Intrinsic muscle properties facilitate locomotor control - a computer simulation study

The History and Future of Neuromusculoskeletal Biomechanics

The Executive Council of the International Society of Biomechanics has initiated and overseen the commemorations of the Society's 50th Anniversary in 2023. This included multiple series of lectures at the ninth World Congress of Biomechanics in 2022 and XXIXth Congress of the International Society of Biomechanics in 2023, all linked to special issues of International Society of Biomechanics' affiliated journals. This special issue of the Journal of Applied Biomechanics is dedicated to the biomechanics of the neuromusculoskeletal system. The reader is encouraged to explore this special issue which comprises 6 papers exploring the current state-of the-art, and future directions and roles for neuromusculoskeletal biomechanics. This editorial presents a very brief history of the science of the neuromusculoskeletal system's 4 main components: the central nervous system, musculotendon units, the musculoskeletal system, and joints, and how they biomechanically integrate to enable an understanding of the generation and control of human movement. This also entails a quick exploration of contemporary neuromusculoskeletal biomechanics and its future with new fields of application.

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.

A reduced-order closed-loop hybrid dynamic model for design and development of lower limb prostheses

This manuscript presents a simplified dynamic human-prosthesis model and simulation framework for the purpose of designing and developing lower limb prosthesis hardware and controllers. The objective was to provide an offline design tool to verify the closed-loop behavior of the prosthesis with the human, in order to avoid relying solely on limiting kinematic and kinetic reference trajectories of (able-bodied) subjects and associated static or inverse dynamic analyses, while not having to resort to complete neuromusculoskeletal models of the human that require extensive optimizations to run. The presented approach employs a reduced-order model that includes only the prosthetic limb and trunk in a multi-body dynamic model. External forces are applied to the trunk during stance phase of the intact leg to represent its presence. Walking is realized by employing the well-known spring-loaded inverted pendulum model, which is shown to generate realistic dynamics on the prosthesis while maintaining a stable and modifiable gait. This simple approach is inspired from the rationale that the human is adaptive, and from the desire to facilitate modifications or inclusions of additional user actions. The presented framework is validated with two use cases, featuring a commercial and research knee prosthesis in combination with a passive ankle prosthesis, performing a continuous sequence of standing still, walking at different velocities and stopping.

Muscle prestimulation tunes velocity preflex in simulated perturbed hopping

Muscle fibres possess unique visco-elastic properties, which generate a stabilising zero-delay response to unexpected perturbations. This instantaneous response-termed "preflex"-mitigates neuro-transmission delays, which are hazardous during fast locomotion due to the short stance duration. While the elastic contribution to preflexes has been studied extensively, the function of fibre viscosity due to the force-velocity relation remains unknown. In this study, we present a novel approach to isolate and quantify the preflex force produced by the force-velocity relation in musculo-skeletal computer simulations. We used our approach to analyse the muscle response to ground-level perturbations in simulated vertical hopping. Our analysis focused on the preflex-phase-the first 30 ms after impact-where neuronal delays render a controlled response impossible. We found that muscle force at impact and dissipated energy increase with perturbation height, helping reject the perturbations. However, the muscle fibres reject only 15% of step-down perturbation energy with constant stimulation. An open-loop rising stimulation, observed in locomotion experiments, amplified the regulatory effects of the muscle fibre's force-velocity relation, resulting in 68% perturbation energy rejection. We conclude that open-loop neuronal tuning of muscle activity around impact allows for adequate feed-forward tuning of muscle fibre viscous capacity, facilitating energy adjustment to unexpected ground-level perturbations.

Muscle model control of knee joint torque in a powered lower-body orthosis

Powered orthoses that employ virtual muscle models for specifying motor commands may better produce natural, human-like joint torque and motion outputs. Here, we design and implement a muscle controller based on the standard 3-element Hill model that outputs a joint torque signal prescribed to the electric motors of a powered orthosis. Real-time simulation of muscle dynamics in a MATLAB/Simulink environment was expressed through a microcontroller on the Parker Hannifin Indego orthosis. To initially demonstrate and examine the force-length and force-velocity relationships of the virtual muscles, we programmed the Indego to perform standard isokinetic and isometric rehabilitation exercises at the knee joint. A Biodex-2 isokinetic dynamometer was used to apply constraints and actively measure changes in knee joint angle, velocity, and torque. The observed torque rise time (∼126 ms) and profiles for torque-angle and torque-velocity for the muscle-model at the knee joint of the orthosis compared favorably to results reported for humans undergoing the same exercises. We further demonstrate potential feasibility for real-world implementation through measures of root mean square error (RMSE) and coefficient of determination (R²), which indicate good matching between the commanded and measured torque outputs. This pilot study represents the first step in developing and implementing control strategies for powered orthoses based on human muscle models.

Predictive Simulations to Replicate Human Gait Adaptations and Energetics With Exoskeletons

Robotic exoskeletons have the potential to restore and enhance human mobility. However, optimally controlling these devices, to work in concert with human users, is challenging. Accurate model simulations of the interaction between exoskeletons and users may expedite the design process and improve control. Here, as a proof of principle, we tested if we could use predictive simulations to replicate human gait adaptations and changes in energy expenditure from an experiment where participants walked with exoskeletons. We recreated a past experimental paradigm, where robotic exoskeletons were used to shift people's energetically optimal step frequency to frequencies higher and lower than normally preferred. To match the experimental controller, we modelled knee-worn exoskeletons that applied resistive torques, either proportional or inversely proportional to step frequency-decreasing or increasing the energy optimal step frequency, respectively. We were able to replicate the experiment, finding higher and lower optimal step frequencies than in natural walking under each respective condition. Our simulated resistive torques and objective landscapes resembled the measured experimental resistive torque and energy landscapes. Individual muscle energetics revealed distinct coordination strategies consistent with each exoskeleton controller condition. Increasing the accuracy of step frequency and energetic predictions was best achieved by increasing the number of virtual participants (varying whole-body anthropometrics), rather than the number of muscle parameter sets (varying muscle anthropometrics). In future, our approach can be used to design controllers in advance of human testing, to help identify reasonable solution spaces or tailor design to individual users.

The control effort to steer self-propelled microswimmers depends on their morphology: comparing symmetric spherical versus asymmetric L-shaped particles

Active goal-directed motion requires real-time adjustment of control signals depending on the system's status, also known as control. The amount of information that needs to be processed depends on the desired motion and control, and on the system's morphology. The morphology of the system may directly effectuate or support the desired motion. This morphology-based reduction to the neuronal 'control effort' can be quantified by a novel information-entropy-based approach. Here, we apply this novel measure of 'control effort' to active microswimmers of different morphology. Their motion is a combination of directed deterministic and stochastic motion. In spherical microswimmers, the active propulsion leads to linear velocities. Active propulsion of asymmetric L-shaped particles leads to circular or-on tilted substrates-directed motion. Thus, the difference in shape, i.e. the morphology of the particles, directly influence the motion. Here, we quantify how this morphology can be exploited by control schemes for the purpose of steering the particles towards targets. Using computer simulations, we found in both cases a significantly lower control effort for L-shaped particles. However, certain movements can only be achieved by spherical particles. This demonstrates that a suitably designed microswimmer's morphology might be exploited to perform specific tasks.

