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

10 Recent years have witnessed breakthroughs in assistive exoskeletons; both passive and active devices have 11 reduced metabolic costs near preferred walking speed by assisting muscle actions. Metabolic reductions at 12 multiple speeds should thus also be attainable. Musculoskeletal simulation can potentially predict the 13 interaction between assistive moments, muscle-tendon mechanics, and walking energetics. In this study, we 14 simulated devices’ optimal assistive moments based on minimal muscle activations during walking with 15 prescribed kinematics and dynamics. We used a generic musculoskeletal model with calibrated muscle -tendon 16 parameters and computed metabolic rates from muscle actions. We then simulated walking across multiple 17 speeds and with two ideal actuation modes – motor-based and spring-based – to assist ankle plantarflexion, 18 knee extension, hip flexion, and hip abduction and compared computed metabolic rates. We found that both 19 actuation modes considerably reduced physiological joint moments but did not always reduce metabolic rates. 20 Compared to unassisted conditions, motor-based ankle plantarflexion and hip flexion assistance reduced 21 metabolic rates, and this effect was more pronounced as walking speed increased. Spring -based hip flexion 22 and abduction assistance increased metabolic rates at some walking speeds despite a moderate decrease in 23 some muscle activations. Both modes of knee extension assistance reduced metabolic rates to a small extent, 24 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint 2 even though the actuation contributed with practically the entire net knee extension moment during stance. 25 Motor-based hip abduction assistance reduced metabolic rates more than spring-based assistance, though this 26 reduction was relatively small. Future work should experimentally validate the effects of assistive moments 27 and refine modeling assumptions accordingly. Our computational workflow is freely available online. 28 29 Author Summary 30 We used simulation to identify ideal assistance at major lower limb joints that can potentially be produced by 31 motor-based or spring-based assistive devices in slow, normal, and fast walking. We found that assistance 32 from both actuation modes decreased muscle activations and net muscle moments to varying extents, 33 depending on joint and walking speed, but they did not always reduce metabolic energy of muscles. Motor-34 based assistance was overall more effective than spring-based assistance, and spring-based assistance at times 35 increased the metabolic energy. The largest metabolic energy reductions occurred with motor-based 36 plantarflexion assistance, followed by motor-based hip flexion assistance, both more notably at higher speeds. 37 Motor-based hip abduction assistance also reduced metabolic energy, somewhat inversely with walking speed. 38 Spring-based assistance was overall less effective than motor-based assistance but did reduce metabolic 39 energy with plantarflexion assistance in slow walking and with hip flexion assistance in fast walking. Knee 40 extension assistance, regardless of actuation mode or walking speed, had little to no influence on metabolic 41 energy. Our simulation findings do not support knee extension assistance at all, nor spring -based hip flexion 42 assistance in slow walking or hip abduction assistance at any speed if a device goal is to reduce muscle 43 activations. 44 45

46 Gait exoskeletons, musculoskeletal modeling, optimal control, locomotion, assistive technology. 47 1. Introduction 48 Multiple lower limb exoskeletons have made breakthroughs in the past decade by improving walking and 49 running efficiency (1). Increasingly efficient actuators and batteries, better strategies for human -device 50 control, and lighter structures and physical interfaces have continuously improved assistance efficiency (2). 51 Current efforts to bridge the gap between laboratory-based observations and real-world benefits focus 52 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint 3 frequently on refining methods to identify optimal assistance (3), integrating human movement intention into 53 exoskeleton control (4), and expanding exoskeleton use to make them suitable across multiple locomotion 54 modes (5). In this regard, musculoskeletal simulations can complement these efforts by guiding hypotheses 55 about muscle-device interaction and revealing causal relationships in experimental observations (6). 56 Prior musculoskeletal simulation studies of exoskeleton assistance have provided insights into muscle-tendon 57 mechanics and energetics, though simulation findings have not always agreed with experimental observations. 