A neuromusculoskeletal tracking method for estimating individual muscle forces in human movement

Bridging the sim2real gap. Investigating deviations between experimental motion measurements and musculoskeletal simulation results-a systematic review

Musculoskeletal simulations can be used to estimate biomechanical variables like muscle forces and joint torques from non-invasive experimental data using inverse and forward methods. Inverse kinematics followed by inverse dynamics (ID) uses body motion and external force measurements to compute joint movements and the corresponding joint loads, respectively. ID leads to residual forces and torques (residuals) that are not physically realistic, because of measurement noise and modeling assumptions. Forward dynamic simulations (FD) are found by tracking experimental data. They do not generate residuals but will move away from experimental data to achieve this. Therefore, there is a gap between reality (the experimental measurements) and simulations in both approaches, the sim2real gap. To answer (patho-) physiological research questions, simulation results have to be accurate and reliable; the sim2real gap needs to be handled. Therefore, we reviewed methods to handle the sim2real gap in such musculoskeletal simulations. The review identifies, classifies and analyses existing methods that bridge the sim2real gap, including their strengths and limitations. Using a systematic approach, we conducted an electronic search in the databases Scopus, PubMed and Web of Science. We selected and included 85 relevant papers that were sorted into eight different solution clusters based on three aspects: how the sim2real gap is handled, the mathematical method used, and the parameters/variables of the simulations which were adjusted. Each cluster has a distinctive way of handling the sim2real gap with accompanying strengths and limitations. Ultimately, the method choice largely depends on various factors: available model, input parameters/variables, investigated movement and of course the underlying research aim. Researchers should be aware that the sim2real gap remains for both ID and FD approaches. However, we conclude that multimodal approaches tracking kinematic and dynamic measurements may be one possible solution to handle the sim2real gap as methods tracking multimodal measurements (some combination of sensor position/orientation or EMG measurements), consistently lead to better tracking performances. Initial analyses show that motion analysis performance can be enhanced by using multimodal measurements as different sensor technologies can compensate each other's weaknesses.

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.

Simulating the effect of ankle plantarflexion and inversion-eversion exoskeleton torques on center of mass kinematics during walking

Walking balance is central to independent mobility, and falls due to loss of balance are a leading cause of death for people 65 years of age and older. Bipedal gait is typically unstable, but healthy humans use corrective torques to counteract perturbations and stabilize gait. Exoskeleton assistance could benefit people with neuromuscular deficits by providing stabilizing torques at lower-limb joints to replace lost muscle strength and sensorimotor control. However, it is unclear how applied exoskeleton torques translate to changes in walking kinematics. This study used musculoskeletal simulation to investigate how exoskeleton torques applied to the ankle and subtalar joints alter center of mass kinematics during walking. We first created muscle-driven walking simulations using OpenSim Moco by tracking experimental kinematics and ground reaction forces recorded from five healthy adults. We then used forward integration to simulate the effect of exoskeleton torques applied to the ankle and subtalar joints while keeping muscle excitations fixed based on our previous tracking simulation results. Exoskeleton torque lasted for 15% of the gait cycle and was applied between foot-flat and toe-off during the stance phase, and changes in center of mass kinematics were recorded when the torque application ended. We found that changes in center of mass kinematics were dependent on both the type and timing of exoskeleton torques. Plantarflexion torques produced upward and backward changes in velocity of the center of mass in mid-stance and upward and smaller forward velocity changes near toe-off. Eversion and inversion torques primarily produced lateral and medial changes in velocity in mid-stance, respectively. Intrinsic muscle properties reduced kinematic changes from exoskeleton torques. Our results provide mappings between ankle plantarflexion and inversion-eversion torques and changes in center of mass kinematics which can inform designers building exoskeletons aimed at stabilizing balance during walking. Our simulations and software are freely available and allow researchers to explore the effects of applied torques on balance and gait.

Coupled exoskeleton assistance simplifies control and maintains metabolic benefits: A simulation study

Assistive exoskeletons can reduce the metabolic cost of walking, and recent advances in exoskeleton device design and control have resulted in large metabolic savings. Most exoskeleton devices provide assistance at either the ankle or hip. Exoskeletons that assist multiple joints have the potential to provide greater metabolic savings, but can require many actuators and complicated controllers, making it difficult to design effective assistance. Coupled assistance, when two or more joints are assisted using one actuator or control signal, could reduce control dimensionality while retaining metabolic benefits. However, it is unknown which combinations of assisted joints are most promising and if there are negative consequences associated with coupled assistance. Since designing assistance with human experiments is expensive and time-consuming, we used musculoskeletal simulation to evaluate metabolic savings from multi-joint assistance and identify promising joint combinations. We generated 2D muscle-driven simulations of walking while simultaneously optimizing control strategies for simulated lower-limb exoskeleton assistive devices to minimize metabolic cost. Each device provided assistance either at a single joint or at multiple joints using massless, ideal actuators. To assess if control could be simplified for multi-joint exoskeletons, we simulated different control strategies in which the torque provided at each joint was either controlled independently or coupled between joints. We compared the predicted optimal torque profiles and changes in muscle and total metabolic power consumption across the single joint and multi-joint assistance strategies. We found multi-joint devices-whether independent or coupled-provided 50% greater metabolic savings than single joint devices. The coupled multi-joint devices were able to achieve most of the metabolic savings produced by independently-controlled multi-joint devices. Our results indicate that device designers could simplify multi-joint exoskeleton designs by reducing the number of torque control parameters through coupling, while still maintaining large reductions in metabolic cost.