Predictive Simulations of Musculoskeletal Function and Jumping Performance in a Generalized Bird

Jumping is a common, but demanding, behavior that many animals employ during everyday activity. In contrast to jump-specialists such as anurans and some primates, jumping biomechanics and the factors that influence performance remains little studied for generalized species that lack marked adaptations for jumping. Computational biomechanical modeling approaches offer a way of addressing this in a rigorous, mechanistic fashion. Here, optimal control theory and musculoskeletal modeling are integrated to generate predictive simulations of maximal height jumping in a small ground-dwelling bird, a tinamou. A three-dimensional musculoskeletal model with 36 actuators per leg is used, and direct collocation is employed to formulate a rapidly solvable optimal control problem involving both liftoff and landing phases. The resulting simulation raises the whole-body center of mass to over double its standing height, and key aspects of the simulated behavior qualitatively replicate empirical observations for other jumping birds. However, quantitative performance is lower, with reduced ground forces, jump heights, and muscle–tendon power. A pronounced countermovement maneuver is used during launch. The use of a countermovement is demonstrated to be critical to the achievement of greater jump heights, and this phenomenon may only need to exploit physical principles alone to be successful; amplification of muscle performance may not necessarily be a proximate reason for the use of this maneuver. Increasing muscle strength or contractile velocity above nominal values greatly improves jump performance, and interestingly has the greatest effect on more distal limb extensor muscles (i.e., those of the ankle), suggesting that the distal limb may be a critical link for jumping behavior. These results warrant a re-evaluation of previous inferences of jumping ability in some extinct species with foreshortened distal limb segments, such as dromaeosaurid dinosaurs.

Simulations prédictives de la fonction musculo-squelettique et des performances de saut chez un oiseau généralisé Sauter est un comportement commun, mais exigeant, que de nombreux animaux utilisent au cours de leurs activités quotidiennes. Contrairement aux spécialistes du saut tels que les anoures et certains primates, la biomécanique du saut et les facteurs qui influencent la performance restent peu étudiés pour les espèces généralisées qui n’ont pas d’adaptations marquées pour le saut. Les approches de modélisation biomécanique computationnelle offrent un moyen d’aborder cette question de manière rigoureuse et mécaniste. Ici, la théorie du contrôle optimal et la modélisation musculo-squelettique sont intégrées pour générer des simulations prédictives du saut en hauteur maximal chez un petit oiseau terrestre, le tinamou. Un modèle musculo-squelettique tridimensionnel avec 36 actionneurs par patte est utilisé, et une méthode numérique nommée “direct collocation” est employée pour formuler un problème de contrôle optimal rapidement résoluble impliquant les phases de décollage et d’atterrissage. La simulation qui en résulte élève le centre de masse du corps entier à plus du double de sa hauteur debout, et les aspects clés du comportement simulé reproduisent qualitativement les observations empiriques d’autres oiseaux sauteurs. Cependant, les performances quantitatives sont moindres, avec une réduction des forces au sol, des hauteurs de saut et de la puissance musculo-tendineuse. Une manœuvre de contre-mouvement prononcée est utilisée pendant le lancement. Il a été démontré que l’utilisation d’un contre-mouvement est essentielle à l’obtention de hauteurs de saut plus importantes, et il se peut que ce phénomène doive exploiter uniquement des principes physiques pour réussir; l’amplification de la performance musculaire n’est pas nécessairement une raison immédiate de l’utilisation de cette manœuvre. L’augmentation de la force musculaire ou de la vitesse de contraction au-dessus des valeurs nominales améliore grandement la performance de saut et, fait intéressant, a le plus grand effet sur les muscles extenseurs des membres plus distaux (c'est-à-dire ceux de la cheville), ce qui suggère que le membre distal peut être un lien critique pour le comportement de saut. Ces résultats justifient une réévaluation des déductions précédentes de la capacité de sauter chez certaines espèces éteintes avec des segments de membres distaux raccourcis, comme les dinosaures droméosauridés.

Voorspellende simulaties van musculoskeletale functie en springprestaties bij een gegeneraliseerde vogel Springen is een veel voorkomend, maar veeleisend, gedrag dat veel dieren toepassen tijdens hun dagelijkse bezigheden. In tegenstelling tot de springspecialisten zoals de anura en sommige primaten, is de biomechanica van het springen en de factoren die de prestaties beïnvloeden nog weinig bestudeerd voor algemene soorten die geen uitgesproken adaptaties voor het springen hebben. Computationele biomechanische modelbenaderingen bieden een manier om dit op een rigoureuze, mechanistische manier aan te pakken. Hier worden optimale controle theorie en musculoskeletale modellering geïntegreerd om voorspellende simulaties te genereren van maximale hoogtesprong bij een kleine grondbewonende vogel, een tinamou. Een driedimensionaal musculoskeletaal model met 36 actuatoren per poot wordt gebruikt, en directe collocatie wordt toegepast om een snel oplosbaar optimaal controleprobleem te formuleren dat zowel de opstijg-als de landingsfase omvat. De resulterende simulatie verhoogt het lichaamszwaartepunt tot meer dan het dubbele van de stahoogte, en belangrijke aspecten van het gesimuleerde gedrag komen kwalitatief overeen met empirische waarnemingen voor andere springende vogels. De kwantitatieve prestaties zijn echter minder, met verminderde grondkrachten, spronghoogtes en spierpeeskracht. Tijdens de lancering wordt een uitgesproken tegenbewegingsmanoeuvre gebruikt. Aangetoond is dat het gebruik van een tegenbeweging van cruciaal belang is voor het bereiken van grotere spronghoogten, en dit fenomeen hoeft alleen op fysische principes te berusten om succesvol te zijn; versterking van de spierprestaties hoeft niet noodzakelijk een proximate reden te zijn voor het gebruik van deze manoeuvre. Het verhogen van de spierkracht of van de contractiesnelheid boven de nominale waarden verbetert de sprongprestatie aanzienlijk, en heeft interessant genoeg het grootste effect op de meer distale extensoren van de ledematen (d.w.z. die van de enkel), wat suggereert dat de distale ledematen een kritieke schakel kunnen zijn voor het springgedrag. Deze resultaten rechtvaardigen een herevaluatie van eerdere conclusies over springvermogen bij sommige uitgestorven soorten met voorgekorte distale ledematen, zoals dromaeosauride dinosauriërs.

