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

Predicting Musculoskeletal Loading at Common Running Injury Locations Using Machine Learning and Instrumented Insoles

INTRODUCTION

Wearables have the potential to provide accurate estimates of tissue loads at common running injury locations. Here we investigate the accuracy by which commercially available instrumented insoles (ARION; ATO-GEAR, Eindhoven, The Netherlands) can predict musculoskeletal loading at common running injury locations.

METHODS

Nineteen runners (10 males) ran at five different speeds, four slopes, with different step frequencies, and forward trunk lean on an instrumented treadmill while wearing instrumented insoles. The insole data were used as input to an artificial neural network that was trained to predict the Achilles tendon strain, and tibia and patellofemoral stress impulses and weighted impulses (damage proxy) as determined with musculoskeletal modeling. Accuracy was investigated using leave-one-out cross-validation and correlations. The effect of different input metrics was also assessed.

RESULTS

The neural network predicted tissue loading with overall relative percentage errors of 1.95 ± 8.40%, -7.37 ± 6.41%, and -12.8 ± 9.44% for the patellofemoral joint, tibia, and Achilles tendon impulse, respectively. The accuracy significantly changed with altered running speed, slope, or step frequency. Mean (95% confidence interval) within-individual correlations between modeled and predicted impulses across conditions were generally nearly perfect, being 0.92 (0.89 to 0.94), 0.95 (0.93 to 0.96), and 0.95 (0.94 to 0.96) for the patellofemoral, tibial, and Achilles tendon stress/strain impulses, respectively.

CONCLUSIONS

This study shows that commercially available instrumented insoles can predict loading at common running injury locations with variable absolute but (very) high relative accuracy. The absolute error was lower than the methods that measure only the step count or assume a constant load per speed or slope. This developed model may allow for quantification of in-field tissue loading and real-time tissue loading-based feedback to reduce injury risk.

A scoping review and evaluation of open-source transtibial amputation musculoskeletal models for female populations

Musculoskeletal modeling is often used to study people with transtibial amputations. Females in this population are of particular interest as they are underrepresented in research, experience unique challenges, and demonstrate gait biomechanics distinct from males. Because generic models often neglect innate variations between populations, it is important to determine whether data used to develop a model are representative of the population studied. The objective of this study was to review and analyze existing transtibial amputation musculoskeletal models, establish a database from the information compiled, and use the database to select the model most relevant for studying female populations. A scoping search was performed and a database was created based on data detailing the eligible models. Models were evaluated through a weighted decision process based on criteria of their representation of females with transtibial amputations, prosthetic functionality, development transparency, overall functionality, and experimental validation methods. The scoping review identified 3 studies, Willson et al., LaPrè et al., and Miller and Esposito. A database detailing these models was established. The Willson model scored highest on all criteria except overall functionality, where the LaPrè model outscored it. Based on the established weightings, the Willson model was classed most appropriate for the stated goals. The created database can be used by other researchers to guide their own modeling studies, irrespective of the population of focus. Of the 3, the Willson model was found most relevant for studying females with transtibial amputations. This model will be used in future work investigating and addressing challenges of females with transtibial amputations.

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.

A novel biomechanical model of the mouse forelimb predicts muscle activity in optimal control simulations of reaching movements

Mice are key model organisms in genetics, neuroscience and motor systems physiology. Fine motor control tasks performed by mice have become widely used in assaying neural and biophysical motor system mechanisms, including lever or joystick manipulation, and reach-to-grasp tasks (Becker et al., 2019; Bollu et al., 2019; Conner at al., 2021). Although fine motor tasks provide useful insights into behaviors which require complex multi-joint motor control, there is no previously developed physiological biomechanical model of the adult mouse forelimb available for estimating kinematics (including joint angles, joint velocities, fiber lengths and fiber velocities) nor muscle activity or kinetics (including forces and moments) during these behaviors. Here we have developed a musculoskeletal model based on high-resolution imaging and reconstruction of the mouse forelimb that includes muscles spanning the neck, trunk, shoulder, and limbs using anatomical data. Physics-based optimal control simulations of the forelimb model were used to estimate in vivo muscle activity present when constrained to the tracked kinematics during mouse reaching movements. The activity of a subset of muscles was recorded via electromyography and used as the ground truth to assess the accuracy of the muscle patterning in simulation. We found that the synthesized muscle patterning in the forelimb model had a strong resemblance to empirical muscle patterning, suggesting that our model has utility in providing a realistic set of estimated muscle excitations over time when provided with a kinematic template. The strength of the resemblance between empirical muscle activity and optimal control predictions increases as mice performance improves throughout learning of the reaching task. Our computational tools are available as open-source in the OpenSim physics and modeling platform (Seth et al., 2018). Our model can enhance research into limb control across broad research topics and can inform analyses of motor learning, muscle synergies, neural patterning, and behavioral research that would otherwise be inaccessible.

Feasibility of predicting changes in gait biomechanics following muscle strength perturbations using optimal control in patients with transfemoral amputation

Bone-anchored limbs (BALs) are socket prosthesis alternatives, directly fixing to residual bone via osseointegrated implant. There is a need to quantify multi-level effects of rehabilitation for transfemoral BAL users (i.e. changes in joint loading and movement patterns). Our primary objective was determining feasibility of using optimal control to predict gait biomechanics compared to ground-truth experimental data from transfemoral BAL users. A secondary objective was examining biomechanical effects from estimated changes in hip abductor muscle strength. We developed and validated a workflow for predicting gait biomechanics in four transfemoral BAL users and investigated the biomechanical effects of altered hip abductor strengths.

Springs vs. motors: Ideal assistance in the lower limbs during walking at different speeds

Recent years have witnessed breakthroughs in assistive exoskeletons; both passive and active devices have reduced metabolic costs near preferred walking speed by assisting muscle actions. Metabolic reductions at multiple speeds should thus also be attainable. Musculoskeletal simulation can potentially predict the interaction between assistive moments, muscle-tendon mechanics, and walking energetics. In this study, we simulated devices' optimal assistive moments based on minimal muscle activations during walking with prescribed kinematics and dynamics. We used a generic musculoskeletal model with tuned muscle-tendon parameters and computed metabolic rates from muscle actions. We then simulated walking across multiple speeds and with two ideal actuation modes-motor-based and spring-based-to assist ankle plantarflexion, knee extension, hip flexion, and hip abduction and compared computed metabolic rates. We found that both actuation modes considerably reduced physiological joint moments but did not always reduce metabolic rates. Compared to unassisted conditions, motor-based ankle plantarflexion and hip flexion assistance reduced metabolic rates, and this effect was more pronounced as walking speed increased. Spring-based hip flexion and abduction assistance increased metabolic rates at some walking speeds despite a moderate decrease in some muscle activations. Both modes of knee extension assistance reduced metabolic rates to a small extent, even though the actuation contributed with practically the entire net knee extension moment during stance. Motor-based hip abduction assistance reduced metabolic rates more than spring-based assistance, though this reduction was relatively small. Our study also suggests that an assistive strategy based on minimal muscle activations might result in a suboptimal reduction of metabolic rates. Future work should experimentally validate the effects of assistive moments and refine modeling assumptions accordingly. Our computational workflow is freely available online.

