Improvement in linearity and regulation of stiffness that results from actions of stretch reflex

A physiologically enhanced muscle spindle model: using a Hill-type model for extrafusal fibers as template for intrafusal fibers

The muscle spindle is an essential proprioceptor, significantly involved in sensing limb position and movement. Although biological spindle models exist for years, the gold-standard for motor control in biomechanics are still sensors built of homogenized spindle output models due to their simpler combination with neuro-musculoskeletal models. Aiming to improve biomechanical simulations, this work establishes a more physiological model of the muscle spindle, aligned to the advantage of easy integration into large-scale musculoskeletal models. We implemented four variations of a spindle model in Matlab/Simulink®: the Mileusnic et al. (2006) model, Mileusnic model without mass, our enhanced Hill-type model, and our enhanced Hill-type model with parallel damping element (PDE). Different stretches in the intrafusal fibers were simulated in all model variations following the spindle afferent recorded in previous experiments in feline soleus muscle. Additionally, the enhanced Hill-type models had their parameters extensively optimized to match the experimental conditions, and the resulting model was validated against data from rats' triceps surae muscle. As result, the Mileusnic models present a better overall performance generating the afferent firings compared to the common data evaluated. However, the enhanced Hill-type model with PDE exhibits a more stable performance than the original Mileusnic model, at the same time that presents a well-tuned Hill-type model as muscle spindle fibers, and also accounts for real sarcomere force-length and force-velocity aspects. Finally, our activation dynamics is similar to the one applied to Hill-type model for extrafusal fibers, making our proposed model more easily integrated in multi-body simulations.

Useful and Useless Misnomers in Motor Control

This article addresses the issue of using terms and concepts in motor control that are ill-defined, undefined, and/or imported from nonbiological fields. In many of such cases, the discourse turns nonscientific and unproductive. Some of such terms are potentially useful but need to be properly and exactly defined. Other terms seem to be misleading and nonfixable. There is also an intermediate group with terms that may or may not be useful if defined properly. The paper presents three examples per group: "reflex," "synergy," and "posture" versus "motor program," "efference copy," and "internal model" versus "muscle tone," "stiffness and impedance," and "redundancy." These terms are analyzed assuming that motor control is a branch of natural science, which must be analyzed using laws of nature, not a subfield of the control theory. In the discussion, we also accept the framework of the theory of movement control with spatial referent coordinates as the only example built on laws of nature with clearly formulated physical and physiological nature of the control parameters.

Neuromechanical Circuits of the Spinal Motor Apparatus

The evolution of mechanisms for terrestrial locomotion has resulted in multi-segmented limbs that allow navigation on irregular terrains, changing of direction, manipulation of external objects, and control over the mechanical properties of limbs important for interaction with the environment, with corresponding changes in neural pathways in the spinal cord. This article is focused on the organization of these pathways, their interactions with the musculoskeletal system, and the integration of these neuromechanical circuits with supraspinal mechanisms to control limb impedance. It is argued that neural pathways from muscle spindles and Golgi tendon organs form a distributive impedance controller in the spinal cord that controls limb impedance and coordination during responses to external disturbances. These pathways include both monosynaptic and polysynaptic components. Autogenic, monosynaptic pathways serve to control the spring-like properties of muscles preserving the nonlinear relationship between stiffness and force. Intermuscular monosynaptic pathways compensate for inertial disparities between the inertial properties of limb segments and help to control inertial coupling between joints and axes of rotation. Reciprocal inhibition controls joint stiffness in conjunction with feedforward cocontraction commands. Excitatory force feedback becomes operational during locomotion and increases muscular stiffness to accommodate the higher inertial loads. Inhibitory force feedback is widely distributed among muscles. It is integrated with excitatory pathways from muscle spindles and Golgi tendon organs to determine limb stiffness and interjoint coordination during interactions with the environment. The intermuscular distribution of force feedback is variable and serves to modulate limb stiffness to meet the physical demands of different motor tasks. © 2024 American Physiological Society. Compr Physiol 14:5789-5838, 2024.

Effect of External Work Magnitude on Mechanical Efficiency of Sledge Jumping

The mechanical efficiency of human locomotion has been studied extensively. The mechanical efficiency of the whole body occasionally exceeds muscle efficiency during bouncing type gaits. It is thought to occur due to elasticity and stiffness of the tendinomuscular system and neuromuscular functions, especially stretch reflexes. In addition, the lower limb joint kinetics affect mechanical efficiency. We investigated the impact of varying external work on mechanical efficiency and lower limb kinetics during repeated sledge jumping. Fifteen male runners performed sledge jumping for 4 minutes at 3 different sledge inclinations. Lower limb kinematics, ground reaction forces, and expired gases were analyzed. Mechanical efficiency did not differ according to sledge inclination. Mechanical efficiency correlated positively with the positive mechanical work of the knee and hip joints and the negative contribution of the hip joints. Conversely, it correlated negatively with both the positive and negative contributions of the ankle joint. This may be attributable to the greater workload in this study versus previous studies. To achieve greater external work, producing more mechanical energy at the proximal joint and transferring it to the distal joint could be an effective strategy for improving mechanical efficiency because of the greater force-generating capability of distal joint muscles.

On the analysis and control of a bipedal legged locomotion model via partial feedback linearization

In this study, we introduce a new model for bipedal locomotion that enhances the classical spring-loaded inverted pendulum (SLIP) model. Our proposed model incorporates a damping term in the leg spring, a linear actuator serially interconnected to the leg, and a rotary actuator affixed to the hip. The distinct feature of this new model is its ability to overcome the non-integrability challenge inherent in the conventional SLIP models through the application of partial feedback linearization. By leveraging these actuators, our model enhances the stability and robustness of the locomotion mechanism, particularly when navigating across varied terrain profiles. To validate the effectiveness and practicality of this model, we conducted detailed simulation studies, benchmarking its performance against other recent models outlined in the literature. Our findings suggest that the redundancy in actuation introduced by our model significantly facilitates both open-loop and closed-loop walking gait, showcasing promising potential for the future of bipedal locomotion, especially for bio-inspired robotics applications in outdoor and rough terrains.

Mechanosensory encoding of forces in walking uphill and downhill: force feedback can stabilize leg movements in stick insects

Force feedback could be valuable in adapting walking to diverse terrains, but the effects of changes in substrate inclination on discharges of sensory receptors that encode forces have rarely been examined. In insects, force feedback is provided by campaniform sensilla, mechanoreceptors that monitor forces as cuticular strains. We neurographically recorded responses of stick insect tibial campaniform sensilla to "naturalistic" forces (joint torques) that occur at the hind leg femur-tibia (FT) joint in uphill, downhill, and level walking. The FT joint torques, obtained in a previous study that used inverse dynamics to analyze data from freely moving stick insects, are quite variable during level walking (including changes in sign) but are larger in magnitude and more consistent when traversing sloped surfaces. Similar to vertebrates, insects used predominantly extension torque in propulsion on uphill slopes and flexion torques to brake forward motion when going downhill. Sensory discharges to joint torques reflected the torque direction but, unexpectedly, often occurred as multiple bursts that encoded the rate of change of positive forces (dF/dt) even when force levels were high. All discharges also showed hysteresis (history dependence), as firing substantially decreased or ceased during transient force decrements. These findings have been tested in simulation in a mathematical model of the sensilla (Szczecinski NS, Dallmann CJ, Quinn RD, Zill SN. Bioinspir Biomim 16: 065001, 2021) that accurately reproduced the biological data. Our results suggest the hypothesis that sensory feedback from the femoro-tibial joint indicating force dynamics (dF/dt) can be used to counter the instability in traversing sloped surfaces in animals and, potentially, in walking machines.NEW & NOTEWORTHY Discharges of sensory receptors (campaniform sensilla) in the hind legs of stick insects can differentially signal forces that occur in walking uphill versus walking downhill. Unexpectedly, sensory firing most closely reflects the rate of change of force (dF/dt) even when the force levels are high. These signals have been replicated in a mathematical model of the receptors and could be used to stabilize leg movements both in the animal and in a walking robot.