Preliminary Validation of Upper Limb Musculoskeletal Model using Static Optimization

Musculoskeletal models are powerful analogues to simulate human motion through kinematic and dynamic analysis. When coupled with feature-rich software, musculoskeletal models form an attractive platform for the integration of machine learning for human motion analysis. Performing realistic simulations using these models provide an avenue to overcome constraints when collecting real-world data sets. This motivates the need to further investigate the validity, efficacy, and accuracy of each available model to ensure that the resultant simulations are transferable to real-world applications. Using the open-source software, OpenSim, the primary aim of this paper is to validate an upper limb musculoskeletal model widely used in research. Muscle activation results from static optimization are evaluated against real-world data. A secondary aim is to investigate the effects of two muscle force generation constraints when evaluating the model's validity. Results show an agreement between the optimized muscle activation trends and real-world sEMG readings. However, it was found that static optimization of the musculoskeletal model is unable to identify voluntary co-contractions since the redundant model has more muscles than the system's degrees of freedom. Thus, future work will look to utilize additional channels of information to incorporate this during analysis.

The impact of anatomical uncertainties on the predictions of a musculoskeletal hand model - a sensitivity study

Outputs of musculoskeletal models should be considered probabilistic rather than deterministic as they are affected by inaccuracies and estimations associated with the development of the model. One of these uncertainties being critical for modeling arises from the determination of the muscles' line of action and the physiological cross-sectional area. Therefore, the aim of this study was to evaluate the outcome sensitivity of model predictions from a musculoskeletal hand model in comparison to the uncertainty of these input parameters. For this purpose, the kinematics and muscle activities of different hand movements (abduction of the fingers, abduction of the thumb, and flexion of the thumb) were recorded. One thousand simulations were calculated for each movement using the Latin hypercube sampling method with a corresponding variation of the muscle origin/insertion points and the cross-sectional area. Comparing the standard hand to simulations incorporating uncertainties of input parameters shows no major deviations in on- and off-set time point of muscle activities. About 60% of simulations are located within a ± 30% interval around the standard model concerning joint reaction forces. The comparison with the variation of the input data leads to the conclusion that the standard hand model is able to provide not over-scattered outcomes and, therefore, can be considered relatively stable. These results are of practical importance to the personalization of a musculoskeletal model with subject-specific bone geometries and hence changed muscle line of action.

In Silico-Enhanced Treatment and Rehabilitation Planning for Patients with Musculoskeletal Disorders: Can Musculoskeletal Modelling and Dynamic Simulations Really Impact Current Clinical Practice?

Over the past decades, the use of computational physics-based models representative of the musculoskeletal (MSK) system has become increasingly popular in many fields of clinically driven research, locomotor rehabilitation in particular. These models have been applied to various functional impairments given their ability to estimate parameters which cannot be readily measured in vivo but are of interest to clinicians. The use of MSK modelling and simulations allows analysis of relevant MSK biomarkers such as muscle and joint contact loading at a number of different stages in the clinical treatment pathway in order to benefit patient functional outcome. Applications of these methods include optimisation of rehabilitation programs, patient stratification, disease characterisation, surgical pre-planning, and assistive device and exoskeleton design and optimisation. This review provides an overview of current approaches, the components of standard MSK models, applications, limitations, and assumptions of these modelling and simulation methods, and finally proposes a future direction.

Curated Model Development Using NEUROiD: A Web-Based NEUROmotor Integration and Design Platform

Decades of research on neuromotor circuits and systems has provided valuable information on neuronal control of movement. Computational models of several elements of the neuromotor system have been developed at various scales, from sub-cellular to system. While several small models abound, their structured integration is the key to building larger and more biologically realistic models which can predict the behavior of the system in different scenarios. This effort calls for integration of elements across neuroscience and musculoskeletal biomechanics. There is also a need for development of methods and tools for structured integration that yield larger in silico models demonstrating a set of desired system responses. We take a small step in this direction with the NEUROmotor integration and Design (NEUROiD) platform. NEUROiD helps integrate results from motor systems anatomy, physiology, and biomechanics into an integrated neuromotor system model. Simulation and visualization of the model across multiple scales is supported. Standard electrophysiological operations such as slicing, current injection, recording of membrane potential, and local field potential are part of NEUROiD. The platform allows traceability of model parameters to primary literature. We illustrate the power and utility of NEUROiD by building a simple ankle model and its controlling neural circuitry by curating a set of published components. NEUROiD allows researchers to utilize remote high-performance computers for simulation, while controlling the model using a web browser.

