units of the desired limb locomotor speed. Furthermore, we performed parametric sensitivity analysis in the context of controlling steering and documented two possible mechanisms associated with either an external drive or intrinsic CPG parameters. The results identify specific propriospinal pathways that may be associated with adaptations within the CPG structure. The model offered several network configurations that may generate the same behavioral outcomes. NEW & NOTEWORTHY Using a simple process of leaky integration, we developed an analytical solution to a robust model of spinal pattern generation. We analyzed the ability of this neural element to exert locomotor control of the signal associated with limb speeds and tested the ability of this simple structure to embed steering control using the velocity signal in the model's inputs or within the internal connectivity of its elements.

Similar Motor Cortical Control Mechanisms for Precise Limb Control during Reaching and Locomotion.

Throughout the course of evolution there has been a parallel development of the complexity and flexibility of the nervous system and the skeletomuscular system that it controls. This development is particularly evident for the cerebral cortical areas and the transformation of the use of the upper limbs from a purely locomotor function to one including, or restricted to, reaching and grasping. This study addresses the issue of whether the control of reaching has involved the development of new cortical circuits or whether the same neurons are used to control both locomotion and reaching. We recorded the activity of pyramidal tract neurons in the motor cortex of the cat both during voluntary gait modifications and during reaching. All cells showed generally similar patterns of activity in both tasks. More specifically, we showed that, in many cases, cells maintained a constant temporal relationship to the activity of synergistic muscle groups in each task. In addition, in some cells the relationship between the intensity of the cell discharge activity and the magnitude of the EMG activity was equally constant during gait modifications and reaching. As such, the results are compatible with the hypothesis that the corticospinal circuits used to control reaching evolved from those used to precisely modify gait.

Muscle anatomy is reflected in the spatial organization of the spinal motoneuron pools.

Neural circuits embed limb dynamics for motor control and sensorimotor integration. The somatotopic organization of motoneuron pools in the spinal cord may support these computations. Here, we tested if the spatial organization of motoneurons is related to the musculoskeletal anatomy. We created a 3D model of motoneuron locations within macaque spinal cord and compared the spatial distribution of motoneurons to the anatomical organization of the muscles they innervate. We demonstrated that the spatial distribution of motoneuron pools innervating the upper limb and the anatomical relationships between the muscles they innervate were similar between macaque and human species. Using comparative analysis, we found that the distances between motoneuron pools innervating synergistic muscles were the shortest, followed by those innervating antagonistic muscles. Such spatial organization can support the co-activation of synergistic muscles and reciprocal inhibition of antagonistic muscles. The spatial distribution of motoneurons may play an important role in embedding musculoskeletal dynamics.

Artificial physics engine for real-time inverse dynamics of arm and hand movement.

Simulating human body dynamics requires detailed and accurate mathematical models. When solved inversely, these models provide a comprehensive description of force generation that considers subject morphology and can be applied to control real-time assistive technology, for example, orthosis or muscle/nerve stimulation. Yet, model complexity hinders the speed of its computations and may require approximations as a mitigation strategy. Here, we use machine learning algorithms to provide a method for accurate physics simulations and subject-specific parameterization. Several types of artificial neural networks (ANNs) with varied architecture were tasked to generate the inverse dynamic transformation of realistic arm and hand movement (23 degrees of freedom). Using a physical model, we generated representative limb movements with bell-shaped end-point velocity trajectories within the physiological workspace. This dataset was used to develop ANN transformations with low torque errors (less than 0.1 Nm). Multiple ANN implementations using kinematic sequences solved accurately and robustly the high-dimensional kinematic Jacobian and inverse dynamics of arm and hand. These results provide further support for the use of ANN architectures that use temporal trajectories of time-delayed values to make accurate predictions of limb dynamics.

Does joint impedance improve dynamic leg simulations with explicit and implicit solvers?

