Hill-type muscle model with serial damping and eccentric force–velocity relation

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

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

Versatile graceful degradation framework for bio-inspired proprioception with redundant soft sensors

Reliable proprioception and feedback from soft sensors are crucial for enabling soft robots to function intelligently in real-world environments. Nevertheless, soft sensors are fragile and are susceptible to various damage sources in such environments. Some researchers have utilized redundant configuration, where healthy sensors compensate instantaneously for lost ones to maintain proprioception accuracy. However, achieving consistently reliable proprioception under diverse sensor degradation remains a challenge. This paper proposes a novel framework for graceful degradation in redundant soft sensor systems, incorporating a stochastic Long Short-Term Memory (LSTM) and a Time-Delay Feedforward Neural Network (TDFNN). The LSTM estimates readings from healthy sensors to compare them with actual data. Then, statistically abnormal readings are zeroed out. The TDFNN receives the processed sensor readings to perform proprioception. Simulation experiments with a musculoskeletal leg that contains 40 nonlinear soft sensors demonstrate the effectiveness of the proposed framework. Results show that the knee angle proprioception accuracy is retained across four distinct degradation scenarios. Notably, the mean proprioception error increases by less than 1.91°(1.36%) when 30 % of the sensors are degraded. These results suggest that the proposed framework enhances the reliability of soft sensor proprioception, thereby improving the robustness of soft robots in real-world applications.

Mechanisms of myosin II force generation: insights from novel experimental techniques and approaches

Myosin II is a molecular motor that converts chemical energy derived from ATP hydrolysis into mechanical work. Myosin II isoforms are responsible for muscle contraction and a range of cell functions relying on the development of force and motion. When the motor attaches to actin, ATP is hydrolyzed and inorganic phosphate (Pi) and ADP are released from its active site. These reactions are coordinated with changes in the structure of myosin, promoting the so-called "power stroke" that causes the sliding of actin filaments. The general features of the myosin-actin interactions are well accepted, but there are critical issues that remain poorly understood, mostly due to technological limitations. In recent years, there has been a significant advance in structural, biochemical, and mechanical methods that have advanced the field considerably. New modeling approaches have also allowed researchers to understand actomyosin interactions at different levels of analysis. This paper reviews recent studies looking into the interaction between myosin II and actin filaments, which leads to power stroke and force generation. It reviews studies conducted with single myosin molecules, myosins working in filaments, muscle sarcomeres, myofibrils, and fibers. It also reviews the mathematical models that have been used to understand the mechanics of myosin II in approaches focusing on single molecules to ensembles. Finally, it includes brief sections on translational aspects, how changes in the myosin motor by mutations and/or posttranslational modifications may cause detrimental effects in diseases and aging, among other conditions, and how myosin II has become an emerging drug target.

A benchmark of muscle models to length changes great and small

Digital human body models are used to simulate injuries that occur as a result of vehicle collisions, vibration, sports, and falls. Given enough time the body's musculature can generate force, affect the body's movements, and change the risk of some injuries. The finite-element code LS-DYNA is often used to simulate the movements and injuries sustained by the digital human body models as a result of an accident. In this work, we evaluate the accuracy of the three muscle models in LS-DYNA (MAT_156, EHTM, and the VEXAT) when simulating a range of experiments performed on isolated muscle: force-length-velocity experiments on maximally and sub-maximally stimulated muscle, active-lengthening experiments, and vibration experiments. The force-length-velocity experiments are included because these conditions are typical of the muscle activity that precedes an accident, while the active-lengthening and vibration experiments mimic conditions that can cause injury. The three models perform similarly during the maximally and sub-maximally activated force-length-velocity experiments, but noticeably differ in response to the active-lengthening and vibration experiments. The VEXAT model is able to generate the enhanced forces of biological muscle during active lengthening, while both the MAT_156 and EHTM produce too little force. In response to vibration, the stiffness and damping of the VEXAT model closely follows the experimental data while the MAT_156 and EHTM models differ substantially. The accuracy of the VEXAT model comes from two additional mechanical structures that are missing in the MAT_156 and EHTM models: viscoelastic cross-bridges, and an active titin filament. To help others build on our work we have made our simulation code publicly available.

Using muscle-tendon load limits to assess unphysiological musculoskeletal model deformation and Hill-type muscle parameter choice

Musculoskeletal simulations are a useful tool for improving our understanding of the human body. However, the physiological validity of predicted kinematics and forces is highly dependent upon the correct calibration of muscle parameters and the structural integrity of a model's internal skeletal structure. In this study, we show how ill-tuned muscle parameters and unphysiological deformations of a model's skeletal structure can be detected by using muscle elements as sensors with which modelling and parameterization inconsistencies can be identified through muscle and tendon strain injury assessment. To illustrate our approach, two modelling issues were recreated. First, a model repositioning simulation using the THUMS AM50 occupant model version 5.03 was performed to show how internal model deformations can occur during a change of model posture. Second, the muscle material parameters of the OpenSim gait2354 model were varied to illustrate how unphysiological muscle forces can arise if material parameters are inadequately calibrated. The simulations were assessed for muscle and tendon strain injuries using previously published injury criteria and a newly developed method to determine tendon strain injury threshold values. Muscle strain injuries in the left and right musculus pronator teres were detected during the model repositioning. This straining was caused by an unphysiologically large gap (12.92 mm) that had formed in the elbow joint. Similarly, muscle and tendon strain injuries were detected in the modified right-hand musculus gastrocnemius medialis of the gait2354 model where an unphysiological reduction of the tendon slack length introduced large pre-strain of the muscle-tendon unit. The results of this work show that the proposed method can quantify the internal distortion behaviour of musculoskeletal human body models and the plausibility of Hill-type muscle parameter choice via strain injury assessment. Furthermore, we highlight possible actions to avoid the presented issues and inconsistencies in literature data concerning the material characteristics of human tendons.

Antagonistic Feedback Control of Muscle Length Changes for Efficient Involuntary Posture Stabilization

Simultaneous and cooperative muscle activation results in involuntary posture stabilization in vertebrates. However, the mechanism through which more muscles than joints contribute to this stabilization remains unclear. We developed a computational human body model with 949 muscle action lines and 22 joints and examined muscle activation patterns for stabilizing right upper or lower extremity motions at a neutral body posture (NBP) under gravity using actor-critic reinforcement learning (ACRL). Two feedback control models (FCM), muscle length change (FCM-ML) and joint angle differences, were applied to ACRL with a normalized Gaussian network (ACRL-NGN) or deep deterministic policy gradient. Our findings indicate that among the six control methods, ACRL-NGN with FCM-ML, utilizing solely antagonistic feedback control of muscle length change without relying on synergy pattern control or categorizing muscles as flexors, extensors, agonists, or synergists, achieved the most efficient involuntary NBP stabilization. This finding suggests that vertebrate muscles are fundamentally controlled without categorization of muscles for targeted joint motion and are involuntarily controlled to achieve the NBP, which is the most comfortable posture under gravity. Thus, ACRL-NGN with FCM-ML is suitable for controlling humanoid muscles and enables the development of a comfortable seat design.

