A physiology based inverse dynamic analysis of human gait: potential and perspectives

Optimal fibre length and maximum isometric force are the most influential parameters when modelling muscular adaptations to unloading using Hill-type muscle models

Introduction: Spaceflight is associated with severe muscular adaptations with substantial inter-individual variability. A Hill-type muscle model is a common method to replicate muscle physiology in musculoskeletal simulations, but little is known about how the underlying parameters should be adjusted to model adaptations to unloading. The aim of this study was to determine how Hill-type muscle model parameters should be adjusted to model disuse muscular adaptations. Methods: Isokinetic dynamometer data were taken from a bed rest campaign and used to perform tracking simulations at two knee extension angular velocities (30°·s-1 and 180°·s-1). The activation and contraction dynamics were solved using an optimal control approach and direct collocation method. A Monte Carlo sampling technique was used to perturb muscle model parameters within physiological boundaries to create a range of theoretical and feasible parameters to model muscle adaptations. Results: Optimal fibre length could not be shortened by more than 67% and 61% for the knee flexors and non-knee muscles, respectively. Discussion: The Hill-type muscle model successfully replicated muscular adaptations due to unloading, and recreated salient features of muscle behaviour associated with spaceflight, such as altered force-length behaviour. Future researchers should carefully adjust the optimal fibre lengths of their muscle-models when trying to model adaptations to unloading, particularly muscles that primarily operate on the ascending and descending limbs of the force-length relationship.

A novel computational framework for the estimation of internal musculoskeletal loading and muscle adaptation in hypogravity

Introduction: Spaceflight is associated with substantial and variable musculoskeletal (MSK) adaptations. Characterisation of muscle and joint loading profiles can provide key information to better align exercise prescription to astronaut MSK adaptations upon return-to-Earth. A case-study is presented of single-leg hopping in hypogravity to demonstrate the additional benefit computational MSK modelling has when estimating lower-limb MSK loading. Methods: A single male participant performed single-leg vertical hopping whilst attached to a body weight support system to replicate five gravity conditions (0.17, 0.25, 0.37, 0.50, 1 g). Experimental joint kinematics, joint kinetics and ground reaction forces were tracked in a data-tracking direct collocation simulation framework. Ground reaction forces, sagittal plane hip, knee and ankle net joint moments, quadriceps muscle forces (Rectus Femoris and three Vasti muscles), and hip, knee and ankle joint reaction forces were extracted for analysis. Estimated quadriceps muscle forces were input into a muscle adaptation model to predict a meaningful increase in muscle cross-sectional area, defined in (DeFreitas et al., 2011). Results: Two distinct strategies were observed to cope with the increase in ground reaction forces as gravity increased. Hypogravity was associated with an ankle dominant strategy with increased range of motion and net plantarflexor moment that was not seen at the hip or knee, and the Rectus Femoris being the primary contributor to quadriceps muscle force. At 1 g, all three joints had increased range of motion and net extensor moments relative to 0.50 g, with the Vasti muscles becoming the main muscles contributing to quadriceps muscle force. Additionally, hip joint reaction force did not increase substantially as gravity increased, whereas the other two joints increased monotonically with gravity. The predicted volume of exercise needed to counteract muscle adaptations decreased substantially with gravity. Despite the ankle dominant strategy in hypogravity, the loading on the knee muscles and joint also increased, demonstrating this provided more information about MSK loading. Discussion: This approach, supplemented with muscle-adaptation models, can be used to compare MSK loading between exercises to enhance astronaut exercise prescription.

Modeling Human Suboptimal Control: A Review

This review paper provides an overview of the approaches to model neuromuscular control, focusing on methods to identify nonoptimal control strategies typical of populations with neuromuscular disorders or children. Where possible, the authors tightened the description of the methods to the mechanisms behind the underlying biomechanical and physiological rationale. They start by describing the first and most simplified approach, the reductionist approach, which splits the role of the nervous and musculoskeletal systems. Static optimization and dynamic optimization methods and electromyography-based approaches are summarized to highlight their limitations and understand (the need for) their developments over time. Then, the authors look at the more recent stochastic approach, introduced to explore the space of plausible neural solutions, thus implementing the uncontrolled manifold theory, according to which the central nervous system only controls specific motions and tasks to limit energy consumption while allowing for some degree of adaptability to perturbations. Finally, they explore the literature covering the explicit modeling of the coupling between the nervous system (acting as controller) and the musculoskeletal system (the actuator), which may be employed to overcome the split characterizing the reductionist approach.

OpenCap: Human movement dynamics from smartphone videos

Measures of human movement dynamics can predict outcomes like injury risk or musculoskeletal disease progression. However, these measures are rarely quantified in large-scale research studies or clinical practice due to the prohibitive cost, time, and expertise required. Here we present and validate OpenCap, an open-source platform for computing both the kinematics (i.e., motion) and dynamics (i.e., forces) of human movement using videos captured from two or more smartphones. OpenCap leverages pose estimation algorithms to identify body landmarks from videos; deep learning and biomechanical models to estimate three-dimensional kinematics; and physics-based simulations to estimate muscle activations and musculoskeletal dynamics. OpenCap's web application enables users to collect synchronous videos and visualize movement data that is automatically processed in the cloud, thereby eliminating the need for specialized hardware, software, and expertise. We show that OpenCap accurately predicts dynamic measures, like muscle activations, joint loads, and joint moments, which can be used to screen for disease risk, evaluate intervention efficacy, assess between-group movement differences, and inform rehabilitation decisions. Additionally, we demonstrate OpenCap's practical utility through a 100-subject field study, where a clinician using OpenCap estimated musculoskeletal dynamics 25 times faster than a laboratory-based approach at less than 1% of the cost. By democratizing access to human movement analysis, OpenCap can accelerate the incorporation of biomechanical metrics into large-scale research studies, clinical trials, and clinical practice.

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

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

Ten steps to becoming a musculoskeletal simulation expert: A half-century of progress and outlook for the future

Over the past half-century, musculoskeletal simulations have deepened our knowledge of human and animal movement. This article outlines ten steps to becoming a musculoskeletal simulation expert so you can contribute to the next half-century of technical innovation and scientific discovery. We advocate looking to the past, present, and future to harness the power of simulations that seek to understand and improve mobility. Instead of presenting a comprehensive literature review, we articulate a set of ideas intended to help researchers use simulations effectively and responsibly by understanding the work on which today's musculoskeletal simulations are built, following established modeling and simulation principles, and branching out in new directions.