Insights into muscle metabolic energetics: Modelling muscle-tendon mechanics and metabolic rates during walking across speeds

The metabolic energy rate of individual muscles is impossible to measure without invasive procedures. Prior studies have produced models to predict metabolic rates based on experimental observations of isolated muscle contraction from various species. Such models can provide reliable predictions of metabolic rates in humans if muscle properties and control are accurately modeled. This study aimed to examine how muscle-tendon model individualization and metabolic energy models influenced estimation of muscle-tendon states and time-series metabolic rates, to evaluate the agreement with empirical data, and to provide predictions of the metabolic rate of muscle groups and gait phases across walking speeds. Three-dimensional musculoskeletal simulations with prescribed kinematics and dynamics were performed. An optimal control formulation was used to compute muscle-tendon states with four levels of individualization, ranging from a scaled generic model and muscle controls based on minimal activations, inclusion of calibrated muscle passive forces, personalization of Achilles and quadriceps tendon stiffnesses, to finally informing muscle controls with electromyography. We computed metabolic rates based on existing models. Simulations with calibrated passive forces and personalized tendon stiffness most accurately estimate muscle excitations and fiber lengths. Interestingly, the inclusion of electromyography did not improve our estimates. The whole-body average metabolic cost was better estimated with a subset of metabolic energy models. We estimated metabolic rate peaks near early stance, pre-swing, and initial swing at all walking speeds. Plantarflexors accounted for the highest cost among muscle groups at the preferred speed and were similar to the cost of hip adductors and abductors combined. Also, the swing phase accounted for slightly more than one-quarter of the total cost in a gait cycle, and its relative cost decreased with walking speed. Our prediction might inform the design of assistive devices and rehabilitation treatment. The code and experimental data are available online.

General Muscle Torque Generator Model for a Two Degree-of-Freedom Shoulder Joint

Muscle torque generators (MTGs) have been developed as an alternative to muscle-force models, reducing the muscle-force model complexity to a single torque at the joint. Current MTGs can only be applied to single Degree-of-freedom (DoF) joints, leading to complications in modeling joints with multiple-DoFs such as the shoulder. This study aimed to develop an MTG model that accounts for the coupling between 2-DoF at the shoulder joint: shoulder plane of elevation (horizontal abduction/adduction) and shoulder elevation (flexion/extension). Three different 2-DoF MTG equations were developed to model the coupling between these two movements. Net joint torques at the shoulder were determined for 20 participants (10 females and 10 males) in isometric, isokinetic, and passive tests. Curve and surface polynomial fitting were used to find the best general fit for the experimental data in terms of the different degrees of coupling. The models were validated against experimental isokinetic torque data. It was determined that implicit coupling that used interpolation between single-DoF MTGs resulted in the lowest root-mean-square percent error of 8.5%. The work demonstrated that general MTG models can predict torque results that are dependent on multiple-DoFs of the shoulder.

Achilles tendon compliance influences tendon loading more than Achilles tendon twist in Achilles tendinopathy: a musculoskeletal modeling approach

The Achilles tendon exhibits anatomical variations in subtendon twist among individuals, and its compliance can change due to conditions like Achilles tendinopathy. However, current musculoskeletal models overlook these material and morphological variations. This study aimed to investigate the impact of altering Achilles subtendon insertion points and compliance on the triceps surae muscle forces, and therefore tendon loading, during dynamic exercises in one Achilles tendinopathy patient. First, subtendon insertion points were altered in the musculoskeletal model based on a subject-specific 3D freehand ultrasound model and for three types of subtendon twists: low, medium, and high. Second, tendon compliance was modeled based on experimental values, creating three musculoskeletal models: compliant, mean, and stiff. Results indicated that tendon compliance had a larger effect than tendon twist on triceps surae muscle forces. Altering subtendon insertion points to the three types of twist showed a maximal change of 2.3% in muscle force contribution compared to the no-twist model. During the eccentric rehabilitation exercise-a common exercise choice during rehabilitation-the compliant tendon model showed substantial differences compared to the generic (control) musculoskeletal model, resulting in decreased gastrocnemius medialis (-3.5%) and gastrocnemius lateralis (-3.2%) contributions and increased soleus contribution (+ 6.6%). Our study results highlight the necessity of incorporating tendon compliance in musculoskeletal models to accurately predict triceps surae muscle forces, especially in individuals with increased tendon compliance, such as patients with Achilles tendinopathy. Such findings contribute to more accurate predictions of muscle forces and hence, personalized rehabilitation strategies.

Experiment-guided tuning of muscle-tendon parameters to estimate muscle fiber lengths and passive forces

The workflow to simulate motion with recorded data usually starts with selecting a generic musculoskeletal model and scaling it to represent subject-specific characteristics. Simulating muscle dynamics with muscle-tendon parameters computed from existing scaling methods in literature, however, yields some inconsistencies compared to measurable outcomes. For instance, simulating fiber lengths and muscle excitations during walking with linearly scaled parameters does not resemble established patterns in the literature. This study presents a tool that leverages reported in vivo experimental observations to tune muscle-tendon parameters and evaluates their influence in estimating muscle excitations and metabolic costs during walking. From a scaled generic musculoskeletal model, we tuned optimal fiber length, tendon slack length, and tendon stiffness to match reported fiber lengths from ultrasound imaging and muscle passive force-length relationships to match reported in vivo joint moment-angle relationships. With tuned parameters, muscle contracted more isometrically, and soleus's operating range was better estimated than with linearly scaled parameters. Also, with tuned parameters, on/off timing of nearly all muscles' excitations in the model agreed with reported electromyographic signals, and metabolic rate trajectories varied significantly throughout the gait cycle compared to linearly scaled parameters. Our tool, freely available online, can customize muscle-tendon parameters easily and be adapted to incorporate more experimental data.

EMG-Constrained and Ultrasound-Informed Muscle-Tendon Parameter Estimation in Post-Stroke Hemiparesis

Secondary morphological and mechanical property changes in the muscle-tendon unit at the ankle joint are often observed in post-stroke individuals. These changes may alter the force generation capacity and affect daily activities such as locomotion. This work aimed to estimate subject-specific muscle-tendon parameters in individuals after stroke by solving the muscle redundancy problem using direct collocation optimal control methods based on experimental electromyography (EMG) signals and measured muscle fiber length. Subject-specific muscle-tendon parameters of the gastrocnemius, soleus, and tibialis anterior were estimated in seven post-stroke individuals and seven healthy controls. We found that the maximum isometric force, tendon stiffness and optimal fiber length in the post-stroke group were considerably lower than in the control group. We also computed the root mean square error between estimated and experimental values of muscle excitation and fiber length. The musculoskeletal model with estimated subject-specific muscle tendon parameters (from the muscle redundancy solver), yielded better muscle excitation and fiber length estimations than did scaled generic parameters. Our findings also showed that the muscle redundancy solver can estimate muscle-tendon parameters that produce force behavior in better accordance with the experimentally-measured value. These muscle-tendon parameters in the post-stroke individuals were physiologically meaningful and may shed light on treatment and/or rehabilitation planning.

A dynamic foot model for predictive simulations of human gait reveals causal relations between foot structure and whole-body mechanics

The unique structure of the human foot is seen as a crucial adaptation for bipedalism. The foot's arched shape enables stiffening the foot to withstand high loads when pushing off, without compromising foot flexibility. Experimental studies demonstrated that manipulating foot stiffness has considerable effects on gait. In clinical practice, altered foot structure is associated with pathological gait. Yet, experimentally manipulating individual foot properties (e.g. arch height or tendon and ligament stiffness) is hard and therefore our understanding of how foot structure influences gait mechanics is still limited. Predictive simulations are a powerful tool to explore causal relationships between musculoskeletal properties and whole-body gait. However, musculoskeletal models used in three-dimensional predictive simulations assume a rigid foot arch, limiting their use for studying how foot structure influences three-dimensional gait mechanics. Here, we developed a four-segment foot model with a longitudinal arch for use in predictive simulations. We identified three properties of the ankle-foot complex that are important to capture ankle and knee kinematics, soleus activation, and ankle power of healthy adults: (1) compliant Achilles tendon, (2) stiff heel pad, (3) the ability to stiffen the foot. The latter requires sufficient arch height and contributions of plantar fascia, and intrinsic and extrinsic foot muscles. A reduced ability to stiffen the foot results in walking patterns with reduced push-off power. Simulations based on our model also captured the effects of walking with anaesthetised intrinsic foot muscles or an insole limiting arch compression. The ability to reproduce these different experiments indicates that our foot model captures the main mechanical properties of the foot. The presented four-segment foot model is a potentially powerful tool to study the relationship between foot properties and gait mechanics and energetics in health and disease.

