Feasibility Theory Reconciles and Informs Alternative Approaches to Neuromuscular Control

A computational study of how an α- to γ-motoneurone collateral can mitigate velocity-dependent stretch reflexes during voluntary movement

The primary motor cortex does not uniquely or directly produce alpha motoneurone (α-MN) drive to muscles during voluntary movement. Rather, α-MN drive emerges from the synthesis and competition among excitatory and inhibitory inputs from multiple descending tracts, spinal interneurons, sensory inputs, and proprioceptive afferents. One such fundamental input is velocity-dependent stretch reflexes in lengthening muscles, which should be inhibited to enable voluntary movement. It remains an open question, however, the extent to which unmodulated stretch reflexes disrupt voluntary movement, and whether and how they are inhibited in limbs with numerous multiarticular muscles. We used a computational model of a Rhesus Macaque arm to simulate movements with feedforward α-MN commands only, and with added velocity-dependent stretch reflex feedback. We found that velocity-dependent stretch reflex caused movement-specific, typically large and variable disruptions to arm movements. These disruptions were greatly reduced when modulating velocity-dependent stretch reflex feedback (i) as per the commonly proposed (but yet to be clarified) idealized alpha-gamma (α-γ) coactivation or (ii) an alternative α-MN collateral projection to homonymous γ-MNs. We conclude that such α-MN collaterals are a physiologically tenable propriospinal circuit in the mammalian fusimotor system. These collaterals could still collaborate with α-γ coactivation, and the few skeletofusimotor fibers (β-MNs) in mammals, to create a flexible fusimotor ecosystem to enable voluntary movement. By locally and automatically regulating the highly nonlinear neuro-musculo-skeletal mechanics of the limb, these collaterals could be a critical low-level enabler of learning, adaptation, and performance via higher-level brainstem, cerebellar, and cortical mechanisms.

An alpha- to gamma-motoneurone collateral can mitigate velocity-dependent stretch reflexes during voluntary movement: A computational study

The primary motor cortex does not uniquely or directly produce alpha motoneurone (α-MN) drive to muscles during voluntary movement. Rather, α-MN drive emerges from the synthesis and competition among excitatory and inhibitory inputs from multiple descending tracts, spinal interneurons, sensory inputs, and proprioceptive afferents. One such fundamental input is velocity-dependent stretch reflexes in lengthening muscles, which should be inhibited to enable voluntary movement. It remains an open question, however, the extent to which unmodulated stretch reflexes disrupt voluntary movement, and whether and how they are inhibited in limbs with numerous multi-articular muscles. We used a computational model of a Rhesus Macaque arm to simulate movements with feedforward α-MN commands only, and with added velocity-dependent stretch reflex feedback. We found that velocity-dependent stretch reflex caused movement-specific, typically large and variable disruptions to arm movements. These disruptions were greatly reduced when modulating velocity-dependent stretch reflex feedback (i) as per the commonly proposed (but yet to be clarified) idealized alpha-gamma (α-γ) co-activation or (ii) an alternative α-MN collateral projection to homonymous γ-MNs. We conclude that such α-MN collaterals are a physiologically tenable, but previously unrecognized, propriospinal circuit in the mammalian fusimotor system. These collaterals could still collaborate with α-γ co-activation, and the few skeletofusimotor fibers (β-MNs) in mammals, to create a flexible fusimotor ecosystem to enable voluntary movement. By locally and automatically regulating the highly nonlinear neuro-musculo-skeletal mechanics of the limb, these collaterals could be a critical low-level enabler of learning, adaptation, and performance via higher-level brainstem, cerebellar and cortical mechanisms.

NSF DARE-Transforming modeling in neurorehabilitation: Four threads for catalyzing progress

We present an overview of the Conference on Transformative Opportunities for Modeling in Neurorehabilitation held in March 2023. It was supported by the Disability and Rehabilitation Engineering (DARE) program from the National Science Foundation's Engineering Biology and Health Cluster. The conference brought together experts and trainees from around the world to discuss critical questions, challenges, and opportunities at the intersection of computational modeling and neurorehabilitation to understand, optimize, and improve clinical translation of neurorehabilitation. We organized the conference around four key, relevant, and promising Focus Areas for modeling: Adaptation & Plasticity, Personalization, Human-Device Interactions, and Modeling 'In-the-Wild'. We identified four common threads across the Focus Areas that, if addressed, can catalyze progress in the short, medium, and long terms. These were: (i) the need to capture and curate appropriate and useful data necessary to develop, validate, and deploy useful computational models (ii) the need to create multi-scale models that span the personalization spectrum from individuals to populations, and from cellular to behavioral levels (iii) the need for algorithms that extract as much information from available data, while requiring as little data as possible from each client (iv) the insistence on leveraging readily available sensors and data systems to push model-driven treatments from the lab, and into the clinic, home, workplace, and community. The conference archive can be found at (dare2023.usc.edu). These topics are also extended by three perspective papers prepared by trainees and junior faculty, clinician researchers, and federal funding agency representatives who attended the conference.

