Wearable exoskeletons have emerged as a solution to enhance locomotion in individuals with impairments and/or weakness. Assistive devices with pneumatic gel muscle actuators (PGMs) are promising for daily use due to their high power-to-weight ratio and compliant structure, enabling potentially easy integration into smart garments. The intrinsic properties of PGMs have been studied over the past decade; however, little is known about how to leverage their dynamics to effectively and optimally assist motion. In this study, we modeled hip joint assistance via two PGMs at each user’s leg and employed musculoskeletal simulations to predict optimal assistive strategies that reduce metabolic costs during walking at various speeds. Specifically, we implemented a bilevel optimization framework to identify optimal control parameters: stiffness, onset time, and duration, under two control modes: coupled and independent, at three actuator placements: medial, neutral, and lateral, relative to the user’s hip joint center. Our results showed that, across walking speeds, PGM actuators with coupled control mode reduced estimated metabolic cost by 5.3–16.0% and with independent control mode by 10.5–17.5%. We also identified that PGM assistance with medial placement with coupled control mode offered the best trade-off between control simplicity and potential metabolic savings at slow walking speeds, which might be particularly useful for enhancing mobility in older adults and in rehabilitation settings. Also, our simulation suggested that neutral placement tended to outperform other actuator placements across speeds in terms of metabolic savings. Future experimental studies may benefit from guiding exoskeleton control as per the predicted assistive strategies in this work.

Introduction: Musculoskeletal simulations can guide the search for optimal strategies to assist motion and reveal causal relationships between assistive moments and muscle dynamics. Assistive devices such as exoskeletons can complement muscle forces based on various aims, such as minimum muscle effort or maximal force distribution. In this study, we present a simulation framework to systematically identify optimal assistance, formulated as a bilevel optimization in a single inverse simulation scheme that seeks optimal assistive moments that fulfill different assistive device aims. Methods: Bilevel optimization of assistive moment was structured as an inner optimization problem to solve the muscle redundancy problem nested within an outer optimization problem that executes the inner problem iteratively, seeking an assistive moment that best satisfies the assistive aim. We used this framework to predict optimal ankle plantarflexion, hip extension, hip flexion, and hip abduction assistance, for three different aims: minimal muscle activations, minimal metabolic rates, and minimal muscle moments. Experimental data from twelve participants walking at preferred speed were used in this study. Results: We found that the optimal moment trajectory is unique for a given assistive aim; i.e., the assistive aim matters. Differences in the assistive trajectories are explained at the muscle level, and as active and passive force contributions to the net muscle moments and muscle mechanical work. Interestingly, the assistive moments for minimal metabolic rates predicted an assistance period and peak timing similar to those reported from experimental studies. Conclusions: Our findings suggest that explicit assistive aim formulation is required to investigate human-device interaction under optimal assistance.

Breakthroughs in assistive exoskeletons have occurred in the recent decade; both active and passive devices that provide partial joint moments in the lower limbs have reduced metabolic costs during walking by assisting muscle action. Musculoskeletal simulation is highly useful in describing the interaction between assistive moments, muscle-tendon mechanics, and walking energetics. In this study, we computed optimal assistive moments in ankle plantarflexion and hip flexion that produce minimal muscle activations during walking, described the muscle energetics, and estimated the potential reduction in metabolic cost. We described with analyses of muscle-tendon mechanics and motor control how reductions in muscle activation do not always result in metabolic cost savings.

The workflow to simulate motion with recorded data usually starts with selecting a generic musculoskeletal model and scaling it to represent subject-specific characteristics. Simulating muscle dynamics with muscle–tendon parameters computed from existing scaling methods in literature, however, yields some inconsistencies compared to measurable outcomes. For instance, simulating fiber lengths and muscle excitations during walking with linearly scaled parameters does not resemble established patterns in the literature. This study presents a tool that leverages reported in vivo experimental observations to tune muscle–tendon parameters and evaluates their influence in estimating muscle excitations and metabolic costs during walking. From a scaled generic musculoskeletal model, we tuned optimal fiber length, tendon slack length, and tendon stiffness to match reported fiber lengths from ultrasound imaging and muscle passive force–length relationships to match reported in vivo joint moment–angle relationships. With tuned parameters, muscle contracted more isometrically, and soleus’s operating range was better estimated than with linearly scaled parameters. Also, with tuned parameters, on/off timing of nearly all muscles’ excitations in the model agreed with reported electromyographic signals, and metabolic rate trajectories varied significantly throughout the gait cycle compared to linearly scaled parameters. Our tool, freely available online, can customize muscle–tendon parameters easily and be adapted to incorporate more experimental data.

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.

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.

Numerous assistive exoskeletons have been developed in recent years to assist walking in individuals with and without motor disorders. A standard metric to measure the efficacy of assistance is the change in the metabolic energy cost between unassisted and assisted conditions. Various experimental methods, such as human-in-the-loop optimization, have been developed to find the optimal exoskeleton control to minimize metabolic energy. Such an approach is powerful yet time- and resource-intensive. In this regard, computational methods might complement state-of-the-art experimental approaches. Developing accurate models of the musculoskeletal system and neuromuscular commands could accelerate the development of exoskeletons and improve our understanding of human-exoskeleton interaction. The aims of the thesis were to model and simulate muscle-tendon mechanics and energetics of walking across speeds in unassisted conditions and with the support of ideal exoskeleton assistance with two modes of assistance: motor-based and spring-based actuators. 