Validity of muscle activation estimated with predicted ground reaction force in inverse dynamics based musculoskeletal simulation during gait

The inverse dynamics based musculoskeletal simulation needs ground reaction forces (GRF) as an external force input. GRF can be predicted from kinematic data. However, the validity of estimated muscle activation using the predicted GRF has remained unclear. Therefore, the purpose of this study was to determine the validity of estimated muscle activation with predicted GRF in the inverse dynamics based musculoskeletal simulation. To perform musculoskeletal simulations, an open-source motion capture dataset that contains gait data from 50 healthy subjects was used. CusToM was used for the musculoskeletal simulations. Two sets of inverse dynamics and static optimization were performed, one used predicted GRF (PRED) and another used experimentally measured GRF (EXP). Pearson's correlation was calculated to evaluate the similarity between EMG and estimated muscle activations for both PRED and EXP. To compare PRED and EXP, paired t-tests were used to compare the trial-wise muscle activation similarity and residuals. Relationships between joint moments and residuals were also tested. The overall muscle activation similarity was comparable in PRED (R = 0.477) and EXP (R = 0.475). The residuals were 2-4 times higher in EXP compared to PRED (P < 0.001). The hip flexion-extension moment was correlated to sagittal plane residual moment (R = 0.467). The muscle activations estimated using predicted GRF were comparable to that with measured GRF in the inverse dynamics based musculoskeletal simulation. Prediction of GRF helps to perform musculoskeletal simulations where the force plates are not available.

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.

Identification of Neural and Non-Neural Origins of Joint Hyper-Resistance Based on a Novel Neuromechanical Model

Joint hyper-resistance is a common symptom in neurological disorders. It has both neural and non-neural origins, but it has been challenging to distinguish different origins based on clinical tests alone. Combining instrumented tests with parameter identification based on a neuromechanical model may allow us to dissociate the different origins of joint hyper-resistance in individual patients. However, this requires that the model captures the underlying mechanisms. Here, we propose a neuromechanical model that, in contrast to previously proposed models, accounts for muscle short-range stiffness (SRS) and its interaction with muscle tone and reflex activity. We collected knee angle trajectories during the pendulum test in 15 children with cerebral palsy (CP) and 5 typically developing children. We did the test in two conditions - hold and pre-movement - that have been shown to alter knee movement. We modeled the lower leg as an inverted pendulum actuated by two antagonistic Hill-type muscles extended with SRS. Reflex activity was modeled as delayed, linear feedback from muscle force. We estimated neural and non-neural parameters by optimizing the fit between simulated and measured knee angle trajectories during the hold condition. The model could fit a wide range of knee angle trajectories in the hold condition. The model with personalized parameters predicted the effect of pre-movement demonstrating that the model captured the underlying mechanism and subject-specific deficits. Our model may help with the identification of neural and non-neural origins of joint hyper-resistance and thereby opens perspectives for improved diagnosis and treatment selection in children with spastic CP, but such applications require further studies to establish the method's reliability.

Increasing midtarsal joint stiffness reduces triceps surae metabolic costs in walking simulations but has little effect on total stance limb metabolic cost

The human foot's arch is thought to be beneficial for efficient gait. This study addresses the extent to which arch stiffness changes alter the metabolic energy requirements of human gait. Computational musculoskeletal simulations of steady state walking using direct collocation were performed. Across a range of foot arch stiffnesses, the metabolic cost of transport decreased by less than 1% with increasing foot arch stiffness. Increasing arch stiffness increased the metabolic efficiency of the triceps surae during push-off, but these changes were almost entirely offset by other muscle groups consuming more energy with increasing foot arch stiffness.

Comparison of Synergy Extrapolation and Static Optimization for Estimating Multiple Unmeasured Muscle Activations during Walking

Background

Calibrated electromyography (EMG)-driven musculoskeletal models can provide great insight into internal quantities (e.g., muscle forces) that are difficult or impossible to measure experimentally. However, the need for EMG data from all involved muscles presents a significant barrier to the widespread application of EMG-driven modeling methods. Synergy extrapolation (SynX) is a computational method that can estimate a single missing EMG signal with reasonable accuracy during the EMG-driven model calibration process, yet its performance in estimating a larger number of missing EMG signals remains unclear.

Methods

This study assessed the accuracy with which SynX can use eight measured EMG signals to estimate muscle activations and forces associated with eight missing EMG signals in the same leg during walking while simultaneously performing EMG-driven model calibration. Experimental gait data collected from two individuals post-stroke, including 16 channels of EMG data per leg, were used to calibrate an EMG-driven musculoskeletal model, providing "gold standard" muscle activations and forces for evaluation purposes. SynX was then used to predict the muscle activations and forces associated with the eight missing EMG signals while simultaneously calibrating EMG-driven model parameter values. Due to its widespread use, static optimization (SO) was also utilized to estimate the same muscle activations and forces. Estimation accuracy for SynX and SO was evaluated using root mean square errors (RMSE) to quantify amplitude errors and correlation coefficient r values to quantify shape similarity, each calculated with respect to "gold standard" muscle activations and forces.

Results

On average, SynX produced significantly more accurate amplitude and shape estimates for unmeasured muscle activations (RMSE 0.08 vs. 0.15 , r value 0.55 vs. 0.12) and forces (RMSE 101.3 N vs. 174.4   N , r value 0.53 vs. 0.07) compared to SO. SynX yielded calibrated Hill-type muscle-tendon model parameter values for all muscles and activation dynamics model parameter values for measured muscles that were similar to "gold standard" calibrated model parameter values.

Conclusions

These findings suggest that SynX could make it possible to calibrate EMG-driven musculoskeletal models for all important lower-extremity muscles with as few as eight carefully chosen EMG signals and eventually contribute to the design of personalized rehabilitation and surgical interventions for mobility impairments.

FARMS: Framework for Animal and Robot Modeling and Simulation

The study of animal locomotion and neuromechanical control offers valuable insights for advancing research in neuroscience, biomechanics, and robotics. We have developed FARMS (Framework for Animal and Robot Modeling and Simulation), an open-source, interdisciplinary framework, designed to facilitate access to neuromechanical simulations for modeling, simulation, and analysis of animal locomotion and bio-inspired robotic systems. By providing an accessible and user-friendly platform, FARMS aims to lower the barriers for researchers to explore the complex interactions between the nervous system, musculoskeletal structures, and their environment. Integrating the MuJoCo physics engine in a modular manner, FARMS enables realistic simulations and fosters collaboration among neuroscientists, biologists, and roboticists. FARMS has already been extensively used to study locomotion in animals such as mice, drosophila, fish, salamanders, and centipedes, serving as a platform to investigate the role of central pattern generators and sensory feedback. This article provides an overview of the FARMS framework, discusses its interdisciplinary approach, showcases its versatility through specific case studies, and highlights its effectiveness in advancing our understanding of locomotion. In particular, we show how we used FARMS to study amphibious locomotion by presenting experimental demonstrations across morphologies and environments based on neural controllers with central pattern generators and sensory feedback circuits models. Overall, the goal of FARMS is to contribute to a deeper understanding of animal locomotion, the development of innovative bio-inspired robotic systems, and promote accessibility in neuromechanical research.

A three-dimensional musculoskeletal model of the pelvis and lower limb of Australopithecus afarensis

OBJECTIVES

Musculoskeletal modeling is a powerful approach for studying the biomechanics and energetics of locomotion. Australopithecus (A.) afarensis is among the best represented fossil hominins and provides critical information about the evolution of musculoskeletal design and locomotion in the hominin lineage. Here, we develop and evaluate a three-dimensional (3-D) musculoskeletal model of the pelvis and lower limb of A. afarensis for predicting muscle-tendon moment arms and moment-generating capacities across lower limb joint positions encompassing a range of locomotor behaviors.