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

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

Stabilizing leaning postures with feedback controlled functional neuromuscular stimulation after trunk paralysis

Spinal cord injury (SCI) can cause paralysis of trunk and hip musculature that negatively impacts seated balance and ability to lean away from an upright posture and interact fully with the environment. Constant levels of electrical stimulation of peripheral nerves can activate typically paralyzed muscles and aid in maintaining a single upright seated posture. However, in the absence of a feedback controller, such seated postures and leaning motions are inherently unstable and unable to respond to perturbations. Three individuals with motor complete SCI who had previously received a neuroprosthesis capable of activating the hip and trunk musculature volunteered for this study. Subject-specific muscle synergies were identified through system identification of the lumbar moments produced via neural stimulation. Synergy-based calculations determined the real-time stimulation parameters required to assume leaning postures. When combined with a proportional, integral, derivative (PID) feedback controller and an accelerometer to infer trunk orientation, all individuals were able to assume non-erect postures of 30-40° flexion and 15° lateral bending. Leaning postures increased forward reaching capabilities by 10.2, 46.7, and 16 cm respectively for each subject when compared with no stimulation. Additionally, the leaning controllers were able to resist perturbations of up to 90 N, and all subjects perceived the leaning postures as moderately to very stable. Implementation of leaning controllers for neuroprostheses have the potential of expanding workspaces, increasing independence, and facilitating activities of daily living for individuals with paralysis.

Generating variability from motor primitives during infant locomotor development

Motor variability is a fundamental feature of developing systems allowing motor exploration and learning. In human infants, leg movements involve a small number of basic coordination patterns called locomotor primitives, but whether and when motor variability could emerge from these primitives remains unknown. Here we longitudinally followed 18 infants on 2-3 time points between birth (~4 days old) and walking onset (~14 months old) and recorded the activity of their leg muscles during locomotor or rhythmic movements. Using unsupervised machine learning, we show that the structure of trial-to-trial variability changes during early development. In the neonatal period, infants own a minimal number of motor primitives but generate a maximal motor variability across trials thanks to variable activations of these primitives. A few months later, toddlers generate significantly less variability despite the existence of more primitives due to more regularity within their activation. These results suggest that human neonates initiate motor exploration as soon as birth by variably activating a few basic locomotor primitives that later fraction and become more consistently activated by the motor system.

Neuromuscular control: from a biomechanist's perspective

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

Temporal control of muscle synergies is linked with alpha-band neural drive

KEY POINTS

It is theorized that the nervous system controls groups of muscles together as functional units, or 'synergies', resulting in correlated electromyographic (EMG) signals among muscles. However, such correlation does not necessarily imply group-level neural control. Oscillatory synchronization (coherence) among EMG signals implies neural coupling, but it is not clear how this relates to control of muscle synergies. EMG was recorded from seven arm muscles of 10 adult participants rotating an upper limb ergometer, and EMG-EMG coherence, EMG amplitude correlations and their relationship with each other were characterized. A novel method to derive multi-muscle synergies from EMG-EMG coherence is presented and these are compared with classically defined synergies. Coherent alpha-band (8-16 Hz) drive was strongest among muscles whose gross activity levels are well correlated within a given task. The cross-muscle distribution and temporal modulation of coherent alpha-band drive suggests a possible role in the neural coordination/monitoring of synergies.

ABSTRACT

During movement, groups of muscles may be controlled together by the nervous system as an adaptable functional entity, or 'synergy'. The rules governing when (or if) this occurs during voluntary behaviour in humans are not well understood, at least in part because synergies are usually defined by correlated patterns of muscle activity without regard for the underlying structure of their neural control. In this study, we investigated the extent to which comodulation of muscle output (i.e. correlation of electromyographic (EMG) amplitudes) implies that muscles share intermuscular neural input (assessed via EMG-EMG coherence analysis). We first examined this relationship among pairs of upper limb muscles engaged in an arm cycling task. We then applied a novel multidimensional EMG-EMG coherence analysis allowing synergies to be characterized on the basis of shared neural drive. We found that alpha-band coherence (8-16 Hz) is related to the degree to which overall muscle activity levels correlate over time. The extension of this coherence analysis to describe the cross-muscle distribution and temporal modulation of alpha-band drive revealed a close match to the temporal and structural features of traditionally defined muscle synergies. Interestingly, the coherence-derived neural drive was inversely associated with, and preceded, changes in EMG amplitudes by ∼200 ms. Our novel characterization of how alpha-band neural drive is dynamically distributed among muscles is a fundamental step forward in understanding the neural origins and correlates of muscle synergies.

