Objective Musculoskeletal models provide a non-invasive means to study human movement and predict the effects of interventions on gait. Our goal was to create an open-source, three-dimensional musculoskeletal model with high-fidelity representations of the lower limb musculature of healthy young individuals that can be used to generate accurate simulations of gait. Methods Our model includes bony geometry for the full body, 37 degrees of freedom to define joint kinematics, Hill-type models of 80 muscle-tendon units actuating the lower limbs, and 17 ideal torque actuators driving the upper body. The model’s musculotendon parameters are derived from previous anatomical measurements of 21 cadaver specimens and magnetic resonance images of 24 young healthy subjects. We tested the model by evaluating its computational time and accuracy of simulations of healthy walking and running. Results Generating muscle-driven simulations of normal walking and running took approximately 10 minutes on a typical desktop computer. The differences between our muscle-generated and inverse dynamics joint moments were within 3% (RMSE) of the peak inverse dynamics joint moments in both walking and running, and our simulated muscle activity showed qualitative agreement with salient features from experimental electromyography data. Conclusion These results suggest that our model is suitable for generating muscle-driven simulations of healthy gait. We encourage other researchers to further validate and apply the model to study other motions of the lower-extremity. Significance The model is implemented in the open source software platform OpenSim. The model and data used to create and test the simulations are freely available at https://simtk.org/home/full_body/, allowing others to reproduce these results and create their own simulations.

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.

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

Wearable robotic devices can restore and enhance mobility. There is growing interest in designing devices that reduce the metabolic cost of walking; however, designers lack guidelines for which joints to assist and when to provide the assistance. To help address this problem, we used musculoskeletal simulation to predict how hypothetical devices affect muscle activity and metabolic cost when walking with heavy loads. We explored 7 massless devices, each providing unrestricted torque at one degree of freedom in one direction (hip abduction, hip flexion, hip extension, knee flexion, knee extension, ankle plantarflexion, or ankle dorsiflexion). We used the Computed Muscle Control algorithm in OpenSim to find device torque profiles that minimized the sum of squared muscle activations while tracking measured kinematics of loaded walking without assistance. We then examined the metabolic savings provided by each device, the corresponding device torque profiles, and the resulting changes in muscle activity. We found that the hip flexion, knee flexion, and hip abduction devices provided greater metabolic savings than the ankle plantarflexion device. The hip abduction device had the greatest ratio of metabolic savings to peak instantaneous positive device power, suggesting that frontal-plane hip assistance may be an efficient way to reduce metabolic cost. Overall, the device torque profiles generally differed from the corresponding net joint moment generated by muscles without assistance, and occasionally exceeded the net joint moment to reduce muscle activity at other degrees of freedom. Many devices affected the activity of muscles elsewhere in the limb; for example, the hip flexion device affected muscles that span the ankle joint. Our results may help experimentalists decide which joint motions to target when building devices and can provide intuition for how devices may interact with the musculoskeletal system. The simulations are freely available online, allowing others to reproduce and extend our work.

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.

Muscles attach to bones via tendons that stretch and recoil, affecting muscle force generation and metabolic energy consumption. In this study, we investigated the effect of tendon compliance on the metabolic cost of running using a full-body musculoskeletal model with a detailed model of muscle energetics. We performed muscle-driven simulations of running at 2–5 m/s with tendon force–strain curves that produced between 1 and 10% strain when the muscles were developing maximum isometric force. We computed the average metabolic power consumed by each muscle when running at each speed and with each tendon compliance. Average whole-body metabolic power consumption increased as running speed increased, regardless of tendon compliance, and was lowest at each speed when tendon strain reached 2–3% as muscles were developing maximum isometric force. When running at 2 m/s, the soleus muscle consumed less metabolic power at high tendon compliance because the strain of the tendon allowed the muscle fibers to operate nearly isometrically during stance. In contrast, the medial and lateral gastrocnemii consumed less metabolic power at low tendon compliance because less compliant tendons allowed the muscle fibers to operate closer to their optimal lengths during stance. The software and simulations used in this study are freely available at simtk.org and enable examination of muscle energetics with unprecedented detail.