Prädiktive Simulationen der muskuloskelettalen Funktion und Sprungleistung bei einem generalisierten Vogel Springen ist ein übliches jedoch anstrengendes Verhalten, das viele Tiere bei ihren täglichen Aktivitäten einsetzen. Im Gegensatz zu Springspezialisten, wie Fröschen und einigen Primaten, sind bei allgemeinen Arten, welche keine ausgeprägten Anpassung für Sprungverhalten aufweisen, die Biomechanik beim Springen und die Faktoren, welche die Leistungsfähigkeit beeinflussen, noch wenig untersucht. Computergestützte biomechanische Modellierungsverfahren bieten hier eine Möglichkeit, dies in einer gründlichen, mechanistischen Weise anzugehen. In dieser Arbeit werden die optimale Steuerungstheorie und Muskel-Skelett-Modellierung zusammen eingesetzt, um die maximale Sprunghöhe eines kleinen bodenlebenden Vogels, eines Perlsteisshuhns, zu simulieren und zu prognostizieren. Es wird ein dreidimensionales Muskel-Skelett-Modell mit 36 Aktuatoren pro Bein verwendet, und durch direkte Kollokation wird ein schnell lösbares optimales Steuerungsproblem formuliert, das sowohl die Abstoss- als auch die Landephase umfasst. Die daraus folgende Simulation bringt den Ganzkörperschwerpunkt auf mehr als das Doppelte seiner Standhöhe und entscheidende Aspekte des simulierten Verhaltens entsprechen qualitativ empirischen Beobachtungen für andere springende Vögel. Allerdings ist die quantitative Leistungsfähigkeit geringer, mit reduzierten Bodenkräften, Sprunghöhen und Muskel-Sehnen-Kräften. Beim Abstossen wird ein ausgeprägtes Gegenbewegungsmanöver durchgeführt. Die Durchführung einer Gegenbewegung ist nachweislich entscheidend für das Erreichen grösserer Sprunghöhen, wobei dieses Phänomen möglicherweise nur physikalische Prinzipien auszuschöpfen braucht, um erfolgreich zu sein. Die Verstärkung der Muskelleistung ist daher möglicherweise nicht zwingend ein unmittelbarer Grund für die Verwendung dieses Manövers. Eine Erhöhung der Muskelkraft oder der Kontraktionsgeschwindigkeit über die Nominalwerte hinaus führt zu einer erheblichen Zunahme der Sprungleistung und hat interessanterweise den grössten Effekt bei den weiter distal gelegenen Streckmuskeln der Beine (d.h. bei denjenigen des Sprunggelenks), was darauf hindeutet, dass die distale Gliedmasse ein entscheidendes Element für das Sprungverhalten sein könnte. Diese Ergebnisse geben Anlass zur Überprüfung früherer Schlussfolgerungen hinsichtlich der Sprungfähigkeit einiger ausgestorbener Arten mit verkürzten distalen Gliedmassen, wie beispielsweise bei dromaeosauriden Dinosauriern.

Computational modelling of muscle fibre operating ranges in the hindlimb of a small ground bird (Eudromia elegans), with implications for modelling locomotion in extinct species

The arrangement and physiology of muscle fibres can strongly influence musculoskeletal function and whole-organismal performance. However, experimental investigation of muscle function during in vivo activity is typically limited to relatively few muscles in a given system. Computational models and simulations of the musculoskeletal system can partly overcome these limitations, by exploring the dynamics of muscles, tendons and other tissues in a robust and quantitative fashion. Here, a high-fidelity, 26-degree-of-freedom musculoskeletal model was developed of the hindlimb of a small ground bird, the elegant-crested tinamou (Eudromia elegans, ~550 g), including all the major muscles of the limb (36 actuators per leg). The model was integrated with biplanar fluoroscopy (XROMM) and forceplate data for walking and running, where dynamic optimization was used to estimate muscle excitations and fibre length changes throughout both gaits. Following this, a series of static simulations over the total range of physiological limb postures were performed, to circumscribe the bounds of possible variation in fibre length. During gait, fibre lengths for all muscles remained between 0.5 to 1.21 times optimal fibre length, but operated mostly on the ascending limb and plateau of the active force-length curve, a result that parallels previous experimental findings for birds, humans and other species. However, the ranges of fibre length varied considerably among individual muscles, especially when considered across the total possible range of joint excursion. Net length change of muscle-tendon units was mostly less than optimal fibre length, sometimes markedly so, suggesting that approaches that use muscle-tendon length change to estimate optimal fibre length in extinct species are likely underestimating this important parameter for many muscles. The results of this study clarify and broaden understanding of muscle function in extant animals, and can help refine approaches used to study extinct species.

Forward dynamic simulation of Japanese macaque bipedal locomotion demonstrates better energetic economy in a virtualised plantigrade posture

A plantigrade foot with a large robust calcaneus is regarded as a distinctive morphological feature of the human foot; it is presumably the result of adaptation for habitual bipedal locomotion. The foot of the Japanese macaque, on the other hand, does not have such a feature, which hampers it from making foot-ground contact at the heel during bipedal locomotion. Understanding how this morphological difference functionally affects the generation of bipedal locomotion is crucial for elucidating the evolution of human bipedalism. In this study, we constructed a forward dynamic simulation of bipedal locomotion in the Japanese macaque based on a neuromusculoskeletal model to evaluate how virtual manipulation of the foot structure from digitigrade to plantigrade affects the kinematics, dynamics, and energetics of bipedal locomotion in a nonhuman primate whose musculoskeletal anatomy is not adapted to bipedalism. The normal bipedal locomotion generated was in good agreement with that of actual Japanese macaques. If, as in human walking, the foot morphology was altered to allow heel contact, the vertical ground reaction force profile became double-peaked and the cost of transport decreased. These results suggest that evolutionary changes in the foot structure were important for the acquisition of human-like efficient bipedal locomotion.

A Conceptual Blueprint for Making Neuromusculoskeletal Models Clinically Useful

The ultimate goal of most neuromusculoskeletal modeling research is to improve the treatment of movement impairments. However, even though neuromusculoskeletal models have become more realistic anatomically, physiologically, and neurologically over the past 25 years, they have yet to make a positive impact on the design of clinical treatments for movement impairments. Such impairments are caused by common conditions such as stroke, osteoarthritis, Parkinson’s disease, spinal cord injury, cerebral palsy, limb amputation, and even cancer. The lack of clinical impact is somewhat surprising given that comparable computational technology has transformed the design of airplanes, automobiles, and other commercial products over the same time period. This paper provides the author’s personal perspective for how neuromusculoskeletal models can become clinically useful. First, the paper motivates the potential value of neuromusculoskeletal models for clinical treatment design. Next, it highlights five challenges to achieving clinical utility and provides suggestions for how to overcome them. After that, it describes clinical, technical, collaboration, and practical needs that must be addressed for neuromusculoskeletal models to fulfill their clinical potential, along with recommendations for meeting them. Finally, it discusses how more complex modeling and experimental methods could enhance neuromusculoskeletal model fidelity, personalization, and utilization. The author hopes that these ideas will provide a conceptual blueprint that will help the neuromusculoskeletal modeling research community work toward clinical utility.

Muscles Reduce Neuronal Information Load: Quantification of Control Effort in Biological vs. Robotic Pointing and Walking

It is hypothesized that the nonlinear muscle characteristic of biomechanical systems simplify control in the sense that the information the nervous system has to process is reduced through off-loading computation to the morphological structure. It has been proposed to quantify the required information with an information-entropy based approach, which evaluates the minimally required information to control a desired movement, i.e., control effort. The key idea is to compare the same movement but generated by different actuators, e.g., muscles and torque actuators, and determine which of the two morphologies requires less information to generate the same movement. In this work, for the first time, we apply this measure to numerical simulations of more complex human movements: point-to-point arm movements and walking. These models consider up to 24 control signals rendering the brute force approach of the previous implementation to search for the minimally required information futile. We therefore propose a novel algorithm based on the pattern search approach specifically designed to solve this constraint optimization problem. We apply this algorithm to numerical models, which include Hill-type muscle-tendon actuation as well as ideal torque sources acting directly on the joints. The controller for the point-to-point movements was obtained by deep reinforcement learning for muscle and torque actuators. Walking was controlled by proprioceptive neural feedback in the muscular system and a PD controller in the torque model. Results show that the neuromuscular models consistently require less information to successfully generate the movement than the torque-driven counterparts. These findings were consistent for all investigated controllers in our experiments, implying that this is a system property, not a controller property. The proposed algorithm to determine the control effort is more efficient than other standard optimization techniques and provided as open source.

