Muscle-driven simulations have been widely adopted to study muscle-tendon behavior; several generic musculoskeletal models have been developed, and their biofidelity improved based on available experimental data and computational feasibility. It is, however, not clear which, if any, of these models accurately estimate muscle-tendon dynamics over a range of walking speeds. In addition, the interaction between model selection, performance criteria to solve muscle redundancy, and approaches for scaling muscle-tendon properties remain unclear. This study aims to compare estimated muscle excitations and muscle fiber lengths, qualitatively and quantitatively, from several model combinations to experimental observations. We tested three generic models proposed by Hamner et al., Rajagopal et al., and Lai-Arnold et al. in combination with performance criteria based on minimization of muscle effort to the power of 2, 3, 5, and 10, and four approaches to scale the muscle-tendon unit properties of maximum isometric force, optimal fiber length, and tendon slack length. We collected motion analysis and electromyography data in eight able-bodied subjects walking at seven speeds and compared agreement between estimated/modelled muscle excitations and observed muscle excitations from electromyography and computed normalized fiber lengths to values reported in the literature. We found that best agreement in on/off timing in vastus lateralis, vastus medialis, tibialis anterior, gastrocnemius lateralis, gastrocnemius medialis, and soleus was estimated with minimum squared muscle effort than to higher exponents, regardless of model and scaling approach. Also, minimum squared or cubed muscle effort with only a subset of muscle-tendon unit scaling approaches produced the best time-series agreement and best estimates of the increment of muscle excitation magnitude across walking speeds. There were discrepancies in estimated fiber lengths and muscle excitations among the models, with the largest discrepancy in the Hamner et al. model. The model proposed by Lai-Arnold et al. best estimated muscle excitation estimates overall, but failed to estimate realistic muscle fiber lengths, which were better estimated with the model proposed by Rajagopal et al. No single model combination estimated the most accurate muscle excitations for all muscles; commonly observed disagreements include onset delay, underestimated co-activation, and failure to estimate muscle excitation increments across walking speeds.

The metabolic energy rate of individual muscles is impossible to measure without invasive procedures. Priorstudies have produced models to predict metabolic rates based on experimental observations of isolated musclecontraction from various species. Such models can provide reliable predictions of metabolic rates in humans ifmuscle properties and control are accurately modelled. This study aimed to examine how muscle-tendon modelcalibration and metabolic energy models influenced estimation of muscle-tendon states and time-seriesmetabolic rates, to evaluate the agreement with empirical data, and to provide predictions of the metabolic rateof muscle groups and gait phases across walking speeds. Three-dimensional musculoskeletal simulations withprescribed kinematics and dynamics were performed. An optimal control formulation was used to computemuscle-tendon states with four levels of individualization, ranging from a scaled generic model and musclecontrols based on minimal activations, to calibration of passive muscle forces, personalization of Achilles andquadriceps tendon stiffnesses, to finally informing muscle controls with electromyography. We computedmetabolic rates based on existing models. Simulations with calibrated passive forces and personalized tendonstiffness most accurately estimate muscle excitations and fiber lengths. Interestingly, the inclusion ofelectromyography did not improve our estimates. The whole-body average metabolic cost was better estimatedusing Bhargava et al. 2004 and Umberger 2010 models. We estimated metabolic rate peaks near early stance,pre-swing, and initial swing at all walking speeds. Plantarflexors accounted for the highest cost among musclegroups at the preferred speed and was similar to the cost of hip adductors and abductors combined. Also, theswing phase accounted for slightly more than one-quarter of the total cost in a gait cycle, and its relative costdecreased with walking speed. Our prediction might inform the design of assistive devices and rehabilitationtreatment. The code and experimental data are available online.

Musculoskeletal simulations can provide insights into the roles of muscles and tendons during motion. Accuratedescriptions of musculoskeletal parameters increase our confidence in the estimations of dynamics andenergetics of muscles, tendons, and joints. In this study, we present a computational tool to tune muscle-tendonparameters based on prior experimental observations in literature and evaluate their influence on estimatedmuscle excitations. From a scaled generic musculoskeletal model, we tuned optimal fiber length, tendon slacklength, and tendon stiffness to match reported digitalized images from ultrasound, and muscle passive curvesto match reported in vivo experimental angle-moment relationship. Our proposed workflow improved theestimation of muscle fiber lengths in the ankle plantarflexors compared to linearly scaling optimal fiber lengthsand tendon slack lengths. Also, with tuned muscle-tendon parameters, estimated the on/off timing of nearly allmuscles’ excitations in the model compared to reported values in literature. Our workflow customizes muscletendonparameters easily and quickly. The computational toolbox is freely available online.Keywords

Recent years have witnessed break throughs in assistive exoskeletons; both passive and active devices have reduced metabolic costs near preferred walking speed by assisting muscle actions. Metabolic reductions at multiple speeds should thus also be attainable. Musculo skeletal simulation can potentially predict the interaction between assistive moments, muscle-tendon mechanics, and walking energetics. In this study, we simulated devices’ optimal assistive moments based on minimal muscle activations during walking with prescribed kinematics and dynamics. We used a generic musculo  skeletal model with calibrated muscle-tendon parameters and computed metabolic rates from muscle actions. We then simulated walking across multiple speeds and with two ideal actuation modes – motor-based and spring-based – to assist ankle plantar flexion,knee extension, hip flexion, and hip abduction and compared computed metabolic rates. We found that both actuation modes considerably reduced physiological joint moments but did not always reduce metabolic rates. Compared to unassisted conditions, motor-based ankle plantar flexion and hip flexion assistance reduced metabolic rates, and this effect was more pronounced as walking speed increased. Spring-based hip flexion and abduction assistance increased metabolic rates at some walking speeds despite a moderate decrease in some muscle activations. Both modes of knee extension assistance reduced metabolic rates to a small extent, eventhough the actuation contributed with practically the entire net knee extension moment during stance. Motorbased hip abduction assistance reduced metabolic rates more than spring-based assistance, though this reduction was relatively small. Future work should experimentally validate the effects of assistive moments andrefine modeling assumptions accordingly. Our computational workflow is freely available online.