Impact of lengthening velocity on the generation of eccentric force by slow-twitch muscle fibers in long stretches

After an initial increase, isovelocity elongation of a muscle fiber can lead to diminishing (referred to as Give in the literature) and subsequently increasing force. How the stretch velocity affects this behavior in slow-twitch fibers remains largely unexplored. Here, we stretched fully activated individual rat soleus muscle fibers from 0.85 to 1.3 optimal fiber length at stretch velocities of 0.01, 0.1, and 1 maximum shortening velocity, vmax, and compared the results with those of rat EDL fast-twitch fibers obtained in similar experimental conditions. In soleus muscle fibers, Give was 7%, 18%, and 44% of maximum isometric force for 0.01, 0.1, and 1 vmax, respectively. As in EDL fibers, the force increased nearly linearly in the second half of the stretch, although the number of crossbridges decreased, and its slope increased with stretch velocity. Our findings are consistent with the concept of a forceful detachment and subsequent crossbridge reattachment in the stretch's first phase and a strong viscoelastic titin contribution to fiber force in the second phase of the stretch. Interestingly, we found interaction effects of stretch velocity and fiber type on force parameters in both stretch phases, hinting at fiber type-specific differences in crossbridge and titin contributions to eccentric force. Whether fiber type-specific combined XB and non-XB models can explain these effects or if they hint at some not fully understood properties of muscle contraction remains to be shown. These results may stimulate new optimization perspectives in sports training and provide a better understanding of structure-function relations of muscle proteins.

A three filament mechanistic model of musculotendon force and impedance

The force developed by actively lengthened muscle depends on different structures across different scales of lengthening. For small perturbations, the active response of muscle is well captured by a linear-time-invariant (LTI) system: a stiff spring in parallel with a light damper. The force response of muscle to longer stretches is better represented by a compliant spring that can fix its end when activated. Experimental work has shown that the stiffness and damping (impedance) of muscle in response to small perturbations is of fundamental importance to motor learning and mechanical stability, while the huge forces developed during long active stretches are critical for simulating and predicting injury. Outside of motor learning and injury, muscle is actively lengthened as a part of nearly all terrestrial locomotion. Despite the functional importance of impedance and active lengthening, no single muscle model has all these mechanical properties. In this work, we present the viscoelastic-crossbridge active-titin (VEXAT) model that can replicate the response of muscle to length changes great and small. To evaluate the VEXAT model, we compare its response to biological muscle by simulating experiments that measure the impedance of muscle, and the forces developed during long active stretches. In addition, we have also compared the responses of the VEXAT model to a popular Hill-type muscle model. The VEXAT model more accurately captures the impedance of biological muscle and its responses to long active stretches than a Hill-type model and can still reproduce the force-velocity and force-length relations of muscle. While the comparison between the VEXAT model and biological muscle is favorable, there are some phenomena that can be improved: the low frequency phase response of the model, and a mechanism to support passive force enhancement.

Wearable high-density EMG sleeve for complex hand gesture classification and continuous joint angle estimation

High-density electromyography (HD-EMG) can provide a natural interface to enhance human-computer interaction (HCI). This study aims to demonstrate the capability of a novel HD-EMG forearm sleeve equipped with up to 150 electrodes to capture high-resolution muscle activity, decode complex hand gestures, and estimate continuous hand position via joint angle predictions. Ten able-bodied participants performed 37 hand movements and grasps while EMG was recorded using the HD-EMG sleeve. Simultaneously, an 18-sensor motion capture glove calculated 23 joint angles from the hand and fingers across all movements for training regression models. For classifying across the 37 gestures, our decoding algorithm was able to differentiate between sequential movements with 97.3 ± 0.3 % accuracy calculated on a 100 ms bin-by-bin basis. In a separate mixed dataset consisting of 19 movements randomly interspersed, decoding performance achieved an average bin-wise accuracy of 92.8 ± 0.8 % . When evaluating decoders for use in real-time scenarios, we found that decoders can reliably decode both movements and movement transitions, achieving an average accuracy of 93.3 ± 0.9 % on the sequential set and 88.5 ± 0.9 % on the mixed set. Furthermore, we estimated continuous joint angles from the EMG sleeve data, achieving a R 2 of 0.884 ± 0.003 in the sequential set and 0.750 ± 0.008 in the mixed set. Median absolute error (MAE) was kept below 10° across all joints, with a grand average MAE of 1.8 ± 0 . 04 ∘ and 3.4 ± 0 . 07 ∘ for the sequential and mixed datasets, respectively. We also assessed two algorithm modifications to address specific challenges for EMG-driven HCI applications. To minimize decoder latency, we used a method that accounts for reaction time by dynamically shifting cue labels in time. To reduce training requirements, we show that pretraining models with historical data provided an increase in decoding performance compared with models that were not pretrained when reducing the in-session training data to only one attempt of each movement. The HD-EMG sleeve, combined with sophisticated machine learning algorithms, can be a powerful tool for hand gesture recognition and joint angle estimation. This technology holds significant promise for applications in HCI, such as prosthetics, assistive technology, rehabilitation, and human-robot collaboration.

Note on hydrostatic skeletons: muscles operating within a pressurized environment

Muscles and muscle fibers are volume-constant constructs that deform when contracted and develop internal pressures. However, muscles embedded in hydrostatic skeletons are also exposed to external pressures generated by their activity. For two examples, the pressure generation in spiders and in annelids, we used simplified biomechanical models to demonstrate that high intracellular pressures diminishing the resulting tensile stress of the muscle fibers are avoided in the hydrostatic skeleton. The findings are relevant for a better understanding of the design and functionality of biological hydrostatic skeletons.

Quantifying the Impact of Spinal Fusion Systems by Multibody Simulation

The established surgical procedure of spinal fusion, in which two or more spinal vertebrae are permanently connected, is constantly increasing worldwide due to new developments in fusion procedures and surgical techniques, as well as improved implants, even though there is still no consensus on whether fusion leads to subsequent degeneration of adjacent spinal segments. We outline the potential biomechanical impacts of mono-segmental and multi-segmental fusion on the spinal structures, especially on the adjacent functional spinal units (FSU), using MultiBody Simulation (MBS). In addition, we investigated the influence of the implant size on the loading situation of the spinal structures by analyzing suitable human MBS models, focusing on a highly detailed spinal region. Our results showed no significant increase in the load on adjacent intervertebral discs (IVD) in the present specific model configurations due to mono-segmental and multi-segmental fusion. Instead, the load was redistributed to the disadvantage of the posterior facet joints in the lumbar spine's upper section. Analysis of the influence of different implant sizes on the spinal structures' load revealed that choosing an implant size that did not correspond to the original IVD space led to a massive increase in the IVD loads.Clinical relevance: gaining new insights to improve surgical outcomes to minimize the risk of adverse effects.