Morphological Computation Increases From Lower- to Higher-Level of Biological Motor Control Hierarchy

Voluntary movements, like point-to-point or oscillatory human arm movements, are generated by the interaction of several structures. High-level neuronal circuits in the brain are responsible for planning and initiating a movement. Spinal circuits incorporate proprioceptive feedback to compensate for deviations from the desired movement. Muscle biochemistry and contraction dynamics generate movement driving forces and provide an immediate physical response to external forces, like a low-level decentralized controller. A simple central neuronal command like "initiate a movement" then recruits all these biological structures and processes leading to complex behavior, e.g., generate a stable oscillatory movement in resonance with an external spring-mass system. It has been discussed that the spinal feedback circuits, the biochemical processes, and the biomechanical muscle dynamics contribute to the movement generation, and, thus, take over some parts of the movement generation and stabilization which would otherwise have to be performed by the high-level controller. This contribution is termed morphological computation and can be quantified with information entropy-based approaches. However, it is unknown whether morphological computation actually differs between these different hierarchical levels of the control system. To investigate this, we simulated point-to-point and oscillatory human arm movements with a neuro-musculoskeletal model. We then quantify morphological computation on the different hierarchy levels. The results show that morphological computation is highest for the most central (highest) level of the modeled control hierarchy, where the movement initiation and timing are encoded. Furthermore, they show that the lowest neuronal control layer, the muscle stimulation input, exploits the morphological computation of the biochemical and biophysical muscle characteristics to generate smooth dynamic movements. This study provides evidence that the system's design in the mechanical as well as in the neurological structure can take over important contributions to control, which would otherwise need to be performed by the higher control levels.

Joint and muscle-tendon coordination strategies during submaximal jumping

Previous research has demonstrated that during submaximal jumping humans prioritize reducing energy consumption by minimizing countermovement depth. However, sometimes movement is constrained to a nonpreferred pattern, and this requires adaptation of neural control that accounts for complex interactions between muscle architecture, muscle properties, and task demands. This study compared submaximal jumping with either a preferred or a deep countermovement depth to examine how joint and muscle mechanics are integrated into the adaptation of coordination strategies in the deep condition. Three-dimensional motion capture, two force plates, electromyography, and ultrasonography were used to examine changes in joint kinetics and kinematics, muscle activation, and muscle kinematics for the lateral gastrocnemius and soleus. Results demonstrated that a decrease in ankle joint work during the deep countermovement depth was due to increased knee flexion, leading to unfavorably short biarticular muscle lengths and reduced active fascicle length change during ankle plantar flexion. Therefore, ankle joint work was likely decreased because of reduced active fascicle length change and operating position on the force-length relationship. Hip joint work was significantly increased as a result of altered muscle activation strategies, likely due to a substantially greater hip extensor muscle activation period compared with plantar flexor muscles during jumping. Therefore, coordination strategies at individual joints are likely influenced by time availability, where a short plantar flexor activation time results in dependence on muscle properties, instead of simply altering muscle activation, while the longer time for contraction of muscles at the hip allows for adjustments to voluntary neural control.

NEW & NOTEWORTHY Using human jumping as a model, we show that adapting movement patterns to altered task demands is achieved differently by muscles across the leg. Because of proximal-to-distal sequencing, distal muscles (i.e., plantar flexors) have reduced activation periods and, as a result, rely on muscle contractile properties (force-length relationship) for adjusting joint kinetics. For proximal muscles that have greater time availability, voluntary activation is modulated to adjust muscle outputs.

Scaling of inertial delays in terrestrial mammals

As part of its response to a perturbation, an animal often needs to reposition its body. Inertia acts to oppose the corrective motion, delaying the completion of the movement-we refer to this elapsed time as inertial delay. As animal size increases, muscle moment arms also increase, but muscles are proportionally weaker, and limb inertia is proportionally larger. Consequently, the scaling of inertial delays is complex. Our intent is to determine how quickly different sized animals can produce corrective movements when their muscles act at their force capacity, relative to the time within which those movements need to be performed. Here, we quantify inertial delay using two biomechanical models representing common scenarios in animal locomotion: a distributed mass pendulum approximating swing limb repositioning (swing task), and an inverted pendulum approximating whole body posture recovery (posture task). We parameterized the anatomical, muscular, and inertial properties of these models using literature scaling relationships, then determined inertial delay for each task across a large range of movement magnitudes and the full range of terrestrial mammal sizes. We found that inertial delays scaled with an average of M0.28 in the swing task and M0.35 in the posture task across movement magnitudes-larger animals require more absolute time to perform the same movement as small animals. The time available to complete a movement also increases with animal size, but less steeply. Consequently, inertial delays comprise a greater fraction of swing duration and other characteristic movement times in larger animals. We also compared inertial delays to the other component delays within the stimulus-response pathway. As movement magnitude increased, inertial delays exceeded these sensorimotor delays, and this occurred for smaller movements in larger animals. Inertial delays appear to be a challenge for motor control, particularly for bigger movements in larger animals.

The influence of added mass on muscle activation and contractile mechanics during submaximal and maximal countermovement jumping in humans

Muscle contractile mechanics induced by the changing demands of human movement have the potential to influence our movement strategies. This study examined fascicle length changes of the triceps surae during jumping with added mass or increasing jump height to determine whether the chosen movement strategies were associated with relevant changes in muscle contractile properties. Sixteen participants jumped at sub-maximal and maximal intensities while total net work was matched via two distinct paradigms: (1) adding mass to the participant or (2) increasing jump height. Electromyography (EMG) and ultrasound analyses were performed to examine muscle activation, fascicle length and fascicle velocity changes of the triceps surae during jumping. Integrated EMG was significantly higher in the added mass paradigm with no difference in mean or maximal EMG, indicating that the muscle was activated for a significantly longer period of time but not activated to a greater intensity. Fascicle shortening velocity was slower with added mass compared than with increasing jump height; therefore, intrinsic force–velocity properties probably enabled increased force production. Improved fascicle contractile mechanics paired with a longer activation period probably produced a consistently larger fascicle force, enabling a greater impulse about the ankle joint. This may explain why previous research found that participants used an ankle-centred strategy for work production in the added mass paradigm and not in the jump height paradigm. The varied architecture of muscles within the lower limb may influence which muscles we choose to employ for work production under different task constraints.

A Novel Optimization Framework to Improve the Computational Cost of Muscle Activation Prediction for a Neuromusculoskeletal System

The high computational cost (CC) of neuromusculoskeletal modeling is usually considered a serious barrier in clinical applications. Different approaches have been developed to lessen CC and amplify the accuracy of muscle activation prediction based on forward and inverse analyses by applying different optimization algorithms. This study is aimed at proposing two novel approaches, inverse muscular dynamics with inequality constraints (IMDIC) and inverse-forward muscular dynamics with inequality constraints (IFMDIC), not only to reduce CC but also to amend the computational errors compared to the well-known approach of extended inverse dynamics (EID). To do that, the equality constraints of optimization problem, which are computationally tough to satisfy, are replaced by inequality constraints, which are easier to satisfy. To verify the practical application of the proposed approaches, the muscle activations of the lower limbs during the half of a gait cycle are quantified. The simulation results of the optimal muscle activations are then compared to the experimental ones. The results reveal that IMDIC requires less CC (87.5%) compared to EID. In addition, CC of IMDIC was about 33.3% improved by the application of IFMDIC. The findings of this study suggest that although the novel approach of IFMDIC decreases CC compared to IMDIC, the convergence of its results is very sensitive to the primary guess of the optimization variables.