58 Researchers have, through simulations, estimated the influence of exoskeleton assistance on tendon energy 59 storage and release (7), on muscle fiber operating lengths and velocities (8), and on muscle activations, all of 60 which influence muscle energetics and metabolic rates (9–11). In theory, a model-based approach can be used 61 to design exoskeleton controllers that result in optimal muscle dynamics and minimal energy cost. For 62 instance, Franks et al. (12) used simulations with prescribed kinematics and dynamics to predict optimal multi-63 joint assistive moments, i.e. leading to minimal metabolic rates during walking. In subsequent experiments 64 with these assistive moments, they indeed observed reduced muscle excitations and metabolic costs, but not 65 as much as the model predicted. Uchida et al. (11) used a similar computational approach to predict optimal 66 assistive moments for running; these were later evaluated experimentally by Lee et al. (13), who reported 67 decreased metabolic cost, but again not as much as the model predicted. Some discrepancies between 68 simulations and experiments are to be expected, as modeling approaches rely on a number of assumptions, 69 including simplified muscle control and dynamics, simplified or no user-device interaction forces, massless 70 devices, and unchanged kinematics. Model-based approaches thus have potential use in informing the design 71 of assistive interventions, more so if they can accurately estimate muscle energetics and metabolic rates. 72 Most musculoskeletal modeling studies aiming to predict optimal assistive moments have focused on gait at or 73 near preferred walking speed, even though daily activities encompass a wide range of speeds and locomotion 74 modes. Several studies have predicted optimal lower limb exoskeleton assistive moments near preferred 75 walking speed in normal and loaded conditions, such as carrying extra weight (6)(9). Other activities, such as 76 walking at various speeds or stair ascent, have been studied less (6). To the best of our knowledge, only two 77 musculoskeletal-based studies have examined optimal assistance during gait at a range of speeds; Uchida et al. 78 examined mechanics and energetics in young adults with ideal actuators during running at 2 and 5 m/s (11), 79 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint 4 and Cseke et al., in elderly adults during walking at self-selected slow (0.86 m/s), comfortable (1.22 m/s) and 80 fast (1.53 m/s) speeds (10). 81 Whereas variable assistive torque profiles that can theoretically be provided by a motor can be expected to 82 reduce metabolic rates, spring-based actuation, i.e., a spring or elastic component that can store potential 83 energy during elongation and then release it during shortening, can also potentially influence muscle dynamics 84 and gait energetics. Spring-based exoskeletons can also potentially be lighter and less cumbersome than 85 motorized exoskeletons. Spring-based assistance should theoretically be effective during gait phases 86 characterized by joint power absorption followed by joint power generation , which is the case with ankle 87 dorsi-/plantarflexion and hip flex-/extension in pre-swing, hip ab-/adduction during midstance, and knee flex-88 /extension during loading response and midstance (14). Spring-based actuators have been observed 89 experimentally to substantially decrease physiological joint moments, i.e., joint moments from muscle actions, 90 but with negligible metabolic reduction (15). Prior musculoskeletal simulation studies have provided insights 91 into the causal relationship between muscle mechanics and spring -based assistive moments near preferred 92 speed (16,17) predictions have agreed with experimental observations to some degree (18,19). Simulations 93 that investigate the influence of spring-based assistance on muscle energetics can potentially inform device 94 design. 95 The objectives of the study were thus to simulate how two modes of assistance, spring -based and motor-96 based, at individual lower limb joints affect computed muscle dynamics and metabolic rates during walking at 97 various speeds. We hypothesized that assistive moments will reduce muscle activations and metabolic rates 98 and that motor-based actuation will be more efficient than spring-based actuation. Also, assisting ankle 99 plantarflexion with any mode of assistance will yield the largest reduction of metabolic rates compared to 100 unassisted conditions among all the muscle groups and at all walking speeds. 101 102 2. Methods 103 2.1 Musculoskeletal simulation workflow 104 We implemented a simulation workflow to estimate muscle dynamics and metabolic rates during walking 105 using musculoskeletal models with calibrated muscle-tendon parameters and recorded motion. We used 106 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint 5 previously reported experimental data (20) and the OpenSim software (21) to scale a generic musculoskeletal 107 model and compute joint kinematics and dynamics. We calibrated muscle-tendon parameters in the scaled 108 musculoskeletal model to better represent fiber lengths and passive angle -moment relationships (22). Then, 109 we performed musculoskeletal simulations while walking with prescribed kinematics and dynamics using 110 trajectory optimization (23) (Fig. 1). 111 112 113 Fig. 1. Simulation workflow per each subject. Inverse kinematics and dynamics are computed using the 114 OpenSim workflow. Moment arms and muscle-tendon lengths are computed from the inverse kinematic 115 solution using the Muscle Analysis tool from OpenSim. We then tuned the muscle -tendon parameters – 116 optimal fiber length, tendon slack length, and tendon stiffness – such that the simulated muscle fiber lengths 117 and excursions matched reported findings from ultrasound imaging. Next, we tuned the muscle passive force 118 curves such that the simulated passive moments matched passive angle -moment joint relationships reported 119 in an in vivo study. Finally, we simulated walking across various speeds with no actuators and with the various 120 assistive actuators. 