MATERIALS AND METHODS

A 3-D musculoskeletal model of an adult A. afarensis pelvis and lower limb was developed based primarily on the A.L. 288-1 partial skeleton. The model includes geometric representations of bones, joints and 35 muscle-tendon units represented using 43 Hill-type muscle models. Two muscle parameter datasets were created from human and chimpanzee sources. 3-D muscle-tendon moment arms and isometric joint moments were predicted over a wide range of joint positions.

RESULTS

Predicted muscle-tendon moment arms generally agreed with skeletal metrics, and corresponded with human and chimpanzee models. Human and chimpanzee-based muscle parameterizations were similar, with some differences in maximum isometric force-producing capabilities. The model is amenable to size scaling from A.L. 288-1 to the larger KSD-VP-1/1, which subsumes a wide range of size variation in A. afarensis.

DISCUSSION

This model represents an important tool for studying the integrated function of the neuromusculoskeletal systems in A. afarensis. It is similar to current human and chimpanzee models in musculoskeletal detail, and will permit direct, comparative 3-D simulation studies.

The Simultaneous Model-Based Estimation of Joint, Muscle, and Tendon Stiffness is Highly Sensitive to the Tendon Force-Strain Relationship

OBJECTIVE

Accurate estimation of stiffness across anatomical levels (i.e., joint, muscle, and tendon) in vivo has long been a challenge in biomechanics. Recent advances in electromyography (EMG)-driven musculoskeletal modeling have allowed the non-invasive estimation of stiffness during dynamic joint rotations. Nevertheless, validation has been limited to the joint level due to a lack of simultaneous in vivo experimental measurements of muscle and tendon stiffness.

METHODS

With a focus on the triceps surae, we employed a novel perturbation-based experimental technique informed by dynamometry and ultrasonography to derive reference stiffness at the joint, muscle, and tendon levels simultaneously. Here, we propose a new EMG-driven model-based approach that does not require external joint perturbation, nor ultrasonography, to estimate multi-level stiffness. We present a novel set of closed-form equations that enables the person-specific tuning of musculoskeletal parameters dictating biological stiffness, including passive force-length relationships in modeled muscles and tendons.

RESULTS

Calibrated EMG-driven musculoskeletal models estimated the reference data with average normalized root-mean-square error ≈ 20%. Moreover, only when calibrated tendons were approximately four times more compliant than typically modeled, our approach could estimate multi-level reference stiffness.

CONCLUSION

EMG-driven musculoskeletal models can be calibrated on a larger set of reference data to provide more realistic values for the biomechanical variables across multiple anatomical levels. Moreover, the tendon models that are typically used in musculoskeletal modeling are too stiff.

SIGNIFICANCE

Calibrated musculoskeletal models informed by experimental measurements give access to an augmented range of biomechanical variables that might not be easily measured with sensors alone.

Scapular morphology variation affects reverse total shoulder arthroplasty biomechanics. A predictive simulation study using statistical and musculoskeletal shoulder models

Reverse total shoulder arthroplasty (RTSA) accounts for over half of shoulder replacement surgeries. At present, the optimal position of RTSA components is unknown. Previous biomechanical studies have investigated the effect of construct placement to quantify mobility, stability and functionality postoperatively. While studies have provided valuable information on construct design and surgical placement, they have not systematically evaluated the importance of scapular morphology on biomechanical outcomes. The aim of this study was to assess the influence of scapular morphology variation on RTSA biomechanics using statistical models, musculoskeletal modeling and predictive simulation. The scapular geometry of a musculoskeletal model was altered across six modes of variation at four levels (±1 and ±3 SD) from a clinically derived statistical shape model. For each model, a standardized virtual surgery was performed to place RTSA components in the same relative position on each model then implemented in 50 predictive simulations of upward and lateral reaching tasks. Results showed morphology affected functional changes in the deltoid moment arms and recruitment for the two tasks. Variation of the anatomy that reduced the efficiency of the deltoids showed increased levels of muscle force production, joint load magnitude and shear. These findings suggest that scapular morphology plays an important role in postoperative biomechanical function of the shoulder with an implanted RTSA. Furthermore a "one-size-fits-all" approach for construct surgical placement may lead to suboptimal patient outcomes across a clinical population. Patient glenoid as well as scapular anatomy may need to be carefully considered when planning RTSA to optimize postoperative success.

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.

A simulation framework to determine optimal strength training and musculoskeletal geometry for sprinting and distance running

Musculoskeletal geometry and muscle volumes vary widely in the population and are intricately linked to the performance of tasks ranging from walking and running to jumping and sprinting. As an alternative to experimental approaches, where it is difficult to isolate factors and establish causal relationships, simulations can be used to independently vary musculoskeletal geometry and muscle volumes, and develop a fundamental understanding. However, our ability to understand how these parameters affect task performance has been limited due to the high computational cost of modelling the necessary complexity of the musculoskeletal system and solving the requisite multi-dimensional optimization problem. For example, sprinting and running are fundamental to many forms of sport, but past research on the relationships between musculoskeletal geometry, muscle volumes, and running performance has been limited to observational studies, which have not established cause-effect relationships, and simulation studies with simplified representations of musculoskeletal geometry. In this study, we developed a novel musculoskeletal simulator that is differentiable with respect to musculoskeletal geometry and muscle volumes. This simulator enabled us to find the optimal body segment dimensions and optimal distribution of added muscle volume for sprinting and marathon running. Our simulation results replicate experimental observations, such as increased muscle mass in sprinters, as well as a mass in the lower end of the healthy BMI range and a higher leg-length-to-height ratio in marathon runners. The simulations also reveal new relationships, for example showing that hip musculature is vital to both sprinting and marathon running. We found hip flexor and extensor moment arms were maximized to optimize sprint and marathon running performance, and hip muscles the main target when we simulated strength training for sprinters. Our simulation results provide insight to inspire future studies to examine optimal strength training. Our simulator can be extended to other athletic tasks, such as jumping, or to non-athletic applications, such as designing interventions to improve mobility in older adults or individuals with movement disorders.

Per-step and cumulative load at three common running injury locations: The effect of speed, surface gradient, and cadence

Understanding how loading and damage on common running injury locations changes across speeds, surface gradients, and step frequencies may inform training programs and help guide progression/rehabilitation after injuries. However, research investigating tissue loading and damage in running is limited and fragmented across different studies, thereby impairing comparison between conditions and injury locations. This study examined per-step peak load and impulse, cumulative impulse, and cumulative weighted impulse (hereafter referred to as cumulative damage) on three common injury locations (patellofemoral joint, tibia, and Achilles tendon) across different speeds, surface gradients, and cadences. We also explored how cumulative damage in the different tissues changed across conditions relative to each other. Nineteen runners ran at five speeds (2.78, 3.0, 3.33, 4.0, 5.0 m s-1 ), and four gradients (-6, -3, +3, +6°), and three cadences (preferred, ±10 steps min-1 ) each at one speed. Patellofemoral, tibial, and Achilles tendon loading and damage were estimated from kinematic and kinetic data and compared between conditions using a linear mixed model. Increases in running speed increased patellofemoral cumulative damage, with nonsignificant increases for the tibia and Achilles tendon. Increases in cadence reduced damage to all tissues. Uphill running increased tibial and Achilles tendon, but decreased patellofemoral damage, while downhill running showed the reverse pattern. Per-step and cumulative loading, and cumulative loading and cumulative damage indices diverged across conditions. Moreover, changes in running speed, surface gradient, and step frequency lead to disproportional changes in relative cumulative damage on different structures. Methodological and practical implications for researchers and practitioners are discussed.

Transfemoral limb loss modestly increases the metabolic cost of optimal control simulations of walking

Background

In transtibial limb loss, computer simulations suggest that the maintenance of muscle strength between pre- and post-limb loss can maintain the pre-limb loss metabolic cost. These results are consistent with comparable costs found experimentally in select cases of high functioning military service members with transtibial limb loss. It is unlikely that similar results would be found with transfemoral limb loss, although the theoretical limits are not known. Here we performed optimal control simulations of walking with and without an above-knee prosthesis to determine if transfemoral limb loss per se increases the metabolic cost of walking.

