Springs vs. motors: Ideal assistance in the lower limbs during walking at different speeds

Multiple lower limb exoskeletons have made breakthroughs in the past decade by improving walking and running efficiency [1]. Increasingly efficient actuators and batteries, better strategies for human-device control, and lighter structures and physical interfaces have continuously improved assistance efficiency [2]. Current efforts to bridge the gap between laboratory-based observations and real-world benefits frequently focus on refining methods to identify optimal assistance [3], integrating human movement intention into exoskeleton control [4], and expanding exoskeleton use to make them suitable across multiple locomotion modes [5]. In this regard, musculoskeletal simulations can complement these efforts by guiding hypotheses about muscle-device interaction and revealing causal relationships in experimental observations [6].

Prior musculoskeletal simulation studies of exoskeleton assistance have provided insights into muscle-tendon mechanics and energetics, though simulation findings have not always agreed with experimental observations. Researchers have, through simulations, estimated the influence of exoskeleton assistance on tendon energy storage and release [7], on muscle fiber operating lengths and velocities [8], and on muscle activations, all of which influence muscle energetics and metabolic rates [9–11]. In theory, a model-based approach can be used to design exoskeleton controllers that result in optimal muscle dynamics and minimal energy cost. For instance, Franks et al. [12] used simulations with prescribed kinematics and dynamics to predict optimal multi-joint assistive moments, i.e. leading to minimal metabolic rates during walking. In subsequent experiments with these assistive moments, they indeed observed reduced muscle excitations and metabolic costs, but not as much as the model predicted. Uchida et al. [10] used a similar computational approach to predict optimal assistive moments for running; these were later evaluated experimentally by Lee et al. [13], who reported decreased metabolic cost, but again not as much as the model predicted. Some discrepancies between simulations and experiments are to be expected, as modeling approaches rely on a number of assumptions, including simplified muscle control and dynamics, simplified or no user-device interaction forces, massless devices, and unchanged kinematics. Model-based approaches thus have potential use in informing the design of assistive interventions, more so if they can accurately estimate muscle energetics and metabolic rates.

Most musculoskeletal modeling studies aiming to predict optimal assistive moments have focused on gait at or near preferred walking speed, even though daily activities encompass a wide range of speeds and locomotion modes. Several studies have predicted optimal lower limb exoskeleton assistive moments near preferred walking speed in normal and loaded conditions, such as carrying extra weight [6,11]. Other activities, such as walking at various speeds or stair ascent, have been studied less [6]. To the best of our knowledge, only two musculoskeletal modeling-based studies have examined optimal assistance during gait at a range of speeds; Uchida et al. examined mechanics and energetics in young adults with ideal actuators during running at 2 and 5 m/s [10], and Cseke et al., in elderly adults during walking at self-selected slow (0.86 m/s), comfortable (1.22 m/s) and fast (1.53 m/s) speeds [9].

Whereas variable assistive torque profiles that can theoretically be provided by a motor can be expected to reduce metabolic rates, spring-based actuation, i.e., a spring or elastic component that can store potential energy during elongation and then release it during shortening, can also potentially influence muscle dynamics and gait energetics. Spring-based exoskeletons can also potentially be lighter and less cumbersome than motorized exoskeletons. Spring-based assistance should theoretically be effective during gait phases characterized by joint power absorption followed by joint power generation, which is the case with ankle dorsi-/plantarflexion and hip flex-/extension in preswing, hip ab-/adduction during midstance, and knee flex-/extension during loading response and midstance [14]. Spring-based actuators have been observed experimentally to substantially decrease physiological joint moments, i.e., joint moments from muscle actions, but with negligible metabolic reduction [15]. Prior musculoskeletal simulation studies have provided insights into the causal relationship between muscle mechanics and spring-based assistive moments near preferred speed [16,17] predictions have agreed with experimental observations to some degree [18,19]. Simulations that investigate the influence of spring-based assistance on muscle energetics can potentially inform device design.