Utilising redundancy in musculoskeletal systems for adaptive stiffness and muscle failure compensation: a model-free inverse statics approach

Vertebrates possess a biomechanical structure with redundant muscles, enabling adaptability in uncertain and complex environments. Harnessing this inspiration, musculoskeletal systems offer advantages like variable stiffness and resilience to actuator failure and fatigue. Despite their potential, the complex structure presents modelling challenges that are difficult to explicitly formulate and control. This difficulty arises from the need for comprehensive knowledge of the musculoskeletal system, including details such as muscle arrangement, and fully accessible muscle and joint states. Whilst existing model-free methods do not need explicit formulations, they also underutilise the benefits of muscle redundancy. Consequently, they necessitate retraining in the event of muscle failure and require manual tuning of parameters to control joint stiffness limiting their applications under unknown payloads. Presented here is a model-free local inverse statics controller for musculoskeletal systems, employing a feedforward neural network trained on motor babbling data. Experiments with a musculoskeletal leg model showcase the controller's adaptability to complex structures, including mono and bi-articulate muscles. The controller can compensate for changes such as weight variations, muscle failures, and environmental interactions, retaining reasonable accuracy without the need for any additional retraining.

Inverting a model of neuromuscular control to estimate descending activation patterns that generate fast-reaching movements

Reaching movements generally show smooth kinematic profiles that are invariant across varying movement speeds even as interaction torques and muscle properties vary nonlinearly with speed. How the brain brings about these invariant profiles is an open question. We developed an analytical inverse dynamics method to estimate descending activation patterns directly from observed joint angle trajectories based on a simple model of the stretch reflex, and of muscle and biomechanical dynamics. We estimated descending activation patterns for experimental data from eight different planar two-joint movements performed at two movement times (fast: 400 ms; slow: 800 ms). The temporal structure of descending activation differed qualitatively across speeds, consistent with the idea that the nervous system uses an internal model to generate anticipatory torques during fast movement. This temporal structure also depended on the cocontraction level of antagonistic muscle groups. Comparing estimated muscle activation and descending activation revealed the contribution of the stretch reflex to movement generation that was found to set in after about 20% of movement time.NEW & NOTEWORTHY By estimating descending activation patterns directly from observed movement kinematics based on a model of the dynamics of the stretch reflex, of muscle force generation, and of the biomechanics of the limb, we observed how brain signals must be temporally structured to enable fast movement.

Why Should Athletes Brake Fast? Influence of Eccentric Velocity on Concentric Performance During Countermovement Jumps at Different Loads

PURPOSE

The aim of the present study was to analyze the effect of different eccentric tempos on eccentric kinetics and kinematics and the subsequent concentric performance when performing countermovement jumps against different loads.

METHODS

After 1-repetition-maximum assessment and 2 familiarization sessions, 13 well-trained participants performed, in randomized order, 12 sets (4 tempos × 3 loads) of 4 repetitions of the loaded countermovement-jump exercise. The eccentric tempos analyzed were 5 and 2 seconds, as fast as possible, and accelerated (ie, without pause between repetitions), while the loads used were 30%, 50%, and 70% of 1-repetition maximum. Several kinetic and kinematic variables during both phases were recorded by linking a linear position transducer to the barbell.

RESULTS

The eccentric work was greater in the accelerated condition despite no changes in the eccentric depth. The peak and mean propulsive velocities were greater in the as-fast-as-possible and accelerated conditions. Correlation analysis showed that, compared with the 5-second condition, the increased concentric performance in the accelerated condition was related to the difference in eccentric work performed in the last 100 milliseconds of the eccentric phase (r > .770).

CONCLUSIONS

Contrary to current practices, the current study highlights the need for performing the eccentric phase of loaded countermovement jumps, a common exercise performed by athletes for both training and evaluation purposes, as fast as possible. This allows not only a greater eccentric work but also improved concentric performance.

An investigation of tendon strains in jersey finger injury load cases using a finite element neuromuscular human body model

Introduction: A common hand injury in American football, rugby and basketball is the so-called jersey finger injury (JFI), in which an eccentric overextension of the distal interphalangeal joint leads to an avulsion of the connected musculus flexor digitorum profundus (FDP) tendon. In the field of automotive safety assessment, finite element (FE) neuromuscular human body models (NHBMs) have been validated and are employed to evaluate different injury types related to car crash scenarios. The goal of this study is to show, how such a model can be modified to assess JFIs by adapting the hand of an FE-NHBM for the computational analysis of tendon strains during a generalized JFI load case. Methods: A jersey finger injury criterion (JFIC) covering the injury mechanisms of tendon straining and avulsion was defined based on biomechanical experiments found in the literature. The hand of the Total Human Model for Safety (THUMS) version 3.0 was combined with the musculature of THUMS version 5.03 to create a model with appropriate finger mobility. Muscle routing paths of FDP and musculus flexor digitorum superficialis (FDS) as well as tendon material parameters were optimized using literature data. A simplified JFI load case was simulated as the gripping of a cylindrical rod with finger flexor activation levels between 0% and 100%, which was then retracted with the velocity of a sprinting college football player to forcefully open the closed hand. Results: The optimization of the muscle routing node positions and tendon material parameters yielded good results with minimum normalized mean absolute error values of 0.79% and 7.16% respectively. Tendon avulsion injuries were detected in the middle and little finger for muscle activation levels of 80% and above, while no tendon or muscle strain injuries of any kind occurred. Discussion: The presented work outlines the steps necessary to adapt the hand model of a FE-NHBM for the assessment of JFIs using a newly defined injury criterion called the JFIC. The injury assessment results are in good agreement with documented JFI symptoms. At the same time, the need to rethink commonly asserted paradigms concerning the choice of muscle material parameters is highlighted.

Development and verification of a physiologically motivated internal controller for the open-source extended Hill-type muscle model in LS-DYNA

Nowadays, active human body models are becoming essential tools for the development of integrated occupant safety systems. However, their broad application in industry and research is limited due to the complexity of incorporated muscle controllers, the long simulation runtime, and the non-regular use of physiological motor control approaches. The purpose of this study is to address the challenges in all indicated directions by implementing a muscle controller with several physiologically inspired control strategies into an open-source extended Hill-type muscle model formulated as LS-DYNA user-defined umat41 subroutine written in the Fortran programming language. This results in increased usability, runtime performance and physiological accuracy compared to the standard muscle material existing in LS-DYNA. The proposed controller code is verified with extensive experimental data that include findings for arm muscles, the cervical spine region, and the whole body. Selected verification experiments cover three different muscle activation situations: (1) passive state, (2) open-loop and closed-loop muscle activation, and (3) reflexive behaviour. Two whole body finite element models, the 50th percentile female VIVA OpenHBM and the 50th percentile male THUMS v5, are used for simulations, complemented by the simplified arm model extracted from the 50th percentile male THUMS v3. The obtained results are evaluated additionally with the CORrelation and Analysis methodology and the mean squared error method, showing good to excellent biofidelity and sufficient agreement with the experimental data. It was shown additionally how the integrated controller allows simplified mimicking of the movements for similar musculoskeletal models using the parameters transfer method. Furthermore, the Hill-type muscle model presented in this paper shows better kinematic behaviour even in the passive case compared to the existing one in LS-DYNA due to its improved damping and elastic properties. These findings provide a solid evidence base motivating the application of the enhanced muscle material with the internal controller in future studies with Active Human Body Models under different loading conditions.