121 122 Experimental data 123 Experimental motion data: marker trajectories and ground reaction force of five unimpaired (2/3 male/female, 124 [mean ± SD] age: 31.4 ± 7.4 years old, height: 1.75 ± 0.03 m, body mass: 69.0 ± 10.3 kg) reported in a previous 125 publication were used for this study (20). In brief, subjects walked on a treadmill at a range of walking speeds, 126 specifically 55%, 70%, 85%, 100%, 115%, 130%, and 145% of their estimated preferred walking speed (PWS) . 127 Subjects then walked along a lab pathway and emulated different walking speeds by matching recorded 128 cadences from treadmill walking. Marker positions (100 Hz), based on the Conventional Gait Model with the 129 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint 6 Extended-foot model (CGM 2.4) and ground reaction forces (1000 Hz) were measured using optical motion 130 capture (Vicon V16, Oxford, UK) and strain gauge force platforms (AMTI, Watertown, MA, USA), respectively. 131 Musculoskeletal model, joint kinematics, and inverse dynamics 132 A generic musculoskeletal model developed by Rajagopal et al. (24) with modified hip abductor muscle paths 133 (25) was selected for this study. We scaled the generic model using OpenSim’s Scale Tool, which adjusted 134 muscle paths, skeletal geometry, and segment inertial properties to fit anthropometric dimensions obtained 135 from a captured static calibration trial. We adjusted the maximum isometric force of the soleus, 136 gastrocnemius, and tibialis anterior as per Arnold et al. (26). 137 Marker trajectories and ground reaction forces throughout three gait cycles per subject at low (55% PWS), 138 normal (100% PWS), and fast (145% PWS) walking speeds were analyzed with inverse kinematics and inverse 139 dynamics using OpenSim 4.1. Marker tracking weights for inverse kinematics were selected to minimize the 140 error between experimental and virtual markers. The subtalar and metatarsal joints were fixed at neutral 141 anatomical positions. 142 Tuning of muscle-tendon parameters 143 We used a computational tool to tune muscle-tendon parameters such that each subject’s muscle excitations, 144 fiber lengths, and passive moments best resembled experimental observations (22). The tuning was done in 145 two steps. First, we tuned optimal fiber lengths, tendon slack lengths, and tendon stiffnesses of the 146 gastrocnemius lateralis, gastrocnemius medialis, soleus, and vasti (lateralis, medialis, and intermedius) to 147 match muscle fiber lengths and excursions obtained from those reported in from ultrasound imaging (27,28). 148 Then, we tuned muscle passive force-length curves to match the reported passive moment at various ankle, 149 knee, and hip joint angles from an in vivo study (29). Compared to simulation with the original generic model, 150 these steps result in estimated muscle excitations that better agree with observed electromyography signals 151 (22). 152 Solving muscle redundancy 153 Our implementation is based on the simulation framework proposed by De Groote et al. (23), which uses 154 direct collocation dynamic optimization and implicitly incorporates activation and contraction dynamics. 155 Muscle excitations, states, and state derivatives were computed based on the assumption that the muscle 156 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint 7 redundancy is solved by the optimization criterion of minimal muscle activations squared. Two other terms are 157 present in the objective function to improve the feasibility and convergence of the formulation. Reserve 158 actuators in each degree of freedom are added to guarantee the problem’s feasibility, and their use is 159 penalized in the objective function. Also, a term that minimizes muscle fiber velocities is included to improve 160 numerical computation (L2 regularization). The objective function is implemented as (1): 161 min (𝑤𝑎 ∫ ∑ 𝑎𝑛 2(𝑡)𝑁 𝑛=1 𝑡𝑓 𝑡𝑖 𝑑𝑡+ +𝑤𝑟 ∫ ∑ 𝑒𝑅𝑗 2 (𝑡)𝐽 𝑗=1 𝑡𝑓 𝑡𝑖 𝑑𝑡+ 𝑤𝑣 ∫ ∑ 𝑣̃𝑛 2(𝑡)𝑁 𝑛=1 𝑡𝑓 𝑡𝑖 𝑑𝑡) (1) 162 Where 𝑎𝑛 is muscle activation of muscle 𝑛, 𝑒𝑅𝑗 is the excitation of the reserve actuator of joint 𝑗, 𝑣̃𝑛 is the 163 normalized fiber velocity of muscle 𝑛, 𝑡𝑓 and 𝑡𝑖 are the initial and final times of the gait cycle, respectively; 𝑁 164 and 𝐽 are the total number of muscles and joints in the musculoskeletal model, respectively; and 𝑤𝑎, 𝑤𝑟 and 165 𝑤𝑣 are the weights of the terms in the objective function related to the muscle activations, reserve actuators, 166 and fiber velocities, respectively. The sum of the moments produced by muscle-tendon and reserve actuators 167 equals the net joint moment obtained from inverse dynamics at each joint. This condition was implemented as 168 a constraint in the optimization problem as in (2) 169 𝜏𝐼𝐷𝑗(𝑡) = 𝜏𝑀𝑈𝑆𝑗(𝑡) + 𝑒𝑅𝑗(𝑡)𝑇𝑅, 𝑗 = 1, … , 𝐽 (2) 170 Where, at joint 𝑗, 𝜏𝐼𝐷𝑗 is the net joint moment, 𝜏𝑀𝑈𝑆𝑗 is the moment produced by the muscle-tendon 171 actuators, subsequently referred to here as “muscle moments”, and 𝑇𝑅 is the magnitude of the reserve 172 actuator. ((Thinking about Svein’s comments, maybe comment about inertia components in the solver?)) 