Estimating kinematics from optical motion capture with skin-mounted markers, referred to as an inverse kinematic (IK) calculation, is the most common experimental technique in human motion analysis. Kinematics are often used to diagnose movement disorders and plan treatment strategies. In many such applications, small differences in joint angles can be clinically significant. Kinematics are also used to estimate joint powers, muscle forces, and other quantities of interest that cannot typically be measured directly. Thus, the accuracy and reproducibility of IK calculations are critical. In this work, we isolate and quantify the uncertainty in joint angles, moments, and powers due to two sources of error during IK analyses: errors in the placement of markers on the model (marker registration) and errors in the dimensions of the model’s body segments (model scaling). We demonstrate that IK solutions are best presented as a distribution of equally probable trajectories when these sources of modeling uncertainty are considered. Notably, a substantial amount of uncertainty exists in the computed kinematics and kinetics even if low marker tracking errors are achieved. For example, considering only 2 cm of marker registration uncertainty, peak ankle plantarflexion angle varied by 15.9°, peak ankle plantarflexion moment varied by 26.6 N⋅m, and peak ankle power at push off varied by 75.9 W during healthy gait. This uncertainty can directly impact the classification of patient movements and the evaluation of training or device effectiveness, such as calculations of push-off power. We provide scripts in OpenSim so that others can reproduce our results and quantify the effect of modeling uncertainty in their own studies.

Accurate computation of joint angles from optical marker data using inverse kinematics methods requires that the locations of markers on a model match the locations of experimental markers on participants. Marker registration is the process of positioning the model markers so that they match the locations of the experimental markers. Markers are typically registered using a graphical user interface (GUI), but this method is subjective and may introduce errors and uncertainty to the calculated joint angles and moments. In this investigation, we use OpenSim to isolate and quantify marker registration–based error from other sources of error by analyzing the gait of a bipedal humanoid robot for which segment geometry, mass properties, and joint angles are known. We then propose a marker registration method that is informed by the orientation of anatomical reference frames derived from surface-mounted optical markers as an alternative to user registration using a GUI. The proposed orientation registration method reduced the average root-mean-square error in both joint angles and joint moments by 67% compared to the user registration method, and eliminated variability among users. Our results show that a systematic method for marker registration that reduces subjective user input can make marker registration more accurate and repeatable.

Movement is fundamental to human and animal life, emerging through interaction of complex neural, muscular, and skeletal systems. Study of movement draws from and contributes to diverse fields, including biology, neuroscience, mechanics, and robotics. OpenSim unites methods from these fields to create fast and accurate simulations of movement, enabling two fundamental tasks. First, the software can calculate variables that are difficult to measure experimentally, such as the forces generated by muscles and the stretch and recoil of tendons during movement. Second, OpenSim can predict novel movements from models of motor control, such as kinematic adaptations of human gait during loaded or inclined walking. Changes in musculoskeletal dynamics following surgery or due to human–device interaction can also be simulated; these simulations have played a vital role in several applications, including the design of implantable mechanical devices to improve human grasping in individuals with paralysis. OpenSim is an extensible and user-friendly software package built on decades of knowledge about computational modeling and simulation of biomechanical systems. OpenSim’s design enables computational scientists to create new state-of-the-art software tools and empowers others to use these tools in research and clinical applications. OpenSim supports a large and growing community of biomechanics and rehabilitation researchers, facilitating exchange of models and simulations for reproducing and extending discoveries. Examples, tutorials, documentation, and an active user forum support this community. The OpenSim software is covered by the Apache License 2.0, which permits its use for any purpose including both nonprofit and commercial applications. The source code is freely and anonymously accessible on GitHub, where the community is welcomed to make contributions. Platform-specific installers of OpenSim include a GUI and are available on simtk.org.

Tools have been used for millions of years to augment the capabilities of the human body, allowing us to accomplish tasks that would otherwise be difficult or impossible. Powered exoskeletons and other assistive devices are sophisticated modern tools that have restored bipedal locomotion in individuals with paraplegia and have endowed unimpaired individuals with superhuman strength. Despite these successes, designing assistive devices that reduce energy consumption during running remains a substantial challenge, in part because these devices disrupt the dynamics of a complex, finely tuned biological system. Furthermore, designers have hitherto relied primarily on experiments, which cannot report muscle-level energy consumption and are fraught with practical challenges. In this study, we use OpenSim to generate muscle-driven simulations of 10 human subjects running at 2 and 5 m/s. We then add ideal, massless assistive devices to our simulations and examine the predicted changes in muscle recruitment patterns and metabolic power consumption. Our simulations suggest that an assistive device should not necessarily apply the net joint moment generated by muscles during unassisted running, and an assistive device can reduce the activity of muscles that do not cross the assisted joint. Our results corroborate and suggest biomechanical explanations for similar effects observed by experimentalists, and can be used to form hypotheses for future experimental studies. The models, simulations, and software used in this study are freely available at simtk.org and can provide insight into assistive device design that complements experimental approaches.

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.

Muscle-driven simulations of human and animal motion are widely used to complement physical experiments for studying movement dynamics. Musculotendon models are an essential component of muscle-driven simulations, yet neither the computational speed nor the biological accuracy of the simulated forces has been adequately evaluated. Here we compare the speed and accuracy of three musculotendon models: two with an elastic tendon (an equilibrium model and a damped equilibrium model) and one with a rigid tendon. Our simulation benchmarks demonstrate that the equilibrium and damped equilibrium models produce similar force profiles but have different computational speeds. At low activation, the damped equilibrium model is 29 times faster than the equilibrium model when using an explicit integrator and 3 times faster when using an implicit integrator; at high activation, the two models have similar simulation speeds. In the special case of simulating a muscle with a short tendon, the rigid-tendon model produces forces that match those generated by the elastic-tendon models, but simulates 2-54 times faster when an explicit integrator is used and 6-31 times faster when an implicit integrator is used. The equilibrium, damped equilibrium, and rigid-tendon models reproduce forces generated by maximally-activated biological muscle with mean absolute errors less than 8.9%, 8.9%, and 20.9% of the maximum isometric muscle force, respectively. When compared to forces generated by submaximally-activated biological muscle, the forces produced by the equilibrium, damped equilibrium, and rigid-tendon models have mean absolute errors less than 16.2%, 16.4%, and 18.5%, respectively. To encourage further development of musculotendon models, we provide implementations of each of these models in OpenSim version 3.1 and benchmark data online, enabling others to reproduce our results and test their models of musculotendon dynamics.