A review of the efforts to develop muscle and musculoskeletal models for biomechanics in the last 50 years

Both the Hill and the Huxley muscle models had already been described by the time the International Society of Biomechanics was founded 50 years ago, but had seen little use before the 1970s due to the lack of computing. As computers and computational methods became available in the 1970s, the field of musculoskeletal modeling developed and Hill type muscle models were adopted by biomechanists due to their relative computational simplicity as compared to Huxley type muscle models. Muscle forces computed by Hill type muscle models provide good agreement in conditions similar to the initial studies, i.e. for small muscles contracting under steady and controlled conditions. However, more recent validation studies have identified that Hill type muscle models are least accurate for natural in vivo locomotor behaviours at submaximal activations, fast speeds and for larger muscles, and thus need to be improved for their use in understanding human movements. Developments in muscle modelling have tackled these shortcomings. However, over the last 50 years musculoskeletal simulations have been largely based on traditional Hill type muscle models or even simplifications of this model that neglected the interaction of the muscle with a compliant tendon. The introduction of direct collocation in musculoskeletal simulations about 15 years ago along with further improvements in computational power and numerical methods enabled the use of more complex muscle models in simulations of whole-body movement. Whereas Hill type models are still the norm, we may finally be ready to adopt more complex muscle models into musculoskeletal simulations of human movement.

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

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

On the estimation of hip joint loads through musculoskeletal modeling

Noninvasive estimation of joint loads is still an open challenge in biomechanics. Although musculoskeletal modeling represents a solid resource, multiple improvements are still necessary to obtain accurate predictions of joint loads and to translate such potential into practical utility. The present study, focused on the hip joint, is aimed at reviewing the state-of-the-art literature on the estimation of hip joint reaction forces through musculoskeletal modeling. Our literature inspection, based on well-defined selection criteria, returned seventeen works, which were compared in terms of methods and results. Deviations between predicted and in vivo measured hip joint loads, taken from the OrthoLoad database, were assessed through quantitative deviation indices. Despite the numerous modeling and computational improvements made over the last two decades, predicted hip joint loads still deviate from their experimental counterparts and typically overestimate them. Several critical aspects have emerged that affect muscle force estimation, hence joint loads. Among them, the physical fidelity of the musculoskeletal model, with its parameters and geometry, plays a crucial role. Also, predicted joint loads are markedly affected by the selected muscle recruitment strategy, which reflects the underlying motor control policy. Practical guidelines for researchers interested in noninvasive estimation of hip joint loads are also provided.

Movement in low gravity environments (MoLo) programme-The MoLo-L.O.O.P. study protocol

BACKGROUND

Exposure to prolonged periods in microgravity is associated with deconditioning of the musculoskeletal system due to chronic changes in mechanical stimulation. Given astronauts will operate on the Lunar surface for extended periods of time, it is critical to quantify both external (e.g., ground reaction forces) and internal (e.g., joint reaction forces) loads of relevant movements performed during Lunar missions. Such knowledge is key to predict musculoskeletal deconditioning and determine appropriate exercise countermeasures associated with extended exposure to hypogravity.

OBJECTIVES

The aim of this paper is to define an experimental protocol and methodology suitable to estimate in high-fidelity hypogravity conditions the lower limb internal joint reaction forces. State-of-the-art movement kinetics, kinematics, muscle activation and muscle-tendon unit behaviour during locomotor and plyometric movements will be collected and used as inputs (Objective 1), with musculoskeletal modelling and an optimisation framework used to estimate lower limb internal joint loading (Objective 2).

METHODS

Twenty-six healthy participants will be recruited for this cross-sectional study. Participants will walk, skip and run, at speeds ranging between 0.56-3.6 m/s, and perform plyometric movement trials at each gravity level (1, 0.7, 0.5, 0.38, 0.27 and 0.16g) in a randomized order. Through the collection of state-of-the-art kinetics, kinematics, muscle activation and muscle-tendon behaviour, a musculoskeletal modelling framework will be used to estimate lower limb joint reaction forces via tracking simulations.

CONCLUSION

The results of this study will provide first estimations of internal musculoskeletal loads associated with human movement performed in a range of hypogravity levels. Thus, our unique data will be a key step towards modelling the musculoskeletal deconditioning associated with long term habitation on the Lunar surface, and thereby aiding the design of Lunar exercise countermeasures and mitigation strategies.

Modifications to the net knee moments lead to the greatest improvements in accelerative sprinting performance: a predictive simulation study

The current body of sprinting biomechanics literature together with the front-side mechanics coaching framework provide various technique recommendations for improving performance. However, few studies have attempted to systematically explore technique modifications from a performance enhancement perspective. The aims of this investigation were therefore to explore how hypothetical technique modifications affect accelerative sprinting performance and assess whether the hypothetical modifications support the front-side mechanics coaching framework. A three-dimensional musculoskeletal model scaled to an international male sprinter was used in combination with direct collocation optimal control to perform (data-tracking and predictive) simulations of the preliminary steps of accelerative sprinting. The predictive simulations differed in the net joint moments that were left 'free' to change. It was found that the 'knee-free' and 'knee-hip-free' simulations resulted in the greatest performance improvements (13.8% and 21.9%, respectively), due to a greater knee flexor moment around touchdown (e.g., 141.2 vs. 70.5 Nm) and a delayed and greater knee extensor moment during stance (e.g., 188.5 vs. 137.5 Nm). Lastly, the predictive simulations which led to the greatest improvements were also found to not exhibit clear and noticeable front-side mechanics technique, thus the underpinning principles of the coaching framework may not be the only key aspect governing accelerative sprinting.

Modeling toes contributes to realistic stance knee mechanics in three-dimensional predictive simulations of walking

Physics-based predictive simulations have been shown to capture many salient features of human walking. Yet they often fail to produce realistic stance knee and ankle mechanics. While the influence of the performance criterion on the predicted walking pattern has been previously studied, the influence of musculoskeletal mechanics has been less explored. Here, we investigated the influence of two mechanical assumptions on the predicted walking pattern: the complexity of the foot model and the stiffness of the Achilles tendon. We found, through three-dimensional muscle-driven predictive simulations of walking, that modeling the toes, and thus using two-segment instead of single-segment foot models, contributed to robustly eliciting physiological stance knee flexion angles, knee extension torques, and knee extensor activity. Modeling toes also slightly decreased the first vertical ground reaction force peak, increasing its agreement with experimental data, and improved stance ankle kinetics. It nevertheless slightly worsened predictions of ankle kinematics. Decreasing Achilles tendon stiffness improved the realism of ankle kinematics, but there remain large discrepancies with experimental data. Overall, this simulation study shows that not only the performance criterion but also mechanical assumptions affect predictive simulations of walking. Improving the realism of predictive simulations is required for their application in clinical contexts. Here, we suggest that using more complex foot models might contribute to such realism.

