Musculoskeletal simulations are used in many different applications, ranging from the design of wearable robots that interact with humans to the analysis of patients with impaired movement. Here, we introduce OpenSim Moco, a software toolkit for optimizing the motion and control of musculoskeletal models built in the OpenSim modeling and simulation package. OpenSim Moco uses the direct collocation method, which is often faster and can handle more diverse problems than other methods for musculoskeletal simulation. Moco frees researchers from implementing direct collocation themselves—which typically requires extensive technical expertise—and allows them to focus on their scientific questions. The software can handle a wide range of problems that interest biomechanists, including motion tracking, motion prediction, parameter optimization, model fitting, electromyography-driven simulation, and device design. Moco is the first musculoskeletal direct collocation tool to handle kinematic constraints, which enable modeling of kinematic loops (e.g., cycling models) and complex anatomy (e.g., patellar motion). To show the abilities of Moco, we first solved for muscle activity that produced an observed walking motion while minimizing squared muscle excitations and knee joint loading. Next, we predicted how muscle weakness may cause deviations from a normal walking motion. Lastly, we predicted a squat-to-stand motion and optimized the stiffness of an assistive device placed at the knee. We designed Moco to be easy to use, customizable, and extensible, thereby accelerating the use of simulations to understand the movement of humans and other animals.

Musculoskeletal simulations of movement can provide insights needed to help humans regain mobility after injuries and design robots that interact with humans. Here, we introduce OpenSim Moco, a software toolkit for optimizing the motion and control of musculoskeletal models built in the OpenSim modeling and simulation package. Open-Sim Moco uses the direct collocation method, which is often faster and can handle more diverse problems than other methods for musculoskeletal simulation but requires extensive technical expertise to implement. Moco frees researchers from implementing direct collocation themselves, allowing them to focus on their scientific questions. The software can handle the wide range of problems that interest biomechanists, including motion tracking, motion prediction, parameter optimization, model fitting, electromyographydriven simulation, and device design. Moco is the first musculoskeletal direct collocation tool to handle kinematic constraints, which are common in musculoskeletal models. To show Moco's abilities, we first solve for muscle activity that produces an observed walking motion while minimizing muscle excitations and knee joint loading. Then, we predict a squat-to-stand motion and optimize the stiffness of a passive assistive knee device. We designed Moco to be easy to use, customizable, and extensible, thereby accelerating the use of simulations to understand human and animal movement.

Accurate prediction of muscle and joint contact forces during human movement could improve treatment planning for disorders such as osteoarthritis, stroke, Parkinson's disease, and cerebral palsy. Recent studies suggest that muscle synergies, a low-dimensional representation of a large set of muscle electromyographic (EMG) signals (henceforth called "muscle excitations"), may reduce the redundancy of muscle excitation solutions predicted by optimization methods. This study explores the feasibility of using muscle synergy information extracted from eight muscle EMG signals (henceforth called "included" muscle excitations) to accurately construct muscle excitations from up to 16 additional EMG signals (henceforth called "excluded" muscle excitations). Using treadmill walking data collected at multiple speeds from two subjects (one healthy, one poststroke), we performed muscle synergy analysis on all possible subsets of eight included muscle excitations and evaluated how well the calculated time-varying synergy excitations could construct the remaining excluded muscle excitations (henceforth called "synergy extrapolation"). We found that some, but not all, eight-muscle subsets yielded synergy excitations that achieved >90% extrapolation variance accounted for (VAF). Using the top 10% of subsets, we developed muscle selection heuristics to identify included muscle combinations whose synergy excitations achieved high extrapolation accuracy. For 3, 4, and 5 synergies, these heuristics yielded extrapolation VAF values approximately 5% lower than corresponding reconstruction VAF values for each associated eight-muscle subset. These results suggest that synergy excitations obtained from experimentally measured muscle excitations can accurately construct unmeasured muscle excitations, which could help limit muscle excitations predicted by muscle force optimizations.

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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.

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 inherently 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 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 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 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 a mapping 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.

Hemiparesis, defined as unilateral muscle weakness, often occurs in people post-stroke or people with cerebral palsy, however it is difficult to understand how this hemiparesis affects movement patterns as it often presents alongside a variety of other neuromuscular impairments. Predictive musculoskeletal modeling presents an opportunity to investigate how impairments affect gait performance assuming a particular cost function. Here, we use predictive simulation to quantify the spatiotemporal asymmetries and changes to metabolic cost that emerge when muscle strength is unilaterally reduced and how reducing spatiotemporal symmetry affects metabolic cost. We modified a 2-D musculoskeletal model by uniformly reducing the peak isometric muscle force unilaterally. We then solved optimal control simulations of walking across a range of speeds by minimizing the sum of the cubed muscle excitations. Lastly, we ran additional optimizations to test if reducing spatiotemporal asymmetry would result in an increase in metabolic cost. Our results showed that the magnitude and direction of effort-optimal spatiotemporal asymmetries depends on both the gait speed and level of weakness. Also, the optimal speed was 1.25 m/s for the symmetrical and 20% weakness models but slower (1.00 m/s) for the 40% and 60% weakness models, suggesting that hemiparesis can account for a portion of the slower gait speed seen in people with hemiparesis. Modifying the cost function to minimize spatiotemporal asymmetry resulted in small increases (~4%) in metabolic cost. Overall, our results indicate that spatiotemporal asymmetry may be optimal for people with hemiparesis. Additionally, the effect of speed and the level of weakness on spatiotemporal asymmetry may help explain the well-known heterogenous distribution of spatiotemporal asymmetries observed in the clinic. Future work could extend our results by testing the effects of other neuromuscular impairments on optimal gait strategies, and therefore build a more comprehensive understanding of the gait patterns observed in clinical populations.

Several neuromuscular impairments, such as weakness (hemiparesis), occur after an individual has a stroke, and these impairments primarily affect one side of the body more than the other. Predictive musculoskeletal modeling presents an opportunity to investigate how a specific impairment affects gait performance post-stroke. Therefore, our aim was to use to predictive simulation to quantify the spatiotemporal asymmetries and changes to metabolic cost that emerge when muscle strength is unilaterally reduced. We also determined how forced spatiotemporal symmetry affects metabolic cost. We modified a 2-D musculoskeletal model by uniformly reducing the peak isometric muscle force in all muscles unilaterally. We then solved optimal control simulations of walking across a range of speeds by minimizing the sum of the cubed muscle excitations across all muscles. Lastly, we ran additional optimizations to test if reducing spatiotemporal asymmetry would result in an increase in metabolic cost. Our results showed that the magnitude and direction of effort-optimal spatiotemporal asymmetries depends on both the gait speed and level of weakness. Also, the optimal metabolic cost of transport was 1.25 m/s for the symmetrical and 20% weakness models but slower (1.00 m/s) for the 40% and 60% weakness models, suggesting that hemiparesis can account for a portion of the slower gait speed seen in people post-stroke. Adding spatiotemporal asymmetry to the cost function resulted in small increases (~4%) in metabolic cost. Overall, our results indicate that spatiotemporal asymmetry may be optimal for people post-stroke, who have asymmetrical neuromuscular impairments. Additionally, the effect of speed and level of weakness on spatiotemporal asymmetry may explain the well-known heterogenous distribution of spatiotemporal asymmetries observed in the clinic. Future work could extend our results by testing the effects of other impairments on optimal gait strategies, and therefore build a more comprehensive understanding of the gait patterns in people post-stroke.