173 3.2 Determining optimal assistive moments 174 Optimal assistive moments were computed using scaled musculoskeletal models with tuned muscle -tendon 175 parameters, inverse kinematics, and inverse dynamics solutions as described above. Constraints and design 176 variables were added when solving the muscle redundancy to model assistive moments at various muscle 177 groups. For each mode of actuation, ideal assistive moments were added at each simulated gait cycle to assist 178 specific muscle groups individually: plantarflexion, knee extension, hip flexion, and hip abduction. Per each 179 subject, nine gait cycles were simulated (three gait cycles per walking speed); therefore, nine assistive 180 moments per mode of actuation and muscle group were determined. 181 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint 8 When solving the muscle redundancy, the objective function was the same as in unassisted conditions but 182 constraints were added to model assistive device moment to assist muscle-tendon actuators in reproducing 183 the inverse dynamics, i.e., the sum of the muscle moment, reserve actuator moment, and assistive device 184 moment equals the net joint moment at each joint, as in (3) 185 𝜏𝐼𝐷𝑗(𝑡) = 𝜏𝑀𝑈𝑆𝑗(𝑡) + 𝑒𝑅𝑗(𝑡)𝑇𝑅 + 𝜏𝐸𝑋𝑂𝑀,𝑆𝑗 (𝑡), 𝑗 = 1, … , 𝐽 (3) 186 Where 𝜏𝐸𝑋𝑂𝑀,𝑆𝑗 is the assistive device moment at joint 𝑗. In this regard, the assistive moments are the optimal 187 solutions to assist muscles based on minimal summed muscle activations squared. 188 Motor-based moment profiles 189 The motor-based actuation was modeled as a unidirectional ideal moment at the corresponding degree of 190 freedom in the musculoskeletal model. The assistive moment ( 𝜏𝐸𝑋𝑂𝑀(𝑡)) was implemented as a time-series 191 design variable. Its magnitude was constrained to assist the aimed muscle group explicitly. For instance, 192 𝜏𝐸𝑋𝑂𝑀(𝑡) < 0 for assisting ankle plantarflexion corresponds to ankle plantarflexion moment (agonist muscle 193 group) and avoids generating ankle dorsiflexion moment (antagonist muscle group). The motor-based 194 actuation was not constrained in its trajectory; hence, it could have any value at each point in time to assist a 195 muscle group. Optimal assistive moment based on motor-based actuation was determined individually for 196 each subject and gait cycle. 197 Spring-based device parameters 198 The spring-based actuator was modeled as a unidirectional torsional spring that engages and disengages in 199 specific joint angles. To implement this, we introduced three design variables: engaged timing (𝑡𝑐), disengaged 200 timing (𝑡𝑑), and spring stiffness (𝑘𝑟), we added a constraint to impose that the angle at which the spring 201 engaged and disengaged are similar as in (4) 202 (𝑞(𝑡𝑐) − 𝑞(𝑡𝑑)) 2 < 0.01 (4) 203 Where 𝑞(𝑡) is the joint angle corresponding to the assisted muscle group. The assistive moment was 204 computed as a product of the spring stiffness and the angle within the period that the spring is engaged as in 205 (5) 206 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint 9 𝜏𝐸𝑋𝑂𝑆(𝑡) = 𝑘𝑟𝑞𝐸𝑋𝑂(𝑡) (5) 207 Where 𝑞𝐸𝑋𝑂(𝑡) is the joint angle displacement from the angle of engagement. This angle was modeled using 208 hyperbolic tangent function as in (6), (7), (8), and (9) 209 𝑇𝑒(𝑡) = 0.5 + 0.5 tanh(𝑏(𝑡𝑖𝑚𝑒(𝑡) − 𝑡𝑐)) (6) 210 𝑇𝑑(𝑡) = 0.5 + 0.5 tanh (𝑏(𝑡𝑑 − 𝑡𝑖𝑚𝑒(𝑡))) (7) 211 𝑇𝑎𝑐𝑡𝑖𝑣𝑒(𝑡) = 𝑇𝑒(𝑡)𝑇𝑑(𝑡) (8) 212 𝑞𝐸𝑋𝑂(𝑡) = 𝑇𝑎𝑐𝑡𝑖𝑣𝑒(𝑡)(𝑞(𝑡) − 𝑞(𝑡𝑐)) (9) 213 Where 𝑇𝑒 is the start of the engaged period, 𝑇𝑑 is the start of the disengagement period, and 𝑇𝑎𝑐𝑡𝑖𝑣𝑒(𝑡) is the 214 period where spring is engaged. 215 We selected 𝑤𝑎, 𝑤𝑟 and 𝑤𝑣 as 1, 1000, and 0.001; thus, the use of reserve actuators was heavily penalized, and 216 the influence of fiber velocities was relatively small. Also, we selected 𝑇𝑅 as 100 Nm, and b as 1000 since it 217 provided a smooth yet steep transition between null to assistive moment generation (Supplementary Fig. 1). 218 Optimal assistive moment based on spring-based actuation was determined individually for each subject and 219 gait cycle. 220 3.3 Metabolic rate computation 221 For each subject/gait cycle, each speed, and each device, the metabolic rate of each muscle was computed 222 based on the muscle excitations, states, and state derivatives obtained from our optimization routine using a 223 metabolic energy model proposed by Bhargava et al. (30), which we previously reported to agree with 224 recorded metabolic rates obtained from spiroergonometry (20). In brief, muscle metabolic rate is computed as 225 in (10) 226 𝐸̇𝑛(𝑡) = 𝑊̇ 𝐶𝐸𝑛(𝑡) + 𝐻̇ 𝑛(𝑡) (10) 227 Where 𝐸̇𝑛, 𝑊̇ 𝐶𝐸𝑛 and 𝐻̇ 𝑛 are the metabolic rate, contractile element work rate, and heat rate, respectively, of 228 muscle 𝑛. The contractile element work rate, also called muscle power, is computed as in (11) 229 𝑊̇ 𝐶𝐸𝑛(𝑡) = 𝐹𝐶𝐸𝑛(𝑡) 𝑉𝐶𝐸𝑛(𝑡) (11) 230 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint 10 Where 𝐹𝐶𝐸𝑛 and 𝑉𝐶𝐸𝑛 are the muscle force and fiber velocity, respectively, of muscle 𝑛. The heat rate depends 231 on muscle mass, muscle activations, fiber velocities, and a function that approximates the size principle of 232 motor recruitment, explained in detail by Bhargava et al. (30). The original formulation did not explicitly 233 address negative metabolic rates, which are possible during eccentric contractions if muscle negative power 234 exceeds the heat rate. As a negative metabolic rate is physiologically questionable, we adjusted it in such cases 235 by updating the heat rate and re-computing the metabolic rate as in (12) and (13) 236 𝐻̇ 𝑛,𝑚𝑜𝑑(𝑡) = −𝑊̇ 𝐶𝐸𝑛(𝑡) − 𝐻̇ 𝑛(𝑡), 𝐸̇𝑛(𝑡) < 0 (12) 237 𝐸̇𝑛(𝑡) = 𝑊̇ 𝐶𝐸𝑛(𝑡) + 𝐻̇ 𝑛,𝑚𝑜𝑑(𝑡) (13) 238 The metabolic rates for one