B. G, João F. Influence of the Musculotendon Dynamics on the Muscle Force-Sharing Problem of the Shoulder—A Fully Inverse Dynamics Approach

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

Predictive Simulations of Neuromuscular Coordination and Joint-Contact Loading in Human Gait

We implemented direct collocation on a full-body neuromusculoskeletal model to calculate muscle forces, ground reaction forces and knee contact loading simultaneously for one cycle of human gait. A data-tracking collocation problem was solved for walking at the normal speed to establish the practicality of incorporating a 3D model of articular contact and a model of foot-ground interaction explicitly in a dynamic optimization simulation. The data-tracking solution then was used as an initial guess to solve predictive collocation problems, where novel patterns of movement were generated for walking at slow and fast speeds, independent of experimental data. The data-tracking solutions accurately reproduced joint motion, ground forces and knee contact loads measured for two total knee arthroplasty patients walking at their preferred speeds. RMS errors in joint kinematics were < 2.0° for rotations and < 0.3 cm for translations while errors in the model-computed ground-reaction and knee-contact forces were < 0.07 BW and < 0.4 BW, respectively. The predictive solutions were also consistent with joint kinematics, ground forces, knee contact loads and muscle activation patterns measured for slow and fast walking. The results demonstrate the feasibility of performing computationally-efficient, predictive, dynamic optimization simulations of movement using full-body, muscle-actuated models with realistic representations of joint function.

Three-dimensional data-tracking dynamic optimization simulations of human locomotion generated by direct collocation

The aim of this study was to perform full-body three-dimensional (3D) dynamic optimization simulations of human locomotion by driving a neuromusculoskeletal model toward in vivo measurements of body-segmental kinematics and ground reaction forces. Gait data were recorded from 5 healthy participants who walked at their preferred speeds and ran at 2m/s. Participant-specific data-tracking dynamic optimization solutions were generated for one stride cycle using direct collocation in tandem with an OpenSim-MATLAB interface. The body was represented as a 12-segment, 21-degree-of-freedom skeleton actuated by 66 muscle-tendon units. Foot-ground interaction was simulated using six contact spheres under each foot. The dynamic optimization problem was to find the set of muscle excitations needed to reproduce 3D measurements of body-segmental motions and ground reaction forces while minimizing the time integral of muscle activations squared. Direct collocation took on average 2.7±1.0h and 2.2±1.6h of CPU time, respectively, to solve the optimization problems for walking and running. Model-computed kinematics and foot-ground forces were in good agreement with corresponding experimental data while the calculated muscle excitation patterns were consistent with measured EMG activity. The results demonstrate the feasibility of implementing direct collocation on a detailed neuromusculoskeletal model with foot-ground contact to accurately and efficiently generate 3D data-tracking dynamic optimization simulations of human locomotion. The proposed method offers a viable tool for creating feasible initial guesses needed to perform predictive simulations of movement using dynamic optimization theory. The source code for implementing the model and computational algorithm may be downloaded at http://simtk.org/home/datatracking.

Neuromusculoskeletal Model Calibration Significantly Affects Predicted Knee Contact Forces for Walking

Though walking impairments are prevalent in society, clinical treatments are often ineffective at restoring lost function. For this reason, researchers have begun to explore the use of patient-specific computational walking models to develop more effective treatments. However, the accuracy with which models can predict internal body forces in muscles and across joints depends on how well relevant model parameter values can be calibrated for the patient. This study investigated how knowledge of internal knee contact forces affects calibration of neuromusculoskeletal model parameter values and subsequent prediction of internal knee contact and leg muscle forces during walking. Model calibration was performed using a novel two-level optimization procedure applied to six normal walking trials from the Fourth Grand Challenge Competition to Predict In Vivo Knee Loads. The outer-level optimization adjusted time-invariant model parameter values to minimize passive muscle forces, reserve actuator moments, and model parameter value changes with (Approach A) and without (Approach B) tracking of experimental knee contact forces. Using the current guess for model parameter values but no knee contact force information, the inner-level optimization predicted time-varying muscle activations that were close to experimental muscle synergy patterns and consistent with the experimental inverse dynamic loads (both approaches). For all the six gait trials, Approach A predicted knee contact forces with high accuracy for both compartments (average correlation coefficient r = 0.99 and root mean square error (RMSE) = 52.6 N medial; average r = 0.95 and RMSE = 56.6 N lateral). In contrast, Approach B overpredicted contact force magnitude for both compartments (average RMSE = 323 N medial and 348 N lateral) and poorly matched contact force shape for the lateral compartment (average r = 0.90 medial and -0.10 lateral). Approach B had statistically higher lateral muscle forces and lateral optimal muscle fiber lengths but lower medial, central, and lateral normalized muscle fiber lengths compared to Approach A. These findings suggest that poorly calibrated model parameter values may be a major factor limiting the ability of neuromusculoskeletal models to predict knee contact and leg muscle forces accurately for walking.