Methods

OpenSim Moco was used to generate optimal control simulations of walking in 15 virtual "subjects" that minimized the weighted sum of (i) deviations from average able-bodied gait mechanics and (ii) the gross metabolic cost of walking, pre-limb loss in models with two intact biological limbs, and post-limb loss with one of the limbs replaced by a prosthetic knee and foot. No other changes were made to the model. Metabolic cost was compared between pre- and post-limb loss simulations in paired t-tests.

Results

Metabolic cost post-limb loss increased by 0.7-9.3% (p < 0.01) depending on whether cost was scaled by total body mass or biological body mass and on whether the prosthetic knee was passive or non-passive.

Conclusions

Given that the post-limb loss model had numerous features that predisposed it to low metabolic cost, these results suggest transfemoral limb loss per se increases the metabolic cost of walking. However, the large differences above able-bodied peers of ∼20-45% in most gait analysis experiments may be avoidable, even when minimizing deviations from able-bodied gait mechanics. Portions of this text were previously published as part of a preprint (https://www.biorxiv.org/content/10.1101/2023.06.26.546515v2.full.pdf).

Higher coactivations of lower limb muscles increase stability during walking on slippery ground in forward dynamics musculoskeletal simulation

The energy efficiency theory of human bipedal locomotion has been widely accepted as a neuro-musculoskeletal control method. However, coactivation of agonist and antagonist muscles in the lower limb has been observed during various limb movements, including walking. The emergence of this coactivation cannot be explained solely by the energy efficiency theory and remains a subject of debate. To shed light on this, we investigated the role of muscle coactivations in walking stability using a forward dynamics musculoskeletal simulation combined with neural-network-based gait controllers. Our study revealed that a gait controller with minimal muscle activations had a high probability of falls under challenging gait conditions such as slippery ground and uneven terrain. Lower limb muscle coactivations emerged in the process of gait controller training on slippery ground. Controllers with physiological coactivation levels demonstrated a significantly reduced probability of falls. Our results suggest that achieving stable walking requires muscle coactivations beyond the minimal level of muscle energy. This study implies that coactivations likely emerge to maintain gait stability under challenging conditions, and both coactivation and energy optimization of lower limb muscles should be considered when exploring the foundational control mechanisms of human walking.

Muscle-driven simulations and experimental data of cycling

Muscle-driven simulations have provided valuable insights in studies of walking and running, but a set of freely available simulations and corresponding experimental data for cycling do not exist. The aim of this work was to develop a set of muscle-driven simulations of cycling and to validate them by comparison with experimental data. We used direct collocation to generate simulations of 16 participants cycling over a range of powers (40-216 W) and cadences (75-99 RPM) using two optimization objectives: a baseline objective that minimized muscle effort and a second objective that additionally minimized tibiofemoral joint forces. We tested the accuracy of the simulations by comparing the timing of active muscle forces in our baseline simulation to timing in experimental electromyography data. Adding a term in the objective function to minimize tibiofemoral forces preserved cycling power and kinematics, improved similarity between active muscle force timing and experimental electromyography, and decreased tibiofemoral joint reaction forces, which better matched previously reported in vivo measurements. The musculoskeletal models, muscle-driven simulations, simulation software, and experimental data are freely shared at https://simtk.org/projects/cycling_sim for others to reproduce these results and build upon this research.

Does enforcing glenohumeral joint stability matter? A new rapid muscle redundancy solver highlights the importance of non-superficial shoulder muscles

The complexity of the human shoulder girdle enables the large mobility of the upper extremity, but also introduces instability of the glenohumeral (GH) joint. Shoulder movements are generated by coordinating large superficial and deeper stabilizing muscles spanning numerous degrees-of-freedom. How shoulder muscles are coordinated to stabilize the movement of the GH joint remains widely unknown. Musculoskeletal simulations are powerful tools to gain insights into the actions of individual muscles and particularly of those that are difficult to measure. In this study, we analyze how enforcement of GH joint stability in a musculoskeletal model affects the estimates of individual muscle activity during shoulder movements. To estimate both muscle activity and GH stability from recorded shoulder movements, we developed a Rapid Muscle Redundancy (RMR) solver to include constraints on joint reaction forces (JRFs) from a musculoskeletal model. The RMR solver yields muscle activations and joint forces by minimizing the weighted sum of squared-activations, while matching experimental motion. We implemented three new features: first, computed muscle forces include active and passive fiber contributions; second, muscle activation rates are enforced to be physiological, and third, JRFs are efficiently formulated as linear functions of activations. Muscle activity from the RMR solver without GH stability was not different from the computed muscle control (CMC) algorithm and electromyography of superficial muscles. The efficiency of the solver enabled us to test over 3600 trials sampled within the uncertainty of the experimental movements to test the differences in muscle activity with and without GH joint stability enforced. We found that enforcing GH stability significantly increases the estimated activity of the rotator cuff muscles but not of most superficial muscles. Therefore, a comparison of shoulder model muscle activity to EMG measurements of superficial muscles alone is insufficient to validate the activity of rotator cuff muscles estimated from musculoskeletal models.

Human force control may trade-off force error with central tendency and recency biases

Understanding how humans control force is useful for understanding human movement behaviors and sensorimotor control. However, it is not well understood how the human nervous system handles different control criteria such as accuracy and energetic cost. We conducted force tracking experiments where participants applied force isometrically while receiving visual force feedback, tracking step changes in target forces. The experiments were designed to disambiguate different plausible objective function components. We found that force tracking error was largely explained by a trade-off between error-reducing tendency and force biases, but we did not need to include an effort-saving tendency. Central tendency bias, which is a shift towards the center of the task distribution, and recency bias, which is a shift towards recent action, were necessary to explain many of our observations. Surprisingly, we did not observe such biases when we removed force requirements for pointing to the target, suggesting that such biases may be task-specific. This study provides insights into the broader field of motor control and human perceptions where behavioral or perceptual biases are involved.

Triceps surae muscle forces during dynamic exercises in patients with Achilles tendinopathy: A cross-sectional study

PURPOSE

The aim of this study was to investigate the individual triceps surae muscle forces during the execution of six different functional movements and rehabilitation exercises in patients with Achilles tendinopathy compared to a control group.

METHODS

Triceps surae muscle forces of 15 participants with Achilles tendinopathy (AT) and 15 healthy controls were estimated through a combination of experimental data and musculo-skeletal modeling. Three-dimensional motion capture and force plates were used to collect the ankle and knee joint angles and moments during three functional movements (walking, heel walking, and toe walking) and three rehabilitation exercises (bilateral heel drop, unilateral heel drop with extended knee and with flexed knee). A dynamic optimization method was used to obtain the modeled triceps surae muscle forces. Force-sharing strategies were calculated at the peak triceps surae muscle force and compared between groups.

RESULTS

Lower peak triceps surae forces were obtained for the AT group during dynamic exercises. Across all exercises, the average contribution of the soleus (SOL) to the total triceps surae muscle force was the largest (60.83 ± 13.89% [AT] > 56.90 ± 16.18% [healthy]), followed by the gastrocnemius medialis (29.87 ± 10.67% [AT] < 32.19 ± 12.90% [healthy]) and the gastrocnemius lateralis (9.30 ± 4.31% [AT] < 10.91 ± 4.66% [healthy]). The triceps surae force-sharing strategy was different for the toe walking, heel walking, and the bilateral and unilateral heel drop with extended knee.

CONCLUSION

This study provides evidence for altered triceps surae muscle force-sharing strategies during dynamic tasks in patients with AT. The influence of altered muscle force-sharing on the subtendon nonuniformity and/or the tendon loading should be explored in future work.