Simulation Analysis of Linear Quadratic Regulator Control of Sagittal-Plane Human Walking-Implications for Exoskeletons

The linear quadratic regulator (LQR) is a classical optimal control approach that can regulate gait dynamics about target kinematic trajectories. Exoskeletons to restore gait function have conventionally utilized time-varying proportional-derivative (PD) control of leg joints. But, these PD parameters are not uniquely optimized for whole-body (full-state) performance. The objective of this study was to investigate the effectiveness of LQR full-state feedback compared to PD control to maintain bipedal walking of a sagittal-plane computational model against force disturbances. Several LQR controllers were uniquely solved with feedback gains optimized for different levels of tracking capability versus control effort. The main implications to future exoskeleton control systems include (1) which LQR controllers out-perform PD controllers in walking maintenance and effort, (2) verifying that LQR desirably produces joint torques that oppose rapidly growing joint state errors, and (3) potentially equipping accurate sensing systems for nonjoint states such as hip-position and torso orientation. The LQR controllers capable of longer walk times than respective PD controllers also required less control effort. During sudden leg collapse, LQR desirably behaved like PD by generating feedback torques that opposed the direction of leg-joint errors. Feedback from nonjoint states contributed to over 50% of the LQR joint torques and appear critical for whole-body LQR control. While LQR control poses implementation challenges, such as more sensors for full-state feedback and operation near the desired trajectories, it offers significant performance advantages over PD control.

An Efficient Inverse Dynamics Optimization Formulation for Musculoskeletal Motion Prediction

In this study, an inverse dynamics optimization formulation and solution procedure is developed for musculoskeletal simulations. The proposed method has three main features: high order recursive B-spline interpolation, partition of unity, and inverse dynamics formulation. First, joint angle and muscle force profiles are represented by recursive B-splines. The formula for high order recursive B-spline derivatives are derived for state variables calculation. Second, partition of unity is used to handle the multi-contact indeterminacy between human and environment during the motion. The global forces and moments are distributed to each contacting point through the corresponding partition ratio. Third, joint torques are inversely calculated from equations of motion based on state variables and contacts to avoid numerical integration of equations of motion. Therefore, the design variables for the optimization problem are joint angle control points, muscle force control points, knot vector, and partition ratios for contacting points. The sum of muscle stress/activity squared is minimized as the cost function. The constraints are imposed for human physical constraints and task-based constraints. The proposed formulation is demonstrated by simulating a trajectory planning problem of a planar musculoskeletal arm with six muscles. In addition, the gait motion of a two-dimensional musculoskeletal model with sixteen muscles is also optimized by using the approach developed in this paper. The gait optimal solution is obtained in about 1 minute CPU time. The predicted kinematics, kinetics, and muscle forces have general trends that are similar to those reported in the literature.

Prediction of human gait trajectories during the SSP using a neuromusculoskeletal modeling: A challenge for parametric optimization

The parametric optimization techniques have been widely employed to predict human gait trajectories; however, their applications to reveal the other aspects of gait are questionable. The aim of this study is to investigate whether or not the gait prediction model is able to justify the movement trajectories for the higher average velocities. A planar, seven-segment model with sixteen muscle groups was used to represent human neuro-musculoskeletal dynamics. At first, the joint angles, ground reaction forces (GRFs) and muscle activations were predicted and validated for normal average velocity (1.55 m/s) in the single support phase (SSP) by minimizing energy expenditure, which is subject to the non-linear constraints of the gait. The unconstrained system dynamics of extended inverse dynamics (USDEID) approach was used to estimate muscle activations. Then by scaling time and applying the same procedure, the movement trajectories were predicted for higher average velocities (from 2.07 m/s to 4.07 m/s) and compared to the pattern of movement with fast walking speed. The comparison indicated a high level of compatibility between the experimental and predicted results, except for the vertical position of the center of gravity (COG). It was concluded that the gait prediction model can be effectively used to predict gait trajectories for higher average velocities.

THEORETICAL PREDICTION OF THE ROLE OF CO-CONTRACTION DURING BALANCE RECOVERY IN ELDERLY

This study aimed to determine the effect of muscle co-contraction on balance recovery by using a simulation model. The muscle-driven forward simulation model included an inverted pendulum with two ankle muscles, a plantar flexor muscle (PF), and a dorsal flexor muscle (DF). The model was created based on experimental data obtained from balance recovery after applying backward platform translation to a standing elderly woman. Baseline simulation was performed using this model. Additionally, we performed two simulations with increased DF excitation at the same level of simulation and at the same pattern of simulation. The same level of simulation had the same PF excitation level as the baseline simulation with increased DF excitation. The same pattern simulation had the same increased or decreased PF excitation pattern but with a constant increase in PF excitation level to offset the increased DF excitation. Our results revealed that the same pattern simulation decreased the maximum dorsal flexion angle after platform translation. During the same level of simulation, the insufficient PF force used to recover balance resulted in a forward fall. These results imply that co-contraction is an effective strategy for recovering balance at the expense of additional muscle excitation in the elderly.

Evolution of Joint-Level Control for Quadrupedal Locomotion

We investigate a hierarchical approach to robot control inspired by joint-level control in animals. The method combines a high-level controller, consisting of an artificial neural network (ANN), with joint-level controllers based on digital muscles. In the digital muscle model (DMM), morphological and control aspects of joints evolve concurrently, emulating the musculoskeletal system of natural organisms. We introduce and compare different approaches for connecting outputs of the ANN to DMM-based joints. We also compare the performance of evolved animats with ANN-DMM controllers with those governed by only high-level (ANN-only) and low-level (DMM-only) controllers. These results show that DMM-based systems outperform their ANN-only counterparts while also exhibiting less complex ANNs in terms of the number of connections and neurons. The main contribution of this work is to explore the evolution of artificial systems where, as in natural organisms, some aspects of control are realized at the joint level.

Muscle Synergies Facilitate Computational Prediction of Subject-Specific Walking Motions

Researchers have explored a variety of neurorehabilitation approaches to restore normal walking function following a stroke. However, there is currently no objective means for prescribing and implementing treatments that are likely to maximize recovery of walking function for any particular patient. As a first step toward optimizing neurorehabilitation effectiveness, this study develops and evaluates a patient-specific synergy-controlled neuromusculoskeletal simulation framework that can predict walking motions for an individual post-stroke. The main question we addressed was whether driving a subject-specific neuromusculoskeletal model with muscle synergy controls (5 per leg) facilitates generation of accurate walking predictions compared to a model driven by muscle activation controls (35 per leg) or joint torque controls (5 per leg). To explore this question, we developed a subject-specific neuromusculoskeletal model of a single high-functioning hemiparetic subject using instrumented treadmill walking data collected at the subject's self-selected speed of 0.5 m/s. The model included subject-specific representations of lower-body kinematic structure, foot-ground contact behavior, electromyography-driven muscle force generation, and neural control limitations and remaining capabilities. Using direct collocation optimal control and the subject-specific model, we evaluated the ability of the three control approaches to predict the subject's walking kinematics and kinetics at two speeds (0.5 and 0.8 m/s) for which experimental data were available from the subject. We also evaluated whether synergy controls could predict a physically realistic gait period at one speed (1.1 m/s) for which no experimental data were available. All three control approaches predicted the subject's walking kinematics and kinetics (including ground reaction forces) well for the model calibration speed of 0.5 m/s. However, only activation and synergy controls could predict the subject's walking kinematics and kinetics well for the faster non-calibration speed of 0.8 m/s, with synergy controls predicting the new gait period the most accurately. When used to predict how the subject would walk at 1.1 m/s, synergy controls predicted a gait period close to that estimated from the linear relationship between gait speed and stride length. These findings suggest that our neuromusculoskeletal simulation framework may be able to bridge the gap between patient-specific muscle synergy information and resulting functional capabilities and limitations.