Our findings indicate that an assistive strategy based on minimal muscle activations does not translate to a decreased metabolic rate. Assistive devices are generally designed to support motion, which might involve reducing net muscle moment, activations, and metabolic rates [2]. The optimal assistive moments in our simulations decreased the overall sum of muscle activation, which in turn reduced muscle forces and, thus, net muscle moment in the assisted muscle groups, though occasionally increasing demand on antagonist muscles. Reduction of metabolic rates was, however, more difficult to achieve. Metabolic energy models estimate muscle energy rates based on heat dissipation and muscle power. Heat dissipation is the sum of various subcomponents that depend on fiber velocities, such as the shortening and lengthening heat rates and the activation and maintenance heat rates [32]. All components are related to muscle activations. As such, metabolic rate is diminished if heat dissipation and muscle power are zero, which only happens when muscle activations are zero. However, assistive moments that submaximally reduce muscle activations, i.e., lower but non-zero activations, can result in higher metabolic rates if the muscle positive power increase outweighs the heat dissipation decrease. We observed two instances in which this was the case, both with spring-based assistance: With plantarflexion assistance during preswing, and with knee extension assistance during midstance, wherein lower activation was associated with higher fiber velocity in the assisted muscles, which increased muscle positive power, and thereby metabolic rates. In several cases, assistive moment resulted in increased demand, and thus muscle positive power and metabolic rates, in antagonist muscles, for instance, with hip flexion assistance during mid-swing and with hip abduction assistance during loading response. It is not a straightforward assumption that assistive moments that reduce overall muscle activations will also reduce metabolic rates. We did, however, identify several cases in which the assistive moment reduced agonist muscle activations to zero, without substantially increasing antagonist muscle activations, and resulted in overall reduced metabolic rates in instances of the gait cycle, specifically with motor-based ankle plantarflexion and knee extension assistance.

Our identified ideal motor-based plantarflexion assistive moment profiles are similar to previously reported moment profiles that were found to reduce metabolic rates. At normal walking speed, the ideal motor-based plantarflexion assistive moment profile was similar to those identified from human-the-loop optimization studies that aimed for minimal metabolic rates [3,33]. The peak in the profile we identified was near 50% of the gait cycle, agreeing with other identified optimal moment trajectories [3,33]. However, our simulation predicts a metabolic reduction (22%) at normal walking speed, which is substantially larger than experimentally reported metabolic rate reduction reported by Zhang et al. at a slightly lower speed (14% metabolic reduction at 1.25 m/s) [33]. We also found that with motor-based plantarflexion assistance, the metabolic reduction should be more pronounced as walking speed increases, in agreement with prior studies [3,33]. The relative metabolic cost of plantarflexion motion respected to the total metabolic cost of the gait cycle increases with walking speeds [20]. Since motor-based plantarflexion assistance did not increase metabolic rates in antagonist or other muscle groups, it is consistent that higher metabolic saving was predicted as walking speed increased.

Our identified ideal spring-based plantarflexion assistive moments disagreed somewhat with prior reported observations. Experimental comparisons with spring-based assistance are more challenging, as very few studies have studied muscle activation changes across walking speeds. In a study from Nuckols and Sawicki using an exoskeleton emulator to mimic spring-like actuation, the optimal spring stiffness to reduce metabolic rates was similar at speeds of 1.25 and 1.75 m/s [34]. This finding does not align with our results, presumably because our optimal assistive moment does not directly minimize metabolic rates. Also, our modeled spring-based device can engage at any instance of the stance phase, while Nuckols and Sawicki engaged the spring at initial foot-ground contact.