How Do Movement Patterns in Weightlifting (Clean) Change When Using Lighter or Heavier Barbell Loads?-A Comparison of Two Principal Component Analysis-Based Approaches to Studying Technique

This study compared whole body kinematics of the clean movement when lifting three different loads, implementing two data analysis approaches based on principal component analysis (PCA). Nine weightlifters were equipped with 39 markers and their motion captured with 8 Vicon cameras at 100 Hz. Lifts of 60, 85, and 95% of the one repetition maximum were analyzed. The first PCA (PCA^trial) analyzed variance among time-normed waveforms compiled from subjects and trials; the second PCA (PCA^posture) analyzed postural positions compiled over time, subjects and trials. Load effects were identified through repeated measures ANOVAs with Bonferroni-corrected post-hocs and through Cousineau-Morey confidence intervals. PCA^trial scores differed in the first (p < 0.016, η_p² = 0.694) and fifth (p < 0.006, η_p² = 0.768) principal component, suggesting that increased barbell load produced higher initial elevation, lower squat position, wider feet position after squatting, and less inclined arms. PCA^posture revealed significant timing differences in all components. We conclude, first, barbell load affects specific aspects of the movement pattern of the clean; second, the PCA^trial approach is better suited for detecting deviations from a mean motion trajectory and its results are easier to interpret; the PCA^posture approach reveals coordination patterns and facilitates comparisons of postural speeds and accelerations.

Learning to use Muscles

The human musculoskeletal system is highly complex mechanically. Its neural control must deal successfully with this complexity to perform the diverse, efficient, robust and usually graceful behaviors of which humans are capable. Most of those behaviors might be performed by many different subsets of its myriad possible states, so how does the nervous system decide which subset to use? One solution that has received much attention over the past 50 years would be for the nervous system to be fundamentally limited in the patterns of muscle activation that it can access, a concept known as muscle synergies or movement primitives. Another solution, based on engineering control methodology, is for the nervous system to compute the single optimal pattern of muscle activation for each task according to a cost function. This review points out why neither appears to be the solution used by humans. There is a third solution that is based on trial-and-error learning, recall and interpolation of sensorimotor programs that are good-enough rather than limited or optimal. The solution set acquired by an individual during the protracted development of motor skills starting in infancy forms the basis of motor habits, which are inherently low-dimensional. Such habits give rise to muscle usage patterns that are consistent with synergies but do not reflect fundamental limitations of the nervous system and can be shaped by training or disability. This habit-based strategy provides a robust substrate for the control of new musculoskeletal structures during evolution as well as for efficient learning, athletic training and rehabilitation therapy.

Autonomous Control of a Tendon-driven Robotic Limb with Elastic Elements Reveals that Added Elasticity can Enhance Learning

Passive elastic elements can contribute to stability, energetic efficiency, and impact absorption in both biological and robotic systems. They also add dynamical complexity which makes them more challenging to model and control. The impact of this added complexity to autonomous learning has not been thoroughly explored. This is especially relevant to tendon-driven limbs whose cables and tendons are inevitably elastic. Here, we explored the efficacy of autonomous learning and control on a simulated bio-plausible tendon-driven leg across different tendon stiffness values. We demonstrate that increasing stiffness of the simulated muscles can require more iterations for the inverse map to converge but can then perform more accurately, especially in discrete tasks. Moreover, the system is robust to subsequent changes in muscle stiffnesses and can adapt on-the-go within 5 attempts. Lastly, we test the system for the functional task of locomotion and found similar effects of muscle stiffness to learning and performance. Given that a range of stiffness values led to improved learning and maximized performance, we conclude the robot bodies and autonomous controllers-at least for tendon-driven systems-can be co-developed to take advantage of elastic elements. Importantly, this opens also the door to development efforts that recapitulate the beneficial aspects of the co-evolution of brains and bodies in vertebrates.