Predictive simulation of post-stroke gait with functional electrical stimulation

Post-stroke patients present various gait abnormalities such as drop foot, stiff-knee gait (SKG), and knee hyperextension. Functional electrical stimulation (FES) improves drop foot gait although the mechanistic basis for this effect is not well understood. To answer this question, we evaluated the gait of a post-stroke patient walking with and without FES by inverse dynamics analysis and compared the results to an optimal control framework. The effect of FES and cause-effect relationship of changes in knee and ankle muscle strength were investigated; personalized muscle–tendon parameters allowed the prediction of pathologic gait. We also predicted healthy gait patterns at different speeds to simulate the subject walking without impairment. The passive moment of the knee played an important role in the estimation of muscle force with knee hyperextension, which was decreased during FES and knee extensor strengthening. Weakening the knee extensors and strengthening the flexors improved SKG. During FES, weak ankle plantarflexors and strong ankle dorsiflexors resulted in increased ankle dorsiflexion, which reduced drop foot. FES also improved gait speed and reduced circumduction. These findings provide insight into compensatory strategies adopted by post-stroke patients that can guide the design of individualized rehabilitation and treatment programs.

Hamstrings Contraction Regulates the Magnitude and Timing of the Peak ACL Loading During the Drop Vertical Jump in Female Athletes

Background

Anterior cruciate ligament (ACL) injury reduction training has focused on lower body strengthening and landing stabilization. In vitro studies have shown that quadriceps forces increase ACL strain, and hamstring forces decrease ACL strain. However, the magnitude of the effect of the quadriceps and hamstrings forces on ACL loading and its timing during in vivo landings remains unclear.

Purpose

To investigate the effect and timing of knee muscle forces on ACL loading during landing.

Study Design

Descriptive laboratory study.

Methods

A total of 13 young female athletes performed drop vertical jump trials, and their movements were recorded with 3-dimensional motion capture. Lower limb joint motion and muscle forces were estimated with OpenSim and applied to a musculoskeletal finite element (FE) model to estimate ACL loading during landings. The FE simulations were performed with 5 different conditions that included/excluded kinematics, ground-reaction force (GRF), and muscle forces.

Results

Simulation of landing kinematics without GRF or muscle forces yielded an estimated median ACL strain and force of 5.1% and 282.6 N. Addition of GRF to kinematic simulations increased ACL strain and force to 6.8% and 418.4 N (P < .05). Addition of quadriceps force to kinematics + GRF simulations nonsignificantly increased ACL strain and force to 7.2% and 478.5 N. Addition of hamstrings force to kinematics + GRF simulations decreased ACL strain and force to 2.6% and 171.4 N (P < .001). Addition of all muscles to kinematics + GRF simulations decreased ACL strain and force to 3.3% and 195.1 N (P < .001). With hamstrings force, ACL loading decreased from initial contact (time of peak: 1-18 milliseconds) while ACL loading without hamstrings force peaked at 47 to 98 milliseconds after initial contact (P = .024-.001). The knee flexion angle increased from 20.9° to 73.1° within 100 milliseconds after initial contact.

Conclusion

Hamstrings activation had greater effect relative to GRF and quadriceps activation on ACL loading, which significantly decreased and regulated the magnitude and timing of ACL loading during in vivo landings.

Clinical Relevance

Clinical training should focus on strategies that influence increased hamstrings activation during landing to reduce ACL loads.

Predictive simulations of running gait reveal a critical dynamic role for the tail in bipedal dinosaur locomotion

Locomotion has influenced the ecology, evolution, and extinction of species throughout history, yet studying locomotion in the fossil record is challenging. Computational biomechanics can provide novel insight by mechanistically relating observed anatomy to whole-animal function and behavior. Here, we leverage optimal control methods to generate the first fully predictive, three-dimensional, muscle-driven simulations of locomotion in an extinct terrestrial vertebrate, the bipedal non-avian theropod dinosaur Coelophysis. Unexpectedly, our simulations involved pronounced lateroflexion movements of the tail. Rather than just being a static counterbalance, simulations indicate that the tail played a crucial dynamic role, with lateroflexion acting as a passive, physics-based mechanism for regulating angular momentum and improving locomotor economy, analogous to the swinging arms of humans. We infer this mechanism to have existed in many other bipedal non-avian dinosaurs as well, and our methodology provides new avenues for exploring the functional diversity of dinosaur tails in the future.

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.

Musculoskeletal modelling of the Nile crocodile (Crocodylus niloticus) hindlimb: Effects of limb posture on leverage during terrestrial locomotion

We developed a three-dimensional, computational biomechanical model of a juvenile Nile crocodile (Crocodylus niloticus) pelvis and hindlimb, composed of 47 pelvic limb muscles, to investigate muscle function. We tested whether crocodiles, which are known to use a variety of limb postures during movement, use limb orientations (joint angles) that optimise the moment arms (leverages) or moment-generating capacities of their muscles during different limb postures ranging from a high walk to a sprawling motion. We also describe the three-dimensional (3D) kinematics of the crocodylian hindlimb during terrestrial locomotion across an instrumented walkway and a treadmill captured via X-ray Reconstruction of Moving Morphology (biplanar fluoroscopy; 'XROMM'). We reconstructed the 3D positions and orientations of each of the hindlimb bones and used dissection data for muscle lines of action to reconstruct a focal, subject-specific 3D musculoskeletal model. Motion data for different styles of walking (a high, crouched, bended and two types of sprawling motion) were fed into the 3D model to identify whether any joints adopted near-optimal poses for leverage across each of the behaviours. We found that (1) the hip adductors and knee extensors had their largest leverages during sprawling postures and (2) more erect postures typically involved greater peak moment arms about the hip (flexion-extension), knee (flexion) and metatarsophalangeal (flexion) joints. The results did not fully support the hypothesis that optimal poses are present during different locomotory behaviours because the peak capacities were not always reached around mid-stance phase. Furthermore, we obtained few clear trends for isometric moment-generating capacities. Therefore, perhaps peak muscular leverage in Nile crocodiles is instead reached either in early/late stance or possibly during swing phase or other locomotory behaviours that were not studied here, such as non-terrestrial movement. Alternatively, our findings could reflect a trade-off between having to execute different postures, meaning that hindlimb muscle leverage is not optimised for any singular posture or behaviour. Our model, however, provides a comprehensive set of 3D estimates of muscle actions in extant crocodiles which can form a basis for investigating muscle function in extinct archosaurs.