The nervous system predicts and executes complex motion of body segments actuated by the coordinated action of muscles. When a stroke or other traumatic injury disrupts neural processing, the impeded behavior has not only kinematic but also kinetic attributes that require interpretation. Biomechanical models could allow medical specialists to observe these dynamic variables and instantaneously diagnose mobility issues that may otherwise remain unnoticed. However, the real-time and subject-specific dynamic computations necessitate the optimization these simulations. In this study, we explored the effects of intrinsic viscoelasticity, choice of numerical integration method, and decrease in sampling frequency on the accuracy and stability of the simulation. The bipedal model with 17 rotational degrees of freedom (DOF)-describing hip, knee, ankle, and standing foot contact-was instrumented with viscoelastic elements with a resting length in the middle of the DOF range of motion. The accumulation of numerical errors was evaluated in dynamic simulations using swing-phase experimental kinematics. The relationship between viscoelasticity, sampling rates, and the integrator type was evaluated. The optimal selection of these three factors resulted in an accurate reconstruction of joint kinematics (err < 1%) and kinetics (err < 5%) with increased simulation time steps. Notably, joint viscoelasticity reduced the integration errors of explicit methods and had minimal to no additional benefit for implicit methods. Gained insights have the potential to improve diagnostic tools and accurize real-time feedback simulations used in the functional recovery of neuromuscular diseases and intuitive control of modern prosthetic solutions.

Does joint impedance improve dynamic leg simulations with explicit and implicit solvers?

The nervous system predicts and executes complex motion of body segments actuated by the coordinated action of muscles. When a stroke or other traumatic injury disrupts neural processing, the impeded behavior has not only kinematic but also kinetic attributes that require interpretation. Biomechanical models could allow medical specialists to observe these dynamic variables and instantaneously diagnose mobility issues that may otherwise remain unnoticed. However, the real-time and subject-specific dynamic computations necessitate the optimization these simulations. In this study, we explored the effects of intrinsic viscoelasticity, choice of numerical integration method, and decrease in sampling frequency on the accuracy and stability of the simulation. The bipedal model with 17 rotational degrees of freedom (DOF)-describing hip, knee, ankle, and standing foot contact-was instrumented with viscoelastic elements with a resting length in the middle of the DOF range of motion. The accumulation of numerical errors was evaluated in dynamic simulations using swing-phase experimental kinematics. The relationship between viscoelasticity, sampling rates, and the integrator type was evaluated. The optimal selection of these three factors resulted in an accurate reconstruction of joint kinematics (err < 1%) and kinetics (err < 5%) with increased simulation time steps. Notably, joint viscoelasticity reduced the integration errors of explicit methods and had minimal to no additional benefit for implicit methods . Gained insights have the potential to improve diagnostic tools and accurize real-time feedback simulations used in the functional recovery of neuromuscular diseases and intuitive control of modern prosthetic solutions.

Surface Electromyography Provides Neuromuscular Insights for Skill Acquisition in Microgravity.

The human motor system has evolved to perform efficient motor control in Earth's gravity. Altered gravity environments, such as microgravity and hypergravity, pose unique challenges for performing fine motor tasks with object manipulation. Altered gravity has been shown to reduce the speed and accuracy of complex manual tasks. This study aims to leverage electromyography (EMG) and virtual reality (VR) technologies to provide insights into the neuromuscular mechanism of object weight compensation. Seven healthy subjects were recruited to perform arm and hand movements, including a customized Box and Block Test with three different block weights, 0 (VR), 0.02, and 0.1 kg. EMG was recorded from 15 muscles of arm and hand while manipulating objects instrumented with force sensors to collect contact forces. Muscle co-contraction extracted from EMGs of antagonistic muscles was used as a measure of joint stiffness for each task. Results show that the co-contraction levels increased in the task with the heavy object and decreased in the VR task. This relationship suggests that the internal expectations of the object weight and the proprioceptive and haptic feedback from the contact with the object are driving the co-contraction of antagonistic muscles.

Young adults perceive small disturbances to their walking balance even when distracted.

BACKGROUND: The ability to perceive disturbances to ongoing locomotion (e.g., slips and trips) may play an important role in walking balance control. However, how well young adults can perceive such disturbances is unknown. RESEARCH QUESTION: The purpose of this study was to identify the perception threshold in young adults to subtle slip-like locomotor disturbances. METHODS: Subjects (n = 12) walked on a split-belt treadmill performing a perturbation discrimination task at their preferred walking speed while randomly experiencing locomotor balance disturbances every 8-12 strides. Balance disturbances were imposed through a short-duration decrease in velocity of a single treadmill belt triggered at heel-strike. The treadmill belt returned to the subject's preferred walking speed during the subsequent swing phase. Locomotor disturbances were given with eight different velocity changes ranging from 0 to 0.4 m/s and were randomized and repeated 5 times. Subjects were prompted to respond when asked if they perceived each disturbance. Using a psychophysical approach, we determined the perception thresholds of slip-like locomotor disturbances (i.e., just noticeable difference). The perturbation discrimination task was repeated with subjects performing a secondary cognitive distraction (counting backward by threes). RESULTS: Subjects perceived small locomotor disturbances during both normal walking (dominant: 0.07 ± 0.03 m/s, non-dominant: 0.08 ± 0.03 m/s) and while performing the secondary cognitive task (dominant: 0.08 ± 0.01 m/s, non-dominant: 0.09 ± 0.02 m/s). There was no significant difference between legs (p = 0.466), with the addition of the cognitive task (p = 0.08), or interaction between leg and task (p = 0.994). SIGNIFICANCE: The ability to perceive subtle slip-like locomotor disturbances was maintained even when performing a cognitively distracting task, suggesting that young adults can perceive very small locomotor disturbances.