EMG-Driven Musculoskeletal Model Calibration With Wrapping Surface Personalization

Muscle forces and joint moments estimated by electromyography (EMG)-driven musculoskeletal models are sensitive to the wrapping surface geometry defining muscle-tendon lengths and moment arms. Despite this sensitivity, wrapping surface properties are typically not personalized to subject movement data. This study developed a novel method for personalizing OpenSim cylindrical wrapping surfaces during EMG-driven model calibration. To avoid the high computational cost of repeated OpenSim muscle analyses, the method uses two-level polynomial surrogate models. Outer-level models specify time-varying muscle-tendon lengths and moment arms as functions of joint angles, while inner-level models specify time-invariant outer-level polynomial coefficients as functions of wrapping surface parameters. To evaluate the method, we used walking data collected from two individuals post-stroke and performed four variations of EMG-driven lower extremity model calibration: 1) no calibration of scaled generic wrapping surfaces (NGA), 2) calibration of outer-level polynomial coefficients for all muscles (SGA), 3) calibration of outer-level polynomial coefficients only for muscles with wrapping surfaces (LSGA), and 4) calibration of cylindrical wrapping surface parameters for muscles with wrapping surfaces (PGA). On average compared to NGA, SGA reduced lower extremity joint moment matching errors by 31%, LSGA by 24%, and PGA by 12%, with the largest reductions occurring at the hip. Furthermore, PGA reduced peak hip joint contact force by 47% bodyweight, which was the most consistent with published in vivo measurements. The proposed method for EMG-driven model calibration with wrapping surface personalization produces physically realistic OpenSim models that reduce joint moment matching errors while improving prediction of hip joint contact force.

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.

Validation of a musculoskeletal model for simulating muscle mechanics and energetics during diverse human hopping tasks

Computational musculoskeletal modelling has emerged as an alternative, less-constrained technique to indirect calorimetry for estimating energy expenditure. However, predictions from modelling tools depend on many assumptions around muscle architecture and function and motor control. Therefore, these tools need to continue to be validated if we are to eventually develop subject-specific simulations that can accurately and reliably model rates of energy consumption for any given task. In this study, we used OpenSim software and experimental motion capture data to simulate muscle activations, muscle fascicle dynamics and whole-body metabolic power across mechanically and energetically disparate hopping tasks, and then evaluated these outputs at a group- and individual-level against experimental electromyography, ultrasound and indirect calorimetry data. Comparing simulated and experimental outcomes, we found weak to strong correlations for peak muscle activations, moderate to strong correlations for absolute fascicle shortening and mean shortening velocity, and strong correlations for gross metabolic power. These correlations tended to be stronger on a group-level rather than individual-level. We encourage the community to use our publicly available dataset from SimTK.org to experiment with different musculoskeletal models, muscle models, metabolic cost models, optimal control policies, modelling tools and algorithms, data filtering etc. with subject-specific simulations being a focal goal.

Simulating Muscle-Level Energetic Cost Savings When Humans Run with a Passive Assistive Device

Connecting the legs with a spring attached to the shoelaces, called an exotendon, can reduce the energetic cost of running, but how the exotendon reduces the energetic burden of individual muscles remains unknown. We generated muscle-driven simulations of seven individuals running with and without the exotendon to discern whether savings occurred during the stance phase or the swing phase, and to identify which muscles contributed to energy savings. We computed differences in muscle-level energy consumption, muscle activations, and changes in muscle-fiber velocity and force between running with and without the exotendon. The seven of nine participants who reduced energy cost when running with the exotendon reduced their measured energy expenditure rate by 0.9 W/kg (8.3%). Simulations predicted a 1.4 W/kg (12.0%) reduction in the average rate of energy expenditure and correctly identified that the exotendon reduced rates of energy expenditure for all seven individuals. Simulations showed most of the savings occurred during stance (1.5 W/kg), though the rate of energy expenditure was also reduced during swing (0.3 W/kg). The energetic savings were distributed across the quadriceps, hip flexor, hip abductor, hamstring, hip adductor, and hip extensor muscle groups, whereas no changes were observed in the plantarflexor or dorsiflexor muscles. Energetic savings were facilitated by reductions in the rate of mechanical work performed by muscles and their estimated rate of heat production. By modeling muscle-level energetics, this simulation framework accurately captured measured changes in whole-body energetics when using an assistive device. This is a useful first step towards using simulation to accelerate device design by predicting how humans will interact with assistive devices that have yet to be built.

Predictive Control of Peak Achilles Tendon Force in a Simulated System of the Human Ankle Joint with a Parallel Artificial Actuator During Hopping

Latest advances in wearable exoskeletons for the human lower extremity predominantly focus on minimising metabolic cost of walking. However, there currently is no robotic exoskeleton that gains control on the mechanics of biological tissues such as biological muscles or series-elastic tendons. Achieving robotic control of biological tissue mechanics would enable prevention of musculoskeletal injuries or the personalization of rehabilitation treatments following injury with levels of precisions not attained before. In this paper, we introduce a new framework that uses nonlinear model predictive control (NMPC) for the closed-loop control of peak tendon force in a simulated system of the human ankle joint with parallel exoskeletal actuation. We propose a computationally efficient NMPC's inner model consisting of explicit, closed-form equations of muscle-tendon dynamics along with those of the ankle joint with parallel actuation. The proposed formulation is tested and verified on movement data collected during dynamic ankle dorsiflexion/plantarflexion rotations executed on a dynamometer as well as during walking and running on a treadmill. The framework designed using the NMPC controller showed a promising performance in keeping the Achilles tendon force under a predefined threshold. Results indicated that our proposed model was generalizable to different muscles and gaits and suitable for real-time applications due to its low computational time.

Muscle Contributions to Take-Off Velocity in the Long Jump

PURPOSE

A key determinant of long jump performance is the ability to increase the vertical velocity of the center of mass (COM) while minimizing the loss in forward velocity (running speed) during the take-off phase, but exactly how this occurs is not fully understood. We combined a three-dimensional musculoskeletal model of the body with dynamic optimization theory to simulate the biomechanics of the long jump take-off and determine the contributions of the individual leg muscles to jump performance.

METHODS

The body was modeled as a 29-degree-of-freedom skeleton actuated by a combination of muscles and net joint torques. A dynamic optimization problem was solved to reproduce full-body motion and ground-force data recorded from experienced subelite jumpers. The optimization solution then was analyzed to determine each muscle's contribution to the ground-force impulse and hence the change in velocity of the COM during the take-off phase.

RESULTS

The hip, knee, and ankle extensors dominated the change in velocity of the COM during take-off. Vasti (VAS) generated the highest support impulse and contributed one-third (33%) of the increase in vertical COM velocity generated by all the muscles. Soleus (SOL) and gluteus maximus (GMAX) also developed substantial support impulses and contributed 24% and 16% of the increase in vertical COM velocity, respectively. VAS also generated the highest braking impulse and contributed approximately one-half (55%) of the loss in forward COM velocity generated by all the muscles, whereas SOL and GMAX made much smaller contributions (12% and 7%, respectively).

CONCLUSIONS

VAS, SOL, and GMAX contributed nearly three-quarters (73%) of the increase in vertical COM velocity at take-off, suggesting that these muscles ought to be prioritized in strength training programs aimed at improving long jump performance.

Predictive Simulations with OpenSim Moco to Investigate the Interaction Between Human and Assistive Exoskeleton

The purpose of this work was to investigate the interaction between human and lower limbs assistive exoskeleton under different levels of assistance, by using computational simulations. To this, a human-exoskeleton interaction model was used and three predictive simulations were carried out with the OpenSim Moco. The results proved that the increase in the level of robot assistance causes a reduction in human effort. In addition, it was possible to verify the RMS torque of both the robot and the human, as well as the muscle activations, for the different levels of assistance simulated. For future work, we intend to run predictive simulations with more complex movements, such as gait free and with obstacles, in addition to using models that can represent a human being with muscle weakness on one side of the body (hemiparesis).

Assisting walking balance using a bio-inspired exoskeleton controller

BACKGROUND

Balance control is important for mobility, yet exoskeleton research has mainly focused on improving metabolic energy efficiency. Here we present a biomimetic exoskeleton controller that supports walking balance and reduces muscle activity.