Neural Data-Driven Musculoskeletal Modeling for Personalized Neurorehabilitation Technologies

OBJECTIVES

The development of neurorehabilitation technologies requires the profound understanding of the mechanisms underlying an individual's motor ability and impairment. A major factor limiting this understanding is the difficulty of bridging between events taking place at the neurophysiologic level (i.e., motor neuron firings) with those emerging at the musculoskeletal level (i.e. joint actuation), in vivo in the intact moving human. This review presents emerging model-based methodologies for filling this gap that are promising for developing clinically viable technologies.

METHODS

We provide a design overview of musculoskeletal modeling formulations driven by recordings of neuromuscular activity with a critical comparison to alternative model-free approaches in the context of neurorehabilitation technologies. We present advanced electromyography-based techniques for interfacing with the human nervous system and model-based techniques for translating the extracted neural information into estimates of motor function.

RESULTS

We introduce representative application areas where modeling is relevant for accessing neuromuscular variables that could not be measured experimentally. We then show how these variables are used for designing personalized rehabilitation interventions, biologically inspired limbs, and human-machine interfaces.

CONCLUSION

The ability of using electrophysiological recordings to inform biomechanical models enables accessing a broader range of neuromechanical variables than analyzing electrophysiological data or movement data individually. This enables understanding the neuromechanical interplay underlying in vivo movement function, pathology, and robot-assisted motor recovery.

SIGNIFICANCE

Filling the gap between our understandings of movement neural and mechanical functions is central for addressing one of the major challenges in neurorehabilitation: personalizing current technologies and interventions to an individual's anatomy and impairment.

Optimizing the Distribution of Leg Muscles for Vertical Jumping

A goal of biomechanics and motor control is to understand the design of the human musculoskeletal system. Here we investigated human functional morphology by making predictions about the muscle volume distribution that is optimal for a specific motor task. We examined a well-studied and relatively simple human movement, vertical jumping. We investigated how high a human could jump if muscle volume were optimized for jumping, and determined how the optimal parameters improve performance. We used a four-link inverted pendulum model of human vertical jumping actuated by Hill-type muscles, that well-approximates skilled human performance. We optimized muscle volume by allowing the cross-sectional area and muscle fiber optimum length to be changed for each muscle, while maintaining constant total muscle volume. We observed, perhaps surprisingly, that the reference model, based on human anthropometric data, is relatively good for vertical jumping; it achieves 90% of the jump height predicted by a model with muscles designed specifically for jumping. Alteration of cross-sectional areas-which determine the maximum force deliverable by the muscles-constitutes the majority of improvement to jump height. The optimal distribution results in large vastus, gastrocnemius and hamstrings muscles that deliver more work, while producing a kinematic pattern essentially identical to the reference model. Work output is increased by removing muscle from rectus femoris, which cannot do work on the skeleton given its moment arm at the hip and the joint excursions during push-off. The gluteus composes a disproportionate amount of muscle volume and jump height is improved by moving it to other muscles. This approach represents a way to test hypotheses about optimal human functional morphology. Future studies may extend this approach to address other morphological questions in ethological tasks such as locomotion, and feature other sets of parameters such as properties of the skeletal segments.

Direct Methods for Predicting Movement Biomechanics Based Upon Optimal Control Theory with Implementation in OpenSim

The aim of this study was to compare the computational performances of two direct methods for solving large-scale, nonlinear, optimal control problems in human movement. Direct shooting and direct collocation were implemented on an 8-segment, 48-muscle model of the body (24 muscles on each side) to compute the optimal control solution for maximum-height jumping. Both algorithms were executed on a freely-available musculoskeletal modeling platform called OpenSim. Direct collocation converged to essentially the same optimal solution up to 249 times faster than direct shooting when the same initial guess was assumed (3.4 h of CPU time for direct collocation vs. 35.3 days for direct shooting). The model predictions were in good agreement with the time histories of joint angles, ground reaction forces and muscle activation patterns measured for subjects jumping to their maximum achievable heights. Both methods converged to essentially the same solution when started from the same initial guess, but computation time was sensitive to the initial guess assumed. Direct collocation demonstrates exceptional computational performance and is well suited to performing predictive simulations of movement using large-scale musculoskeletal models.