Robotic lower limb prosthesis design through simultaneous computer optimizations of human and prosthesis costs

Robotic lower limb prostheses can improve the quality of life for amputees. Development of such devices, currently dominated by long prototyping periods, could be sped up by predictive simulations. In contrast to some amputee simulations which track experimentally determined non-amputee walking kinematics, here, we explicitly model the human-prosthesis interaction to produce a prediction of the user’s walking kinematics. We obtain simulations of an amputee using an ankle-foot prosthesis by simultaneously optimizing human movements and prosthesis actuation, minimizing a weighted sum of human metabolic and prosthesis costs. The resulting Pareto optimal solutions predict that increasing prosthesis energy cost, decreasing prosthesis mass, and allowing asymmetric gaits all decrease human metabolic rate for a given speed and alter human kinematics. The metabolic rates increase monotonically with speed. Remarkably, by performing an analogous optimization for a non-amputee human, we predict that an amputee walking with an appropriately optimized robotic prosthesis can have a lower metabolic cost – even lower than assuming that the non-amputee’s ankle torques are cost-free.

Neural representation of muscle dynamics in voluntary movement control

Several theories of motor control posit that the nervous system has access to a neural representation of muscle dynamics. Yet, this has not been tested experimentally. Should such a representation exist, it was hypothesized that subjects who learned to control a virtual limb using virtual muscles would improve performance faster and show greater generalization than those who learned with a less dynamically complex virtual force generator. Healthy adults practiced using their biceps brachii activity to move a myoelectrically controlled virtual limb from rest to a standard target position with maximum speed and accuracy. Throughout practice, generalization was assessed with untrained target trials and sensitivity to actuator dynamics was probed by unexpected actuator model switches. In a muscle model subject group (n = 10), the biceps electromyographic signal activated a virtual muscle that pulled on the virtual limb with a force governed by muscle dynamics, defined by a nonlinear force-length-velocity relation and series elastic stiffness. A force generator group (n = 10) performed the same task, but the actuation force was a linear function of the biceps activation signal. Both groups made significant errors with unexpected actuator dynamics switches, supporting task sensitivity to actuator dynamics. The muscle model group improved performance as fast as the force generator group and showed greater generalization in early practice, despite using an actuator with more complex dynamics. These results are consistent with a preexisting neural representation of muscle dynamics, which may have offset any learning challenges associated with the more dynamically complex virtual muscle model.

A comparison of muscle energy models for simulating human walking in three dimensions

The popular Hill model for muscle activation and contractile dynamics has been extended with several different formulations for predicting the metabolic energy expenditure of human muscle actions. These extended models differ considerably in their approach to computing energy expenditure, particularly in their treatment of active lengthening and eccentric work, but their predictive abilities have never been compared. In this study, we compared the predictions of five different Hill-based muscle energy models in 3D forward dynamics simulations of normal human walking. In a data-tracking simulation that minimized muscle fatigue, the energy models predicted metabolic costs that varied over a three-fold range (2.45-7.15 J/m/kg), with the distinction arising from whether or not eccentric work was subtracted from the net heat rate in the calculation of the muscle metabolic rate. In predictive simulations that optimized neuromuscular control to minimize the metabolic cost, all five models predicted similar speeds, step lengths, and stance phase durations. However, some of the models predicted a hip circumduction strategy to minimize metabolic cost, while others did not, and the accuracy of the predicted knee and ankle angles and ground reaction forces also depended on the energy model used. The results highlights the need to clarify how eccentric work should be treated when calculating muscle energy expenditure, the difficulty in predicting realistic metabolic costs in simulated walking even with a detailed 3D musculoskeletal model, the potential for using such models to predict energetically-optimal gait modifications, and the room for improvement in existing muscle energy models and locomotion simulation frameworks.

Quantifying control effort of biological and technical movements: an information-entropy-based approach

In biomechanics and biorobotics, muscles are often associated with reduced movement control effort and simplified control compared to technical actuators. This is based on evidence that the nonlinear muscle properties positively influence movement control. It is, however, open how to quantify the simplicity aspect of control effort and compare it between systems. Physical measures, such as energy consumption, stability, or jerk, have already been applied to compare biological and technical systems. Here a physical measure of control effort based on information entropy is presented. The idea is that control is simpler if a specific movement is generated with less processed sensor information, depending on the control scheme and the physical properties of the systems being compared. By calculating the Shannon information entropy of all sensor signals required for control, an information cost function can be formulated allowing the comparison of models of biological and technical control systems. Exemplarily applied to (bio-)mechanical models of hopping, the method reveals that the required information for generating hopping with a muscle driven by a simple reflex control scheme is only I=32 bits versus I=660 bits with a DC motor and a proportional differential controller. This approach to quantifying control effort captures the simplicity of a control scheme and can be used to compare completely different actuators and control approaches.

Biomechanical and metabolic responses to seat-tube angle variation during cycling in tri-athletes

One of the most physically demanding parts of triathlon is the transition from cycling to running. Many tri-athletes believe that increasing seat-tube angle (STA) can bring advantages in the following running part. The aim of this study was to evaluate the effects of inverting the support of the seat, for increasing STA, on the metabolic response and on the muscle activation pattern, maintaining a controlled kinematic. Moreover, a muscle-skeletal model was applied to evaluate the hypothesis that increasing STA changes force-producing capabilities of muscles crossing the hip. Ten tri-athletes cycled at two different power levels and with two different STA's. Gas exchange data, kinematics and surface electromyography (sEMG) were acquired during the tests. sEMG was measured from eight muscles of the right side of the body. A model of muscle mechanics and energy expenditure was applied to estimate variations of force production capabilities and muscle energy consumption between the two STA configurations. Inverting the support of the seat showed no significant effects on kinematic, Oxygen consumption, muscle activations and muscle power production capabilities. Nevertheless, an interesting advantage can be the tendency to less activate gastrocnemius and biceps femoris: this could lead to minor muscle fatigue during the following running phase.

A bio-robotic platform for integrating internal and external mechanics during muscle-powered swimming

To explore the interplay between muscle function and propulsor shape in swimming animals, we built a robotic foot to mimic the morphology and hind limb kinematics of Xenopus laevis frogs. Four foot shapes ranging from low aspect ratio (AR = 0.74) to high (AR = 5) were compared to test whether low-AR feet produce higher propulsive drag force resulting in faster swimming. Using feedback loops, two complementary control modes were used to rotate the foot: force was transmitted to the foot either from (1) a living plantaris longus (PL) muscle stimulated in vitro or (2) an in silico mathematical model of the PL. To mimic forward swimming, foot translation was calculated in real time from fluid force measured at the foot. Therefore, bio-robot swimming emerged from muscle-fluid interactions via the feedback loop. Among in vitro-robotic trials, muscle impulse ranged from 0.12 ± 0.002 to 0.18 ± 0.007 N s and swimming velocities from 0.41 ± 0.01 to 0.43 ± 0.00 m s(-1), similar to in vivo values from prior studies. Trends in in silico-robotic data mirrored in vitro-robotic observations. Increasing AR caused a small (∼10%) increase in peak bio-robot swimming velocity. In contrast, muscle force-velocity effects were strongly dependent on foot shape. Between low- and high-AR feet, muscle impulse increased ∼50%, while peak shortening velocity decreased ∼50% resulting in a ∼20% increase in net work. However, muscle-propulsion efficiency (body center of mass work/muscle work) remained independent of AR. Thus, we demonstrate how our experimental technique is useful for quantifying the complex interplay among limb morphology, muscle mechanics and hydrodynamics.