METHODS

Humans restore balance after a perturbation by adjusting activity of the muscles actuating the ankle in proportion to deviations from steady-state center of mass kinematics. We designed a controller that mimics the neural control of steady-state walking and the balance recovery responses to perturbations. This controller uses both feedback from ankle kinematics in accordance with an existing model and feedback from the center of mass velocity. Control parameters were estimated by fitting the experimental relation between kinematics and ankle moments observed in humans that were walking while being perturbed by push and pull perturbations. This identified model was implemented on a bilateral ankle exoskeleton.

RESULTS

Across twelve subjects, exoskeleton support reduced calf muscle activity in steady-state walking by 19% with respect to a minimal impedance controller (p < 0.001). Proportional feedback of the center of mass velocity improved balance support after perturbation. Muscle activity is reduced in response to push and pull perturbations by 10% (p = 0.006) and 16% (p < 0.001) and center of mass deviations by 9% (p = 0.026) and 18% (p = 0.002) with respect to the same controller without center of mass feedback.

CONCLUSION

Our control approach implemented on bilateral ankle exoskeletons can thus effectively support steady-state walking and balance control and therefore has the potential to improve mobility in balance-impaired individuals.

Model-based estimation of muscle and ACL forces during turning maneuvers in alpine skiing

In alpine skiing, estimation of the muscle forces and joint loads such as the forces in the ACL of the knee are essential to quantify the loading pattern of the skier during turning maneuvers. Since direct measurement of these forces is generally not feasible, non-invasive methods based on musculoskeletal modeling should be considered. In alpine skiing, however, muscle forces and ACL forces have not been analyzed during turning maneuvers due to the lack of three dimensional musculoskeletal models. In the present study, a three dimensional musculoskeletal skier model was successfully applied to track experimental data of a professional skier. During the turning maneuver, the primary activated muscles groups of the outside leg, bearing the highest loads, were the gluteus maximus, vastus lateralis as well as the medial and lateral hamstrings. The main function of these muscles was to generate the required hip extension and knee extension moments. The gluteus maximus was also the main contributor to the hip abduction moment when the hip was highly flexed. Furthermore, the lateral hamstrings and gluteus maximus contributed to the hip external rotation moment in addition to the quadratus femoris. Peak ACL forces reached 211 N on the outside leg with the main contribution in the frontal plane due to an external knee abduction moment. Sagittal plane contributions were low due to consistently high knee flexion (> 60[Formula: see text]), substantial co-activation of the hamstrings and the ground reaction force pushing the anteriorly inclined tibia backwards with respect to the femur. In conclusion, the present musculoskeletal simulation model provides a detailed insight into the loading of a skier during turning maneuvers that might be used to analyze appropriate training loads or injury risk factors such as the speed or turn radius of the skier, changes of the equipment or neuromuscular control parameters.

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.

How Connecting the Legs with a Spring Improves Human Running Economy

Connecting the legs with a spring attached to the shoelaces reduces the energy cost of running, but how the spring reduces the energy burden of individual muscles remains unknown. We generated muscle-driven simulations of seven individuals running with and without the spring to discern whether savings occurred during the stance phase or the swing phase, and to identify which muscles contributed to energy savings. We computed differences in muscle-level energy consumption, muscle activations, and changes in muscle-fiber velocity and force between running with and without the spring. Across participants, running with the spring reduced the measured rate of energy expenditure by 0.9 W/kg (8.3%). Simulations predicted a 1.4 W/kg (12.0%) reduction in the average rate of energy expenditure and correctly identified that the spring reduced rates of energy expenditure for all participants. Simulations showed most of the savings occurred during stance (1.5 W/kg), though the rate of energy expenditure was also reduced during swing (0.3 W/kg). The energetic savings were distributed across the quadriceps, hip flexor, hip abductor, hamstring, hip adductor, and hip extensor muscle groups, whereas no changes in the rate of energy expenditure were observed in the plantarflexor or dorsiflexor muscles. Energetic savings were facilitated by reductions in the rate of mechanical work performed by muscles and their estimated rate of heat production. The simulations provide insight into muscle-level changes that occur when utilizing an assistive device and the mechanisms by which a spring connecting the legs improves running economy.

Minimum effort simulations of split-belt treadmill walking exploit asymmetry to reduce metabolic energy expenditure

Walking on a split-belt treadmill elicits an adaptation response that changes baseline step length asymmetry. The underlying causes of this adaptation, however, are difficult to determine. It has been proposed that effort minimization may drive this adaptation, based on the idea that adopting longer steps on the fast belt, or positive step length asymmetry (SLA), can cause the treadmill to exert net-positive mechanical work on a bipedal walker. However, humans walking on split-belt treadmills have not been observed to reproduce this behavior when allowed to freely adapt. To determine if an effort-minimization motor control strategy would result in experimentally observed adaptation patterns, we conducted simulations of walking on different combinations of belt speeds with a human musculoskeletal model that minimized muscle excitations and metabolic rate. The model adopted increasing amounts of positive SLA and decreased its net metabolic rate with increasing belt speed difference, reaching +42.4% SLA and -5.7% metabolic rate relative to tied-belt walking at our maximum belt speed ratio of 3:1. These gains were primarily enabled by an increase in braking work and a reduction in propulsion work on the fast belt. The results suggest that a purely effort minimization driven split-belt walking strategy would involve substantial positive SLA, and that the lack of this characteristic in human behavior points to additional factors influencing the motor control strategy, such as aversion to excessive joint loads, asymmetry, or instability.NEW & NOTEWORTHY Behavioral observations of split-belt treadmill adaptation have been inconclusive toward its underlying causes. To estimate gait patterns when driven exclusively by one of these possible underlying causes, we simulated split-belt treadmill walking with a musculoskeletal model that minimized its summed muscle excitations. Our model took significantly longer steps on the fast belt and reduced its metabolic rate below tied-belt walking, unlike experimental observations. This suggests that asymmetry is energetically optimal, but human adaptation involves additional factors.

Limiting radial pedal forces greatly reduces maximal power output and efficiency in sprint cycling: an optimal control study

A cyclist's performance depends critically on the generated average mechanical power output (AMPO). The instantaneous mechanical power output equals the product of crank angular velocity, crank length, and the tangential pedal force. Radial pedal forces do not contribute to mechanical power. It has been suggested that radial pedal forces arise from suboptimal pedaling technique and that limiting these would increase AMPO and efficiency. Here, we presented an optimal control musculoskeletal model of a cyclist (consisting of five segments driven by nine Hill-type muscle-tendon units) to predict maximal AMPO during sprint cycling at different levels of allowed radial pedal forces. Our findings showed that limiting radial pedal forces has a detrimental effect on maximal AMPO; it dropped from 1,115 W without a limit on radial forces to 528 W when no radial forces were allowed (both at 110 rpm). We explained that avoiding radial pedal forces causes ineffective use of muscles: muscles deliver less positive power and have a higher muscle power dissipation ratio (average mechanical power dissipated per unit of average positive power delivered). We concluded that radial pedal forces are an unavoidable by-product when optimizing for maximal AMPO and that limiting these leads to a performance decrease.NEW & NOTEWORTHY In the literature, but also in the "cycling field" [e.g., trainers, coaches, and (professional) cyclists], it is often suggested that trying to limit/avoid radial pedal forces enhances cycling technique and with that maximal average power output and efficiency. In this paper, we introduce an optimal control model of a human cyclists (consisting of five segments and driven by nine Hill-type muscle-tendon complex models). With that we not only show, but also explain why limiting radial forces is a bad idea: it will decrease maximal attainable AMPO and will decrease efficiency.

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.