Behavioral Motor Performance

The human sensorimotor control system has exceptional abilities to perform skillful actions. We easily switch between strenuous tasks that involve brute force, such as lifting a heavy sewing machine, and delicate movements such as threading a needle in the same machine. Using a structure with different control architectures, the motor system is capable of updating its ability to perform through our daily interaction with the fluctuating environment. However, there are issues that make this a difficult computational problem for the brain to solve. The brain needs to control a nonlinear, nonstationary neuromuscular system, with redundant and occasionally undesired degrees of freedom, in an uncertain environment using a body in which information transmission is subject to delays and noise. To gain insight into the mechanisms of motor control, here we survey movement laws and invariances that shape our everyday motion. We then examine the major solutions to each of these problems in the three parts of the sensorimotor control system, sensing, planning, and acting. We focus on how the sensory system, the control architectures, and the structure and operation of the muscles serve as complementary mechanisms to overcome deviations and disturbances to motor behavior and give rise to skillful motor performance. We conclude with possible future research directions based on suggested links between the operation of the sensorimotor system across the movement stages. © 2024 American Physiological Society. Compr Physiol 14:5179-5224, 2024.

Evaluation of stretch reflex synergies in the upper limb using principal component analysis (PCA)

The dynamic nature of movement and muscle activation emphasizes the importance of a sound experimental design. To ensure that an experiment determines what we intend, the design must be carefully evaluated. Before analyzing data, it is imperative to limit the number of outliers, biases, and skewness. In the present study, a simple center-out experiment was performed by 16 healthy volunteers. The experiment included three load conditions, two preparatory delays, two perturbations, and four targets placed along a diagonal path on a 2D plane. While the participants performed the tasks, the activity of seven arm muscles were monitored using surface electromyography (EMG). Principal component analysis (PCA) was used to evaluate the study design, identify muscle synergies, and assess the effects of individual quirks. With PCA, we can identify the trials that trigger stretch reflexes and pinpoint muscle synergies. The posterior deltoid, triceps long head, and brachioradialis were engaged when targets were in the direction of muscle shortening and the perturbation was applied in the opposite direction. Similarly, the pectoralis and anterior deltoid were engaged when the targets were in the direction of muscle shortening and the perturbation was applied in the opposite direction. The stretch reflexes were not triggered when the perturbation brought the hand in the direction of, or into the target, except if the muscle was pre-loaded. The use of PCA was also proven valuable when evaluating participant performance. While individual quirks are to be expected, failure to perform trials as expected can adversely affect the study results.

Identifying spinal tracts transmitting distant effects of trans-spinal magnetic stimulation

Estimating the state of tract-specific inputs to spinal motoneurons is critical to understanding movement deficits induced by neurological injury and potential pathways to recovery but remains challenging in humans. In this study, we explored the capability of trans-spinal magnetic stimulation (TSMS) to modulate distal reflex circuits in young adults. TSMS was applied over the thoracic spine to condition soleus H-reflexes involving sacral-level motoneurons. Three TSMS intensities below the motor threshold were applied at interstimulus intervals (ISIs) between 2 and 20 ms relative to peripheral nerve stimulation (PNS). Although low-intensity TSMS yielded no changes in H-reflexes across ISIs, the two higher stimulus intensities yielded two phases of H-reflex inhibition: a relatively long-lasting period at 2- to 9-ms ISIs, and a short phase at 11- to 12-ms ISIs. H-reflex inhibition at 2-ms ISI was uniquely dependent on TSMS intensity. To identify the candidate neural pathways contributing to H-reflex suppression, we constructed a tract-specific conduction time estimation model. Based upon our model, H-reflex inhibition at 11- to 12-ms ISIs is likely a manifestation of orthodromic transmission along the lateral reticulospinal tract. In contrast, the inhibition at 2-ms ISI likely reflects orthodromic transmission along sensory fibers with activation reaching the brain, before descending along motor tracts. Multiple pathways may contribute to H-reflex modulation between 4- and 9-ms ISIs, orthodromic transmission along sensorimotor tracts, and antidromic transmission of multiple motor tracts. Our findings suggest that noninvasive TSMS can influence motoneuron excitability at distal segments and that the contribution of specific tracts to motoneuron excitability may be distinguishable based on conduction velocities.NEW & NOTEWORTHY This study explored the capability of trans-spinal magnetic stimulation (TSMS) over the thoracic spine to modulate distal reflex circuits, H-reflexes involving sacral-level motoneurons, in young adults. TSMS induced two inhibition phases of H-reflex across interstimulus intervals (ISIs): a relatively long-lasting period at 2- to 9-ms ISIs, and a short phase at 11- to 12-ms ISIs. An estimated probability model constructed from tract-specific conduction velocities allowed the identification of potential spinal tracts contributing to the changes in motoneuron excitability.

History-dependent muscle resistance to stretch remains high after small, posturally relevant pre-movements

The contributions of intrinsic muscle fiber resistance during mechanical perturbations to standing and other postural behaviors are unclear. Muscle short-range stiffness is known to vary depending on the current level and history of the muscle's activation, as well as the muscle's recent movement history; this property has been referred to as history dependence or muscle thixotropy. However, we currently lack sufficient data about the degree to which muscle stiffness is modulated across posturally relevant characteristics of muscle stretch and activation. We characterized the history dependence of muscle's resistance to stretch in single, permeabilized, activated, muscle fibers in posturally relevant stretch conditions and activation levels. We used a classic paired muscle stretch paradigm, varying the amplitude of a 'conditioning' triangular stretch-shorten cycle followed by a 'test' ramp-and-hold imposed after a variable inter-stretch interval. We tested low (<15%), intermediate (15-50%) and high (>50%) muscle fiber activation levels, evaluating short-range stiffness and total impulse in the test stretch. Muscle fiber resistance to stretch remained high at conditioning amplitudes of <1% optimal fiber length, L0, and inter-stretch intervals of >1 s, characteristic of healthy standing postural sway. An ∼70% attenuation of muscle resistance to stretch was reached at conditioning amplitudes of >3% L0 and inter-stretch intervals of <0.1 s, characteristic of larger, faster postural sway in balance-impaired individuals. The thixotropic changes cannot be predicted solely on muscle force at the time of stretch. Consistent with the disruption of muscle cross-bridges, muscle resistance to stretch during behavior can be substantially attenuated if the prior motion is large enough and/or frequent enough.

Muscle preflex response to perturbations in locomotion: In vitro experiments and simulations with realistic boundary conditions

Neuromuscular control loops feature substantial communication delays, but mammals run robustly even in the most adverse conditions. In vivo experiments and computer simulation results suggest that muscles' preflex-an immediate mechanical response to a perturbation-could be the critical contributor. Muscle preflexes act within a few milliseconds, an order of magnitude faster than neural reflexes. Their short-lasting action makes mechanical preflexes hard to quantify in vivo. Muscle models, on the other hand, require further improvement of their prediction accuracy during the non-standard conditions of perturbed locomotion. Our study aims to quantify the mechanical work done by muscles during the preflex phase (preflex work) and test their mechanical force modulation. We performed in vitro experiments with biological muscle fibers under physiological boundary conditions, which we determined in computer simulations of perturbed hopping. Our findings show that muscles initially resist impacts with a stereotypical stiffness response-identified as short-range stiffness-regardless of the exact perturbation condition. We then observe a velocity adaptation to the force related to the amount of perturbation similar to a damping response. The main contributor to the preflex work modulation is not the change in force due to a change in fiber stretch velocity (fiber damping characteristics) but the change in magnitude of the stretch due to the leg dynamics in the perturbed conditions. Our results confirm previous findings that muscle stiffness is activity-dependent and show that also damping characteristics are activity-dependent. These results indicate that neural control could tune the preflex properties of muscles in expectation of ground conditions leading to previously inexplicable neuromuscular adaptation speeds.