A predictive model of muscle excitations based on muscle modularity for a large repertoire of human locomotion conditions

Humans can efficiently walk across a large variety of terrains and locomotion conditions with little or no mental effort. It has been hypothesized that the nervous system simplifies neuromuscular control by using muscle synergies, thus organizing multi-muscle activity into a small number of coordinative co-activation modules. In the present study we investigated how muscle modularity is structured across a large repertoire of locomotion conditions including five different speeds and five different ground elevations. For this we have used the non-negative matrix factorization technique in order to explain EMG experimental data with a low-dimensional set of four motor components. In this context each motor components is composed of a non-negative factor and the associated muscle weightings. Furthermore, we have investigated if the proposed descriptive analysis of muscle modularity could be translated into a predictive model that could: (1) Estimate how motor components modulate across locomotion speeds and ground elevations. This implies not only estimating the non-negative factors temporal characteristics, but also the associated muscle weighting variations. (2) Estimate how the resulting muscle excitations modulate across novel locomotion conditions and subjects. The results showed three major distinctive features of muscle modularity: (1) the number of motor components was preserved across all locomotion conditions, (2) the non-negative factors were consistent in shape and timing across all locomotion conditions, and (3) the muscle weightings were modulated as distinctive functions of locomotion speed and ground elevation. Results also showed that the developed predictive model was able to reproduce well the muscle modularity of un-modeled data, i.e., novel subjects and conditions. Muscle weightings were reconstructed with a cross-correlation factor greater than 70% and a root mean square error less than 0.10. Furthermore, the generated muscle excitations matched well the experimental excitation with a cross-correlation factor greater than 85% and a root mean square error less than 0.09. The ability of synthetizing the neuromuscular mechanisms underlying human locomotion across a variety of locomotion conditions will enable solutions in the field of neurorehabilitation technologies and control of bipedal artificial systems. Open-access of the model implementation is provided for further analysis at https://simtk.org/home/p-mep/.

Is my model good enough? Best practices for verification and validation of musculoskeletal models and simulations of movement

Computational modeling and simulation of neuromusculoskeletal (NMS) systems enables researchers and clinicians to study the complex dynamics underlying human and animal movement. NMS models use equations derived from physical laws and biology to help solve challenging real-world problems, from designing prosthetics that maximize running speed to developing exoskeletal devices that enable walking after a stroke. NMS modeling and simulation has proliferated in the biomechanics research community over the past 25 years, but the lack of verification and validation standards remains a major barrier to wider adoption and impact. The goal of this paper is to establish practical guidelines for verification and validation of NMS models and simulations that researchers, clinicians, reviewers, and others can adopt to evaluate the accuracy and credibility of modeling studies. In particular, we review a general process for verification and validation applied to NMS models and simulations, including careful formulation of a research question and methods, traditional verification and validation steps, and documentation and sharing of results for use and testing by other researchers. Modeling the NMS system and simulating its motion involves methods to represent neural control, musculoskeletal geometry, muscle-tendon dynamics, contact forces, and multibody dynamics. For each of these components, we review modeling choices and software verification guidelines; discuss variability, errors, uncertainty, and sensitivity relationships; and provide recommendations for verification and validation by comparing experimental data and testing robustness. We present a series of case studies to illustrate key principles. In closing, we discuss challenges the community must overcome to ensure that modeling and simulation are successfully used to solve the broad spectrum of problems that limit human mobility.

Musculoskeletal shoulder models: A technical review and proposals for research foci

Musculoskeletal shoulder models allow non-invasive prediction of parameters that cannot be measured, particularly the loading applied to morphological structures and neurological control. This insight improves treatment and avoidance of pathology and performance evaluation and optimisation. A lack of appropriate validation and knowledge of model parameters’ accuracy may cause reduced clinical success for these models. Instrumented implants have recently been used to validate musculoskeletal models, adding important information to the literature. This development along with increasing prevalence of shoulder models necessitates a fresh review of available models and their utility. The practical uses of models are described. Accuracy of model inputs, modelling techniques and model sensitivity is the main technical review undertaken. Collection and comparison of these parameters are vital to understanding disagreement between model outputs. Trends in shoulder modelling are highlighted: validation through instrumented prostheses, increasing openness and strictly constrained, optimised, measured kinematics. Future directions are recommended: validation through focus on model sub-sections, increased subject specificity with imaging techniques determining muscle and body segment parameters and through different scaling and kinematics optimisation approaches.

An improved inverse dynamics formulation for estimation of external and internal loads during human sagittal plane movements

Planar musculoskeletal models are common in the inverse dynamics analysis of human movements such as walking, running and jumping. The continued interest in such models is justified by their simplicity and computational efficiency. Related to a human planar model, a unified formulation for both the flying and support phases of the sagittal plane movements is developed. The actuation involves muscle forces in the lower limbs and the resultant muscle torques in the other body joints. The dynamic equations, introduced in absolute coordinates of the segments, are converted into useful compact forms using the projective technique. The solution to a determinate inverse dynamics problem allows for the explicit determination of the external reactions (presumed to vanish during the flying phases) and the resultant muscle torques in all the model joints. The indeterminate inverse dynamics problem is then focused on the assessment of muscle forces and joint reaction forces selectively in the supporting lower limb. Numerical results of the inverse dynamics simulation of sample sagittal plane movements are reported to illustrate the validity and effectiveness of the improved formulation.