The goal of this study was to gain insight into how ankle exoskeletons affect the behavior of the plantarflexor muscles during walking. Using data from previous experiments, we performed electromyographydriven simulations of musculoskeletal dynamics to explore how changes in exoskeleton assistance affected plantarflexor muscletendon mechanics, particularly for the soleus. We used a model of muscle energy consumption to estimate individual muscle metabolic rate. As average exoskeleton torque was increased, while no net exoskeleton work was provided, a reduction in tendon recoil led to an increase in positive mechanical work performed by the soleus muscle fibers. As net exoskeleton work was increased, both soleus muscle fiber force and positive mechanical work decreased. Trends in the sum of the metabolic rates of the simulated muscles correlated well with trends in experimentally observed whole-body metabolic rate (R 2 =0.9), providing confidence in our model estimates. Our simulation results suggest that different exoskeleton behaviors can alter the functioning of the muscles and tendons acting at the assisted joint. Furthermore, our results support the idea that the series tendon helps reduce positive work done by the muscle fibers by storing and returning energy elastically. We expect the results from this study to promote the use of electromyography-driven simulations to gain insight into the operation of muscle-tendon units and to guide the design and control of assistive devices.

Algorithmic differentiation (AD) is an alternative to finite differences (FD) for evaluating function derivatives. The primary aim of this study was to demonstrate the computational benefits of using AD instead of FD in OpenSim-based trajectory optimization of human movement. The secondary aim was to evaluate computational choices including different AD tools, different linear solvers, and the use of first-or second-order derivatives. First, we enabled the use of AD in OpenSim through a custom source code transformation tool and through the operator overloading tool ADOL-C. Second, we developed an interface between OpenSim and CasADi to solve trajectory optimization problems. Third, we evaluated computational choices through simulations of perturbed balance, two-dimensional predictive simulations of walking, and three-dimensional tracking simulations of walking. We performed all simulations using direct collocation and implicit differential equations. Using AD through our custom tool was between 1.8 ± 0.1 and 17.8 ± 4.9 times faster than using FD, and between 3.6 ± 0.3 and 12.3 ± 1.3 times faster than using AD through ADOL-C. The linear solver efficiency was problem-dependent and no solver was consistently more efficient. Using second-order derivatives was more efficient for balance simulations but less efficient for walking simulations. The walking simulations were physiologically realistic. These results highlight how the use of AD drastically decreases computational time of trajectory optimization problems as compared to more common FD. Overall, combining AD with direct collocation and implicit differential equations decreases the computational burden of trajectory optimization of human movement, which will facilitate their use for biomechanical applications requiring the use of detailed models of the musculoskeletal system. Algorithmic differentiation speeds up trajectory optimization of human movement PLOS ONE | https://doi.Fig 2.Flowchart depicting the optimal control framework. We developed two approaches (AD-ADOLC and AD-Recorder) to make an OpenSim function F and its forward (F fwd) and reverse (F rev) directional derivatives available within the CasADi environment for use by the NLP solver during the optimization. In the AD-ADOLC approach (top), ADOL-C's algorithms are used in a C++ code to provide F fwd and F rev. In the AD-Recorder approach (bottom), Recorder provides the expression graph of F as MATLAB source code from which CasADi's C-code generator generates C-code containing F, F fwd, and F rev. The AD-Recorder approach combines operator overloading, when generating the expression graph, and source code transformation, when processing the expression graph to generate C-code for F, F fwd, and F rev. In both approaches, the code comprising F, F fwd, and F rev is compiled as a Dynamic-link Library (DLL), which is imported as an external function within the CasADi environment. In our application, F represents the multi-body dynamics and is called when formulating the optimal control problem. The latte...