Coordinating upper limbs for octave playing on the piano via neuro-musculoskeletal modeling

Understanding the coordination of multiple biomechanical degrees of freedom in biological organisms is crucial for unraveling the neurophysiological control of sophisticated motor tasks. This study focuses on the cooperative behavior of upper-limb motor movements in the context of octave playing on the piano. While the vertebrate locomotor system has been extensively investigated, the coherence and precision timing of rhythmic movements in the upper-limb system remain incompletely understood. Inspired by the spinal cord neuronal circuits (central pattern generator, CPG), a computational neuro-musculoskeletal model is proposed to explore the coordination of upper-limb motor movements during octave playing across varying tempos and volumes. The proposed model incorporates a CPG-based nervous system, a physiologically-informed mechanical body, and a piano environment to mimic human joint coordination and expressiveness. The model integrates neural rhythm generation, spinal reflex circuits, and biomechanical muscle dynamics while considering piano playing quality and energy expenditure. Based on real-world human subject experiments, the model has been refined to study tempo transitions and volume control during piano playing. This computational approach offers insights into the neurophysiological basis of upper-limb motor coordination in piano playing and its relation to expressive features.

Effect of neglecting passive spinal structures: a quantitative investigation using the forward-dynamics and inverse-dynamics musculoskeletal approach

Purpose: Inverse-dynamics (ID) analysis is an approach widely used for studying spine biomechanics and the estimation of muscle forces. Despite the increasing structural complexity of spine models, ID analysis results substantially rely on accurate kinematic data that most of the current technologies are not capable to provide. For this reason, the model complexity is drastically reduced by assuming three degrees of freedom spherical joints and generic kinematic coupling constraints. Moreover, the majority of current ID spine models neglect the contribution of passive structures. The aim of this ID analysis study was to determine the impact of modelled passive structures (i.e., ligaments and intervertebral discs) on remaining joint forces and torques that muscles must balance in the functional spinal unit. Methods: For this purpose, an existing generic spine model developed for the use in the demoa software environment was transferred into the musculoskeletal modelling platform OpenSim. The thoracolumbar spine model previously used in forward-dynamics (FD) simulations provided a full kinematic description of a flexion-extension movement. By using the obtained in silico kinematics, ID analysis was performed. The individual contribution of passive elements to the generalised net joint forces and torques was evaluated in a step-wise approach increasing the model complexity by adding individual biological structures of the spine. Results: The implementation of intervertebral discs and ligaments has significantly reduced compressive loading and anterior torque that is attributed to the acting net muscle forces by -200% and -75%, respectively. The ID model kinematics and kinetics were cross-validated against the FD simulation results. Conclusion: This study clearly shows the importance of incorporating passive spinal structures on the accurate computation of remaining joint loads. Furthermore, for the first time, a generic spine model was used and cross-validated in two different musculoskeletal modelling platforms, i.e., demoa and OpenSim, respectively. In future, a comparison of neuromuscular control strategies for spinal movement can be investigated using both approaches.

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.

Eccentric muscle contractions: from single muscle fibre to whole muscle mechanics

Eccentric muscle loading encompasses several unique features compared to other types of contractions. These features include increased force, work, and performance at decreased oxygen consumption, reduced metabolic cost, improved energy efficiency, as well as decreased muscle activity. This review summarises explanatory approaches to long-standing questions in terms of muscular contraction dynamics and molecular and cellular mechanisms underlying eccentric muscle loading. Moreover, this article intends to underscore the functional link between sarcomeric components, emphasising the fundamental role of titin in skeletal muscle. The giant filament titin reveals versatile functions ranging from sarcomere organisation and maintenance, providing passive tension and elasticity, and operates as a mechanosensory and signalling platform. Structurally, titin consists of a viscoelastic spring segment that allows activation-dependent coupling to actin. This titin-actin interaction can explain linear force increases in active lengthening experiments in biological systems. A three-filament model of skeletal muscle force production (mediated by titin) is supposed to overcome significant deviations between experimental observations and predictions by the classic sliding-filament and cross-bridge theories. Taken together, this review intends to contribute to a more detailed understanding of overall muscle behaviour and force generation-from a microscopic sarcomere level to a macroscopic multi-joint muscle level-impacting muscle modelling, the understanding of muscle function, and disease.

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.

Inertia-Constrained Reinforcement Learning to Enhance Human Motor Control Modeling

Locomotor impairment is a highly prevalent and significant source of disability and significantly impacts the quality of life of a large portion of the population. Despite decades of research on human locomotion, challenges remain in simulating human movement to study the features of musculoskeletal drivers and clinical conditions. Most recent efforts to utilize reinforcement learning (RL) techniques are promising in the simulation of human locomotion and reveal musculoskeletal drives. However, these simulations often fail to mimic natural human locomotion because most reinforcement strategies have yet to consider any reference data regarding human movement. To address these challenges, in this study, we designed a reward function based on the trajectory optimization rewards (TOR) and bio-inspired rewards, which includes the rewards obtained from reference motion data captured by a single Inertial Moment Unit (IMU) sensor. The sensor was equipped on the participants' pelvis to capture reference motion data. We also adapted the reward function by leveraging previous research on walking simulations for TOR. The experimental results showed that the simulated agents with the modified reward function performed better in mimicking the collected IMU data from participants, which means that the simulated human locomotion was more realistic. As a bio-inspired defined cost, IMU data enhanced the agent's capacity to converge during the training process. As a result, the models' convergence was faster than those developed without reference motion data. Consequently, human locomotion can be simulated more quickly and in a broader range of environments, with a better simulation performance.

Numerical instability of Hill-type muscle models

Hill-type muscle models are highly preferred as phenomenological models for musculoskeletal simulation studies despite their introduction almost a century ago. The use of simple Hill-type models in simulations, instead of more recent cross-bridge models, is well justified since computationally 'light-weight'-although less accurate-Hill-type models have great value for large-scale simulations. However, this article aims to invite discussion on numerical instability issues of Hill-type muscle models in simulation studies, which can lead to computational failures and, therefore, cannot be simply dismissed as an inevitable but acceptable consequence of simplification. We will first revisit the basic premises and assumptions on the force-length and force-velocity relationships that Hill-type models are based upon, and their often overlooked but major theoretical limitations. We will then use several simple conceptual simulation studies to discuss how these numerical instability issues can manifest as practical computational problems. Lastly, we will review how such numerical instability issues are dealt with, mostly in an ad hoc fashion, in two main areas of application: musculoskeletal biomechanics and computer animation.