A rolling constraint reproduces ground reaction forces and moments in dynamic simulations of walking, running, and crouch gait

Recent advances in computational technology have dramatically increased the use of muscle-driven simulation to study accelerations produced by muscles during gait. Accelerations computed from muscle-driven simulations are sensitive to the model used to represent contact between the foot and ground. A foot-ground contact model must be able to calculate ground reaction forces and moments that are consistent with experimentally measured ground reaction forces and moments. We show here that a rolling constraint can model foot-ground contact and reproduce measured ground reaction forces and moments in an induced acceleration analysis of muscle-driven simulations of walking, running, and crouch gait. We also illustrate that a point constraint and a weld constraint used to model foot-ground contact in previous studies produce inaccurate reaction moments and lead to contradictory interpretations of muscle function. To enable others to use and test these different constraint types (i.e., rolling, point, and weld constraints) we have included them as part of an induced acceleration analysis in OpenSim, a freely-available biomechanics simulation package.

Ultrasound-based subject-specific parameters improve fascicle behaviour estimation in Hill-type muscle model

The estimation of muscle fascicle behaviour is decisive in a Hill-type model as they are related to muscle force by the force-length-velocity relationship and the tendon force-strain relationship. This study was aimed at investigating the influence of subject-specific tendon force-strain relationship and initial fascicle geometry (IFG) on the estimation of muscle forces and fascicle behaviour during isometric contractions. Ultrasonography was used to estimate the in vivo muscle fascicle behaviour and compare the muscle fascicle length and pennation angle estimated from the Hill-type model. The calibration-prediction process of the electromyography-driven model was performed using generic or subject-specific tendon definition with or without IFG as constraint. The combination of subject-specific tendon definition and IFG led to muscle fascicle behaviour closer to ultrasound data and significant lower forces of the ankle dorsiflexor and plantarflexor muscles compared to the other conditions. Thus, subject-specific ultrasound measurements improve the accuracy of Hill-type models on muscle fascicle behaviour.

Adjusting kinematics and kinetics in a feedback-controlled toe walking model

BACKGROUND

In clinical gait assessment, the correct interpretation of gait kinematics and kinetics has a decisive impact on the success of the therapeutic programme. Due to the vast amount of information from which primary anomalies should be identified and separated from secondary compensatory changes, as well as the biomechanical complexity and redundancy of the human locomotion system, this task is considerably challenging and requires the attention of an experienced interdisciplinary team of experts. The ongoing research in the field of biomechanics suggests that mathematical modeling may facilitate this task. This paper explores the possibility of generating a family of toe walking gait patterns by systematically changing selected parameters of a feedback-controlled model.

METHODS

From the selected clinical case of toe walking we identified typical toe walking characteristics and encoded them as a set of gait-oriented control objectives to be achieved in a feedback-controlled walking model. They were defined as fourth order polynomials and imposed via feedback control at the within-step control level. At the between-step control level, stance leg lengthening velocity at the end of the single support phase was adaptively adjusted after each step so as to facilitate gait velocity control. Each time the gait velocity settled at the desired value, selected intra-step gait characteristics were modified by adjusting the polynomials so as to mimic the effect of a typical therapeutical intervention - inhibitory casting.

RESULTS

By systematically adjusting the set of control parameters we were able to generate a family of gait kinematic and kinetic patterns that exhibit similar principal toe walking characteristics, as they were recorded by means of an instrumented gait analysis system in the selected clinical case of toe walking. We further acknowledge that they to some extent follow similar improvement tendencies as those which one can identify in gait kinematics and kinetics in the selected clinical case after inhibitory casting.

CONCLUSIONS

The proposed walking model that is based on a two-level control strategy has the ability to generate different gait kinematics and kinetics when the set of control parameters that define walking premises change. Such a framework does not have only educational value, but may also prove to have practical implications in pathological gait diagnostics and treatment.