leg (𝐸̇𝐿) is computed as the sum of all the individual muscle metabolic rates as in 239 (14) 240 𝐸̇𝐿(𝑡) = ∑ 𝐸̇𝑛(𝑡)𝑁 𝑛=1 (14) 241 F. Data and statistical analysis 242 We evaluated the change of muscle activations, physiological joint moments, and metabolic rates between 243 unassisted and assisted with two actuation modes during walking across speeds. Muscle activations were the 244 sum of all the muscle activations in one leg obtained from solving the muscle redundancy and divided by the 245 number of muscles. Net muscle moments are defined here as the net joint moments minus the assistive 246 moments (3). Net muscle moments for agonists (plantarflexion, knee extension, hip flexion, and hip abduction) 247 and antagonists (dorsiflexion, knee flexion, hip extension, and hip adduction) were computed in 248 correspondence to the muscle group assisted, e.g., with ideal plantarflexion assistive moments, plantarflexion 249 and dorsiflexion net muscle moments were presented. Metabolic rates were the sum of all the muscle 250 metabolic rates in one leg (13). Average muscle activations, agonist and antagonist net muscle moment, and 251 metabolic rates in unassisted and assisted conditions over each gait cycle were computed as the integral of its 252 corresponding time-series divided by the gait cycle duration as in (15) 253 𝑋̅ = 1 𝑡𝑓−𝑡𝑖 ∫ 𝑋 𝑡𝑓 𝑡𝑖 𝑑𝑡 (15) 254 Where 𝑋̅ are the average values of the muscle activations, agonist and antagonist net muscle moment, and 255 metabolic rates over a gait cycle. To facilitate comparison, we computed the change ( ∆) in the average muscle 256 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint 11 activations, net muscle moment, and metabolic rates for each gait cycle between unassisted and assisted 257 conditions, and presented it as a percentage of that value in unassisted conditions as in (16) 258 ∆ = 𝑋̅𝑢𝑛𝑎𝑠𝑠𝑖𝑠𝑡𝑒𝑑−𝑋̅𝑎𝑠𝑠𝑖𝑠𝑡𝑒𝑑 𝑋̅𝑢𝑛𝑎𝑠𝑠𝑖𝑠𝑡𝑒𝑑 𝑥 100% (16) 259 Where 𝑋̅𝑢𝑛𝑎𝑠𝑠𝑖𝑠𝑡𝑒𝑑 and 𝑋̅𝑎𝑠𝑠𝑖𝑠𝑡𝑒𝑑 are the average values of the muscle activations, agonist and antagonist net 260 muscle moment, and metabolic rates over the gait cycle in unassisted and assisted conditions, respectively. For 261 each walking speed, we computed the average values for all subjects and gait cycles and presented the change 262 in average metabolic rates vs. change in average muscle activations, as well as the time -series of muscle 263 activations, agonist and antagonist net muscle moment, and metabolic rates between unassisted and assisted 264 walking at slow (55% PWS), normal (100% PWS), and fast walking speeds (145% PWS). In addition, to 265 complement the description of the estimated muscle-tendon mechanics and energetics, we presented the 266 activations, work rates (obtained from (11)), and metabolic rates of individual muscles for unassisted and 267 assisted conditions at normal walking speed in the supplementary material (average values among all subjects 268 and gait cycles). 269 270 3. Results 271 3.1. Influence of assistive moments on relative muscle activations and metabolic rates 272 Compared to unassisted conditions, with either actuation mode, relative muscle activation changes varied, 273 depending on the joint and muscle group assisted and with walking speed (Fig. 2). With motor -based 274 actuation, muscle activation reduced most overall with hip flexion assistance at a high walking speed; this 275 change decreased with decreasing walking speeds. The next highest muscle activation reduction was observed 276 with hip abduction assistance, which, in contrast to hip flexion assistance, was proportionally higher as walking 277 speed decreased. Muscle activations were reduced moderately with plantarflexion assistance, with a small 278 relation to walking speed. Muscle activations were nearly unchanged with knee extension assistance at any 279 walking speed. 280 With spring-based actuation, relative muscle activations were nearly with identical trends as with motor -based 281 actuation, though all proportionally lower, with one major contrast, that muscle activation changes with 282 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint 12 plantarflexion assistance were inversely proportional to walking speed, and were practically zero at fast 283 walking speed. 284 While relative muscle activation changes were largely proportional to relative metabolic rate changes, they did 285 not always translate to reduced metabolic cost; spring-based assistance actually resulted in 2-4% higher 286 metabolic rates, most notably with hip flexion assistance at slow and normal speeds and with hip abduction 287 assistance at fast speed. The largest reduction (average ca. 7%) of relative metabolic rate with spring -based 288 actuation resulted from ankle plantarflexion assistance at slow speed, followed ca. 5% reduction with hip 289 flexion reduction at fast speed. 290 Motor-based assistance always caused a decrease in metabolic rates, wherein the highest relative reduction 291 (average ca. 24%) was observed with ankle plantarflexion assistance at fast speed, followed by ankle 292 plantarflexion assistance at lower speeds (22% at normal and 16% at slow speeds) then by hip flexion 293 assistance (15%) at high walking speed. Hip flexion assistance at low speed had practically no effect on 294 metabolic rate change, nor did knee extension assistance at any speed. 295 Analyses of the influence of ideal assistive moments at each joint are described in more detail in the next 296 section. 