Three-dimensional data-tracking simulations of sprinting using a direct collocation optimal control approach

Biomechanical simulation and modelling approaches have the possibility to make a meaningful impact within applied sports settings, such as sprinting. However, for this to be realised, such approaches must first undergo a thorough quantitative evaluation against experimental data. We developed a musculoskeletal modelling and simulation framework for sprinting, with the objective to evaluate its ability to reproduce experimental kinematics and kinetics data for different sprinting phases. This was achieved by performing a series of data-tracking calibration (individual and simultaneous) and validation simulations, that also featured the generation of dynamically consistent simulated outputs and the determination of foot-ground contact model parameters. The simulated values from the calibration simulations were found to be in close agreement with the corresponding experimental data, particularly for the kinematics (average root mean squared differences (RMSDs) less than 1.0° and 0.2 cm for the rotational and translational kinematics, respectively) and ground reaction force (highest average percentage RMSD of 8.1%). Minimal differences in tracking performance were observed when concurrently determining the foot-ground contact model parameters from each of the individual or simultaneous calibration simulations. The validation simulation yielded results that were comparable (RMSDs less than 1.0° and 0.3 cm for the rotational and translational kinematics, respectively) to those obtained from the calibration simulations. This study demonstrated the suitability of the proposed framework for performing future predictive simulations of sprinting, and gives confidence in its use to assess the cause-effect relationships of technique modification in relation to performance. Furthermore, this is the first study to provide dynamically consistent three-dimensional muscle-driven simulations of sprinting across different phases.

Anterior Cruciate Ligament Loading Increases With Pivot-Shift Mechanism During Asymmetrical Drop Vertical Jump in Female Athletes

Background:

Frontal plane trunk lean with a side-to-side difference in lower extremity kinematics during landing increases unilateral knee abduction moment and consequently anterior cruciate ligament (ACL) injury risk. However, the biomechanical features of landing with higher ACL loading are still unknown. Validated musculoskeletal modeling offers the potential to quantify ACL strain and force during a landing task.

Purpose:

To investigate ACL loading during a landing and assess the association between ACL loading and biomechanical factors of individual landing strategies.

Study Design:

Descriptive laboratory study.

Methods:

Thirteen young female athletes performed drop vertical jump trials, and their movements were recorded with 3-dimensional motion capture. Electromyography-informed optimization was performed to estimate lower limb muscle forces with an OpenSim musculoskeletal model. A whole-body musculoskeletal finite element model was developed. The joint motion and muscle forces obtained from the OpenSim simulations were applied to the musculoskeletal finite element model to estimate ACL loading during participants’ simulated landings with physiologic knee mechanics. Kinematic, muscle force, and ground-reaction force waveforms associated with high ACL strain trials were reconstructed via principal component analysis and logistic regression analysis, which were used to predict trials with high ACL strain.

Results:

The median (interquartile range) values of peak ACL strain and force during the drop vertical jump were 3.3% (–1.9% to 5.1%) and 195.1 N (53.9 to 336.9 N), respectively. Four principal components significantly predicted high ACL strain trials, with 100% sensitivity, 78% specificity, and an area of 0.91 under the receiver operating characteristic curve (P < .001). High ACL strain trials were associated with (1) knee motions that included larger knee abduction, internal tibial rotation, and anterior tibial translation and (2) motion that included greater vertical and lateral ground-reaction forces, lower gluteus medius force, larger lateral pelvic tilt, and increased hip adduction.

Conclusion:

ACL loads were higher with a pivot-shift mechanism during a simulated landing with asymmetry in the frontal plane. Specifically, knee abduction can create compression on the posterior slope of the lateral tibial plateau, which induces anterior tibial translation and internal tibial rotation.

Clinical Relevance:

Athletes are encouraged to perform interventional and preventive training to improve symmetry during landing.

Physics-Based Simulations to Predict the Differential Effects of Motor Control and Musculoskeletal Deficits on Gait Dysfunction in Cerebral Palsy: A Retrospective Case Study

Physics-based simulations of walking have the theoretical potential to support clinical decision-making by predicting the functional outcome of treatments in terms of walking performance. Yet before using such simulations in clinical practice, their ability to identify the main treatment targets in specific patients needs to be demonstrated. In this study, we generated predictive simulations of walking with a medical imaging based neuro-musculoskeletal model of a child with cerebral palsy presenting crouch gait. We explored the influence of altered muscle-tendon properties, reduced neuromuscular control complexity, and spasticity on gait dysfunction in terms of joint kinematics, kinetics, muscle activity, and metabolic cost of transport. We modeled altered muscle-tendon properties by personalizing Hill-type muscle-tendon parameters based on data collected during functional movements, simpler neuromuscular control by reducing the number of independent muscle synergies, and spasticity through delayed muscle activity feedback from muscle force and force rate. Our simulations revealed that, in the presence of aberrant musculoskeletal geometries, altered muscle-tendon properties rather than reduced neuromuscular control complexity and spasticity were the primary cause of the crouch gait pattern observed for this child, which is in agreement with the clinical examination. These results suggest that muscle-tendon properties should be the primary target of interventions aiming to restore an upright gait pattern for this child. This suggestion is in line with the gait analysis following muscle-tendon property and bone deformity corrections. Future work should extend this single case analysis to more patients in order to validate the ability of our physics-based simulations to capture the gait patterns of individual patients pre- and post-treatment. Such validation would open the door for identifying targeted treatment strategies with the aim of designing optimized interventions for neuro-musculoskeletal disorders.

Knee abduction moment is predicted by lower gluteus medius force and larger vertical and lateral ground reaction forces during drop vertical jump in female athletes

Prospective knee abduction moments measured during the drop vertical jump task identify those at increased risk for anterior cruciate ligament injury. The purpose of this study was to determine which muscle forces and frontal plane biomechanical features contribute to large knee abduction moments. Thirteen young female athletes performed three drop vertical jump trials. Subject-specific musculoskeletal models and electromyography-informed simulations were developed to calculate the frontal plane biomechanics and lower limb muscle forces. The relationships between knee abduction moment and frontal plane biomechanics were examined. Knee abduction moment was positively correlated to vertical (R = 0.522, P < 0.001) and lateral ground reaction forces (R = 0.395, P = 0.016), hip adduction angle (R = 0.358, P < 0.023) and lateral pelvic tilt (R = 0.311, P = 0.061). A multiple regression showed that knee abduction moment was predicted by reduced gluteus medius force and increased vertical and lateral ground reaction forces (P < 0.001, R² = 0.640). Hip adduction is indicative of lateral pelvic shift during landing. The coupled hip adduction and lateral pelvic tilt were associated to the increased vertical and lateral ground reaction forces, propagating into higher knee abduction moments. These biomechanical features are associated with ACL injury and may be limited in a landing with increased activation of the gluteus medius. Targeted neuromuscular training to control the frontal pelvic and hip motion may help to avoid injurious ground reaction forces and consequent knee abduction moment and ACL injury risk.