Assessing shoulder muscle stretch reflexes following breast cancer treatment and postmastectomy breast reconstruction

Muscle stiffness is altered following postmastectomy breast reconstruction and breast cancer treatment. The exact mechanisms underlying these alterations are unknown; however, muscle stretch reflexes may play a role. This work examined short- (SLR) and long-latency (LLR) shoulder muscle stretch reflexes in breast cancer survivors. Forty-nine patients who had undergone postmastectomy breast reconstruction, 17 who had undergone chemoradiation, and 18 healthy, age-matched controls were enrolled. Muscle activity was recorded from the clavicular and sternocostal regions of the pectoralis major and anterior, middle, and posterior deltoids during vertical ab/adduction or horizontal flex/extension perturbations while participants maintained minimal torques. SLR and LLR were quantified for each muscle. Our major finding was that following postmastectomy breast reconstruction, SLR and LLR are impaired in the clavicular region of the pectoralis major. Individuals who had chemoradiation had impaired stretch reflexes in the clavicular and sternocostal region of the pectoralis major, anterior, middle, and posterior deltoid. These findings indicate that breast cancer treatments alter the regulation of shoulder muscle stretch reflexes and may be associated with surgical or nonsurgical damage to the pectoral fascia, muscle spindles, and/or sensory Ia afferents.NEW & NOTEWORTHY Shoulder muscle stretch reflexes may be impacted following postmastectomy breast reconstruction and chemoradiation. Here, we examined short- and long-latency shoulder muscle stretch reflexes in two experiments following common breast reconstruction procedures and chemoradiation. We show impairments in pectoralis major stretch reflexes following postmastectomy breast reconstruction and pectoralis major and deltoid muscle stretch reflexes following chemoradiation. These findings indicate that breast cancer treatments alter the regulation of shoulder muscle stretch reflexes.

Assistive Loading Promotes Goal-Directed Tuning of Stretch Reflex Gains

Voluntary movements are prepared before they are executed. Preparatory activity has been observed across the CNS and recently documented in first-order neurons of the human PNS (i.e., in muscle spindles). Changes seen in sensory organs suggest that independent modulation of stretch reflex gains may represent an important component of movement preparation. The aim of the current study was to further investigate the preparatory modulation of short-latency stretch reflex responses (SLRs) and long-latency stretch reflex responses (LLRs) of the dominant upper limb of human subjects. Specifically, we investigated how different target parameters (target distance and direction) affect the preparatory tuning of stretch reflex gains in the context of goal-directed reaching, and whether any such tuning depends on preparation duration and the direction of background loads. We found that target distance produced only small variations in reflex gains. In contrast, both SLR and LLR gains were strongly modulated as a function of target direction, in a manner that facilitated the upcoming voluntary movement. This goal-directed tuning of SLR and LLR gains was present or enhanced when the preparatory delay was sufficiently long (>250 ms) and the homonymous muscle was unloaded [i.e., when a background load was first applied in the direction of homonymous muscle action (assistive loading)]. The results extend further support for a relatively slow-evolving process in reach preparation that functions to modulate reflexive muscle stiffness, likely via the independent control of fusimotor neurons. Such control can augment voluntary goal-directed movement and is triggered or enhanced when the homonymous muscle is unloaded.

The force response of muscles to activation and length perturbations depends on length history

Recent studies have demonstrated that muscle force is not determined solely by activation under dynamic conditions, and that length history has an important role in determining dynamic muscle force. Yet, the mechanisms for how muscle force is produced under dynamic conditions remain unclear. To explore this, we investigated the effects of muscle stiffness, activation and length perturbations on muscle force. First, submaximal isometric contraction was established for whole soleus muscles. Next, the muscles were actively shortened at three velocities. During active shortening, we measured muscle stiffness at optimal muscle length (L0) and the force response to time-varying activation and length perturbations. We found that muscle stiffness increased with activation but decreased as shortening velocity increased. The slope of the relationship between maximum force and activation amplitude differed significantly among shortening velocities. Also, the intercept and slope of the relationship between length perturbation amplitude and maximum force decreased with shortening velocity. As shortening velocities were related to muscle stiffness, the results suggest that length history determines muscle stiffness and the history-dependent muscle stiffness influences the contribution of activation and length perturbations to muscle force. A two-parameter viscoelastic model including a linear spring and a linear damper in parallel with measured stiffness predicted history-dependent muscle force with high accuracy. The results and simulations support the hypothesis that muscle force under dynamic conditions can be accurately predicted as the force response of a history-dependent viscoelastic material to length perturbations.

Virtual Stiffness: A Novel Biomechanical Approach to Estimate Limb Stiffness of a Multi-Muscle and Multi-Joint System

In recent years, different groups have developed algorithms to control the stiffness of a robotic device through the electromyographic activity collected from a human operator. However, the approaches proposed so far require an initial calibration, have a complex subject-specific muscle model, or consider the activity of only a few pairs of antagonist muscles. This study described and tested an approach based on a biomechanical model to estimate the limb stiffness of a multi-joint, multi-muscle system from muscle activations. The "virtual stiffness" method approximates the generated stiffness as the stiffness due to the component of the muscle-activation vector that does not generate any endpoint force. Such a component is calculated by projecting the vector of muscle activations, estimated from the electromyographic signals, onto the null space of the linear mapping of muscle activations onto the endpoint force. The proposed method was tested by using an upper-limb model made of two joints and six Hill-type muscles and data collected during an isometric force-generation task performed with the upper limb. The null-space projection of the muscle-activation vector approximated the major axis of the stiffness ellipse or ellipsoid. The model provides a good approximation of the voluntary stiffening performed by participants that could be directly implemented in wearable myoelectric controlled devices that estimate, in real-time, the endpoint forces, or endpoint movement, from the mapping between muscle activation and force, without any additional calibrations.

A robot for overground physical human-robot interaction experiments

Many anticipated physical human-robot interaction (pHRI) applications in the near future are overground tasks such as walking assistance. For investigating the biomechanics of human movement during pHRI, this work presents Ophrie, a novel interactive robot dedicated for physical interaction tasks with a human in overground settings. Unique design requirements for pHRI were considered in implementing the one-arm mobile robot, such as the low output impedance and the ability to apply small interaction forces. The robot can measure the human arm stiffness, an important physical quantity that can reveal human biomechanics during overground pHRI, while the human walks alongside the robot. This robot is anticipated to enable novel pHRI experiments and advance our understanding of intuitive and effective overground pHRI.

A Biorealistic Computational Model Unfolds Human-Like Compliant Properties for Control of Hand Prosthesis

Objective: Human neuromuscular reflex control provides a biological model for a compliant hand prosthesis. Here we present a computational approach to understanding the emerging human-like compliance, force and position control, and stiffness adaptation in a prosthetic hand with a replica of human neuromuscular reflex. Methods: A virtual twin of prosthetic hand was constructed in the MuJoCo environment with a tendon-driven anthropomorphic hand structure. Biorealistic mathematic models of muscle, spindle, spiking-neurons and monosynaptic reflex were implemented in neuromorphic chips to drive the virtual hand for real-time control. Results: Simulation showed that the virtual hand acquired human-like ability to control fingertip position, force and stiffness for grasp, as well as the capacity to interact with soft objects by adaptively adjusting hand stiffness. Conclusion: The biorealistic neuromorphic reflex model restores human-like neuromuscular properties for hand prosthesis to interact with soft objects.

Heksor: the central nervous system substrate of an adaptive behaviour

Over the past half-century, the largely hardwired central nervous system (CNS) of 1970 has become the ubiquitously plastic CNS of today, in which change is the rule not the exception. This transformation complicates a central question in neuroscience: how are adaptive behaviours - behaviours that serve the needs of the individual - acquired and maintained through life? It poses a more basic question: how do many adaptive behaviours share the ubiquitously plastic CNS? This question compels neuroscience to adopt a new paradigm. The core of this paradigm is a CNS entity with unique properties, here given the name heksor from the Greek hexis. A heksor is a distributed network of neurons and synapses that changes itself as needed to maintain the key features of an adaptive behaviour, the features that make the behaviour satisfactory. Through their concurrent changes, the numerous heksors that share the CNS negotiate the properties of the neurons and synapses that they all use. Heksors keep the CNS in a state of negotiated equilibrium that enables each heksor to maintain the key features of its behaviour. The new paradigm based on heksors and the negotiated equilibrium they create is supported by animal and human studies of interactions among new and old adaptive behaviours, explains otherwise inexplicable results, and underlies promising new approaches to restoring behaviours impaired by injury or disease. Furthermore, the paradigm offers new and potentially important answers to extant questions, such as the generation and function of spontaneous neuronal activity, the aetiology of muscle synergies, and the control of homeostatic plasticity.