Compensatory Strategies Due to Knee Flexion Constraint during Gait of Non-Disabled Adults.

Constraining knee flexion of non-disabled individuals could further our understanding regarding the importance of knee joint during gait, which is a common disturbance in individuals with gait impairment. In this study we investigated whether a mechanical constraint of knee flexion in non-disabled adults would lead to compensatory strategies. Eleven non-disabled male adults walked without and with an orthosis that permitted full extension and limited knee flexion up to either 45° or 30°. We analyzed the temporal organization of lower limb kinematics and electromyograms of the rectus femoris, vastus medialis and lateralis, tibialis anterior, semitendinosus, biceps femoris, and gastrocnemius medialis and lateralis. Non-disabled adults compensated for the reduced knee flexion by increasing hip and ankle joint excursions and ankle flexor activation amplitude. Also, these adults shortened pre-swing and lengthened swing duration in the constrained limb and increased the activity of bifunctional hip extensor and knee flexor muscles in the constrained limb in relation to the unconstrained limb. The use of an orthosis that limited knee flexion in non-disabled adults leaded to compensatory strategies in the temporal organization of joint excursions and muscle activations in the constrained limb. The compensatory effects were correlated with the extent of knee flexion constraint.

Sequential activation of motor cortical neurons contributes to intralimb coordination during reaching in the cat by modulating muscle synergies.

We examined the contribution of the motor cortex to the control of intralimb coordination during reaching in the standing cat. We recorded the activity of 151 pyramidal tract neurons (PTNs) in the forelimb representation of three cats during a task in which the cat reached forward from a standing position to press a lever. We simultaneously recorded the activity of muscles in the contralateral forelimb acting around each of the major joints. Cell activity was recorded with and without the presence of an obstacle requiring a modification of limb trajectory. The majority of the PTNs (134/151, 89%) modulated their discharge activity at some period of the reach while 84/151 (56%) exhibited a significant peak or trough of activity as the limb was transported from its initial position to the lever. These phasic changes of activity were distributed sequentially throughout the transport phase. A cluster analysis of muscle activity in two of the cats showed the presence of five muscle synergies during this transport period. One of the synergies was related to the lift of the paw from the support surface, two to flexion of the limb and dorsiflexion of the paw, one to preparation for contact with the lever, and one to the transport of the entire limb forward; a sixth synergy was activated during the lever press. An analysis of the phase of cell activity with respect to the phase of activity of muscles selected to represent each of these synergies showed that different populations of PTNs were activated sequentially and coincidentally with each synergy. We suggest that this sequential activation of populations of PTNs is compatible with a contribution to the initiation and modulation of functionally distinct groups of synergistic muscles and ultimately serves to ensure the appropriate multiarticular, intralimb coordination of the limb during reaching.

Solving musculoskeletal biomechanics with machine learning.

Deep learning is a relatively new computational technique for the description of the musculoskeletal dynamics. The experimental relationships of muscle geometry in different postures are the high-dimensional spatial transformations that can be approximated by relatively simple functions, which opens the opportunity for machine learning (ML) applications. In this study, we challenged general ML algorithms with the problem of approximating the posture-dependent moment arm and muscle length relationships of the human arm and hand muscles. We used two types of algorithms, light gradient boosting machine (LGB) and fully connected artificial neural network (ANN) solving the wrapping kinematics of 33 muscles spanning up to six degrees of freedom (DOF) each for the arm and hand model with 18 DOFs. The input-output training and testing datasets, where joint angles were the input and the muscle length and moment arms were the output, were generated by our previous phenomenological model based on the autogenerated polynomial structures. Both models achieved a similar level of errors: ANN model errors were 0.08 ± 0.05% for muscle lengths and 0.53 ± 0.29% for moment arms, and LGB model made similar errors-0.18 ± 0.06% and 0.13 ± 0.07%, respectively. LGB model reached the training goal with only 103 samples, while ANN required 106 samples; however, LGB models were about 39 times slower than ANN models in the evaluation. The sufficient performance of developed models demonstrates the future applicability of ML for musculoskeletal transformations in a variety of applications, such as in advanced powered prosthetics.