Habitual foot strike pattern does not affect simulated triceps surae muscle metabolic energy consumption during running

Foot strike pattern affects ankle joint work and triceps surae muscle-tendon dynamics during running. Whether these changes in muscle-tendon dynamics also affect triceps surae muscle energy consumption is still unknown. In addition, as the triceps surae muscle accounts for a substantial amount of the whole-body metabolic energy consumption, changes in triceps surae energy consumption may affect whole-body metabolic energy consumption. However, direct measurements of muscle metabolic energy consumption during dynamic movements is difficult. Model-based approaches can be used to estimate individual muscle and whole-body metabolic energy consumption based on Hill type muscle models. In this study, we use an integrated experimental and dynamic optimization approach to compute muscle states (muscle forces, lengths, velocities, excitations and activations) of 10 habitual midfoot/forefoot striking and nine habitual rearfoot striking runners while running at 10 and 14 km h^-1 The Achilles tendon stiffness of the musculoskeletal model was adapted to fit experimental ultrasound data of the gastrocnemius medialis muscle during ground contact. Next, we calculated triceps surae muscle and whole-body metabolic energy consumption using four different metabolic energy models provided in the literature. Neither triceps surae metabolic energy consumption (P>0.35) nor whole-body metabolic energy consumption (P>0.14) was different between foot strike patterns, regardless of the energy model used or running speed tested. Our results provide new evidence that midfoot/forefoot and rearfoot strike patterns are metabolically equivalent.

Ultrasound-Based Optimal Parameter Estimation Improves Assessment of Calf Muscle-Tendon Interaction During Walking

We present and evaluate a new approach to estimate calf muscle-tendon parameters and calculate calf muscle-tendon function during walking. We used motion analysis, ultrasound, and EMG data of the calf muscles collected in six young and six older adults during treadmill walking as inputs to a new optimal estimation algorithm. We used estimated parameters or scaled generic parameters in an existing approach to calculate muscle fiber lengths and activations. We calculated the fit with experimental data in terms of root mean squared differences (RMSD) and coefficients of determination (R²). We also calculated the calf muscle metabolic energy cost. RMSD between measured and calculated fiber lengths and activations decreased and R² increased when estimating parameters compared to using scaled generic parameters. Moreover, R² between measured and calculated gastrocnemius medialis fiber length and soleus activations increased by 19 and 70%, and calf muscle metabolic energy decreased by 25% when using estimated parameters compared to using scaled generic parameters at speeds not used for estimation. This new approach estimates calf muscle-tendon parameters in good accordance with values reported in literature. The approach improves calculations of calf muscle-tendon interaction during walking and highlights the importance of individualizing calf muscle-tendon parameters.

Algorithmic differentiation improves the computational efficiency of OpenSim-based trajectory optimization of human movement

Algorithmic differentiation (AD) is an alternative to finite differences (FD) for evaluating function derivatives. The primary aim of this study was to demonstrate the computational benefits of using AD instead of FD in OpenSim-based trajectory optimization of human movement. The secondary aim was to evaluate computational choices including different AD tools, different linear solvers, and the use of first- or second-order derivatives. First, we enabled the use of AD in OpenSim through a custom source code transformation tool and through the operator overloading tool ADOL-C. Second, we developed an interface between OpenSim and CasADi to solve trajectory optimization problems. Third, we evaluated computational choices through simulations of perturbed balance, two-dimensional predictive simulations of walking, and three-dimensional tracking simulations of walking. We performed all simulations using direct collocation and implicit differential equations. Using AD through our custom tool was between 1.8 ± 0.1 and 17.8 ± 4.9 times faster than using FD, and between 3.6 ± 0.3 and 12.3 ± 1.3 times faster than using AD through ADOL-C. The linear solver efficiency was problem-dependent and no solver was consistently more efficient. Using second-order derivatives was more efficient for balance simulations but less efficient for walking simulations. The walking simulations were physiologically realistic. These results highlight how the use of AD drastically decreases computational time of trajectory optimization problems as compared to more common FD. Overall, combining AD with direct collocation and implicit differential equations decreases the computational burden of trajectory optimization of human movement, which will facilitate their use for biomechanical applications requiring the use of detailed models of the musculoskeletal system.

Rapid predictive simulations with complex musculoskeletal models suggest that diverse healthy and pathological human gaits can emerge from similar control strategies

Physics-based predictive simulations of human movement have the potential to support personalized medicine, but large computational costs and difficulties to model control strategies have limited their use. We have developed a computationally efficient optimal control framework to predict human gaits based on optimization of a performance criterion without relying on experimental data. The framework generates three-dimensional muscle-driven simulations in 36 min on average—more than 20 times faster than existing simulations—by using direct collocation, implicit differential equations and algorithmic differentiation. Using this framework, we identified a multi-objective performance criterion combining energy and effort considerations that produces physiologically realistic walking gaits. The same criterion also predicted the walk-to-run transition and clinical gait deficiencies caused by muscle weakness and prosthesis use, suggesting that diverse healthy and pathological gaits can emerge from the same control strategy. The ability to predict the mechanics and energetics of a broad range of gaits with complex three-dimensional musculoskeletal models will allow testing novel hypotheses about gait control and hasten the development of optimal treatments for neuro-musculoskeletal disorders.

Effect of habitual foot-strike pattern on the gastrocnemius medialis muscle-tendon interaction and muscle force production during running

The interaction between gastrocnemius medialis (GM) muscle and Achilles tendon, i.e., muscle-tendon unit (MTU) interaction, plays an important role in minimizing the metabolic cost of running. Foot-strike pattern (FSP) has been suggested to alter MTU interaction and subsequently the metabolic cost of running. However, metabolic data from experimental studies on FSP are inconsistent, and a comparison of MTU interaction between FSP is still lacking. We, therefore, investigated the effect of habitual rearfoot and mid-/forefoot striking on MTU interaction, ankle joint work, and plantar flexor muscle force production while running at 10 and 14 km/h. GM muscle fascicles of 9 rearfoot and 10 mid-/forefoot strikers were tracked using dynamic ultrasonography during treadmill running. We collected kinetic and kinematic data and used musculoskeletal models to determine joint angles and calculate MTU lengths. In addition, we used dynamic optimization to assess plantar flexor muscle forces. During ground contact, GM fascicle shortening ( P = 0.02) and average contraction velocity ( P = 0.01) were 40-45% greater in rearfoot strikers than mid-/forefoot strikers. Differences in contraction velocity were especially prominent during early ground contact. Moreover, GM ( P = 0.02) muscle force was greater during early ground contact in mid-/forefoot strikers than rearfoot strikers. Interestingly, we did not find differences in stretch or recoil of the series elastic element between FSP. Our results suggest that, for the GM, the reduced muscle energy cost associated with lower fascicle contraction velocity in mid-/forefoot strikers may be counteracted by greater muscle forces during early ground contact. NEW & NOTEWORTHY Kinetic and kinematic differences between foot-strike patterns during running imply (not previously reported) altered muscle-tendon interaction. Here, we studied muscle-tendon interaction using ultrasonography. We found greater fascicle contraction velocities and lower muscle forces in rearfoot compared with mid-/forefoot strikers. Our results suggest that the higher metabolic energy demand due to greater fascicle contraction velocities might offset the lower metabolic energy demand due to lower muscle forces in rearfoot compared with mid-/forefoot strikers.