Our findings of decreased muscle activation but increased muscle positive power during early midstance with knee extension assistance might explain why previous experimental studies with this aim have failed to reduce metabolic rates during walking. Metabolic rate reduction with knee extension assistance has only been achieved with motor-based actuation compared to wearing a powered-off exoskeleton [35,36] or in challenging environments such as carrying loads while walking on an inclined surface [37]. Vastus lateralis, a major knee extensor muscle, contracts nearly isometrically during loading response and midstance in unassisted conditions [30], which results in low metabolic rate demands. Our simulation suggests that, with knee extensor assistance, some increase in metabolic rates is observed due to the detuning of the force generation capacity associated with the fiber contraction velocity. The knee extension assistive moment decreased the knee extension muscle forces during loading response, resulting in shorter tendon elongation because the elongation of the tendons, modeled as non-linear springs [23], depends on the force they are subject to, e.g., elongation is shorter with a lower force. Furthermore, since the muscle-tendon unit length is unchanged between unassisted and assisted conditions, i.e., motion is prescribed in both conditions, shorter tendon elongation directly implies larger muscle fiber excursion. A low reduction in metabolic rates was predicted because the metabolic rate associated with knee extension is relatively small (i.e., the metabolic peak of knee extension muscles ~0.4 w/kg in unassisted conditions), and muscle fiber velocities increased during early midstance, increasing muscle positive power and metabolic rates compared to unassisted conditions. Jackson et al. reported a similar finding that even if muscle moment is reduced with an ankle exoskeleton, the metabolic cost can increase if the muscle moment corresponds to increasing muscle positive work [7]. In our study, we found little to no potential benefit from knee extensor assistance, regardless of actuation mode or walking speed.

Spring-based and especially motor-based hip flexion assistance shows promise in reducing metabolic rates, particularly at fast walking speeds. Only a few studies have evaluated the effects of hip flexion assistance with powered devices [38–40]. Studies of devices that reduced metabolic cost parametrized the assistive profile such that it began at maximum hip extension [40] or provided a power burst during a predefined time window (corresponding to 25% of the gait cycle) [39]; both studies found that the optimal peak assistive moment should be later than the net hip flexion moment. These assistive trajectories disagree somewhat with the optimal assistive moments that we identified. We also found that the increased antagonist hip extensor muscle moment during the swing phase counterintuitively reduced metabolic rate, in agreement with findings reported in another simulation study [11]. It is possible that this counterintuitive benefit from simulation studies might not translate experimentally; it has, to the best of our knowledge, not been tested experimentally. Furthermore, previous experimental studies reported a metabolic decrease of 8.8% with hip flexion assistance compared to unassisted conditions [40] and 6.1% compared with a powered-off exoskeleton [39], which agrees with our predictions (9% near preferred walking speed). With spring-based hip flexion assistance, only two experimental studies reported metabolic rate reduction [19,41]. Zhou et al. reported 7.2% metabolic rate reduction at 1.5 m/s and suggested that optimal assistive is likely speed-dependent [19]. We found no metabolic reduction with spring-based assistance at preferred walking speed but a small decrease (4%) in fast walking. To the best of our knowledge, no previous study has evaluated the influence of hip flexion assistance, neither spring- or motor-based, at different walking speeds. Our simulation supports a hypothesis that hip flexion assistance from either actuation mode can potentially decrease metabolic rate as walking speed increases.

Our findings indicate little potential for hip abduction assistance to reduce metabolic rates substantially. Recent studies have evaluated metabolic rate reduction assisting hip abduction using soft exosuits [42] and rigid frame-based exoskeletons [43]. Park et al. used a soft exosuit to explore the interaction between metabolic rates and balance based on assistive moments that mimic peak abduction moments and power [42]. They found that mimicking the physiological second peak moment (~45% of the gait cycle) reduced metabolic rates by 11% compared to unassisted conditions. Interestingly, we estimated two assistive moment peaks with motor-based assistance, both aligned with the physiological moment peaks. Yet, the first assistive moment peak increased the time-series metabolic rates of the hip adduction (antagonist) muscle group, while the second assistive moment peak (~50% of the gait cycle) decreased the time-series metabolic rates of the hip adduction muscle group. On the other hand, Kim et al. used a rigid frame-based exoskeleton to explore the metabolic reduction based on assistive moments obtained from human-in-the-loop optimization, mimicking the net hip moment in the frontal plane, and optimal assistance from musculoskeletal simulation [43]. They found none of them reduced metabolic rates compared to the unpowered exoskeleton. The simulation-based optimal assistance used by Kim et al. was based on the predicted value from Dembia et al. [11] and resembled our predicted assistive moment trajectory. In this regard, our finding suggests that predicting assistive moments based on minimal muscle activations may not be the most advantageous strategy for metabolic rate reduction. Also, our estimation suggests that applying an abduction assistive moment during ~50% of the gait cycle might decrease metabolic rates as it does not involve a substantial increase in the metabolic rate of the hip adductor muscle group across walking speeds. Future studies experimental studies might confirm or refine our observations.

