Physics-based simulation generate movement patterns based on a neuro-musculoskeletal model without relying on experimental movement data, offering a powerful approach to study how neuro-musculoskeletal properties shape locomotion. Yet, simulated gait patterns and metabolic powers do not always agree with experiments, pointing to modeling errors reflecting gaps in our understanding. Here, we systematically evaluated the predictive capability of simulations based on a 3D musculoskeletal model to predict gait mechanics, muscle activity, and metabolic power across gait conditions. We simulated the effect of adding mass to body segments, variations in walking speed, inclined walking, and crouched walking. We chose tasks that are relatively straightforward to model to limit the contribution of errors in modeling the task to prediction errors. The simulations predicted stride frequency and walking kinematics with reasonable accuracy but underestimated variation in metabolic power across conditions. In particular, simulations underestimated changes in metabolic power with respect to level walking in tasks requiring substantial positive mechanical work, such as incline walking (27% underestimation). We identified two possible errors in simulated metabolic power. First, the phenomenological metabolic power model produced high maximal mechanical efficiency (average 0.58) during concentric contractions, compared to the observed 0.2-0.3 in laboratory experiments. Second, when we multiplied the mechanical work with more realistic estimates of mechanical efficiency (i.e., 0.25), simulations overestimated the metabolic power by 84%. This suggests that positive work by muscle fibers was overestimated in the simulations. This overestimation may be caused by several assumptions and errors in (the parameters of) the musculoskeletal model including its interaction with the environment or in the cost function. This study highlights the need for more accurate models of musculoskeletal mechanics, energetics, passive elastic structures, and neural control (e.g., optimality criteria) to improve the realism of human movement simulations. Validating simulations across a broad range of conditions is important to pinpoint shortcomings in model-based simulations.

The unique structure of the human foot is seen as a crucial adaptation for bipedalism. The foot's arched shape enables stiffening the foot to withstand high loads when pushing off, without compromising foot flexibility. Experimental studies demonstrated that manipulating foot stiffness has considerable effects on gait. In clinical practice, altered foot structure is associated with pathological gait. Yet, experimentally manipulating individual foot properties (e.g. arch height or tendon and ligament stiffness) is hard and therefore our understanding of how foot structure influences gait mechanics is still limited. Predictive simulations are a powerful tool to explore causal relationships between musculoskeletal properties and whole-body gait. However, musculoskeletal models used in three-dimensional predictive simulations assume a rigid foot arch, limiting their use for studying how foot structure influences three-dimensional gait mechanics. Here, we developed a four-segment foot model with a longitudinal arch for use in predictive simulations. We identified three properties of the ankle-foot complex that are important to capture ankle and knee kinematics, soleus activation, and ankle power of healthy adults: (1) compliant Achilles tendon, (2) stiff heel pad, (3) the ability to stiffen the foot. The latter requires sufficient arch height and contributions of plantar fascia, and intrinsic and extrinsic foot muscles. A reduced ability to stiffen the foot results in walking patterns with reduced push-off power. Simulations based on our model also captured the effects of walking with anaesthetised intrinsic foot muscles or an insole limiting arch compression. The ability to reproduce these different experiments indicates that our foot model captures the main mechanical properties of the foot. The presented four-segment foot model is a potentially powerful tool to study the relationship between foot properties and gait mechanics and energetics in health and disease.

Recent years have witnessed breakthroughs 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. Musculoskeletal 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 musculoskeletal model with tuned 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 plantarflexion, 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 plantarflexion 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, even though the actuation contributed with practically the entire net knee extension moment during stance. Motor-based hip abduction assistance reduced metabolic rates more than spring-based assistance, though this reduction was relatively small. Our study also suggests that an assistive strategy based on minimal muscle activations might result in a suboptimal reduction of metabolic rates. Future work should experimentally validate the effects of assistive moments and refine modeling assumptions accordingly. Our computational workflow is freely available online.

The metabolic energy rate of individual muscles is impossible to measure without invasive procedures. Prior studies have produced models to predict metabolic rates based on experimental observations of isolated muscle contraction from various species. Such models can provide reliable predictions of metabolic rates in humans if muscle properties and control are accurately modeled. This study aimed to examine how muscle-tendon model individualization and metabolic energy models influenced estimation of muscle-tendon states and time-series metabolic rates, to evaluate the agreement with empirical data, and to provide predictions of the metabolic rate of muscle groups and gait phases across walking speeds. Three-dimensional musculoskeletal simulations with prescribed kinematics and dynamics were performed. An optimal control formulation was used to compute muscle-tendon states with four levels of individualization, ranging from a scaled generic model and muscle controls based on minimal activations, inclusion of calibrated muscle passive forces, personalization of Achilles and quadriceps tendon stiffnesses, to finally informing muscle controls with electromyography. We computed metabolic rates based on existing models. Simulations with calibrated passive forces and personalized tendon stiffness most accurately estimate muscle excitations and fiber lengths. Interestingly, the inclusion of electromyography did not improve our estimates. The whole-body average metabolic cost was better estimated with a subset of metabolic energy 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 muscle groups at the preferred speed and were similar to the cost of hip adductors and abductors combined. Also, the swing phase accounted for slightly more than one-quarter of the total cost in a gait cycle, and its relative cost decreased with walking speed. Our prediction might inform the design of assistive devices and rehabilitation treatment. The code and experimental data are available online.

Standing and walking balance control in humans relies on the transformation of sensory information to motor commands that drive muscles. Here, we evaluated whether sensorimotor transformations underlying walking balance control can be described by task-level center of mass kinematics feedback similar to standing balance control. We found that delayed linear feedback of center of mass position and velocity, but not delayed linear feedback from ankle angles and angular velocities, can explain reactive ankle muscle activity and joint moments in response to perturbations of walking across protocols (discrete and continuous platform translations and discrete pelvis pushes). Feedback gains were modulated during the gait cycle and decreased with walking speed. Our results thus suggest that similar task-level variables, i.e. center of mass position and velocity, are controlled across standing and walking but that feedback gains are modulated during gait to accommodate changes in body configuration during the gait cycle and in stability with walking speed. These findings have important implications for modelling the neuromechanics of human balance control and for biomimetic control of wearable robotic devices. The feedback mechanisms we identified can be used to extend the current neuromechanical models that lack balance control mechanisms for the ankle joint. When using these models in the control of wearable robotic devices, we believe that this will facilitate shared control of balance between the user and the robotic device.