Estimation of muscle activation during different walking speeds with two mathematical approaches compared to surface EMG

BACKGROUND

Muscle force estimation could improve clinical gait analysis by enhancing insight into causes of impairments and informing targeted treatments. However, it is not currently standard practice to use muscle force models to augment clinical gait analysis, partly, because robust validations of estimated muscle activations, underpinning force modelling processes, against recorded electromyography (EMG) are lacking.

RESEARCH QUESTION

Therefore, in order to facilitate future clinical use, this study sought to validate estimated lower limb muscle activation using two mathematical models (static optimisation SO, computed muscle control CMC) against recorded muscle activations of ten healthy participants.

METHODS

Participants walked at five speeds. Visual agreement in activation onset and offset as well as linear correlation (r) and mean absolute error (MAE) between models and EMG were evaluated.

RESULTS

MAE between measured and recorded activations were variable across speeds (SO vs EMG 15-68%, CMC vs EMG 13-69%). Slower speeds resulted in smaller deviations (mean MAE < 30%) than faster speeds. Correlation was high (r > 0.5) for only 11/40 (CMC) and 6/40 (SO) conditions (muscles X speeds) compared to EMG.

SIGNIFICANCE

Modelling approaches do not yet show sufficient consistency of agreement between estimated and recorded muscle activation to support recommending immediate clinical adoption of muscle force modelling. This may be because assumptions underlying muscle activation estimations (e.g. muscles' anatomy and maximum voluntary contraction) are not yet sufficiently individualizable. Future research needs to find timely and cost efficient ways to scale musculoskeletal models for better individualisation to facilitate future clinical implementation.

Influence of the Musculotendon Dynamics on the Muscle Force-Sharing Problem of the Shoulder—A Fully Inverse Dynamics Approach

Most dynamic simulations are based on inverse dynamics, being the time-dependent physiological nature of the muscle properties rarely considered due to numerical challenges. Since the influence of muscle physiology on the consistency of inverse dynamics simulations remains unclear, the purpose of the present study is to evaluate the computational efficiency and biological validity of four musculotendon models that differ in the simulation of the muscle activation and contraction dynamics. Inverse dynamic analyses are performed using a spatial musculoskeletal model of the upper limb. The muscle force-sharing problem is solved for five repetitions of unloaded and loaded motions of shoulder abduction and shoulder flexion. The performance of the musculotendon models is evaluated by comparing muscle activation predictions with electromyography (EMG) signals, measured synchronously with motion for 11 muscles, and the glenohumeral joint reaction forces estimated numerically with those measured in vivo. The results show similar muscle activations for all muscle models. Overall, high cross-correlations are computed between muscle activations and the EMG signals measured for all movements analyzed, which provides confidence in the results. The glenohumeral joint reaction forces estimated compare well with those measured in vivo, but the influence of the muscle dynamics is found to be negligible. In conclusion, for slow-speed, standard movements of the upper limb, as those studied here, the activation and musculotendon contraction dynamics can be neglected in inverse dynamic analyses without compromising the prediction of muscle and joint reaction forces.

A systematic review of approaches to modelling lower limb muscle forces during gait: Applicability to clinical gait analyses

Computational methods to estimate muscle forces during walking are becoming more common in biomechanical research but not yet in clinical gait analysis. This systematic review aims to identify the current state-of-the-art, examine the differences between approaches, and consider applicability of the current approaches in clinical gait analysis. A systematic database search identified studies including estimated muscle force profiles of the lower limb during healthy walking. These were rated for quality and the muscle force profiles digitised for comparison. From 13.449 identified studies, 22 were finally included which used four modelling approaches: static optimisation, enhanced static optimisation, forward dynamics and EMG-driven. These used a range of different musculoskeletal models, muscle-tendon characteristics and cost functions. There is visually broad agreement between and within approaches about when muscles are active throughout the gait cycle. There remain, considerable differences (CV 7%-151%, range of timing of peak forces in gait cycle 1%-31%) in patterns and magnitudes of force between and within modelling approaches. The main source of this variability is not clear. Different musculoskeletal models, experimental protocols, and modelling approaches will clearly have an effect as will the variability of joint kinetics between healthy individuals. Limited validation of modelling approaches, particularly at the level of individual participants, makes it difficult to conclude if any of the approaches give consistently better estimates than others. While muscle force modelling has clear potential to enhance clinical gait analyses future research is needed to improve validation, accuracy and feasibility of implementation in clinical practice.

Joint torque variability and repeatability during cyclic flexion-extension of the elbow

Background

Joint torques are generally of primary importance for clinicians to analyze the effect of a surgery and to obtain an indicator of functional capability to perform a motion. Given the current need to standardize the functional evaluation of the upper limb, the aim of this paper is to assess (1) the variability of the calculated maximal elbow joint torque during cyclic elbow flexion-extension movements and (2) participant test-retest repeatability in healthy young adults. Calculations were based on an existing non-invasive method including kinematic identification and inverse dynamics processes.

Methods

Twelve healthy young adults (male n = 6) performed 10 elbow flexion-extension movement carrying five different dumbbells (0, 1, 2, 3 and 4 kg) with several flexion-extension frequencies (½, ¹/₃, ¼ Hz) to evaluate peak elbow joint torques.

Results

Whatever the condition, the variability coefficient of trial peak torques remained under 4 %. Bland and Altman plot also showed good test-retest, whatever the frequency conditions for the 0, 1, 2, and 3 kg conditions.

Conclusion

The good repeatability of the flexion-extension peak torques represents a key step to standardize the functional evaluation of the upper limb.