The two major limitations of our study are 1) the assumption that motion patterns in unassisted and assisted conditions are unchanged, which is a dilemma in all musculoskeletal simulations with constrained kinematics, and 2) the optimal assistive moments defined with the objective function in the muscle redundancy solver that seeks the task-specific exoskeleton moments that minimize the sum of squared muscle activations. The assumption of unchanged kinematics might be reasonable in spring-based devices at the ankle [18] and hip [19], as they can be made lightweight and reasonably comfortable. With powered ankle and hip assistive devices, despite evidence suggesting that joint angles and net joint moments might be preserved [38,44], human-device adaptation is complex and more likely to alter the user’s motor control strategy and, thereby, joint kinematics and moments [45]. The motion adaptation accompanying optimal assistance can be inferred by adopting a more complex scheme, such as predictive simulation. However, enabling the prediction of joint mechanics does not necessarily imply more realism in the simulated outcome. For instance, Nikoo and Uchida showed that the predicted optimal assistance varies substantially according to the selected objective function, and the corresponding kinematic adaptation does not necessarily reflect experimentally reported values; simulation of gait with an ankle plantarflexion device and multiple objective functions [46] predicted knee flexion throughout the gait cycle which was not observed experimentally [47]. Accurate prediction of motion adaptation using exoskeleton devices might derive from a more physiologically plausible neuromuscular control model, which constitutes an active line of research. Moreover, accounting for motion adaptation is likely more relevant in conditions where assistive devices might drastically change motion patterns, such as when using devices that span multiple joints [36] or in people with motion disorders [48,49].

Regarding the second limitation, we formulated the optimization problem to solve muscle redundancy and to identify optimal assistive moments using the same objective function, specifically minimal muscle activation. We assumed the paradigm that human walking is achieved with a minimum summed of squared muscle activations, and that metabolic efficiency is driven by this neuromuscular strategy. As such, the assistive moments in our simulation represent the optimal for minimal muscle activations, but we demonstrated that reduction of muscle activations does not directly translate to reduction of metabolic rates. Our findings warrant further simulation studies that identify assistive moments with optimization goals other than minimal activations, ideally with goals of minimal metabolic cost. In this regard, it might be beneficial to explicitly incorporate the goal of the assistive moment separately from the objective function to solve muscle redundancy. This can theoretically be achieved by adopting a bilevel optimization scheme as proposed by Nguyen et al. [50], in which a low-level optimization problem might deal with solving muscle redundancy, while a upper-level problem searches for optimal assistance with a task criterion, e.g., maximal walking stability or minimal metabolic cost. Future studies might unveil unexplored human-device interaction by explicitly formulating the goals of the assistive devices.

Finally, other venues to improve our understanding of the human-device performance based on musculoskeletal simulations lie in further examining the model sensibility to predict optimal assistance. Our study aims to provide insights into the interaction between muscle dynamics and assistive moments among types of devices when assisting gait. Yet, estimations of the optimal assistance are likely subject to simplifications of the modeled musculoskeletal system [51] and human-device interface [52]. For instance, we neglected anatomical variations of the muscle-tendon geometries such as muscle-tendon length and moment arm around the hip joint, though they influence muscle forces [53] and, thus, potentially muscle energetics in unassisted and assisted conditions. Similarly, we modeled assistive devices as massless and frictionless actuators. As such, our estimation does not consider any possible inefficiency in force transmission exerted by the device to the body segments. Future studies might benefit from evaluating the sensibility of the predicted optimal assistance in correspondence with the modeled musculoskeletal geometry and human-device interface. Establishing the relationship between model selection and muscle dynamics on assistive moment might refine the prediction of the optimal assistance and guide the design of the assistive device control and structure.