Quantifying Performance in Robotic Surgery Training Using Muscle-Based Activity Metrics.

Training to perform robotic surgery is time-consuming with uncertain metrics of the level of achieved skill. We tested the feasibility of using muscle co-contraction as a metric to quantify robotic surgical skill in a virtual simulation environment. We recruited six volunteers with varying skill levels in robotic surgery. The volunteers performed virtual tasks using a robotic console while we recorded their muscle activity. A co-contraction metric was then derived from the activity of pairs of opposing hand muscles and compared to the scores assigned by the training software. We found that muscle-based metrics were more sensitive than motion-based scores in quantifying the different levels of skill between simulated tasks and in novices vs. experts across different tasks. Therefore, muscle-based metrics may help quantify in general terms the level of robotic surgical skill and could potentially be used for biofeedback to increase the rate of learning.

A segmented forearm model of hand pronation-supination approximates joint moments for real time applications.

Musculoskeletal modeling is a new computational tool to reverse engineer human control systems, which require efficient algorithms running in real-time. Human hand pronation-supination movement is accomplished by movement of the radius and ulna bones relative to each other via the complex proximal and distal radioulnar joints, each with multiple degrees of freedom (DOFs). Here, we report two simplified models of this complex kinematic transformation implemented as a part of a 20 DOF model of the hand and forearm. The pronation/supination DOF was implemented as a single rotation joint either within the forearm segment or separating proximal and distal parts of the forearm segment. Torques produced by the inverse dynamic simulations with anatomical architecture of the forearm (OpenSim model) were used as the "gold standard" in the comparison of two simple models. Joint placement was iteratively optimized to achieve the closest representation of torques during realistic hand movements. The model with a split forearm segment performed better than the model with a solid forearm segment in simulating pronation/supination torques. We conclude that simplifying pronation/supination DOF as a single-axis rotation between arm segments is a viable strategy to reduce the complexity of multi-DOF dynamic simulations.

Computational evidence for nonlinear feedforward modulation of fusimotor drive to antagonistic co-contracting muscles.

The sensorimotor integration during unconstrained reaching movements in the presence of variable environmental forces remains poorly understood. The objective of this study was to quantify how much the primary afferent activity of muscle spindles can contribute to shaping muscle coactivation patterns during reaching movements with complex dynamics. To achieve this objective, we designed a virtual reality task that guided healthy human participants through a set of planar reaching movements with controlled kinematic and dynamic conditions that were accompanied by variable muscle co-contraction. Next, we approximated the Ia afferent activity using a phenomenological model of the muscle spindle and muscle lengths derived from a musculoskeletal model. The parameters of the spindle model were altered systematically to evaluate the effect of fusimotor drive on the shape of the temporal profile of afferent activity during movement. The experimental and simulated data were analyzed with hierarchical clustering. We found that the pattern of co-activation of agonistic and antagonistic muscles changed based on whether passive forces in each movement played assistive or resistive roles in limb dynamics. The reaching task with assistive limb dynamics was associated with the most muscle co-contraction. In contrast, the simulated Ia afferent profiles were not changing between tasks and they were largely reciprocal with homonymous muscle activity. Simulated physiological changes to the fusimotor drive were not sufficient to reproduce muscle co-contraction. These results largely rule out the static set and α-γ coactivation as the main types of fusimotor drive that transform the monosynaptic Ia afferent feedback into task-dependent co-contraction of antagonistic muscles. We speculate that another type of nonlinear transformation of Ia afferent signals that is independent of signals modulating the activity of α motoneurons is required for Ia afferent-based co-contraction. This transformation could either be applied through a complex nonlinear profile of fusimotor drive that is not yet experimentally observed or through presynaptic inhibition.

Cortical mechanisms involved in visuomotor coordination during precision walking.