Evaluation of Direct Collocation Optimal Control Problem Formulations for Solving the Muscle Redundancy Problem

Estimation of muscle forces during motion involves solving an indeterminate problem (more unknown muscle forces than joint moment constraints), frequently via optimization methods. When the dynamics of muscle activation and contraction are modeled for consistency with muscle physiology, the resulting optimization problem is dynamic and challenging to solve. This study sought to identify a robust and computationally efficient formulation for solving these dynamic optimization problems using direct collocation optimal control methods. Four problem formulations were investigated for walking based on both a two and three dimensional model. Formulations differed in the use of either an explicit or implicit representation of contraction dynamics with either muscle length or tendon force as a state variable. The implicit representations introduced additional controls defined as the time derivatives of the states, allowing the nonlinear equations describing contraction dynamics to be imposed as algebraic path constraints, simplifying their evaluation. Problem formulation affected computational speed and robustness to the initial guess. The formulation that used explicit contraction dynamics with muscle length as a state failed to converge in most cases. In contrast, the two formulations that used implicit contraction dynamics converged to an optimal solution in all cases for all initial guesses, with tendon force as a state generally being the fastest. Future work should focus on comparing the present approach to other approaches for computing muscle forces. The present approach lacks some of the major limitations of established methods such as static optimization and computed muscle control while remaining computationally efficient.

Subject-specific geometrical detail rather than cost function formulation affects hip loading calculation

This study assessed the relative importance of introducing an increasing level of medical image-based subject-specific detail in bone and muscle geometry in the musculoskeletal model, on calculated hip contact forces during gait. These forces were compared to introducing minimization of hip contact forces in the optimization criterion. With an increasing level of subject-specific detail, specifically MRI-based geometry and wrapping surfaces representing the hip capsule, hip contact forces decreased and were more comparable to contact forces measured using instrumented prostheses (average difference of 0.69 BW at the first peak compared to 1.04 BW for the generic model). Inclusion of subject-specific wrapping surfaces in the model had a greater effect than altering the cost function definition.

FEASIBILITY STUDY FOR ANFIS AND EMG UTILIZATION IN MODELING PROSTHESIS FOR TRANS-FEMORAL CUT REHABILITATION AND GAIT CYCLE RESTORATION

Rehabilitation of lower limbs with high-level amputation (Trans-femoral Cut) requires an alternative method of inverse and forward dynamics to be employed. Inverse and forward dynamics are capable of solving the problem of redundancy of muscles in human lower limbs. Furthermore, inverse and forward dynamics can be used for estimating joints moments, predicting body segment kinematics, and estimating the distribution of forces between the agonist/antagonist muscle group with reasonable accuracy [Riener R, Lünenburger L, Colombo G, Human-Centered robotics applied to gait training and assessment robert, J Rehabil Res Dev43:679, 2006; Keller T, Perry JC, Rehabilitation robotics for outpatient clinical and domestic use, WC IFMBE Proc25:291, 2009; Crespo LM, Reinkensmeyer DJ, Review of control strategies for robotic movement training after neurologic injury, J Neuroeng Rehabil6:20, 2009; Hillman MI, Rehabilitation robotics from past to present — A historical prespective, Adv Rehabil Robotics, Lect Notes Contr Inf306:25, 2004.]. However, the application of these methods, in rehabilitation, is still limited due to their dependence on multiple input data that cannot be measured using conventional measurement tools. This study is aimed at verifying and validating new models which are capable of predicting body segment kinematics accurately using features obtained from electromyography (EMG) and adaptive neuro fuzzy inference system (ANFIS). These features are used to model a set of (input\output) dynamic data. EMG signals obtained from full gait cycle trials of a subject are used to calculate joint moments. Kinematics of the body segments are obtained by applying Euler numerical integration. The relative percentage root mean square (RMS) error between predicted kinematics from ANFIS and measured values for hip, knee, and ankle were 2.23%, 0.98%, and 0.69%, respectively. However, the achieved minimal reasonable accuracy for minimum number of measured inputs depends on the characteristics of the gait parameters such as cyclic nature and delayed symmetric activities between right and left leg about mid sagittal plane. Results of the combined model show that higher prediction accuracy of the gait cycle is achieved and so rehabilitation of lower limbs is feasible.

Muscle optimization techniques impact the magnitude of calculated hip joint contact forces

In musculoskeletal modelling, several optimization techniques are used to calculate muscle forces, which strongly influence resultant hip contact forces (HCF). The goal of this study was to calculate muscle forces using four different optimization techniques, i.e., two different static optimization techniques, computed muscle control (CMC) and the physiological inverse approach (PIA). We investigated their subsequent effects on HCFs during gait and sit to stand and found that at the first peak in gait at 15-20% of the gait cycle, CMC calculated the highest HCFs (median 3.9 times peak GRF (pGRF)). When comparing calculated HCFs to experimental HCFs reported in literature, the former were up to 238% larger. Both static optimization techniques produced lower HCFs (median 3.0 and 3.1 pGRF), while PIA included muscle dynamics without an excessive increase in HCF (median 3.2 pGRF). The increased HCFs in CMC were potentially caused by higher muscle forces resulting from co-contraction of agonists and antagonists around the hip. Alternatively, these higher HCFs may be caused by the slightly poorer tracking of the net joint moment by the muscle moments calculated by CMC. We conclude that the use of different optimization techniques affects calculated HCFs, and static optimization approached experimental values best.

CONTRIBUTION OF MUSCLE TENSION FORCE TO MEDIAL KNEE CONTACT FORCE AT FAST WALKING SPEED

Fast walking is considered as a factor that causes pain in patients suffering from knee disorders. This study examined the effect of walking speed on the medial knee contact force and identified contributions to the muscle tension on the medial knee contact force during fast walking using musculoskeletal simulation analysis. The muscle contribution to the medial knee contact force was calculated based on the joint angles and ground reaction force for the normal and fast walking experiments of seven subjects. The muscle force and joint reaction force were used to estimate the medial knee contact force. Results showed, in average, 70% increase in medial knee contact force at the first peak and 34% increase at the second peak with a fast walking speed, compared to when they walked at a normal walking speed. The remarkable increase in the first peak was mainly contributed by the increase in the quadriceps force resisting the external knee flexion moment. In contrast, the moderate increase of second peak was contributed by the increase in the gastrocnemius muscle force. These results suggest that the increase in medial knee contact force at fast walking speeds is caused by the increased muscle force.