The first three studies examined multiple musculoskeletal models, calibration methods of the muscle-tendon architecture, performance criteria for solving the muscle redundancy, and metabolic energy models to accurately estimate muscle excitations, fiber lengths, and metabolic energy cost compared to available experimental data. The musculoskeletal model proposed by Rajagopal et al. with calibrated muscle passive fiber-length curves and personalized Achilles and patellar tendon stiffness provided good agreement with muscle excitations and fiber lengths obtained from electromyographic signal and ultrasound imaging, respectively. Also, among multiple metabolic energy models in the literature, the model proposed by Bhargava et al. best estimated the average metabolic rates of the whole body compared to experimental measurements computed from spiroergometry. With the best estimations of muscle-tendon mechanics and energetics, the relative cost of the stance phase was predicted to increase significantly with walking speeds, and the metabolic cost of ankle plantarflexors was the highest among muscle groups and increased with walking speeds. The fourth study examined the optimal assistance to reduce muscle activations using motor-based and spring-based assistance of ankle plantarflexor, knee extensor, hip flexor, and hip abductor muscle groups. The largest reduction of muscle activation compared to unassisted conditions was obtained with hip flexor assistance with both actuation systems at high walking speeds. The reduction of metabolic rates compared to unassisted conditions was greater with walking speed with motor-based ankle plantarflexor assistance. In contrast, assisting this muscle group with spring-based actuation resulted in lower metabolic cost compared to unassisted conditions as walking speed increased. Interestingly, the decrease in muscle activations did not necessarily imply a reduction of metabolic energy cost compared to unassisted conditions, for instance with spring-based hip flexor and abductor assistance at some walking speeds. Metabolic energy rates during specific periods of the gait cycle were larger than in unassisted conditions due to increased muscle positive work, which is associated with high metabolic cost. 

The computational methods in the thesis might inspire future studies in the field. The software to calibrate muscle-tendon parameters, such as tendon compliance based on electromyography and muscle passive force-length curves based on ultrasound imaging, and to simulate exoskeleton assistance, are available in public repositories and can be adapted to integrate more experimental observations and simulate other motions than walking. Future studies will validate the predicted muscle-tendon mechanics with exoskeleton assistance.

Flera exoskelett har utvecklats under de senaste åren för att hjälpa personer med och utan motoriska funktionsnedsättningar att gå. Ett standardmått för att utvärdera prestation hos ett exoskelett är förändringen i metabola energikostnad mellan oassisterad och assisterad gång. Flera experimentella metoder, t.ex. human-in-the-loop-optimering, har utvecklats för att identifiera den optimala exoskelettassistansen som minimerar den metabola energin. Sådan metoder är mycket kraftfulla men är också mycket tids- och resurskrävande. I detta avseende kan beräkningsmetoder komplettera de experimentella metoderna. Noggranna modeller av rörelsesystemet och dess motoriska kontroll kan påskynda exoskelettutvecklingen och ge viktig information om samspeket mellan en människa och ett exoskelett. Syftet med avhandlingen är att modellera och simulera muskelmekanik och energiförbrukning vid gång i olika hastigheter, både utan assistans och med ett exoskelett med idealisk assistans från motorer och från fjädrar. 

I de tre första studierna undersökte vi flera modellvariationer för att identifiera den kombination vars resultat bäst matchade experimentella fynd.  Specifikt undersökte vi: flera biomekaniska modeller, olika metoder för att kalibrera muskelarkitekturen, flera kriterier för att lösa det underbestämda muskelkraftsystemet, och flera ekvationer som uppskattar metabolisk energi. Vi jämförde våra resultat med uppmätta eller tillgängliga experimentella data, såsom muskelaktivering, muskelfiberlängd och metabolisk energikostnad. Den biomekaniska modellen av Rajagopal et al. med justeringar för passiva muskelkrafter och häl- och patellarsenstelhet uppskattade muskelaktiveringar och muskelfiberlängder som överensstämde med experiment eller befintlig data.  Bland metabolisk energimodeller, resultaten från modellen av Bhargava et al. stämde bäst med experimentella mätningar från spiroergometri. Med den modellkombinationen som bäst uppskattade muskeldynamiken kunde vi mäta att den relativa metabola kostnad för stödfasen ökar med gånghastighet, där vadmusklerna stod för den största energiförbrukningen. I den fjärde studien uppskattade vi optimal assistans vid varje nedre extremitetsled som minimerar muskelaktiveringar, både från simulerade motorer och fjädrar. De största minskningarna av muskelaktivering uppnåddes med höftböjarassistans från antigen en motor eller en fjäder vid höga gånghastigheter. Vadmuskelassistans med motorer minskade metabola kostnader mer när gånghastigheten ökade. Däremot minskade inte metabola kostnader med vadmuskelassistans från fjädrar när gånghastigheten ökade. Det är intressant att påpeka att exoskelett som minskade muskelaktiveringar inte alltid minskade den metabola kostnaden, t.ex. med höftböjare och höftabduktorassistans från fjädrar. I vissa gångfaser var metabola energin till och med högre med assistans än utan, eftersom muskelarbete var högre vid dessa ögonblick.

De beräkningsmetoder som presenterades i avhandlingen kan inspirera och påskynda framtida studier inom området. Källkoden för kalibrering och justering av muskelparametrar samt senor och muskelpassiva egenskaper är fritt tillgänglig online i ett datarepository, liksom källkoden för simulering av exoskelettassistans. Framtida studier med exoskelettprototyper syftar till att validera simuleringarna.

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.

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