Effects of geometric individualisation of a human spine model on load sharing: neuro-musculoskeletal simulation reveals significant differences in ligament and muscle contribution

In spine research, two possibilities to generate models exist: generic (population-based) models representing the average human and subject-specific representations of individuals. Despite the increasing interest in subject specificity, individualisation of spine models remains challenging. Neuro-musculoskeletal (NMS) models enable the analysis and prediction of dynamic motions by incorporating active muscles attaching to bones that are connected using articulating joints under the assumption of rigid body dynamics. In this study, we used forward-dynamic simulations to compare a generic NMS multibody model of the thoracolumbar spine including fully articulated vertebrae, detailed musculature, passive ligaments and linear intervertebral disc (IVD) models with an individualised model to assess the contribution of individual biological structures. Individualisation was achieved by integrating skeletal geometry from computed tomography and custom-selected muscle and ligament paths. Both models underwent a gravitational settling process and a forward flexion-to-extension movement. The model-specific load distribution in an equilibrated upright position and local stiffness in the L4/5 functional spinal unit (FSU) is compared. Load sharing between occurring internal forces generated by individual biological structures and their contribution to the FSU stiffness was computed. The main finding of our simulations is an apparent shift in load sharing with individualisation from an equally distributed element contribution of IVD, ligaments and muscles in the generic spine model to a predominant muscle contribution in the individualised model depending on the analysed spine level.

Neuro-cognitive assessment of intentional control methods for a soft elbow exosuit using error-related potentials

Soft exosuits offer promise to support users in everyday workload tasks by providing assistance. However, acceptance of such systems remains low due to the difficulty of control compared with rigid mechatronic systems. Recently, there has been progress in developing control schemes for soft exosuits that move in line with user intentions. While initial results have demonstrated sufficient device performance, the assessment of user experience via the cognitive response has yet to be evaluated. To address this, we propose a soft pneumatic elbow exosuit designed based on our previous work to provide assistance in line with user expectations utilizing two existing state-of-the-art control methods consisting of a gravity compensation and myoprocessor based on muscle activation. A user experience study was conducted to assess whether the device moves naturally with user expectations and the potential for device acceptance by determining when the exosuit violated user expectations through the neuro-cognitive and motor response. Brain activity from electroencephalography (EEG) data revealed that subjects elicited error-related potentials (ErrPs) in response to unexpected exosuit actions, which were decodable across both control schemes with an average accuracy of 76.63 ± 1.73% across subjects. Additionally, unexpected exosuit actions were further decoded via the motor response from electromyography (EMG) and kinematic data with a grand average accuracy of 68.73 ± 6.83% and 77.52 ± 3.79% respectively. This work demonstrates the validation of existing state-of-the-art control schemes for soft wearable exosuits through the proposed soft pneumatic elbow exosuit. We demonstrate the feasibility of assessing device performance with respect to the cognitive response through decoding when the device violates user expectations in order to help understand and promote device acceptance.

Design and Scaling of Exoskeleton Power Units Considering Load Cycles of Humans

Exoskeletons are powerful tools for aiding humans with pathological conditions, in dangerous environments or in manually exhausting tasks. Typically, they are designed for specific maximum scenarios without taking into account the diversity of tasks and the individuality of the user. To address this discrepancy, a framework was developed for personalizing an exoskeleton by scaling the components, especially the electrical machine, based on different simulated human muscle forces. The main idea was to scale a numerical arm model based on body mass and height to predict different movements representing both manual labor and daily activities. The predicted torques necessary to produce these movements were then used to generate a load/performance cycle for the power unit design. Considering these torques, main operation points of this load cycle were defined and a reference power unit was scaled and optimized. Therefore, a scalability model for an electrical machine is introduced. This individual adaptation and scaling of the power unit for different users leads to a better performance and a lighter design.

Evaluation of muscle strain injury severity in active human body models

Even though significant efforts in the field of injury detection with finite element active human body models (FE AHBMs) have been made, injuries of the muscle-tendon unit (MTU) have not yet been taken into consideration. Therefore, the goal of this study was to define a muscle strain injury criterion (MSIC) to evaluate the damage sustained by the musculature during muscle driven movement scenarios. The MSIC was derived from biomechanical tests found in the literature and the proposed threshold values were substantiated through a comparison to an estimate of the ultimate tensile strength of human skeletal muscle and the forces acting on the biceps femoris long head muscle during one sprinting gait cycle. The application of the MSIC to state-of-the-art FE AHBMs was demonstrated by evaluating the strain injury severity of selected neck muscles of a full-body AHBM during two seat rotation load cases. The results of the MSIC substantiation suggest that all three injury threshold values proposed in this work fall in a plausible corridor of forces acting on the MTU. The combined results of the AHBM simulations indicate that neither of the two examined seat rotations are likely to cause strain injury to the neck muscles and that the proposed MSIC can easily be applied to current AHBMs without further modification of the model architecture or the muscle parameters. The MSIC was also used to formulate a hypothesis on the aetiology of muscle strain injuries, through which it was demonstrated that material inhomogeneities in the MTU might be the cause for strain injuries sustained during otherwise physiological movements. This work is a first step in the direction of the definition of a wholistic injury criterion for the human skeletal muscle fibre.

A review of motor neural system robotic modeling approaches and instruments

In this review, we are considering an actively developing tool in neuroscience-robotic modeling. The new perspective and existing application fields, tools, and methods are discussed. We try to determine starting positions and approaches that are useful at the beginning of new research in this field. Among multiple directions of the research is robotic modeling on the level of muscles fibers and their afferents, skin surface sensors, muscles, and joints proprioceptors. Some examples of technical implementation for physical modeling are reviewed. They are software and hardware tools like event-related modeling algorithms, reduced neuron models, robotic drives constructions. We observe existing drives technologies and prospective electric motor types: switched reluctance and transverse flux motors. Next, we look at the existing examples and approaches for robotic modeling of the cerebellum and spinal cord neural networks. These examples show practical methods for the model neural network architecture and adaptation. Those methods allow the use of cortical and spinal cord reflexes for the network training and apply additional artificial blocks for data processing in other brain structures that transmit and receive data from biologically realistic models.

The Need for Eccentric Speed: A Narrative Review of the Effects of Accelerated Eccentric Actions During Resistance-Based Training

Eccentric training as a method to enhance athletic performance is a topic of increasing interest to both practitioners and researchers. However, data regarding the effects of performing the eccentric actions of an exercise at increased velocities are limited. This narrative review aimed to provide greater clarity for eccentric methods and classification with regard to temporal phases of exercises. Between March and April 2021, we used key terms to search the PubMed, SPORTDiscus, and Google Scholar databases within the years 1950-2021. Search terms included 'fast eccentric', 'fast velocity eccentric', 'dynamic eccentric', 'accentuated eccentric loading', and 'isokinetic eccentric', analysing both the acute and the chronic effects of accelerated eccentric training in human participants. Review of the 26 studies that met the inclusion criteria identified that completing eccentric tempos of < 2 s increased subsequent concentric one repetition maximum performance, velocity, and power compared with > 4 s tempos. Tempos of > 4 s duration increased time under tension (TUT), whereas reduced tempos allowed for greater volume to be completed. Greater TUT led to larger accumulation of blood lactate, growth hormone, and testosterone when volume was matched to that of the reduced tempos. Overall, evidence supports eccentric actions of < 2 s duration to improve subsequent concentric performance. There is no clear difference between using eccentric tempos of 2-6 s if the aim is to increase hypertrophic response and strength. Future research should analyse the performance of eccentric actions at greater velocities or reduced time durations to determine more factors such as strength response. Tempo studies should aim to complete the same TUT for protocols to determine measures for hypertrophic response.