297 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint 13 298 299 Fig. 2. Change in metabolic rates vs. reduction of muscle activations, shown as % of unassisted conditions, at 300 slow, normal, and fast walking speeds with motor-based and spring-based assistance. The values shown are 301 average  1 standard deviation among all subjects and gait cycles. 302 303 3.2. Ankle plantarflexion assistance 304 The computed ideal motor-based plantarflexion assistance contributed with more than half of the net ankle 305 plantarflexion moment, and only increased slightly in magnitude with increasing speed; the net plantarflexion 306 muscle moment was reduced by approximately 60% at all speeds (Fig. 3), while the net dorsiflexor muscle 307 moment increased by up to 4%. With motor-based assistance, the total metabolic rate peak at all speeds was 308 reduced near terminal stance and pre-swing phases. Overall, these differences resulted in a 16% reduction in 309 overall metabolic rate in slow walking and a 24% reduction in fast walking. Soleus activation was nearly 310 Decrease Increase .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint 14 entirely reduced with motor-based plantarflexion assistance, and, to a lower extent, gastrocnemius activation 311 (Supplementary Fig. 2). The gastrocnemius still generated a moment during midstance, contributing to the 312 ankle plantarflexion and knee flexion moments. Tibialis anterior activation remains nearly the same compared 313 to unassisted conditions during mid-stance. 314 Ideal spring-based plantarflexion assistance contributed with more overall moments in slow walking than in 315 normal or fast walking; the plantarflexor muscle moment was reduced by more than half (55%) in slow 316 walking, by 43% in normal and 27% in fast walking. With spring-based assistance, the total metabolic rate peak 317 was reduced by 7% in slow walking, 2% in normal, and 1% in fast walking. The peak ankle dorsiflexion angle, 318 which sets the assistive moment peak, occurs earlier in the gait cycle as walking speed increases; the spring 319 can thus not maximally assist the muscle plantarflexor moment peak at pre -swing to the same extent as 320 motor-based actuation can. During terminal stance, soleus and gastrocnemius activations were reduced with 321 spring-based assistance, but tibialis anterior activations were increased. Muscle fiber velocities increased in 322 the soleus and gastrocnemius during push-off, and, as a result, muscle positive power increased 323 (supplementary Fig. 2 and 3), resulting in increased total metabolic rate peak at all speeds even though the 324 average metabolic rate over the gait cycle decreased (supplementary Fig. 4). 325 Fig. 3. Assistive device moments [first column], net muscle moments [second column], muscle activations 326 [third column], and metabolic rates [fourth column] in unassisted conditions and with motor -based and spring-327 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint 15 based assistance during slow (upper row), normal (middle row), and fast (lower row) walking speed, shown as 328 average values among all subjects and gait cycles. Positive moment refers to ankle plantarflexion, and negative 329 to ankle dorsiflexion. Change in ankle plantarflexion (𝛥𝜏𝑃) and ankle dorsiflexion (ΔτD) moments, muscle 330 activations (Δa), and metabolic rates (ΔE), shown as % of unassisted conditions, are presented. 331 332 3.3. Knee extensor assistance 333 Ideal motor-based knee extensor assistance was only effectual in loading response and early midstance, where 334 it contributed with nearly all knee extensor moments at all walking speeds (Fig. 4). The assistive moment 335 resulted in a net muscle moment decrease of 47-50% at all speeds. The assistive moment resulted in a slightly 336 increased knee flexion moment just after initial contact, more so at high walking speed. With assistance, 337 during loading response, vasti activations decreased, but muscle power increased (supplementary Fig. 2 and 338 3); knee extension assistance resulted in decreased vasti tendon force, which decreased tendon strain and 339 thus increased fiber velocities. As a result, both muscle negative power during loading response and muscle 340 positive power in early midstance increased. Consequently, metabolic rates from vasti dynamics decreased in 341 loading response and increased slightly in early midstance (supplementary Fig. 4). Overall, the motor -based 342 assistance resulted in a 2-3% metabolic rate reduction at all walking speeds. 343 Ideal spring-based knee extensor assistance was likewise only effectual in loading response and early 344 midstance, to practically the same degree as motor-based assistance. It resulted in similar reductions in muscle 345 activations, net muscle moments, and metabolic energy rates, yet to a somewhat lower magnitude; with 346 assistance, the total metabolic rate was reduced by approximately 2% at all speeds. 347 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint 16 348 Fig. 4. Assistive device moments [first column], net muscle moments [second column], muscle activations 349 [third column], and metabolic rates [fourth column] in unassisted conditions and with motor -based and spring-350 based assistance during slow (upper row), normal (middle row), and fast (lower row) walking speed, shown as 351 average values among all subjects and gait cycles. Positive moment refers to knee extension, and negative to 352 knee flexion. Change in knee extension (𝛥𝜏𝐸) and knee flexion (ΔτF) moments, muscle activations (Δa), and 353 metabolic rates (ΔE), shown as % of unassisted conditions, are presented. 