Soleus H-reflex modulation during a double-legged drop landing task

Muscle spindle afferent feedback is modulated during different phases of locomotor tasks in a way that facilitates task goals. However, only a few studies have studied H-reflex modulation during landing. This study aimed to characterize soleus (SOL) H-reflex modulation during the flight and early landing period of drop landings. Since landing presumably involves a massive increase in spindle afferent firing due to rapid SOL muscle stretching, we hypothesized H-reflex size would decrease near landing reflecting neural modulation to prevent excessive motoneuron excitation. The soleus H-reflex was recorded during drop landings from a 30 cm height in nine healthy adults. Electromyography (SOL, tibialis anterior (TA), medial gastrocnemius, and vastus lateralis), ankle and knee joint motion and ground reaction force were recorded during landings. Tibial nerve stimulation was timed to elicit H-reflexes during the flight and early ground contact period (five 30 ms Bins from 90 ms before to 60 ms after landing). The H-reflexes recorded after landing (0-30 and 30-60 ms) were significantly smaller (21-36% less) than that recorded during the flight periods (90-0 ms before ground contact; P ≤ 0.004). The decrease in H-reflex size not occurring until after ground contact indicates a time-critical modulation of reflex gain during the last 30 ms of flight (i.e., time of tibial nerve stimulation). H-reflex size reduction after ground contact supports a probable neural strategy to prevent excessive reflex-mediated muscle activation and thereby facilitates appropriate musculotendon and joint stiffness.

Translations of the Humeral Head Elicit Reflexes in Rotator Cuff Muscles That Are Larger Than Those in the Primary Shoulder Movers

Muscle activation helps stabilize the glenohumeral joint and prevent dislocations, which are more common at the shoulder than at any other human joint. Feedforward control of shoulder muscles is important for protecting the glenohumeral joint from harm caused by anticipated external perturbations. However, dislocations are frequently caused by unexpected perturbations for which feedback control is essential. Stretch-evoked reflexes elicited by translations of the glenohumeral joint may therefore be an important mechanism for maintaining joint integrity, yet little is known about them. Specifically, reflexes elicited by glenohumeral translations have only been studied under passive conditions, and there have been no investigations of how responses are coordinated across the functional groupings of muscles found at the shoulder. Our objective was to characterize stretch-evoked reflexes elicited by translations of the glenohumeral joint while shoulder muscles are active. We aimed to determine how these responses differ between the rotator cuff muscles, which are essential for maintaining glenohumeral stability, and the primary shoulder movers, which are essential for the large mobility of this joint. We evoked reflexes using anterior and posterior translations of the humeral head while participants produced voluntary isometric torque in six directions spanning the three rotational degrees-of-freedom about the shoulder. Electromyograms were used to measure the stretch-evoked reflexes elicited in nine shoulder muscles. We found that reflex amplitudes were larger in the rotator cuff muscles than in the primary shoulder movers, in part due to increased background activation during torque generation but more so due to an increased scaling of reflex responses with background activation. The reflexes we observed likely arose from the diversity of proprioceptors within the muscles and in the passive structures surrounding the shoulder. The large reflexes observed in the rotator cuff muscles suggest that feedback control of the rotator cuff augments the feedforward control that serves to compress the humeral head into the glenoid. This coordination may serve to stabilize the shoulder rapidly when preparing for and responding to unexpected disturbances.

What is an artificial muscle? A comparison of soft actuators to biological muscles

Interest in emulating the properties of biological muscles that allow for fast adaptability and control in unstructured environments has motivated researchers to develop new soft actuators, often referred to as 'artificial muscles'. The field of soft robotics is evolving rapidly as new soft actuator designs are published every year. In parallel, recent studies have also provided new insights for understanding biological muscles as 'active' materials whose tunable properties allow them to adapt rapidly to external perturbations. This work presents a comparative study of biological muscles and soft actuators, focusing on those properties that make biological muscles highly adaptable systems. In doing so, we briefly review the latest soft actuation technologies, their actuation mechanisms, and advantages and disadvantages from an operational perspective. Next, we review the latest advances in understanding biological muscles. This presents insight into muscle architecture, the actuation mechanism, and modeling, but more importantly, it provides an understanding of the properties that contribute to adaptability and control. Finally, we conduct a comparative study of biological muscles and soft actuators. Here, we present the accomplishments of each soft actuation technology, the remaining challenges, and future directions. Additionally, this comparative study contributes to providing further insight on soft robotic terms, such as biomimetic actuators, artificial muscles, and conceptualizing a higher level of performance actuator named artificial supermuscle. In conclusion, while soft actuators often have performance metrics such as specific power, efficiency, response time, and others similar to those in muscles, significant challenges remain when finding suitable substitutes for biological muscles, in terms of other factors such as control strategies, onboard energy integration, and thermoregulation.

Muscle as a tunable material: implications for achieving muscle-like function in robotic prosthetic devices

An ideal prosthesis should perform as well as or better than the missing limb it was designed to replace. Although this ideal is currently unattainable, recent advances in design have significantly improved the function of prosthetic devices. For the lower extremity, both passive prostheses (which provide no added power) and active prostheses (which add propulsive power) aim to emulate the dynamic function of the ankle joint, whose adaptive, time-varying resistance to applied forces is essential for walking and running. Passive prostheses fail to normalize energetics because they lack variable ankle impedance that is actively controlled within each gait cycle. By contrast, robotic prostheses can normalize energetics for some users under some conditions. However, the problem of adaptive and versatile control remains a significant issue. Current prosthesis-control algorithms fail to adapt to changes in gait required for walking on level ground at different speeds or on ramps and stairs. A new paradigm of 'muscle as a tunable material' versus 'muscle as a motor' offers insights into the adaptability and versatility of biological muscles, which may provide inspiration for prosthesis design and control. In this new paradigm, neural activation tunes muscle stiffness and damping, adapting the response to applied forces rather than instructing the timing and amplitude of muscle force. A mechanistic understanding of muscle function is incomplete and would benefit from collaboration between biologists and engineers. An improved understanding of the adaptability of muscle may yield better models as well as inspiration for developing prostheses that equal or surpass the functional capabilities of biological limbs across a wide range of conditions.

Non-uniform upregulation of the autogenic stretch reflex among hindlimb extensors following lateral spinal lesion in the cat

Successful propagation throughout the step cycle is contingent on adequate regulation of whole-limb stiffness by proprioceptive feedback. Following spinal cord injury (SCI), there are changes in the strength and organization of proprioceptive feedback that can result in altered joint stiffness. In this study, we measured changes in autogenic feedback of five hindlimb extensor muscles following chronic low thoracic lateral hemisection (LSH) in decerebrate cats. We present three features of the autogenic stretch reflex obtained using a mechanographic method. Stiffness was a measure of the resistance to stretch during the length change. The dynamic index documented the extent of adaptation or increase of the force response during the hold phase, and the impulse measured the integral of the response from initiation of a stretch to the return to the initial length. The changes took the form of variable and transient increases in the stiffness of vastus (VASTI) group, soleus (SOL), and flexor hallucis longus (FHL), and either increased (VASTI) or decreased adaptation (GAS and PLANT). The stiffness of the gastrocnemius group (GAS) was also variable over time but remained elevated at the final time point. An unexpected finding was that these effects were observed bilaterally. Potential reasons for this finding and possible sources of increased excitability to this muscle group are discussed.