Muscular strategy shift in human running: dependence of running speed on hip and ankle muscle performance

Humans run faster by increasing a combination of stride length and stride frequency. In slow and medium-paced running, stride length is increased by exerting larger support forces during ground contact, whereas in fast running and sprinting, stride frequency is increased by swinging the legs more rapidly through the air. Many studies have investigated the mechanics of human running, yet little is known about how the individual leg muscles accelerate the joints and centre of mass during this task. The aim of this study was to describe and explain the synergistic actions of the individual leg muscles over a wide range of running speeds, from slow running to maximal sprinting. Experimental gait data from nine subjects were combined with a detailed computer model of the musculoskeletal system to determine the forces developed by the leg muscles at different running speeds. For speeds up to 7 m s(-1), the ankle plantarflexors, soleus and gastrocnemius, contributed most significantly to vertical support forces and hence increases in stride length. At speeds greater than 7 m s(-1), these muscles shortened at relatively high velocities and had less time to generate the forces needed for support. Thus, above 7 m s(-1), the strategy used to increase running speed shifted to the goal of increasing stride frequency. The hip muscles, primarily the iliopsoas, gluteus maximus and hamstrings, achieved this goal by accelerating the hip and knee joints more vigorously during swing. These findings provide insight into the strategies used by the leg muscles to maximise running performance and have implications for the design of athletic training programs.

Comparison of different methods for estimating muscle forces in human movement

The aim of this study was to compare muscle-force estimates derived for human locomotion using three different methods commonly reported in the literature: static optimisation (SO), computed muscle control (CMC) and neuromusculoskeletal tracking (NMT). In contrast with SO, CMC and NMT calculate muscle forces dynamically by including muscle activation dynamics. Furthermore, NMT utilises a time-dependent performance criterion, wherein a single optimisation problem is solved over the entire time interval of the task. Each of these methods was used in conjunction with musculoskeletal modelling and experimental gait data to determine lower-limb muscle forces for self-selected speeds of walking and running. Correlation analyses were performed for each muscle to quantify differences between the various muscle-force solutions. The patterns of muscle loading predicted by the three methods were similar for both walking and running. The correlation coefficient between any two sets of muscle-force solutions ranged from 0.46 to 0.99 ( p < 0.001 for all muscles). These results suggest that the robustness and efficiency of static optimisation make it the most attractive method for estimating muscle forces in human locomotion.

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

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

OpenSim: a musculoskeletal modeling and simulation framework for in silico investigations and exchange

Movement science is driven by observation, but observation alone cannot elucidate principles of human and animal movement. Biomechanical modeling and computer simulation complement observations and inform experimental design. Biological models are complex and specialized software is required for building, validating, and studying them. Furthermore, common access is needed so that investigators can contribute models to a broader community and leverage past work. We are developing OpenSim, a freely available musculoskeletal modeling and simulation application and libraries specialized for these purposes, by providing: musculoskeletal modeling elements, such as biomechanical joints, muscle actuators, ligament forces, compliant contact, and controllers; and tools for fitting generic models to subject-specific data, performing inverse kinematics and forward dynamic simulations. OpenSim performs an array of physics-based analyses to delve into the behavior of musculoskeletal models by employing Simbody, an efficient and accurate multibody system dynamics code. Models are publicly available and are often reused for multiple investigations because they provide a rich set of behaviors that enables different lines of inquiry. This report will discuss one model developed to study walking and applied to gain deeper insights into muscle function in pathological gait and during running. We then illustrate how simulations can test fundamental hypotheses and focus the aims of in vivo experiments, with a postural stability platform and human model that provide a research environment for performing human posture experiments in silico. We encourage wide adoption of OpenSim for community exchange of biomechanical models and methods and welcome new contributors.

Reactive control and its operation limits in responding to a novel slip in gait

The purposes of this study were: (1) to examine the reactive control of the resultant joint moments at the lower limbs in response to a novel and unannounced slip; (2) to establish individualized forward-dynamics models; and (3) to explore personal potential by determining the operation limits of these moments at each lower limb joint, beyond which the resulting motion at this or other joints will exceed its/their normal range(s). Ten young subjects' kinematics and kinetics, collected during regular walking and during their first exposure to a novel and unannounced slip, were randomly selected from an existing database. An inverse-dynamics approach was applied to derive their (original) resultant joint moments, which were then used as input to establish forward-dynamics models, each including an individualized 16-element foot model to simulate ground reaction force. A simulated annealing (SA) algorithm was applied to modify the original moments, so that the subsequent output (baseline) moments can closely reproduce these subjects' recorded motion. A systematic alteration of the baseline moments was employed to determine the operation limits. The results revealed that the subjects reactively increased the hip extensor and knee flexor moments and reduced their ankle plantar flexor moments of their single-stance limb following slip onset. The "baseline" correction of the original moments can reach as much as 21% of the original moments. The analysis of the operation limits revealed that these individuals may be able to further increase their knee flexors more so than increase the hip extensors or reduce ankle plantar flexors before causing abnormal joint movement. Such systematic approach opens the possibility to properly assess an individual's rehabilitation potential, and to identify whether this person's strength is the limiting factor for stability training.