Goal-directed locomotion, in particular in situations where there is a need to step over or around obstacles, is largely guided by visual information. To negotiate an obstacle successfully, subjects must first plan how to perform the movement and then must execute that plan. In cats, this information must also be stored and used to guide the hindlimbs, which are moved in the absence of direct visual input. Experiments in cats have shown that the motor cortex makes an important contribution to the execution of gait modifications and is involved both in specifying limb trajectory and, when necessary, where the paw will be placed. We suggest that, in both situations, subpopulations of pyramidal tract neurons in the motor cortex act to regulate the duration, level and timing of small groups of synergistic muscles, active at different times during the gait modification. However, the available evidence suggests that the motor cortex plays little role in the planning of these gait modifications. Instead, recent work suggests that the posterior parietal cortex (PPC) may contribute to this function. In agreement with this proposal, we have found that lesions to this structure lead to errors in forelimb placement in front of an advancing obstacle and may produce deficits in forelimb-hindlimb coordination. Single-unit recordings from neurons in the PPC support a role for the PPC in these two aspects of visually guided locomotion and further show that the signal in this structure might be limb-independent.

Analytical CPG model driven by limb velocity input generates accurate temporal locomotor dynamics.

The ability of vertebrates to generate rhythm within their spinal neural networks is essential for walking, running, and other rhythmic behaviors. The central pattern generator (CPG) network responsible for these behaviors is well-characterized with experimental and theoretical studies, and it can be formulated as a nonlinear dynamical system. The underlying mechanism responsible for locomotor behavior can be expressed as the process of leaky integration with resetting states generating appropriate phases for changing body velocity. The low-dimensional input to the CPG model generates the bilateral pattern of swing and stance modulation for each limb and is consistent with the desired limb speed as the input command. To test the minimal configuration of required parameters for this model, we reduced the system of equations representing CPG for a single limb and provided the analytical solution with two complementary methods. The analytical and empirical cycle durations were similar (R 2 = 0.99) for the full range of walking speeds. The structure of solution is consistent with the use of limb speed as the input domain for the CPG network. Moreover, the reciprocal interaction between two leaky integration processes representing a CPG for two limbs was sufficient to capture fundamental experimental dynamics associated with the control of heading direction. This analysis provides further support for the embedded velocity or limb speed representation within spinal neural pathways involved in rhythm generation.

A novel method of identifying motor primitives using wavelet decomposition.

This study reports a new technique for extracting muscle synergies using continuous wavelet transform. The method allows to quantify coincident activation of muscle groups caused by the physiological processes of fixed duration, thus enabling the extraction of wavelet modules of arbitrary groups of muscles. Hierarchical clustering and identification of the repeating wavelet modules across subjects and across movements, was used to identify consistent muscle synergies. Results indicate that the most frequently repeated wavelet modules comprised combinations of two muscles that are not traditional agonists and span different joints. We have also found that these wavelet modules were flexibly combined across different movement directions in a pattern resembling directional tuning. This method is extendable to multiple frequency domains and signal modalities.

Correction: Biomechanical Constraints Underlying Motor Primitives Derived from the Musculoskeletal Anatomy of the Human Arm.

[This corrects the article DOI: 10.1371/journal.pone.0164050.].

The neuromechanical tuning hypothesis.

Simulations performed with neuromechanical models are providing insight into the neural control of locomotion that would be hard if not impossible to obtain in any other way. We first discuss the known properties of the neural mechanisms controlling locomotion, with a focus on mammalian systems. The rhythm-generating properties of central pattern generators (CPGs) are discussed in light of results indicating that cycle characteristics may be preset by tonic drive to spinal interneuronal networks. We then describe neuromechanical simulations that have revealed some basic rules of interaction between CPGs, sensory-mediated switching mechanisms and the biomechanics of locomotor movements. We posit that the spinal CPG timer and the sensory-mediated switch operate in parallel, the former being driven primarily by descending inputs and the latter by the kinematics. The CPG timer produces extensor and flexor phase durations, which covary along specific lines in a plot of phase- versus cycle-duration. We coined the term "phase-duration characteristics" to describe such plots. Descending input from higher centers adjusts the operating points on the phase-duration characteristics according to anticipated biomechanical requirements. In well-predicted movements, CPG-generated phase durations closely match those required by the kinematics, minimizing the corrections in phase duration required of the sensory switching mechanism. We propose the term "neuromechanical tuning" to describe this process of matching the CPG to the kinematics.