Evaluation of force feedback in walking using joint torques as "naturalistic" stimuli

Control of adaptive walking requires the integration of sensory signals of muscle force and load. We have studied how mechanoreceptors (tibial campaniform sensilla) encode “naturalistic” stimuli derived from joint torques of stick insects walking on a horizontal substrate. Previous studies showed that forces applied to the legs using the mean torque profiles of a proximal joint were highly effective in eliciting motor activities. However, substantial variations in torque direction and magnitude occurred at the more distal femorotibial joint, which can generate braking or propulsive forces and provide lateral stability. To determine how these forces are encoded, we used torque waveforms of individual steps that had maximum values in stance in the directions of flexion or extension. Analysis of kinematic data showed that the torques in different directions tended to occur in different ranges of joint angles. Variations within stance were not accompanied by comparable changes in joint angle but often reflected vertical ground reaction forces and leg support of body load. Application of torque waveforms elicited sensory discharges with variations in firing frequency similar to those seen in freely walking insects. All sensilla directionally encoded the dynamics of force increases and showed hysteresis to transient force decreases. Smaller receptors exhibited more tonic firing. Our findings suggest that dynamic sensitivity in force feedback can modulate ongoing muscle activities to stabilize distal joints when large forces are generated at proximal joints. Furthermore, use of “naturalistic” stimuli can reproduce characteristics seen in freely moving animals that are absent in conventional restrained preparations.

NEW & NOTEWORTHY Sensory encoding of forces during walking by campaniform sensilla was characterized in stick insects using waveforms of joint torques calculated by inverse dynamics as mechanical stimuli. Tests using the mean joint torque and torques of individual steps showed the system is highly sensitive to force dynamics (dF/dt). Use of “naturalistic” stimuli can reproduce characteristics of sensory discharges seen in freely walking insects, such as load transfer among legs.

Somatosensory deafferentation reveals lateralized roles of proprioception in feedback and adaptive feedforward control of movement and posture

Proprioception provides crucial information necessary for determining limb position and movement, and plausibly also for updating internal models that might underlie the control of movement and posture. Seminal studies of upper-limb movements in individuals living with chronic, large fiber deafferentation have provided evidence for the role of proprioceptive information in the hypothetical formation and maintenance of internal models to produce accurate motor commands. Vision also contributes to sensorimotor functions but cannot fully compensate for proprioceptive deficits. More recent work has shown that posture and movement control processes are lateralized in the brain, and that proprioception plays a fundamental role in coordinating the contributions of these processes to the control of goal-directed actions. In fact, the behavior of each limb in a deafferented individual resembles the action of a controller in isolation. Proprioception, thus, provides state estimates necessary for the nervous system to efficiently coordinate multiple motor control processes.

BIOMECHANICAL EFFECTS OF HYPERPRONATION ON MULTIDIRECTIONAL ANKLE ANGULAR DISPLACEMENT AND STIFFNESS

Hyperpronation of the foot is believed to contribute to ankle hypermobility and associated stiffness reduction, but the underlying biomechanical mechanisms remain unknown. This study aimsed to investigate multidirectional ankle displacement and associated stiffness when a posterior–anterior impact force was applied to the posterior knee compartment. Forty healthy adults with and without foot hyperpronation were recruited. A three-dimensional motion capture system and force plates were used to acquire angular displacement and ankle joint moment data. The independent [Formula: see text]-test and Mann–Whitney [Formula: see text] test were used to compare the group differences in ankle angular displacement, moment, and stiffness. Spearman’s rho test was performed to determine the relationship between ankle angular displacement and stiffness. The hyperpronation group demonstrated significantly greater sagittal ([Formula: see text]) and frontal plane ([Formula: see text]) angular displacements and reduced sagittal plane ankle stiffness ([Formula: see text]) than the neutral group. The Spearman’s correlation analysis showed a close inverse relationship between the ankle angular displacement and stiffness, ranging from [Formula: see text] to [Formula: see text]. The biomechanical data in our study suggest that individuals with foot hyperpronation present with multidirectional hypermobility and a reduction in ankle stiffness. These factors contribute to an increased risk of ankle-foot injury in individuals with foot hyperpronation.

Neuromorphic Model of Reflex for Realtime Human-Like Compliant Control of Prosthetic Hand

Current control of prosthetic hands is ineffective when grasping deformable, irregular, or heavy objects. In humans, grasping is achieved under spinal reflexive control of the musculotendon skeletal structure, which produces a hand stiffness commensurate with the task. We hypothesize that mimicking reflex on a prosthetic hand may improve grasping performance and safety when interacting with human. Here, we present a design of compliant controller for prosthetic hand with a neuromorphic model of human reflex. The model includes 6 motoneuron pools containing 768 spiking neurons, 1 muscle spindle with 128 spiking afferents, and 1 modified Hill-type muscle. Models are implemented using neuromorphic hardware with 1 kHz real-time computing. Experimental tests showed that the prosthetic hand could sustain a 40 N load compared to 95 N for an adult. Stiffness range was adjustable from 60 to 640 N/m, about 46.6% of that of human hand. The grasping velocity could be ramped up to 14.4 cm/s, or 24% of the human peak velocity. The complaint control could switch between free movement and contact force when pressing a deformable beam. The amputee can achieve a 47% information throughput of healthy humans. Overall, the reflex-enabled prosthetic hand demonstrated the attributes of human compliant grasping with the neuromorphic model of spinal neuromuscular reflex.

Laws of nature that define biological action and perception

We describe a physical approach to biological functions, with the emphasis on the motor and sensory functions. The approach assumes the existence of biology-specific laws of nature uniting salient physical variables and parameters. In contrast to movements in inanimate nature, actions are produced by changes in parameters of the corresponding laws of nature. For movements, parameters are associated with spatial referent coordinates (RCs) for the effectors. Stability of motor actions is ensured by the abundant mapping of RCs across hierarchical control levels. The sensory function is viewed as based on an interaction of efferent and afferent signals leading to an iso-perceptual manifold where percepts of salient sensory variables are stable. This approach offers novel interpretations for a variety of known neurophysiological and behavioral phenomena and makes a number of novel testable predictions. In particular, we discuss novel interpretations for the well-known phenomena of agonist-antagonist co-activation and vibration-induced illusions of both position and force. We also interpret results of several new experiments with unintentional force changes and with analysis of accuracy of perception of variables produced by elements of multi-element systems. Recently, this approach has been expanded to interpret motor disorders including spasticity and consequences of subcortical disorders (such as Parkinson's disease). We suggest that the approach can be developed for cognitive functions.

Neuromotor Regulation of Ankle Stiffness is Comparable to Regulation of Joint Position and Torque at Moderate Levels

Joint mechanical impedance, which describes the instantaneous relationship between kinematic perturbations and the resulting torque response, plays an important role in the way humans ambulate, interact with the environment, and respond to disturbances. Recent studies have quantified how the stiffness component of mechanical impedance varies during walking. However, the extent to which humans can voluntarily regulate leg joint stiffness is not yet known. Our study sought to quantify the accuracy and precision of the neuromotor system to voluntarily regulate ankle joint stiffness while seated, and compare these data to the well-known abilities to regulate ankle joint torque and position. We tested individuals’ ability to to regulate these quantities at three different magnitudes: 20%, 40%, and 60% of a maximum value. Our results showed that subjects were able to voluntarily regulate ankle joint stiffness, and that the normalized accuracy and precision of stiffness regulation were not different than those of position or torque for targets at magnitudes of 20% of a maximum value. However, the accuracy and precision of stiffness regulation were statistically different than those of position and torque for targets at magnitudes of 40% of the maximum values. At moderate targets, the similarity of the ability to regulate ankle joint stiffness when compared to the abilities to regulate joint torque and position highlights the importance of a comprehensive description of lower-limb biomechanics that includes consideration of joint mechanical impedance, in addition to the common descriptions of joint torque and position.