A Differentiable Dynamic Model for Musculoskeletal Simulation and Exoskeleton Control

An exoskeleton, a wearable device, was designed based on the user's physical and cognitive interactions. The control of the exoskeleton uses biomedical signals reflecting the user intention as input, and its algorithm is calculated as an output to make the movement smooth. However, the process of transforming the input of biomedical signals, such as electromyography (EMG), into the output of adjusting the torque and angle of the exoskeleton is limited by a finite time lag and precision of trajectory prediction, which result in a mismatch between the subject and exoskeleton. Here, we propose an EMG-based single-joint exoskeleton system by merging a differentiable continuous system with a dynamic musculoskeletal model. The parameters of each muscle contraction were calculated and applied to the rigid exoskeleton system to predict the precise trajectory. The results revealed accurate torque and angle prediction for the knee exoskeleton and good performance of assistance during movement. Our method outperformed other models regarding the rate of convergence and execution time. In conclusion, a differentiable continuous system merged with a dynamic musculoskeletal model supported the effective and accurate performance of an exoskeleton controlled by EMG signals.

‘Falling heads’: investigating reflexive responses to head–neck perturbations

Background

Reflexive responses to head–neck perturbations affect the injury risk in many different situations ranging from sports-related impact to car accident scenarios. Although several experiments have been conducted to investigate these head–neck responses to various perturbations, it is still unclear why and how individuals react differently and what the implications of these different responses across subjects on the potential injuries might be. Therefore, we see a need for both experimental data and biophysically valid computational Human Body Models with bio-inspired muscle control strategies to understand individual reflex responses better.

Methods

To address this issue, we conducted perturbation experiments of the head–neck complex and used this data to examine control strategies in a simulation model. In the experiments, which we call ’falling heads’ experiments, volunteers were placed in a supine and a prone position on a table with an additional trapdoor supporting the head. This trapdoor was suddenly released, leading to a free-fall movement of the head until reflexive responses of muscles stopped the downwards movement.

Results

We analysed the kinematic, neuronal and dynamic responses for all individuals and show their differences for separate age and sex groups. We show that these results can be used to validate two simple reflex controllers which are able to predict human biophysical movement and modulate the response necessary to represent a large variability of participants.

Conclusions

We present characteristic parameters such as joint stiffness, peak accelerations and latency times. Based on this data, we show that there is a large difference in the individual reflexive responses between participants. Furthermore, we show that the perturbation direction (supine vs. prone) significantly influences the measured kinematic quantities. Finally, ’falling heads’ experiments data are provided open-source to be used as a benchmark test to compare different muscle control strategies and to validate existing active Human Body Models directly.

Deep reinforcement learning for modeling human locomotion control in neuromechanical simulation

Modeling human motor control and predicting how humans will move in novel environments is a grand scientific challenge. Researchers in the fields of biomechanics and motor control have proposed and evaluated motor control models via neuromechanical simulations, which produce physically correct motions of a musculoskeletal model. Typically, researchers have developed control models that encode physiologically plausible motor control hypotheses and compared the resulting simulation behaviors to measurable human motion data. While such plausible control models were able to simulate and explain many basic locomotion behaviors (e.g. walking, running, and climbing stairs), modeling higher layer controls (e.g. processing environment cues, planning long-term motion strategies, and coordinating basic motor skills to navigate in dynamic and complex environments) remains a challenge. Recent advances in deep reinforcement learning lay a foundation for modeling these complex control processes and controlling a diverse repertoire of human movement; however, reinforcement learning has been rarely applied in neuromechanical simulation to model human control. In this paper, we review the current state of neuromechanical simulations, along with the fundamentals of reinforcement learning, as it applies to human locomotion. We also present a scientific competition and accompanying software platform, which we have organized to accelerate the use of reinforcement learning in neuromechanical simulations. This “Learn to Move” competition was an official competition at the NeurIPS conference from 2017 to 2019 and attracted over 1300 teams from around the world. Top teams adapted state-of-the-art deep reinforcement learning techniques and produced motions, such as quick turning and walk-to-stand transitions, that have not been demonstrated before in neuromechanical simulations without utilizing reference motion data. We close with a discussion of future opportunities at the intersection of human movement simulation and reinforcement learning and our plans to extend the Learn to Move competition to further facilitate interdisciplinary collaboration in modeling human motor control for biomechanics and rehabilitation research

Intuitive assessment of modeled lumbar spinal motion by clustering and visualization of finite helical axes

A variety of medical imaging procedures, cadaver experiments, and computer models have been utilized to capture, depict, and understand the motion of the human lumbar spine. Particular interest lies in assessing the relative movement between two adjacent vertebrae, which can be represented by a temporal evolution of finite helical axes (FHA). Mathematically, this FHA evolution constitutes a seven-dimensional quantity: one dimension for the time, two for the (normalized) direction vector, another two for the (unique) position vector, as well as one for each the angle of rotation around and the amount of translation along the axis. Predominantly in the literature, however, movements are assumed to take place in certain physiological planes on which FHA are projected. The resulting three-dimensional quantity - the so-called centrode - is easily presentable but leaves out substantial pieces of available data. Here, we investigate and assess several possibilities to visualize subsets of FHA data of increasing dimensionality. Finally, we utilize an agglomerative hierarchical clustering algorithm and propose a novel visualization technique, namely the quiver principal axis plot (QPAP), to depict the entirety of information inherent to hundreds or thousands of FHA. The QPAP method is applied to flexion-extension, lateral bending, and axial rotation movements of a lumbar spine within both a reduced model as well as a complex upper body system.

Power Amplification Increases With Contraction Velocity During Stretch-Shortening Cycles of Skinned Muscle Fibers

Muscle force, work, and power output during concentric contractions (active muscle shortening) are increased immediately following an eccentric contraction (active muscle lengthening). This increase in performance is known as the stretch-shortening cycle (SSC)-effect. Recent findings demonstrate that the SSC-effect is present in the sarcomere itself. More recently, it has been suggested that cross-bridge (XB) kinetics and non-cross-bridge (non-XB) structures (e.g., titin and nebulin) contribute to the SSC-effect. As XBs and non-XB structures are characterized by a velocity dependence, we investigated the impact of stretch-shortening velocity on the SSC-effect. Accordingly, we performed in vitro isovelocity ramp experiments with varying ramp velocities (30, 60, and 85% of maximum contraction velocity for both stretch and shortening) and constant stretch-shortening magnitudes (17% of the optimum sarcomere length) using single skinned fibers of rat soleus muscles. The different contributions of XB and non-XB structures to force production were identified using the XB-inhibitor Blebbistatin. We show that (i) the SSC-effect is velocity-dependent-since the power output increases with increasing SSC-velocity. (ii) The energy recovery (ratio of elastic energy storage and release in the SSC) is higher in the Blebbistatin condition compared with the control condition. The stored and released energy in the Blebbistatin condition can be explained by the viscoelastic properties of the non-XB structure titin. Consequently, our experimental findings suggest that the energy stored in titin during the eccentric phase contributes to the SSC-effect in a velocity-dependent manner.