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

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

A clinically applicable model to estimate the opposing muscle groups contributions to isometric and dynamic tasks

This article presents an EMG-to-moment optimization model suitable for clinical studies to estimate the contribution of agonist and antagonist muscle groups to the net ankle joint moment during dynamic and isometric tasks. The proposed EMG-to-moment model took into account realistic muscle properties such as the electromechanical delay, and a force-length-velocity relationship with subject-specific muscle anthropometric data. Subjects performed isometric ankle plantar-flexion (fixed-end contraction) and dynamic tasks (heel-raise) in two positions, seated and upright. Two models were compared: the proposed EMG-to-moment model calibrated on eight dynamic and isometric tasks (Model 8-tasks) and on two dynamic tasks (Model 2-tasks), and a published reference model. First, each model was calibrated at the ankle joint on 10 subjects by adjusting individual set of parameters to estimate the muscle groups contributions. Then, the model was used to predict the ankle net joint moment. The model developed in this study showed good prediction. The Model 8-tasks predicted net joint moment with an average RMS error of 6.11 +/- 4.41 N m and a mean R (2) of 0.67 +/- 0.26 across dynamic and isometric tasks. The proposed EMG-to-moment model was simple and required few calibration tasks without oversimplifying muscle properties, satisfying requirements for clinical settings.

Optimal estimation of dynamically consistent kinematics and kinetics for forward dynamic simulation of gait

Forward dynamic simulation provides a powerful framework for characterizing internal loads and for predicting changes in movement due to injury, impairment or surgical intervention. However, the computational challenge of generating simulations has greatly limited the use and application of forward dynamic models for simulating human gait. In this study, we introduce an optimal estimation approach to efficiently solve for generalized accelerations that satisfy the overall equations of motion and best agree with measured kinematics and ground reaction forces. The estimated accelerations are numerically integrated to enforce dynamic consistency over time, resulting in a forward dynamic simulation. Numerical optimization is then used to determine a set of initial generalized coordinates and speeds that produce a simulation that is most consistent with the measured motion over a full cycle of gait. The proposed method was evaluated with synthetically created kinematics and force plate data in which both random noise and bias errors were introduced. We also applied the method to experimental gait data collected from five young healthy adults walking at a preferred speed. We show that the proposed residual elimination algorithm (REA) converges to an accurate solution, reduces the detrimental effects of kinematic measurement errors on joint moments, and eliminates the need for residual forces that arise in standard inverse dynamics. The greatest improvements in joint kinetics were observed proximally, with the algorithm reducing joint moment errors due to marker noise by over 20% at the hip and over 50% at the low back. Simulated joint angles were generally within 1 deg of recorded values when REA was used to generate a simulation from experimental gait data. REA can thus be used as a basis for generating accurate simulations of subject-specific gait dynamics.

Limitations of parallel global optimization for large-scale human movement problems

Global optimization algorithms (e.g., simulated annealing, genetic, and particle swarm) have been gaining popularity in biomechanics research, in part due to advances in parallel computing. To date, such algorithms have only been applied to small- or medium-scale optimization problems (<100 design variables). This study evaluates the applicability of a parallel particle swarm global optimization algorithm to large-scale human movement problems. The evaluation was performed using two large-scale (660 design variables) optimization problems that utilized a dynamic, 27 degree-of-freedom, full-body gait model to predict new gait motions from a nominal gait motion. Both cost functions minimized a quantity that reduced the external knee adduction torque. The first one minimized footpath errors corresponding to an increased toe out angle of 15 degrees, while the second one minimized the knee adduction torque directly without changing the footpath. Constraints on allowable changes in trunk orientation, joint angles, joint torques, centers of pressure, and ground reactions were handled using a penalty method. For both problems, a single run with a gradient-based nonlinear least squares algorithm found a significantly better solution than did 10 runs with the global particle swarm algorithm. Due to the penalty terms, the physically realistic gradient-based solutions were located within a narrow "channel" in design space that was difficult to enter without gradient information. Researchers should exercise caution when extrapolating the performance of parallel global optimizers to human movement problems with hundreds of design variables, especially when penalty terms are included in the cost function.

OpenSim: open-source software to create and analyze dynamic simulations of movement

Dynamic simulations of movement allow one to study neuromuscular coordination, analyze athletic performance, and estimate internal loading of the musculoskeletal system. Simulations can also be used to identify the sources of pathological movement and establish a scientific basis for treatment planning. We have developed a freely available, open-source software system (OpenSim) that lets users develop models of musculoskeletal structures and create dynamic simulations of a wide variety of movements. We are using this system to simulate the dynamics of individuals with pathological gait and to explore the biomechanical effects of treatments. OpenSim provides a platform on which the biomechanics community can build a library of simulations that can be exchanged, tested, analyzed, and improved through a multi-institutional collaboration. Developing software that enables a concerted effort from many investigators poses technical and sociological challenges. Meeting those challenges will accelerate the discovery of principles that govern movement control and improve treatments for individuals with movement pathologies.