Change the direction: 3D optimal control simulation by directly tracking marker and ground reaction force data

Optimal control simulations of musculoskeletal models can be used to reconstruct motions measured with optical motion capture to estimate joint and muscle kinematics and kinetics. These simulations are mutually and dynamically consistent, in contrast to traditional inverse methods. Commonly, optimal control simulations are generated by tracking generalized coordinates in combination with ground reaction forces. The generalized coordinates are estimated from marker positions using, for example, inverse kinematics. Hence, inaccuracies in the estimated coordinates are tracked in the simulation. We developed an approach to reconstruct arbitrary motions, such as change of direction motions, using optimal control simulations of 3D full-body musculoskeletal models by directly tracking marker and ground reaction force data. For evaluation, we recorded three trials each of straight running, curved running, and a v-cut for 10 participants. We reconstructed the recordings with marker tracking simulations, coordinate tracking simulations, and inverse kinematics and dynamics. First, we analyzed the convergence of the simulations and found that the wall time increased three to four times when using marker tracking compared to coordinate tracking. Then, we compared the marker trajectories, ground reaction forces, pelvis translations, joint angles, and joint moments between the three reconstruction methods. Root mean squared deviations between measured and estimated marker positions were smallest for inverse kinematics (e.g., 7.6 ± 5.1 mm for v-cut). However, measurement noise and soft tissue artifacts are likely also tracked in inverse kinematics, meaning that this approach does not reflect a gold standard. Marker tracking simulations resulted in slightly higher root mean squared marker deviations (e.g., 9.5 ± 6.2 mm for v-cut) than inverse kinematics. In contrast, coordinate tracking resulted in deviations that were nearly twice as high (e.g., 16.8 ± 10.5 mm for v-cut). Joint angles from coordinate tracking followed the estimated joint angles from inverse kinematics more closely than marker tracking (e.g., root mean squared deviation of 1.4 ± 1.8 deg vs. 3.5 ± 4.0 deg for v-cut). However, we did not have a gold standard measurement of the joint angles, so it is unknown if this larger deviation means the solution is less accurate. In conclusion, we showed that optimal control simulations of change of direction running motions can be created by tracking marker and ground reaction force data. Marker tracking considerably improved marker accuracy compared to coordinate tracking. Therefore, we recommend reconstructing movements by directly tracking marker data in the optimal control simulation when precise marker tracking is required.

Musculoskeletal-Modeling-Based, Full-Body Load-Assessment Tool for Ergonomists (MATE): Method Development and Proof of Concept Case Studies

A new ergonomic-risk-assessment tool was developed that combines musculoskeletal-model-based loading estimates with insights from fatigue failure theory to evaluate full-body musculoskeletal loading during dynamic tasks. Musculoskeletal-modeling output parameters, i.e., joint contact forces and muscle forces, were combined with tissue-specific injury thresholds that account for loading frequency to determine the injury risk for muscles, lower back, and hip cartilage. The potential of this new risk-assessment tool is demonstrated for defining ergonomic interventions in terms of lifting characteristics, back and shoulder exoskeleton assistance, box transferring, stoop lifting, and an overhead wiring task, respectively. The MATE identifies the risk of WMSDs in different anatomical regions during occupational tasks and allows for the evaluation of the impact of interventions that modify specific lifting characteristics, i.e., load weight versus task repetition. Furthermore, and in clear contrast to currently available ergonomic assessment scores, the effects of the exoskeleton assistance level on the risk of WMSDs of full-body musculoskeletal loading (in particular, the muscles, lower back, and hips) can be evaluated and shows small reductions in musculoskeletal loading but not in injury risk. Therefore, the MATE is a risk-assessment tool based on a full-body, musculoskeletal-modeling approach combined with insights from the fatigue failure theory that shows the proof of concept of a shoulder and back exoskeleton. Furthermore, it accounts for subject-specific characteristics (age and BMI), further enhancing individualized ergonomic-risk assessment.

Characterization of muscle recruitment during gait of bilateral transfemoral and through-knee persons with limb loss

Introduction: Due to loss in musculoskeletal capacity, there is an increased burden on the residual limbs of bilateral transfemoral and through-knee persons with limb loss. This reduced capacity is associated with an increased cost of walking that is detrimental to functionality. Compensatory gait strategies are adopted by this population. However, how these strategies relate to specific muscle recruitment is not known. The primary aim of this study is to characterize muscle recruitment during gait of this population. The secondary aim is to assess whether the measured kinematics can be actuated when the endurance of specific muscles is reduced and if this is the case, which alternative muscles facilitate this. Methods: 3D gait data and high-resolution magnetic resonance images were acquired from six bilateral transfemoral and through-knee persons with limb loss. Subject-specific anatomical muscle models were developed for each participant, and a validated musculoskeletal model was used to quantify muscle forces in two conditions: during normal gait (baseline) and when muscles, which were identified as functioning above a "healthy" level at baseline, have a reduced magnitude of maximum force capacity (reduced endurance simulation). To test the hypothesis that there are differences in muscle forces between the baseline trials and the simulations with reduced muscular endurance, a Bonferroni corrected two-way ANOVA with repeated measures was completed between the two states. Results: The baseline analysis showed that the hip flexors experience relatively high muscle activations during gait. The reduced endurance simulation found two scenarios. First, for 5 out of the 12 simulations, the baseline kinematics could not be reproduced with the reduced muscular capacity. Second, for 7 out of 12 cases where the baseline kinematics were achieved, this was possible with compensatory increased activation of some muscles with similar functions (p ≤ 0.003). Discussion: Evidently, due to the loss of the ankle plantar flexors, gait imposes a high demand on the flexor muscle group of the residual limb. This study highlights how the elevated cost of gait in this population manifests in muscle recruitment. To enhance functionality, it is critical to consider the mechanical demand on the hip flexors and to develop rehabilitation interventions accordingly.

Towards improving the accuracy of musculoskeletal simulation of dynamic three-dimensional spine rotations with optimizing model and algorithm

BACKGROUND

The accuracy of musculoskeletal simulations greatly relies on model structures and optimization algorithms. This study investigated the unclarified influence of accounting for several commonly-simplified different model components and optimization criteria on spinal musculoskeletal simulations.

METHODS

The study constructed a full-body musculoskeletal model with passive components of functional spinal units and spinal muscles subject-specifically refined. A muscle redundancy solver was built with 15 optimization criteria. Three-dimensional spine rotations and spinal muscle activities were measured using optical motion capture and electromyogram techniques when eight healthy volunteers performed standing, flexion/extension, lateral bending, and axial rotation. The effect of the model with four different conditions of the passive components and the sensitivity of the 15 optimization criteria on simulations were investigated.

RESULTS

Accounting for the refined passive components significantly improved the simulation accuracy. Different optimization criteria behaved distinctly for different motions. Generally minimizing the sum of squared muscle activations outperformed the others, with the highest averaged correlation coefficient (0.82) between the estimated erector spinae muscle activations and measured electromyography and with the estimated joint compression forces comparable to in vivo reference data.

CONCLUSION

This study highlights the importance of passive model components and proposes a suitable optimization framework for realistic spinal musculoskeletal simulations.

Generating Human Arm Kinematics Using Reinforcement Learning to Train Active Muscle Behavior in Automotive Research

Computational human body models (HBMs) are important tools for predicting human biomechanical responses under automotive crash environments. In many scenarios, the prediction of the occupant response will be improved by incorporating active muscle control into the HBMs to generate biofidelic kinematics during different vehicle maneuvers. In this study, we have proposed an approach to develop an active muscle controller based on reinforcement learning (RL). The RL muscle activation control (RL-MAC) approach is a shift from using traditional closed-loop feedback controllers, which can mimic accurate active muscle behavior under a limited range of loading conditions for which the controller has been tuned. Conversely, the RL-MAC uses an iterative training approach to generate active muscle forces for desired joint motion and is analogous to how a child develops gross motor skills. In this study, the ability of a deep deterministic policy gradient (DDPG) RL controller to generate accurate human kinematics is demonstrated using a multibody model of the human arm. The arm model was trained to perform goal-directed elbow rotation by activating the responsible muscles and investigated using two recruitment schemes: as independent muscles or as antagonistic muscle groups. Simulations with the trained controller show that the arm can move to the target position in the presence or absence of externally applied loads. The RL-MAC trained under constant external loads was able to maintain the desired elbow joint angle under a simplified automotive impact scenario, implying the robustness of the motor control approach.