Task constraints and minimization of muscle effort result in a small number of muscle synergies during gait

Finding muscle activity generating a given motion is a redundant problem, since there are many more muscles than degrees of freedom. The control strategies determining muscle recruitment from a redundant set are still poorly understood. One theory of motor control suggests that motion is produced through activating a small number of muscle synergies, i.e., muscle groups that are activated in a fixed ratio by a single input signal. Because of the reduced number of input signals, synergy-based control is low dimensional. But a major criticism on the theory of synergy-based control of muscles is that muscle synergies might reflect task constraints rather than a neural control strategy. Another theory of motor control suggests that muscles are recruited by optimizing performance. Optimization of performance has been widely used to calculate muscle recruitment underlying a given motion while assuming independent recruitment of muscles. If synergies indeed determine muscle recruitment underlying a given motion, optimization approaches that do not model synergy-based control could result in muscle activations that do not show the synergistic muscle action observed through electromyography (EMG). If, however, synergistic muscle action results from performance optimization and task constraints (joint kinematics and external forces), such optimization approaches are expected to result in low-dimensional synergistic muscle activations that are similar to EMG-based synergies. We calculated muscle recruitment underlying experimentally measured gait patterns by optimizing performance assuming independent recruitment of muscles. We found that the muscle activations calculated without any reference to synergies can be accurately explained by on average four synergies. These synergies are similar to EMG-based synergies. We therefore conclude that task constraints and performance optimization explain synergistic muscle recruitment from a redundant set of muscles.

The development of lower limb musculoskeletal models with clinical relevance is dependent upon the fidelity of the mathematical description of the lower limb. Part I: Equations of motion

Contemporary musculoskeletal modelling research is based upon the assumption that such models will evolve into clinical tools that can be used to guide therapeutic interventions. However, there are a number of questions that must be addressed before this becomes a reality. At its heart, musculoskeletal modelling is a process of formulating and then solving the equations of motion that describe the movement of body segments. Both of these steps are challenging. This article argues that traditional approaches to musculoskeletal modelling have been heavily influenced by the need to simplify this process (and in particular the solution process), and that this has to some degree resulted in approaches that are contrary to the principles of classical mechanics. It is suggested that future work is required to understand how these simplifications affect the outputs of musculoskeletal modelling studies. Equally, to increase their clinical relevance, the models of the future should adhere more closely to the classical mechanics on which they are based.

Influence of joint models on lower-limb musculo-tendon forces and three-dimensional joint reaction forces during gait

Several three-dimensional (3D) lower-limb musculo-skeletal models have been developed for gait analysis and different hip, knee and ankle joint models have been considered in the literature. Conversely to the influence of the musculo-tendon geometry, the influence of the joint models - i.e. number of degrees of freedom and passive joint moments - on the estimated musculo-tendon forces and 3D joint reaction forces has not been extensively examined.

In this paper musculo-tendon forces and 3D joint reaction forces have been estimated for one subject and one gait cycle with nine variations of a musculoskeletal model and outputs have been compared to measured electromyographic signals and knee joint contact forces. The model outputs are generally in line with the measured signals. However, the 3D joint reaction forces were higher than published values and the contact forces measured for the subject. The results of this study show that, with more degrees of freedom in the model, the musculo-tendon forces and the 3D joint reaction forces tend to increase but with some redistribution between the muscles. In addition, when taking into account passive joint moments, the 3D joint reaction forces tend to decrease during the stance phase and increase during the swing phase.

Although further investigations are needed, a five-degree-of-freedom lower-limb musculo-skeletal model with some angle-dependent joint coupling and stiffness seems to provide satisfactory musculo-tendon forces and 3D joint reaction forces.

The development of lower limb musculoskeletal models with clinical relevance is dependent upon the fidelity of the mathematical description of the lower limb. Part 2: patient-specific geometry

Musculoskeletal models have the potential to evolve into sensitive clinical tools that provide relevant therapeutic guidance. A key impediment to this is the lack of understanding as to the function of such models. In order to improve this it is useful to recognise that musculoskeletal modelling is the mathematical description of musculoskeletal movement – a process that involves the construction and solution of equations of motion. These equations are derived from standard mechanical considerations and the mathematical representation of anatomy. The fidelity of musculoskeletal models is highly dependent on the assumption that such representations also describe the function of the musculoskeletal geometry. In addition, it is important to understand the sensitivity of such representations to patient-specific variations in anatomy. The exploration of these twin considerations will be fundamental to the creation of musculoskeletal modelling tools with clinical relevance and a systematic enquiry of these key parameters is recommended.

Analytical and numerical analysis of inverse optimization problems: conditions of uniqueness and computational methods

One of the key problems of motor control is the redundancy problem, in particular how the central nervous system (CNS) chooses an action out of infinitely many possible. A promising way to address this question is to assume that the choice is made based on optimization of a certain cost function. A number of cost functions have been proposed in the literature to explain performance in different motor tasks: from force sharing in grasping to path planning in walking. However, the problem of uniqueness of the cost function(s) was not addressed until recently. In this article, we analyze two methods of finding additive cost functions in inverse optimization problems with linear constraints, so-called linear-additive inverse optimization problems. These methods are based on the Uniqueness Theorem for inverse optimization problems that we proved recently (Terekhov et al., J Math Biol 61(3):423-453, 2010). Using synthetic data, we show that both methods allow for determining the cost function. We analyze the influence of noise on the both methods. Finally, we show how a violation of the conditions of the Uniqueness Theorem may lead to incorrect solutions of the inverse optimization problem.

Sensitivity of dynamic simulations of gait and dynamometer experiments to hill muscle model parameters of knee flexors and extensors

We assessed and compared sensitivities of dynamic simulations to musculotendon (MT) parameters for gait and dynamometer experiments. Our aim with this comparison was to investigate whether dynamometer experiments could provide information about MT-parameters that are important to reliably study MT-function during gait. This would mean that dynamometer experiments could be used to estimate these parameters. Muscle contribution to the joint torque (MT-torque) rather than relative MT-force primarily affects the resulting gait pattern and torque measured by the dynamometer. In contrast to recent studies, therefore, we assessed the sensitivity of the MT-torque, rather than the sensitivity of the relative MT-force. Based on sensitivity of the MT-torque to a parameter perturbation, MT-parameters of the knee flexors and extensors were classified in three categories: low, medium, and high. For gait, classification was based on the average sensitivity during a gait cycle. For isometric and isokinetic dynamometer experiments, classification was based on the highest sensitivity found in the experiments. The calculated muscle contributions to the knee torque during gait and dynamometer experiments had a high sensitivity to only a limited number of MT-parameters of the knee flexors and extensors, suggesting that not all MT-parameters need to be estimated. In general, the highest sensitivity was found for tendon slack length. However, for some muscles the sensitivity to the optimal fibre length or the maximal isometric muscle force was also high or medium. The classification of the individual MT-parameters for gait and dynamometer experiments was largely similar. We therefore conclude that dynamometer experiments provide information about MT-parameters important to reliably study MT-function during gait, so that subject-specific estimates of MT-parameters could be made based on dynamometer experiments.