A geometry- and muscle-based control architecture for synthesising biological movement

A key problem for biological motor control is to establish a link between an idea of a movement and the generation of a set of muscle-stimulating signals that lead to the movement execution. The number of signals to generate is thereby larger than the body's mechanical degrees of freedom in which the idea of the movement may be easily expressed, as the movement is actually executed in this space. A mathematical formulation that provides a solving link is presented in this paper in the form of a layered, hierarchical control architecture. It is meant to synthesise a wide range of complex three-dimensional muscle-driven movements. The control architecture consists of a 'conceptional layer', where the movement is planned, a 'structural layer', where the muscles are stimulated, and between both an additional 'transformational layer', where the muscle-joint redundancy is resolved. We demonstrate the operativeness by simulating human stance and squatting in a three-dimensional digital human model (DHM). The DHM considers 20 angular DoFs and 36 Hill-type muscle-tendon units (MTUs) and is exposed to gravity, while its feet contact the ground via reversible stick-slip interactions. The control architecture continuously stimulates all MTUs ('structural layer') based on a high-level, torque-based task formulation within its 'conceptional layer'. Desired states of joint angles (postural plan) are fed to two mid-level joint controllers in the 'transformational layer'. The 'transformational layer' communicates with the biophysical structures in the 'structural layer' by providing direct MTU stimulation contributions and further input signals for low-level MTU controllers. Thereby, the redundancy of the MTU stimulations with respect to the joint angles is resolved, i.e. a link between plan and execution is established, by exploiting some properties of the biophysical structures modelled. The resulting joint torques generated by the MTUs via their moment arms are fed back to the conceptional layer, closing the high-level control loop. Within our mathematical formulations of the Jacobian matrix-based layer transformations, we identify the crucial information for the redundancy solution to be the muscle moment arms, the stiffness relations of muscle and tendon tissue within the muscle model, and the length-stimulation relation of the muscle activation dynamics. The present control architecture allows the straightforward feeding of conceptional movement task formulations to MTUs. With this approach, the problem of movement planning is eased, as solely the mechanical system has to be considered in the conceptional plan.

Biomechanics of the human thumb and the evolution of dexterity

Systematic tool production and use is one of humanity's defining characteristics, possibly originating as early as >3 million years ago.^1-3 Although heightened manual dexterity is considered to be intrinsically intertwined with tool use and manufacture, and critical for human evolution, its role in the emergence of early culture remains unclear. Most previous research on this question exclusively relied on direct morphological comparisons between early hominin and modern human skeletal elements, assuming that the degree of a species' dexterity depends on its similarity with the modern human form. Here, we develop a new approach to investigate the efficiency of thumb opposition, a fundamental component of manual dexterity, in several species of fossil hominins. Our work for the first time takes into account soft tissue as well as bone anatomy, integrating virtual modeling of musculus opponens pollicis and its interaction with three-dimensional bone shape form. Results indicate that a fundamental aspect of efficient thumb opposition appeared approximately 2 million years ago, possibly associated with our own genus Homo, and did not characterize Australopithecus, the earliest proposed stone tool maker. This was true also of the late Australopithecus species, Australopithecus sediba, previously found to exhibit human-like thumb proportions. In contrast, later Homo species, including the small-brained Homo naledi, show high levels of thumb opposition dexterity, highlighting the increasing importance of cultural processes and manual dexterity in later human evolution.

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.

Development of a musculoskeletal model of the wrist to predict frictional work dissipated due to tendon gliding resistance in the carpal tunnel

Carpal tunnel syndrome is an entrapment neuropathy that has been associated with the aggravation of tendon gliding resistance due to forceful, high velocity, awkwardly angled, and repetitive wrist motions. Cadaveric and epidemiological studies have shown that combinations of these risk factors have a more than additive effect. The aim of the current study was to develop a musculoskeletal model of the wrist that could evaluate these risk factors by simulating frictional work dissipated due to the gliding resistance of the third flexor digitorum superficialis tendon. Three flexion angle zones, three extension angle zones, five levels of task repetitiveness, and five levels of task effort were derived from ergonomic standards. Of the simulations performed by systematically combining these parameters, the extreme wrist flexion zone, at peak task repetitiveness and effort, dissipated the most frictional work. This zone dissipated approximately double the amount of frictional work compared to its equivalent zone in extension. For all motions, a multiplicative effect of the combination of task repetitiveness and effort on frictional work was identified by the musculoskeletal model, corroborating previous epidemiological and experimental studies. Overall, these results suggest that the ergonomic standards for wrist flexion-extension may need to be adjusted to reflect equivalent biomechanical impact and that workplace tasks should be designed to minimise exposure to combinations of highly repetitive and highly forceful work, especially when the wrist is highly flexed.

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.

Reverse-engineering and modeling the 3D passive and active responses of skeletal muscle using a data-driven, non-parametric, spline-based procedure

In this work we present a non-parametric data-driven approach to reverse-engineer and model the 3D passive and active responses of skeletal muscle, applied to tibialis anterior muscle of Wistar rats. We assume a Hill-type additive relation for the stored energy into passive and active contributions. The terms of the stored energy have no upfront assumed shape, nor material parameters. These terms are determined directly from experimental data in spline form solving numerically the functional equations of the tests from which experimental data is available. To characterize typical longitudinal-to-transverse behavior in rodent's muscle, experiments from Morrow et al. (J. Mech. Beh. Biomed. Mater. 2010; 3: 124-129) are employed. Then, the passive and active behaviors of Wistar rats are determined from the experiments of Calvo et al. (J. Bomech. 2010; 43:318-325) and Ramirez et al. (J. Theor. Biol. 2010; 267:546-553). The twitch shape is not assumed, but reverse-engineered from experimental data. The influence of the strain and the stimulus voltage and frequency in the active response, are also modeled. A convenient stimulus power-related variable is proposed to comprise both voltage and frequency dependencies in the active response. Then, the behavior of the resulting muscle model depends only on the muscle strain maintained during isometric tests in the muscle and the stimulus power variable, along the time from initiation of the tetanus state.