Predicting Perturbed Human Arm Movements in a Neuro-Musculoskeletal Model to Investigate the Muscular Force Response

Human movement is generated by a dynamic interplay between the nervous system, the biomechanical structures, and the environment. To investigate this interaction, we propose a neuro-musculoskeletal model of human goal-directed arm movements. Using this model, we simulated static perturbations of the inertia and damping properties of the arm, as well as dynamic torque perturbations for one-degree-of freedom movements around the elbow joint. The controller consists of a feed-forward motor command and feedback based on muscle fiber length and contraction velocity representing short-latency (25 ms) or long-latency (50 ms) stretch reflexes as the first neuronal responses elicited by an external perturbation. To determine the open-loop control signal, we parameterized the control signal resulting in a piecewise constant stimulation over time for each muscle. Interestingly, such an intermittent open-loop signal results in a smooth movement that is close to experimental observations. So, our model can generate the unperturbed point-to-point movement solely by the feed-forward command. The feedback only contributed to the stimulation in perturbed movements. We found that the relative contribution of this feedback is small compared to the feed-forward control and that the characteristics of the musculoskeletal system create an immediate and beneficial reaction to the investigated perturbations. The novelty of these findings is (1) the reproduction of static as well as dynamic perturbation experiments in one neuro-musculoskeletal model with only one set of basic parameters. This allows to investigate the model's neuro-muscular response to the perturbations that-at least to some degree-represent stereotypical interactions with the environment; (2) the demonstration that in feed-forward driven movements the muscle characteristics generate a mechanical response with zero-time delay which helps to compensate for the perturbations; (3) that this model provides enough biomechanical detail to allow for the prediction of internal forces, including joint loads and muscle-bone contact forces which are relevant in ergonomics and for the development of assistive devices but cannot be observed in experiments.

Stochastic optimal open-loop control as a theory of force and impedance planning via muscle co-contraction

Understanding the underpinnings of biological motor control is an important issue in movement neuroscience. Optimal control theory is a leading framework to rationalize this problem in computational terms. Previously, optimal control models have been devised either in deterministic or in stochastic settings to account for different aspects of motor control (e.g. average behavior versus trial-to-trial variability). While these approaches have yielded valuable insights about motor control, they typically fail in explaining muscle co-contraction. Co-contraction of a group of muscles associated to a motor function (e.g. agonist and antagonist muscles spanning a joint) contributes to modulate the mechanical impedance of the neuromusculoskeletal system (e.g. joint viscoelasticity) and is thought to be mainly under the influence of descending signals from the brain. Here we present a theory suggesting that one primary goal of motor planning may be to issue feedforward (open-loop) motor commands that optimally specify both force and impedance, according to noisy neuromusculoskeletal dynamics and to optimality criteria based on effort and variance. We show that the proposed framework naturally accounts for several previous experimental findings regarding the regulation of force and impedance via muscle co-contraction in the upper-limb. Stochastic optimal (closed-loop) control, preprogramming feedback gains but requiring on-line state estimation processes through long-latency sensory feedback loops, may then complement this nominal feedforward motor command to fully determine the limb’s mechanical impedance. The proposed stochastic optimal open-loop control theory may provide new insights about the general articulation of feedforward/feedback control mechanisms and justify the occurrence of muscle co-contraction in the neural control of movement.

This study presents a novel computational theory to explain the planning of force and impedance (e.g. viscoelasticity) in the neural control of movement. It assumes that one main goal of motor planning is to elaborate feedforward motor commands that determine both the force and the impedance required for the task at hand. These feedforward motor commands (i.e. that are defined prior to movement execution) are designed to minimize effort and variance costs considering the uncertainty arising from sensorimotor or environmental noise. A major outcome of this mathematical framework is the explanation of muscle co-contraction (i.e. the concurrent contraction of a group of muscles involved in a motor function). Muscle co-contraction has been shown to occur in many situations but previous modeling works struggled to account for it. Although effortful, co-contraction contributes to increase the robustness of motor behavior (e.g. small variance) upstream of sophisticated optimal closed-loop control processes that require state estimation from delayed sensory feedback to function. This work may have implications regarding our understanding of the neural control of movement in computational terms. It also provides a theoretical ground to explain how to optimally plan force and impedance within a general and versatile framework.

Ultrasound imaging links soleus muscle neuromechanics and energetics during human walking with elastic ankle exoskeletons

Unpowered exoskeletons with springs in parallel to human plantar flexor muscle-tendons can reduce the metabolic cost of walking. We used ultrasound imaging to look 'under the skin' and measure how exoskeleton stiffness alters soleus muscle contractile dynamics and shapes the user's metabolic rate during walking. Eleven participants (4F, 7M; age: 27.7 ± 3.3 years) walked on a treadmill at 1.25 m s-1 and 0% grade with elastic ankle exoskeletons (rotational stiffness: 0-250 Nm rad-1) in one training and two testing days. Metabolic savings were maximized (4.2%) at a stiffness of 50 Nm rad-1. As exoskeleton stiffness increased, the soleus muscle operated at longer lengths and improved economy (force/activation) during early stance, but this benefit was offset by faster shortening velocity and poorer economy in late stance. Changes in soleus activation rate correlated with changes in users' metabolic rate (p = 0.038, R2 = 0.44), highlighting a crucial link between muscle neuromechanics and exoskeleton performance; perhaps informing future 'muscle-in-the loop' exoskeleton controllers designed to steer contractile dynamics toward more economical force production.

Adaptation to slope in locomotor-trained spinal cats with intact and self-reinnervated lateral gastrocnemius and soleus muscles

Sensorimotor training providing motion-dependent somatosensory feedback to spinal locomotor networks restores treadmill weight-bearing stepping on flat surfaces in spinal cats. In this study, we examined if locomotor ability on flat surfaces transfers to sloped surfaces and the contribution of length-dependent sensory feedback from lateral gastrocnemius (LG) and soleus (Sol) to locomotor recovery after spinal transection and locomotor training. We compared kinematics and muscle activity at different slopes (±10° and ±25°) in spinalized cats (n = 8) trained to walk on a flat treadmill. Half of those animals had their right hindlimb LG/Sol nerve cut and reattached before spinal transection and locomotor training, a procedure called muscle self-reinnervation that leads to elimination of autogenic monosynaptic length feedback in spinally intact animals. All spinal animals trained on a flat surface were able to walk on slopes with minimal differences in walking kinematics and muscle activity between animals with/without LG/Sol self-reinnervation. We found minimal changes in kinematics and muscle activity at lower slopes (±10°), indicating that walking patterns obtained on flat surfaces are robust enough to accommodate low slopes. Contrary to results in spinal intact animals, force responses to muscle stretch largely returned in both SELF-REINNERVATED muscles for the trained spinalized animals. Overall, our results indicate that the locomotor patterns acquired with training on a level surface transfer to walking on low slopes and that spinalization may allow the recovery of autogenic monosynaptic length feedback following muscle self-reinnervation.NEW & NOTEWORTHY Spinal locomotor networks locomotor trained on a flat surface can adapt the locomotor output to slope walking, up to ±25° of slope, even with total absence of supraspinal CONTROL. Autogenic length feedback (stretch reflex) shows signs of recovery in spinalized animals, contrary to results in spinally intact animals.

Stabilizing stretch reflexes are modulated independently from the rapid release of perturbation-triggered motor plans

Responses elicited after the shortest latency spinal reflexes but prior to the onset of voluntary activity can display sophistication beyond a stereotypical reflex. Two distinct behaviors have been identified for these rapid motor responses, often called long-latency reflexes. The first is to maintain limb stability by opposing external perturbations. The second is to quickly release motor actions planned prior to the disturbance, often called a triggered reaction. This study investigated their interaction when motor tasks involve both limb stabilization and motor planning. We used a robotic manipulator to change the stability of the haptic environment during 2D arm reaching tasks, and to apply perturbations that could elicit rapid motor responses. Stabilizing reflexes were modulated by the orientation of the haptic environment (field effect) whereas triggered reactions were modulated by the target to which subjects were instructed to reach (target effect). We observed that there were no significant interactions between the target and field effects in the early (50–75 ms) portion of the long-latency reflex, indicating that these components of the rapid motor response are initially controlled independently. There were small but significant interactions for two of the six relevant muscles in the later portion (75–100 ms) of the reflex response. In addition, the target effect was influenced by the direction of the perturbation used to elicit the motor response, indicating a later feedback correction in addition to the early component of the triggered reaction. Together, these results demonstrate how distinct components of the long-latency reflex can work independently and together to generate sophisticated rapid motor responses that integrate planning with reaction to uncertain conditions.