Predictive simulation of gait at low gravity reveals skipping as the preferred locomotion strategy

The investigation of gait strategies at low gravity environments gained momentum recently as manned missions to the Moon and to Mars are reconsidered. Although reports by astronauts of the Apollo missions indicate alternative gait strategies might be favored on the Moon, computational simulations and experimental investigations have been almost exclusively limited to the study of either walking or running, the locomotion modes preferred under Earth's gravity. In order to investigate the gait strategies likely to be favored at low gravity a series of predictive, computational simulations of gait are performed using a physiological model of the musculoskeletal system, without assuming any particular type of gait. A computationally efficient optimization strategy is utilized allowing for multiple simulations. The results reveal skipping as more efficient and less fatiguing than walking or running and suggest the existence of a walk-skip rather than a walk-run transition at low gravity. The results are expected to serve as a background to the design of experimental investigations of gait under simulated low gravity.

Stabilisation of walking by intrinsic muscle properties revealed in a three-dimensional muscle-driven simulation

A fundamental question in movement science is how humans perform stable movements in the presence of disturbances such as contact with objects. It remains unclear how the nervous system, with delayed responses to disturbances, maintains the stability of complex movements. We hypothesised that intrinsic muscle properties (i.e. the force-length-velocity properties of muscle fibres and tendon elasticity) may help stabilise human walking by responding instantaneously to a disturbance and providing forces that help maintain the movement trajectory. To investigate this issue, we generated a 3D muscle-driven simulation of walking and analysed the changes in the simulation's motion when a disturbance was applied to models with and without intrinsic muscle properties. Removing the intrinsic properties reduced the stability; this was true when the disturbing force was applied at a variety of times and in different directions. Thus, intrinsic muscle properties play a unique role in stabilising walking, complementing the delayed response of the central nervous system.

Integration of intrinsic muscle properties, feed-forward and feedback signals for generating and stabilizing hopping

It was hypothesized that a tight integration of feed-forward and feedback-driven muscle activation with the characteristic intrinsic muscle properties is a key feature of locomotion in challenging environments. In this simulation study it was investigated whether a combination of feed-forward and feedback signals improves hopping stability compared with those simulations with one individual type of activation. In a reduced one-dimensional hopping model with a Hill-type muscle (one contractile element, neither serial nor parallel elastic elements), the level of detail of the muscle's force-length-velocity relation and the type of activation generation (feed-forward, feedback and combination of both) were varied to test their influence on periodic hopping. The stability of the hopping patterns was evaluated by return map analysis. It was found that the combination of feed-forward and proprioceptive feedback improved hopping stability. Furthermore, the nonlinear Hill-type representation of intrinsic muscle properties led to a faster reduction of perturbations than a linear approximation, independent of the type of activation. The results emphasize the ability of organisms to exploit the stabilizing properties of intrinsic muscle characteristics.

Energy management that generates terrain following versus apex-preserving hopping in man and machine

While hopping, 12 subjects experienced a sudden step down of 5 or 10 cm. Results revealed that the hopping style was "terrain following". It means that the subjects pursued to keep the distance between maximum hopping height (apex) and ground profile constant. The spring-loaded inverse pendulum (SLIP) model, however, which is currently considered as template for stable legged locomotion would predict apex-preserving hopping, by which the absolute maximal hopping height is kept constant regardless of changes of the ground level. To get more insight into the physics of hopping, we outlined two concepts of energy management: "constant energy supply", by which in each bounce--regardless of perturbations--the same amount of mechanical energy is injected, and "lost energy supply", by which the mechanical energy that is going to be dissipated in the current cycle is assessed and replenished. When tested by simulations and on a robot testbed capable of hopping, constant energy supply generated stable and robust terrain following hopping, whereas lost energy supply led to something like apex-preserving hopping, which, however, lacks stability as well as robustness. Comparing simulated and machine hopping with human hopping suggests that constant energy supply has a good chance to be used by humans to generate hopping.

MUSCULOSKELETAL STABILIZATION OF THE ELBOW — COMPLEX OR REAL

Both sensory information and mechanical properties of the musculoskeletal system are necessary for fast and appropriate reactions of humans and animals to environmental perturbations. In this paper, we focus on the musculoskeletal system and study the stability of a human elbow in an equilibrium state. We derive a biomechanical model of the human elbow, including an antagonistic pair of muscles, and investigate the stability analytically based on the theory of Ljapunov. Depending on the elbow angle and the level of coactivation, we obtain the following three qualitatively different behaviors: unstable, stable with real eigenvalues, and stable with complex eigenvalues. If the eigenvalues are real, then the system is critically damped; for complex eigenvalues, solutions near the equilibrium are oscillating. Based on experimental data, we found that in principle real and complex behaviors may occur in human arm movements. The experiments support the analytical predictions. Furthermore, in agreement with the simulations, we found differences in the experimental results among the subjects. The results of this study support the assumption that arm movements around an equilibrium point may be self-stabilized without sensory feedback or motor control, based only on mechanical properties of musculoskeletal systems.

Limitations to maximum sprinting speed imposed by muscle mechanical properties

It has been suggested that the force-velocity relationship of skeletal muscle plays a critical limiting role in the maximum speed at which humans can sprint. However, this theory has not been tested directly, and it is possible that other muscle mechanical properties play limiting roles as well. In this study, forward dynamics simulations of human sprinting were generated using a 2D musculoskeletal model actuated by Hill muscle models. The initial simulation results compared favorably to kinetic, kinematic, and electromyographic data recorded from sprinting humans. Muscle mechanical properties were then removed in isolation to quantify their effect on maximum sprinting speed. Removal of the force-velocity, excitation-activation, and force-length relationships increased the maximum speed by 15, 8, and 4%, respectively. Removal of the series elastic force-extension relationship decreased the maximum speed by 26%. Each relationship affected both stride length and stride frequency except for the force-length relationship, which mainly affected stride length. Removal of all muscular properties entirely (optimized joint torques) increased speed (+22%) to a greater extent than the removal of any single contractile property. The results indicate that the force-velocity relationship is indeed the most important contractile property of muscle regarding limits to maximum sprinting speed, but that other muscular properties also play important roles. Interactions between the various muscular properties should be considered when explaining limits to maximal human performance.