354 355 3.4. Hip flexor assistance 356 Ideal motor-based hip flexor assistance was effectual largely in terminal stance and preswing , increasing with 357 walking speed, and mid- to late swing (Fig. 5) and to a very small amount immediately after initial contact. The 358 assistive moment resulted in substantially decreased hip flexion muscle moment, ranging from 66% reduction 359 at slow and 80% at fast walking speeds, mostly observed in terminal stance and preswing, but also increased 360 hip extensor muscle moment in mid- to late swing. The increase in hip extensor muscle moment was relatively 361 similar at all speeds but led to a particularly remarkable 168% increase in net hip extensor muscle moment in 362 slow walking, during which the extensor moment was negligible without assistance. The increase in hip 363 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint 17 extension muscle moment reflects a trade-off between decreased activations in the hip flexion muscle group 364 (see psoas in supplementary Fig. 2) at the expense of slightly increased activations in other muscle groups (see 365 biceps femoris long head and vastus lateralis in supplementary Fig. 2). As a result, with assistance, metabolic 366 rates were reduced during terminal stance and pre-swing but increased during early to mid-swing. Overall, 367 with motor-based hip flexor assistance, the total metabolic rate decreased by 15% in fast walking, 9% in 368 normal and 1% in slow walking. Without assistance, the vasti were most active during loading response and 369 mid-stance, but with motor-based assistance, the vasti were also active during mid-swing, likely as antagonists 370 for the increased biceps femoris long head activation. This activation pattern resulted in increased vasti force 371 and power during the swing phase (supplementary Fig. 3), which caused vasti negative power during initial 372 swing and positive power during mid-swing. As muscle positive power is associated with higher metabolic 373 rates, motor-based assistance resulted in slightly increased metabolic rates during mid-swing. 374 Ideal spring-based hip flexor assistance was only effectual during terminal stance and preswing, as it is set by 375 spring engagement as the hip extends during mid-stance and disengagement as the hip flexes in early swing 376 (Fig. 5). With assistance, the hip flexor muscle moment was greatly reduced during this phase; the net hip 377 flexor muscle moment was reduced by 64 in slow and 69-70% in faster walking. However, its engagement 378 during midstance, which accommodated energy storage during hip extension, resulted in increased hip 379 extensor muscle during midstance. With assistance, the gluteus maximum and semimembranosus activations 380 increased in midstance, and vasti activation increased in initial swing (Supplementary Fig. 2), resulting in higher 381 muscle positive power and, thereby, metabolic rates during the mid- to terminal stance. In contrast, the 382 increased vasti activation corresponded to higher muscle negative power, which did not increase metabolic 383 rates (supplementary Fig. 3 and 4). Overall, with spring-based hip flexor assistance, the total metabolic rate 384 decreased only during fast walking (4%) but increased by 2-4% in normal and slow walking. 385 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint 18 Fig. 5. Assistive device moments [first column], net muscle moments [second column], muscle activations 386 [third column], and metabolic rates [fourth column] in unassisted conditions and with motor -based and spring-387 based assistance during slow (upper row), normal (middle row), and fast (lower row) walking speed, shown as 388 average values among all subjects and gait cycles. Positive moment refers to hip extension, and negative to hip 389 flexion. Change in hip extension (𝛥𝜏𝐸) and hip flexion (ΔτF) moments, muscle activations (Δa), and metabolic 390 rates (ΔE), shown as % of unassisted conditions, are presented. 391 392 3.5. Hip abduction assistance 393 Ideal motor-based hip abduction assistance was effectual throughout nearly the entire stance phase, 394 accounting for the majority of net hip abduction moment, reducing the hip abductor muscle moment by more 395 than 70% at all walking speeds and more at slower speeds (Fig. 6). The assistive moment peaked at 396 approximately 20 and 50% of the gait cycle. Whereas the first assistive peak reduced the net muscle hip 397 abduction moments and hip abductor muscle activations, the second peak increased the net hip adduction 398 moment and adductor muscle activations (Supplementary Fig. 2), with correspondingly higher hip adductor 399 muscle positive power and metabolic rates (supplementary Fig. 3 and 4). Overall, with motor -based hip 400 abduction assistance, the total metabolic rate decreased by 7-8% in normal and fast walking and by 5% in slow 401 walking. 