Dysregulation of mechanosensory circuits coordinating the actions of antagonist motor pools following peripheral nerve injury and muscle reinnervation

Movement disorders observed following peripheral nerve injury and muscle reinnervation suggest discoordination in the activation of antagonist muscles. Although underlying mechanisms remain undecided, dysfunction in spinal reflex circuits is a reasonable candidate. Based on the well known role of reflex inhibition between agonist and antagonist muscles in normal animals, we hypothesized its reduction following muscle reinnervation, similar to that associated with other disorders exhibiting antagonist discoordination, e.g. spinal cord injury and dystonia. Experiments performed on acutely-decerebrated rats examined interactions of mechanosensory reflexes between ipsilateral muscles acting as mechanical antagonists at the ankle joint: ankle extensor, gastrocnemii (G) muscles (agonists) and ankle flexor, tibialis anterior (TA) muscle (antagonist). The force of agonist stretch reflex contraction was measured for its suppression or facilitation by concurrent conditioning stretch of the antagonist muscle. Data were compared between two groups of adult rats, an antagonist reinnervation group with TA muscle reinnervated and a control group with TA normally innervated. Results revealed a three-fold increase in reflex suppression in the antagonist reinnervation group, contrary to our predicted decrease. Reflex facilitation also increased, not only in strength, seven-fold, but also in its frequency of stochastic occurrence across stimulus trials. These observations suggest dysregulation in specific spinal reflex circuits as novel candidate origins of modified antagonist muscle coordination following peripheral nerve injury and muscle reinnervation.

Sloppy, But Acceptable, Control of Biological Movement: Algorithm-Based Stabilization of Subspaces in Abundant Spaces

In this paper, we develop an algorithm-based approach to the problem of stability of salient performance variables during motor actions. This problem is reformulated as stabilizing subspaces within high-dimensional spaces of elemental variables. Our main idea is that the central nervous system does not solve such problems precisely, but uses simple rules that achieve success with sufficiently high probability. Such rules can be applied even if the central nervous system has no knowledge of the mapping between small changes in elemental variables and changes in performance. We start with a rule ”Act on the most nimble” (the AMN-rule), when changes in the local feedback-based loops occur for the most unstable variable first. This rule is implemented in a task-specific coordinate system that facilitates local control. Further, we develop and supplement the AMN-rule to improve the success rate. Predictions of implementation of such algorithms are compared with the results of experiments performed on the human hand with both visual and mechanical perturbations. We conclude that physical, including neural, processes associated with everyday motor actions can be adequately represented with a set of simple algorithms leading to sloppy, but satisfactory, solutions. Finally, we discuss implications of this scheme for motor learning and motor disorders.

Stiffness as a control factor for object manipulation

During manipulation, force is exerted with the expectation that an object will move in an intended manner. This prediction is a learned coordination between force and movement. Mechanically, impedance is a way to describe this coordination, and object interaction could be anticipated by setting impedance before the hand moves the object. This strategy would be especially important at the end of a reach, because feedback is ineffective for rapid force changes. Since mechanical impedance is not subject to the time delays of feedback, it can, if set properly, produce the desired motion on impact. We examined this possibility by instructing subjects to move a handle to a specific target position along a track. The handle was locked in place until the subject exerted enough force to cross a threshold; the handle was then released abruptly to move along the track. We hypothesized that this ballistic release task would encourage subjects to modify impedance in anticipation of the upcoming movement and found that one component of impedance, stiffness, varied in a way that matched the behavioral demands of the task. Analysis suggests that this stiffness was set before the handle moved and governed the subsequent motion. We also found separate components of muscle activity that corresponded to stiffness and to changes in force. Our results show that subjects used a robust and efficient strategy to coordinate force and displacement by modulating muscle activity in a way that was behaviorally relevant in the task.NEW & NOTEWORTHY The arm can behave like a spring, and this mechanical behavior can be advantageous in situations requiring rapid changes in force and/or displacement. Selection of a proper "virtual" spring before the occurrence of a rapid transient could facilitate a desired responsive movement. We show that these spring-like arm mechanics, set in anticipation of an instantaneous force change, function as an efficient strategy to control movement when feedback is ineffective.

Muscle Function from Organisms to Molecules

Gaps in our understanding of muscle contraction at the molecular level limit the ability to predict in vivo muscle forces in humans and animals during natural movements. Because muscles function as motors, springs, brakes, or struts, it is not surprising that uncertainties remain as to how sarcomeres produce these different behaviors. Current theories fail to explain why a single extra stimulus, added shortly after the onset of a train of stimuli, doubles the rate of force development. When stretch and doublet stimulation are combined in a work loop, muscle force doubles and work increases by 50% per cycle, yet no theory explains why this occurs. Current theories also fail to predict persistent increases in force after stretch and decreases in force after shortening. Early studies suggested that all of the instantaneous elasticity of muscle resides in the cross-bridges. Subsequent cross-bridge models explained the increase in force during active stretch, but required ad hoc assumptions that are now thought to be unreasonable. Recent estimates suggest that cross-bridges account for only ∼12% of the energy stored by muscles during active stretch. The inability of cross-bridges to account for the increase in force that persists after active stretching led to development of the sarcomere inhomogeneity theory. Nearly all predictions of this theory fail, yet the theory persists. In stretch-shortening cycles, muscles with similar activation and contractile properties function as motors or brakes. A change in the phase of activation relative to the phase of length changes can convert a muscle from a motor into a spring or brake. Based on these considerations, it is apparent that the current paradigm of muscle mechanics is incomplete. Recent advances in our understanding of giant muscle proteins, including twitchin and titin, allow us to expand our vision beyond cross-bridges to understand how muscles contribute to the biomechanics and control of movement.

Damping Perception During Active Ankle and Knee Movement

The mechanical impedance of the leg governs many important aspects of locomotion, including energy storage, transfer, and dissipation between joints. These mechanical properties, including stiffness and damping, have been recently quantified at the ankle joint during walking. However, little is known about the human ability to sense changes in impedance. Here, we investigate the ability to detect small changes in damping coefficients when interacting with a mechanical system coupled to the ankle or knee joint. Using a psychophysical experiment (adaptive, weighted staircase method) and an admittance-controlled dynamometer, we determined the 75% minimum detectable change by tasking subjects to compare the damping values of different virtual spring-mass-damper systems. The Weber fraction for damping coefficient ranged from 12% to 31%, with similar performance across the ankle and knee. Damping perception performance was similar to previous stiffness perception results, suggesting that both the stiffness and damping of the environment are important for the human sensorimotor system and motivating further investigation on the role of damping in biomechanics, motor control, and wearable robotic technologies.

Difference of neuromuscular responses by additional loads during plyometric jump

Plyometric training is a training method to increase the motor output, stretch-shortening cycle which could be associated with power output. To increase the neuromuscular output, various training variables have been incorporated in training programs. Weight vest is one of the variables to develop it. However, how much load can effectively develop the neural response is still not clearly understood. The aim of this study was to identify the effects of additional external loads on neuromuscular response of lower body during plyometric jump. Total 19 men performed jump tests with weight vest (two jumps in each additional load; 0%, 10%, 15% and 20% of bodyweight [BW]). During the tests, neuromuscular responses of lower extremity were measured. In vertical jump, 0%BW group was higher than the other heavier loads. In rate of force development (RFD), 10%BW was higher than 15%BW and 20%BW. In 0-30 msec of interval RFD, the heavier load groups were greater than 0%BW and in 0-50 msec, 15%BW and 20%BW were higher than 0%BW. In neuromuscular efficiency (NME), 15%BW and 20%BW were greater than 0%BW in ankle joint. This research indicated that plyometric jump with additional load causes greater RFD and NME of lower extremity compared with jump training without additional load. During weight vest plyometric jump, 10%-20% of BW load is advantageous to NME of lower body and 10% of BW load is effective to develop RFD of lower extremity.