An EMG-driven model applied for predicting metabolic energy consumption during movement

The relationship between mechanical work and metabolic energy cost during movement is not yet clear. Many studies demonstrated the utility of forward-dynamic musculoskeletal models combined with experimental data to address such question. The aim of this study was to evaluate the applicability of a muscle energy expenditure model at whole body level, using an EMG-driven approach. Four participants performed a 5-min squat exercise on unilateral leg press at two different frequencies and two load levels. Data collected were kinematics, EMG, forces and moments under the foot and gas-exchange data. This same task was simulated using a musculoskeletal model, which took EMG and kinematics as inputs and gave muscle forces and muscle energetics as outputs. Model parameters were taken from literature, but maximal isometric muscle force was optimized in order to match predicted joint moments with measured ones. Energy rates predicted by the model were compared with energy consumption measured by the gas-exchange data. Model results on metabolic energy consumption were close to the values obtained through indirect calorimetry. At the higher frequency level, the model underestimated measured energy consumption. This underestimation can be explained with an increase in energy consumption of the non-muscular mass with movement velocity. In conclusion, results obtained in comparing model predictions with experimental data were promising. More research is needed to evaluate this way of computing mechanical and metabolic work.

Sensitivity analysis of an energetic muscle model applied at whole body level in recumbent pedalling

Musculoskeletal models are used in order to describe and analyse the mechanics of human movement. In order to get a complete evaluation of the human movement, energetic muscle models were developed and were shown to be promising. The aim of this work is to determine the sensitivity of muscle mechanical and energetic model estimates to changes in parameters during recumbent pedalling. Inputs of the model were electromyography and joint angles, collected experimentally on one participant. The sensitivity analysis was performed on muscle-specific tension, physiological cross-sectional area, muscle maximal force, tendon rest length and percentage of fast-twitch fibres using an integrated sensitivity ratio. Soleus, gastrocnemius, vasti, gluteus and medial hamstrings were selected for the analyses. The energetic model was found to be always less sensitive to parameter changes than the mechanical model. Tendon slack length was found to be the most critical parameter for both energetic and mechanical models even if the effect on the energetic output was smaller than on muscle force and joint moments.

A method to simulate motor control strategies to recover from perturbations: application to a stumble recovery during gait

Perturbations during human gait such as a trip or a slip can result in a fall, especially among frail populations such as the elderly. In order to recover from a trip or a stumble during gait, humans perform different types of recovery strategies. It is very useful to uncover the mechanisms of the recovery to improve training methods for populations at risk of falling. Moreover, human recovery strategies could be applied to implement controllers for bipedal robot walker, as an application of biomimetic design. A biomechanical model of the response to a trip during gait might uncover the control mechanisms underlying the different recovery strategies and the adaptation of the responses found during the execution of successive perturbation trials. This paper introduces a model of stumble in the multibody system framework. This model is used to assess different feedforward strategies to recover from a trip. First of all, normal gait patterns for the musculoskeletal system model are obtained by solving an optimal control problem. Secondly, the reference gait is perturbed by the application of forces on the swinging foot in different ways: as an instantaneous inelastic collision of the foot with an obstacle, as an impulsive horizontal force or using a force curve measured experimentally during gait perturbation experiments. The influence of the type of perturbation, the timing of the collision with respect to the gait cycle, as well as of the coefficient of restitution was investigated previously. Finally, in order to test the effects of different muscle excitation levels on the initial phases of the recovery response, several muscle excitations were added to selected muscles of the legs, thus providing a simulation of the recovery reactions. These results pave the way for future analysis and modeling of the control mechanisms of gait.

Concurrent musculoskeletal dynamics and finite element analysis predicts altered gait patterns to reduce foot tissue loading

Current computational methods for simulating locomotion have primarily used muscle-driven multibody dynamics, in which neuromuscular control is optimized. Such simulations generally represent joints and soft tissue as simple kinematic or elastic elements for computational efficiency. These assumptions limit application in studies such as ligament injury or osteoarthritis, where local tissue loading must be predicted. Conversely, tissue can be simulated using the finite element method with assumed or measured boundary conditions, but this does not represent the effects of whole body dynamics and neuromuscular control. Coupling the two domains would overcome these limitations and allow prediction of movement strategies guided by tissue stresses. Here we demonstrate this concept in a gait simulation where a musculoskeletal model is coupled to a finite element representation of the foot. Predictive simulations incorporated peak plantar tissue deformation into the objective of the movement optimization, as well as terms to track normative gait data and minimize fatigue. Two optimizations were performed, first without the strain minimization term and second with the term. Convergence to realistic gait patterns was achieved with the second optimization realizing a 44% reduction in peak tissue strain energy density. The study demonstrated that it is possible to alter computationally predicted neuromuscular control to minimize tissue strain while including desired kinematic and muscular behavior. Future work should include experimental validation before application of the methodology to patient care.

Stance and swing phase costs in human walking

Leg swing in human walking has historically been viewed as a passive motion with little metabolic cost. Recent estimates of leg swing costs are equivocal, covering a range from 10 to 33 per cent of the net cost of walking. There has also been a debate as to whether the periods of double-limb support during the stance phase dominate the cost of walking. Part of this uncertainty is because of our inability to measure metabolic energy consumption in individual muscles during locomotion. Therefore, the purpose of this study was to investigate the metabolic cost of walking using a modelling approach that allowed instantaneous energy consumption rates in individual muscles to be estimated over the full gait cycle. At a typical walking speed and stride rate, leg swing represented 29 per cent of the total muscular cost. During the stance phase, the double-limb and single-limb support periods accounted for 27 and 44 per cent of the total cost, respectively. Performing step-to-step transitions, which encompasses more than just the double-support periods, represented 37 per cent of the total cost of walking. Increasing stride rate at a constant speed led to greater double-limb support costs, lower swing phase costs and no change in single-limb support costs. Together, these results provide unique insight as to how metabolic energy is expended over the human gait cycle.

Distribution of Forces Between Synergistics and Antagonistics Muscles Using an Optimization Criterion Depending on Muscle Contraction Behavior

In this paper, a new neuromusculoskeletal simulation strategy is proposed. It is based on a cascade control approach with an inner muscular-force control loop and an outer joint-position control loop. The originality of the work is located in the optimization criterion used to distribute forces between synergistic and antagonistic muscles. The cost function and the inequality constraints depend on an estimation of the muscle fiber length and its time derivative. The advantages of a such criterion are exposed by theoretical analysis and numerical tests. The simulation model used in the numerical tests consists in an anthropomorphic arm model composed by two joints and six muscles. Each muscle is modeled as a second-order dynamical system including activation and contraction dynamics. Contraction dynamics is represented using a classical Hill’s model.

The role of intrinsic muscle properties for stable hopping--stability is achieved by the force-velocity relation

A reductionist approach was presented to investigate which level of detail of the physiological muscle is required for stable locomotion. Periodic movements of a simplified one-dimensional hopping model with a Hill-type muscle (one contractile element, neither serial nor parallel elastic elements) were analyzed. Force-length and force-velocity relations of the muscle were varied in three levels of approximation (constant, linear and Hill-shaped nonlinear) resulting in nine different hopping models of different complexity. Stability of these models was evaluated by return map analysis and the performance by the maximum hopping height. The simplest model (constant force-length and constant force-velocity relations) outperformed all others in the maximum hopping height but was unstable. Stable hopping was achieved with linear and Hill-shaped nonlinear characteristic of the force-velocity relation. The characteristics of the force-length relation marginally influenced hopping stability. The results of this approach indicate that the intrinsic properties of the contractile element are responsible for stabilization of periodic movements. This connotes that (a) complex movements like legged locomotion could benefit from stabilizing effects of muscle properties, and (b) technical systems could benefit from the emerging stability when implementing biological characteristics into artificial muscles.