Muscle-driven and torque-driven centrodes during modeled flexion of individual lumbar spines are disparate

Lumbar spine biomechanics during the forward-bending of the upper body (flexion) are well investigated by both in vivo and in vitro experiments. In both cases, the experimentally observed relative motion of vertebral bodies can be used to calculate the instantaneous center of rotation (ICR). The timely evolution of the ICR, the centrode, is widely utilized for validating computer models and is thought to serve as a criterion for distinguishing healthy and degenerative motion patterns. While in vivo motion can be induced by physiological active structures (muscles), in vitro spinal segments have to be driven by external torque-applying equipment such as spine testers. It is implicitly assumed that muscle-driven and torque-driven centrodes are similar. Here, however, we show that centrodes qualitatively depend on the impetus. Distinction is achieved by introducing confidence regions (ellipses) that comprise centrodes of seven individual multi-body simulation models, performing flexion with and without preload. Muscle-driven centrodes were generally directed superior–anterior and tail-shaped, while torque-driven centrodes were located in a comparably narrow region close to the center of mass of the caudal vertebrae. We thus argue that centrodes resulting from different experimental conditions ought to be compared with caution. Finally, the applicability of our method regarding the analysis of clinical syndromes and the assessment of surgical methods is discussed.

Parameter estimation and experimental design for Hill-type muscles: Impulses from optimization-based modeling

The benefits of optimization-based modeling for parameter estimation of Hill-type muscle models are demonstrated. Therefore, we examined the model and data of Günther et al. (2007), who analyzed isometric, concentric, and quick-release contractions of a piglet calf muscle. We found that the isometric experiments are suitable for derivative-based parameter estimation while the others did not provide any additional value. During the estimation process, certain parameters had to be fixed. We give possible reasons and provide impulses for modelers. Subsequently, unnecessarily complex or deprecated model parts were exchanged and the new model was fitted to the data. In order to be able to provide a reliable estimation of the whole parameter set, we propose two isometric and two quick-release experiments, which are real-life feasible and together allow an identification of all parameters based on a local sensitivity analysis. These experiments can be used as qualitative guidelines for practitioners to reduce the experimental effort when estimating parameters for macroscopic muscle models.

Energy Expenditure of Dynamic Submaximal Human Plantarflexion Movements: Model Prediction and Validation by in-vivo Magnetic Resonance Spectroscopy

To understand the organization and efficiency of biological movement, it is important to evaluate the energy requirements on the level of individual muscles. To this end, predicting energy expenditure with musculoskeletal models in forward-dynamic computer simulations is currently the most promising approach. However, it is challenging to validate muscle models in-vivo in humans, because access to the energy expenditure of single muscles is difficult. Previous approaches focused on whole body energy expenditure, e.g., oxygen consumption (VO2), or on thermal measurements of individual muscles by tracking blood flow and heat release (through measurements of the skin temperature). This study proposes to validate models of muscular energy expenditure by using functional phosphorus magnetic resonance spectroscopy (³¹P-MRS). ³¹P-MRS allows to measure phosphocreatine (PCr) concentration which changes in relation to energy expenditure. In the first 25 s of an exercise, PCr breakdown rate reflects ATP hydrolysis, and is therefore a direct measure of muscular enthalpy rate. This method was applied to the gastrocnemius medialis muscle of one healthy subject during repetitive dynamic plantarflexion movements at submaximal contraction, i.e., 20% of the maximum plantarflexion force using a MR compatible ergometer. Furthermore, muscle activity was measured by surface electromyography (EMG). A model (provided as open source) that combines previous models for muscle contraction dynamics and energy expenditure was used to reproduce the experiment in simulation. All parameters (e.g., muscle length and volume, pennation angle) in the model were determined from magnetic resonance imaging or literature (e.g., fiber composition), leaving no free parameters to fit the experimental data. Model prediction and experimental data on the energy supply rates are in good agreement with the validation phase (<25 s) of the dynamic movements. After 25 s, the experimental data differs from the model prediction as the change in PCr does not reflect all metabolic contributions to the energy expenditure anymore and therefore underestimates the energy consumption. This shows that this new approach allows to validate models of muscular energy expenditure in dynamic movements in vivo.

Comparative Study of a Biomechanical Model-based and Black-box Approach for Subject-Specific Movement Prediction. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2020;2020:4775-4778. [PMID: 33019058 DOI: 10.1109/embc44109.2020.9176600] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

The performance and safety of human robot interaction (HRI) can be improved by using subject-specific movement prediction. Typical models include biomechanical (parametric) or black-box (non-parametric) models. The current work aims to investigate the benefits and drawbacks of these approaches by comparing elbow-joint torque predictions based on electromyography signals of the elbow flexors and extensors. To this end, a parameterized biomechanical model is compared to a non-parametric (Gaussian-process) approach. Both models showed adequate results in predicting the elbow-joint torques. While the non-parametric model requires minimal modeling effort, the parameterized biomechanical model can lead to deeper insight of the underlying subject specific musculoskeletal system.

Optimality Principles in Human Point-to-Manifold Reaching Accounting for Muscle Dynamics

Human arm movements are highly stereotypical under a large variety of experimental conditions. This is striking due to the high redundancy of the human musculoskeletal system, which in principle allows many possible trajectories toward a goal. Many researchers hypothesize that through evolution, learning, and adaption, the human system has developed optimal control strategies to select between these possibilities. Various optimality principles were proposed in the literature that reproduce human-like trajectories in certain conditions. However, these studies often focus on a single cost function and use simple torque-driven models of motion generation, which are not consistent with human muscle-actuated motion. The underlying structure of our human system, with the use of muscle dynamics in interaction with the control principles, might have a significant influence on what optimality principles best model human motion. To investigate this hypothesis, we consider a point-to-manifold reaching task that leaves the target underdetermined. Given hypothesized motion objectives, the control input is generated using Bayesian optimization, which is a machine learning based method that trades-off exploitation and exploration. Using numerical simulations with Hill-type muscles, we show that a combination of optimality principles best predicts human point-to-manifold reaching when accounting for the muscle dynamics.

Exhaustion of Skeletal Muscle Fibers Within Seconds: Incorporating Phosphate Kinetics Into a Hill-Type Model

Initiated by neural impulses and subsequent calcium release, skeletal muscle fibers contract (actively generate force) as a result of repetitive power strokes of acto-myosin cross-bridges. The energy required for performing these cross-bridge cycles is provided by the hydrolysis of adenosine triphosphate (ATP). The reaction products, adenosine diphosphate (ADP) and inorganic phosphate (P i ), are then used-among other reactants, such as creatine phosphate-to refuel the ATP energy storage. However, similar to yeasts that perish at the hands of their own waste, the hydrolysis reaction products diminish the chemical potential of ATP and thus inhibit the muscle's force generation as their concentration rises. We suggest to use the term "exhaustion" for force reduction (fatigue) that is caused by combined P i and ADP accumulation along with a possible reduction in ATP concentration. On the basis of bio-chemical kinetics, we present a model of muscle fiber exhaustion based on hydrolytic ATP-ADP-P i dynamics, which are assumed to be length- and calcium activity-dependent. Written in terms of differential-algebraic equations, the new sub-model allows to enhance existing Hill-type excitation-contraction models in a straightforward way. Measured time courses of force decay during isometric contractions of rabbit M. gastrocnemius and M. plantaris were employed for model verification, with the finding that our suggested model enhancement proved eminently promising. We discuss implications of our model approach for enhancing muscle models in general, as well as a few aspects regarding the significance of phosphate kinetics as one contributor to muscle fatigue.

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

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