Sampling-Based Nonlinear Stochastic Optimal Control for Neuromechanical Systems

Determining how the nervous system controls tendon-driven bodies remains an open question. Stochastic optimal control (SOC) has been proposed as a plausible analogy in the neuroscience community. SOC relies on solving the Hamilton-Jacobi-Bellman equation, which seeks to minimize a desired cost function for a given task with noisy controls. We evaluate and compare three SOC methodologies to produce tapping by a simulated planar 3-joint human index finger: iterative Linear Quadratic Gaussian (iLQG), Model-Predictive Path Integral Control (MPPI), and Deep Forward-Backward Stochastic Differential Equations (FBSDE). We show that averaged over 128 repeats these methodologies can place the fingertip at the desired final joint angles but-because of kinematic redundancy and the presence of noise-they each have joint trajectories and final postures with different means and variances. iLQG in particular, had the largest kinematic variance and departure from the final desired joint angles. We demonstrate that MPPI and FBSDE have superior performance for such nonlinear, tendon-driven systems with noisy controls.Clinical relevance- The mathematical framework provided by MPPI and FBSDE may be best suited for tendon-driven anthropomorphic robots, exoskeletons, and prostheses for amputees.

Simple Kinematic Feedback Enhances Autonomous Learning in Bio-Inspired Tendon-Driven Systems

Error feedback is known to improve performance by correcting control signals in response to perturbations. Here we show how adding simple error feedback can also accelerate and robustify autonomous learning in a tendon-driven robot. We have implemented two versions of the General-to-Particular (G2P) autonomous learning algorithm using a tendon-driven leg with two joints and three tendons: one with and one without real-time kinematic feedback. We have performed a rigorous study on the performance of each system, for both simulation and physical implementation cases, over a wide range of tasks. As expected, feedback improved performance in simulation and hardware. However, we see these improvements even in the presence of sensory delays of up to 100 ms and when experiencing substantial contact collisions. Importantly, feedback accelerates learning and enhances G2P's continual refinement of the initial inverse map by providing the system with more relevant data to train on. This allows the system to perform well even after only 60 seconds of initial motor babbling.

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.

Humans use multi-objective control to regulate lateral foot placement when walking

A fundamental question in human motor neuroscience is to determine how the nervous system generates goal-directed movements despite inherent physiological noise and redundancy. Walking exhibits considerable variability and equifinality of task solutions. Existing models of bipedal walking do not yet achieve both continuous dynamic balance control and the equifinality of foot placement humans exhibit. Appropriate computational models are critical to disambiguate the numerous possibilities of how to regulate stepping movements to achieve different walking goals. Here, we extend a theoretical and computational Goal Equivalent Manifold (GEM) framework to generate predictive models, each posing a different experimentally testable hypothesis. These models regulate stepping movements to achieve any of three hypothesized goals, either alone or in combination: maintain lateral position, maintain lateral speed or “heading”, and/or maintain step width. We compared model predictions against human experimental data. Uni-objective control models demonstrated clear redundancy between stepping variables, but could not replicate human stepping dynamics. Most multi-objective control models that balanced maintaining two of the three hypothesized goals also failed to replicate human stepping dynamics. However, multi-objective models that strongly prioritized regulating step width over lateral position did successfully replicate all of the relevant step-to-step dynamics observed in humans. Independent analyses confirmed this control was consistent with linear error correction and replicated step-to-step dynamics of individual foot placements. Thus, the regulation of lateral stepping movements is inherently multi-objective and balances task-specific trade-offs between competing task goals. To determine how people walk in their environment requires understanding both walking biomechanics and how the nervous system regulates movements from step-to-step. Analogous to mechanical “templates” of locomotor biomechanics, our models serve as “control templates” for how humans regulate stepping movements from each step to the next. These control templates are symbiotic with well-established mechanical templates, providing complimentary insights into walking regulation.

When we walk, we walk in real-world contexts and with specific goal to achieve. Side-to-side movements are paramount because walking bipeds (humans, animals, robots, etc.) are inherently more unstable laterally. This is particularly important in older adults as sideways falls greatly increase hip fracture risk. Additionally, we normally walk on paths that limit (more or less) our lateral movements. Appropriately regulating lateral stepping movements is thus critical to achieving successful locomotion in any such context. Here, we use appropriate models to test competing hypotheses about how humans regulate lateral stepping movements from each step to the next to identify what task goals they try to achieve. Our work both bridges and unifies perspectives from dynamic walking and computational motor control to provide a coherent theoretical and computational framework from which to study motor regulation in the context of goal-directedness across a wide range of walking tasks and/or conditions.