An Initial Passive Phase That Limits the Time to Recover and Emphasizes the Role of Proprioceptive Information

In the present experiments, multiple balance perturbations were provided by unpredictable support-surface translations in various directions and velocities. The aim of this study was to distinguish the passive and the active phases during the pre-impact period of a fall. It was hypothesized that it should be feasible if one uses a specific quantitative kinematic analysis to evaluate the dispersion of the body segments trajectories across trials. Moreover, a multi-joint kinematical model was created for each subject, based on a new 3-D minimally invasive stereoradiographic X-ray images to assess subject-specific geometry and inertial parameters. The simulations allowed discriminating between the contributions of the passive (inertia-induced properties) and the active (neuromuscular response) components during falls. Our data show that there is limited time to adjust the way one fall from a standing position. We showed that the pre-impact period is truncated of 200 ms. During the initial part of a fall, the observed trajectory results from the interaction between the destabilizing external force and the body: inertial properties intrinsic to joints, ligaments and musculotendinous system have then a major contribution, as suggested for the regulation of static upright stance. This passive phase is later followed by an active phase, which consists of a corrective response to the postural perturbation. We believe that during a fall from standing height, it takes about 300 ms for postural responses to start correcting the body trajectory, while the impact is expected to occur around 700 ms. It has been argued that this time is sufficient to change the way one falls and that this makes it possible to apply safer ways of falling, for example by using martial arts fall techniques. Also, our results imply visual and vestibular information are not congruent with the beginning of the on-going fall. This consequence is to be noted as subjects prepare to the impact on the basis of sensory information, which would be uniquely mainly of proprioceptive origin at the fall onset. One limitation of the present analysis is that no EMG was included so far but these data are the subject of a future study.

Interaction between muscle tone, short-range stiffness and increased sensory feedback gains explains key kinematic features of the pendulum test in spastic cerebral palsy: A simulation study

The pendulum test is a sensitive clinical assessment of spasticity where the lower leg is dropped from the horizontal position and features of limb motion are recorded. Three key kinematic features are associated with the degree of severity of spasticity in children with cerebral palsy: decreased initial limb excursion, reduced number of limb oscillations, and a non-vertical resting limb angle. While spasticity is attributed to increased velocity-dependent resistance to motion, prior models simulating increased sensorimotor feedback of muscle velocity fail to explain the key pendulum test kinematic outcomes in spastic individuals. Here we hypothesized that increased muscle tone, causing a transient increase in muscle force, i.e. short-range stiffness, could account for reduced first swing excursion and non-vertical resting limb angle. We further hypothesized that hyperreflexia modeled based on muscle fiber force, and not velocity, feedback would be necessary to reduce the number of oscillations because of its interaction with transiently increased muscle force due to short-range stiffness. We simulated the lower leg as a torque-driven single-link pendulum. Muscle tone was modeled as a constant baseline joint torque, short-range stiffness torque was dependent on the level of muscle tone, and delayed sensory feedback torque to simulate reflex activity was based on either muscle velocity or force. Muscle tone and transient short-range stiffness were necessary to simulate decreased initial swing excursion and non-vertical resting leg angle. Moreover, the reduction in the number of oscillations was best reproduced by simulating stretch reflex activity in terms of force, and not velocity, feedback. Varying only baseline muscle torque and reflex gain, we simulated a range of pendulum test kinematics observed across different levels of spasticity. Our model lends insight into physiological mechanisms of spasticity whose contributions can vary on an individual-specific basis, and potentially across different neurological disorders that manifest spasticity as a symptom.

Perturbation velocity affects linearly estimated neuromechanical wrist joint properties

The dynamic behavior of the wrist joint is governed by nonlinear properties, yet applied mathematical models, used to describe the measured input-output (perturbation-response) relationship, are commonly linear. Consequently, the linearly estimated model parameters will depend on properties of the applied perturbation properties (such perturbation amplitude and velocity). We aimed to systematically address the effects of perturbation velocity on linearly estimated neuromechanical parameters. Using a single axis manipulator ramp and hold perturbations were applied to the wrist joint. Effects of perturbation velocity (0.5, 1 and 3 rad/s) were investigated at multiple background torque levels (0, 0.5 and 1 N·m). With increasing perturbation velocity, estimated joint stiffness remained constant, while damping and reflex gain decreased. This variation in model parameters is dependent on background torque levels, i.e. muscle contraction. These observations support the future development of nonlinear models that are capable of describing wrist joint behavior over a larger range of loading conditions, exceeding the restricted range of operation that is required for linearization.

Case Study: A Bio-Inspired Control Algorithm for a Robotic Foot-Ankle Prosthesis Provides Adaptive Control of Level Walking and Stair Ascent

Powered ankle-foot prostheses assist users through plantarflexion during stance and dorsiflexion during swing. Provision of motor power permits faster preferred walking speeds than passive devices, but use of active motor power raises the issue of control. While several commercially available algorithms provide torque control for many intended activities and variations of terrain, control approaches typically exhibit no inherent adaptation. In contrast, muscles adapt instantaneously to changes in load without sensory feedback due to the intrinsic property that their stiffness changes with length and velocity. We previously developed a “winding filament” hypothesis (WFH) for muscle contraction that accounts for intrinsic muscle properties by incorporating the giant titin protein. The goals of this study were to develop a WFH-based control algorithm for a powered prosthesis and to test its robustness during level walking and stair ascent in a case study of two subjects with 4–5 years of experience using a powered prosthesis. In the WFH algorithm, ankle moments produced by virtual muscles are calculated based on muscle length and activation. Net ankle moment determines the current applied to the motor. Using this algorithm implemented in a BiOM T2 prosthesis, we tested subjects during level walking and stair ascent. During level walking at variable speeds, the WFH algorithm produced plantarflexion angles (range = −8 to −19°) and ankle moments (range = 1 to 1.5 Nm/kg) similar to those produced by the BiOM T2 stock controller and to people with no amputation. During stair ascent, the WFH algorithm produced plantarflexion angles (range −15 to −19°) that were similar to persons with no amputation and were ~5 times larger on average at 80 steps/min than those produced by the stock controller. This case study provides proof-of-concept that, by emulating muscle properties, the WFH algorithm provides robust, adaptive control of level walking at variable speed and stair ascent with minimal sensing and no change in parameters.

Muscle coactivation: definitions, mechanisms, and functions

The phenomenon of agonist-antagonist muscle coactivation is discussed with respect to its consequences for movement mechanics (such as increasing joint apparent stiffness, facilitating faster movements, and effects on action stability), implication for movement optimization, and involvement of different neurophysiological structures. Effects of coactivation on movement stability are ambiguous and depend on the effector representing a kinematic chain with a fixed origin or free origin. Furthermore, coactivation is discussed within the framework of the equilibrium-point hypothesis and the idea of hierarchical control with spatial referent coordinates. Relations of muscle coactivation to changes in one of the basic commands, the c-command, are discussed and illustrated. A hypothesis is suggested that agonist-antagonist coactivation reflects a deliberate neural control strategy to preserve effector-level control and avoid making it degenerate and facing the necessity to control at the level of signals to individual muscles. This strategy, in particular, allows stabilizing motor actions by covaried adjustments in spaces of control variables. This hypothesis is able to account for higher levels of coactivation in young healthy persons performing challenging tasks and across various populations with movement impairments.

Distributed force feedback in the spinal cord and the regulation of limb mechanics

This review is an update on the role of force feedback from Golgi tendon organs in the regulation of limb mechanics during voluntary movement. Current ideas about the role of force feedback are based on modular circuits linking idealized systems of agonists, synergists, and antagonistic muscles. In contrast, force feedback is widely distributed across the muscles of a limb and cannot be understood based on these circuit motifs. Similarly, muscle architecture cannot be understood in terms of idealized systems, since muscles cross multiple joints and axes of rotation and further influence remote joints through inertial coupling. It is hypothesized that distributed force feedback better represents the complex mechanical interactions of muscles, including the stresses in the musculoskeletal network born by muscle articulations, myofascial force transmission, and inertial coupling. Together with the strains of muscle fascicles measured by length feedback from muscle spindle receptors, this integrated proprioceptive feedback represents the mechanical state of the musculoskeletal system. Within the spinal cord, force feedback has excitatory and inhibitory components that coexist in various combinations based on motor task and integrated with length feedback at the premotoneuronal and motoneuronal levels. It is concluded that, in agreement with other investigators, autogenic, excitatory force feedback contributes to propulsion and weight support. It is further concluded that coexistent inhibitory force feedback, together with length feedback, functions to manage interjoint coordination and the mechanical properties of the limb in the face of destabilizing inertial forces and positive force feedback, as required by the accelerations and changing directions of both predator and prey.