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.

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...

The arrangement and physiology of muscle fibres can strongly influence musculoskeletal function and whole-organismal performance. However, experimental investigation of muscle function during in vivo activity is typically limited to relatively few muscles in a given system. Computational models and simulations of the musculoskeletal system can partly overcome these limitations, by exploring the dynamics of muscles, tendons and other tissues in a robust and quantitative fashion. Here, a high-fidelity, 26-degree-of-freedom musculoskeletal model was developed of the hindlimb of a small ground bird, the elegant-crested tinamou (Eudromia elegans, ~550 g), including all the major muscles of the limb (36 actuators per leg). The model was integrated with biplanar fluoroscopy (XROMM) and forceplate data for walking and running, where dynamic optimization was used to estimate muscle excitations and fibre length changes throughout both gaits. Following this, a series of static simulations over the total range of physiological limb postures were performed, to circumscribe the bounds of possible variation in fibre length. During gait, fibre lengths for all muscles remained between 0.5 to 1.21 times optimal fibre length, but operated mostly on the ascending limb and plateau of the active force-length curve, a result that parallels previous experimental findings for birds, humans and other species. However, the ranges of fibre length varied considerably among individual muscles, especially when considered across the total possible range of joint excursion. Net length change of muscle–tendon units was mostly less than optimal fibre length, sometimes markedly so, suggesting that approaches that use muscle–tendon length change to estimate optimal fibre length in extinct species are likely underestimating this important parameter for many muscles. The results of this study clarify and broaden understanding of muscle function in extant animals, and can help refine approaches used to study extinct species.

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.

Knowledge of human-exoskeleton interaction 1 forces is crucial to assess user comfort and effectiveness 2 of the interaction. The subject-exoskeleton collaborative 3 movement and its interaction forces can be predicted in 4 silico using computational modeling techniques. We devel-5 oped an optimal control framework that consisted of three 6 phases. First, the foot-ground (Phase A) and the subject-7 exoskeleton (Phase B) contact models were calibrated 8 using three experimental sit-to-stand trials. Then, the collab-9 orative movement and the subject-exoskeleton interaction 10 forces, of six different sit-to-stand trials were predicted 11 (Phase C). The results show that the contact models were 12 able to reproduce experimental kinematics of calibration 13 trials (mean root mean square differences (RMSD) coor-14 dinates ≤ 1.1°and velocities ≤ 6.8°/s), ground reaction 15 forces (mean RMSD≤ 22.9 N), as well as the interaction 16 forces at the pelvis, thigh, and shank (mean RMSD ≤ 5.4 N). 17 Phase C could predict the collaborative movements of pre-18 diction trials (mean RMSD coordinates ≤ 3.5°and veloc-19 ities ≤ 15.0°/s), and their subject-exoskeleton interaction 20 forces (mean RMSD ≤ 13.1 N). In conclusion, this optimal 21 control framework could be used while designing exoskele-22 tons to have in silico knowledge of new optimal movements 23 and their interaction forces.

Locomotion results from complex interactions between the central nervous system and the musculoskeletal system with its many degrees of freedom and muscles. Gaining insight into how the properties of each subsystem shape human gait is challenging as experimental methods to manipulate and assess isolated subsystems are limited. Simulations that predict movement patterns based on a mathematical model of the neuro-musculoskeletal system without relying on experimental data can reveal principles of locomotion by elucidating cause–effect relationships. New computational approaches have enabled the use of such predictive simulations with complex neuro-musculoskeletal models. Here, we review recent advances in predictive simulations of human movement and how those simulations have been used to deepen our knowledge about the neuromechanics of gait. In addition, we give a perspective on challenges towards using predictive simulations to gain new fundamental insight into motor control of gait, and to help design personalized treatments in patients with neurological disorders and assistive devices that improve gait performance. Such applications will require more detailed neuro-musculoskeletal models and simulation approaches that take uncertainty into account, tools to efficiently personalize those models, and validation studies to demonstrate the ability of simulations to predict gait in novel circumstances.

Physics-based simulations of walking have the theoretical potential to support clinical decision-making by predicting the functional outcome of treatments in terms of walking performance. Yet before using such simulations in clinical practice, their ability to identify the main treatment targets in specific patients needs to be demonstrated. In this study, we generated predictive simulations of walking with a medical imaging based neuro-musculoskeletal model of a child with cerebral palsy presenting crouch gait. We explored the influence of altered muscle-tendon properties, reduced neuromuscular control complexity, and spasticity on gait dysfunction in terms of joint kinematics, kinetics, muscle activity, and metabolic cost of transport. We modeled altered muscle-tendon properties by personalizing Hill-type muscle-tendon parameters based on data collected during functional movements, simpler neuromuscular control by reducing the number of independent muscle synergies, and spasticity through delayed muscle activity feedback from muscle force and force rate. Our simulations revealed that, in the presence of aberrant musculoskeletal geometries, altered muscle-tendon properties rather than reduced neuromuscular control complexity and spasticity were the primary cause of the crouch gait pattern observed for this child, which is in agreement with the clinical examination. These results suggest that muscle-tendon properties should be the primary target of interventions aiming to restore an upright gait pattern for this child. This suggestion is in line with the gait analysis following muscle-tendon property and bone deformity corrections. Future work should extend this single case analysis to more patients in order to validate the ability of our physics-based simulations to capture the gait patterns of individual patients pre-and post-treatment. Such validation would open the door for identifying targeted treatment strategies with the aim of designing optimized interventions for neuro-musculoskeletal disorders.