402 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint 19 Ideal spring-based hip abduction assistance was likewise effectual during nearly the entire stance phase. With 403 spring-based assistance, the hip abductor muscle moment decreased by approximately 60% at all walking 404 speeds. However, the overall metabolic rate was nearly unchanged; with assistance, the metabolic rate 405 decreased by 2% in slow walking, was unchanged in normal walking, and increased by 2% in fast walking. The 406 spring-based assistance had a less pronounced peak in terminal stance than motor -based assistance, as it was 407 set by the hip adduction angle, and a hip abductor muscle moment was still required in this phase, though 408 lower than without assistance. Similar to motor-based assistance, spring-based assistance involved a trade-off 409 between decreased hip abductor muscle activation and increased hip adductor muscle activation 410 (supplementary Fig. 2). This trade-off was, however, even less effective in reducing activations and metabolic 411 rates than the motor-based assistance. While metabolic rates decreased in gluteus medialis and minimus, and 412 tensor fasciae latae with spring-based assistance, they did not decrease as much as with motor -based 413 assistance. Also, metabolic rates in the gluteus maximum during mid-stance were higher with spring-based 414 than with motor-based assistance. 415 416 Fig. 6. Assistive device moments [first column], net muscle moments [second column], muscle activations 417 [third column], and metabolic rates [fourth column] in unassisted conditions and with motor -based and spring-418 based assistance during slow (upper row), normal (middle row), and fast (lower row) walking speed, shown as 419 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint 20 average values among all subjects and gait cycles. Positive moment refers to hip abduction, and negative to hip 420 adduction. Change in hip abduction (𝛥𝜏𝐵) and hip adduction (ΔτD) moments, muscle activations (Δa), and 421 metabolic rates (ΔE), shown as % of unassisted conditions, are presented. 422 423 4. Discussion 424 In this simulation study, ideal assistive moments were identified, defined as those that reduced the squared 425 sum of muscle activations. The assistive moment profiles in a motor -based actuator could have a variable 426 profile, but those with the spring-based actuators were constrained by joint kinematics. The ideal assistive 427 moments in both actuator modes substantially decreased net muscle moments, i.e., the net joint moment 428 minus the assistive moment. Whereas motor-based assistance always reduced total metabolic rates to some 429 extent, varying among joints and speeds, spring-based assistance did not always reduce metabolic rates. The 430 most notable reductions in metabolic rates resulted from motor-based plantarflexion assistance, followed by 431 motor-based hip flexion assistance, both more effective at higher speeds. Motor -based hip abduction 432 assistance also reduced metabolic rate, interestingly inversely with walking speed. Spring -based hip flexion 433 assistance at slow and normal speeds and hip abduction assistance at normal and fast speeds reduced muscle 434 activations to some extent, but these reductions did not translate to reduced metabolic rates; rates were 435 unchanged or even increased slightly. Knee extension assistance, regardless of actuation mode or walking 436 speed, had little to no effect on metabolic rates, even though it was able to contribute to a majority of the net 437 extensor moment in loading response. 438 Our findings indicate that an assistive strategy based on minimal muscle activations does not translate to a 439 decreased metabolic rate. Assistive devices are generally designed to support motion, which might involve 440 reducing net muscle moment, activations, and metabolic rates (2). The optimal assistive moments in our 441 simulations decreased the overall sum of muscle activation, which in turn reduced muscle forces and, thus, net 442 muscle moment in the assisted muscle groups, though occasionally increasing demand on antagonist muscles. 443 Reduction of metabolic rates was, however, more difficult to achieve. Metabolic energy models estimate 444 muscle energy rates based on heat dissipation and muscle power. Heat dissipation is the sum of various 445 subcomponents that depend on fiber velocities, such as the shortening and lengthening heat rates and the 446 activation and maintenance heat rates (30). All components are related to muscle activations. As such, 447 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint 21 metabolic rate is diminished if heat dissipation and muscle power are zero, which only happens when muscle 448 activations are zero. However, assistive moments that submaximally reduce muscle activations, i.e. lower but 449 non-zero activations, can result in higher metabolic rates if the muscle positive power increase outweighs the 450 heat dissipation decrease. We observed two instances in which this was the case, both with spring -based 451 assistance: With plantarflexion assistance during preswing, and with knee extension assistance during mid -452 stance, wherein lower activation was associated with higher fiber velocity in the assisted muscles, which 453 increased muscle positive power, and thereby metabolic rates. In several cases, assistive moment resulted in 454 increased demand, and thus muscle positive power and metabolic rates, in antagonist muscles, for instance, 455 with hip flexion assistance during mid-swing and with hip abduction assistance during loading response. It is 456 not a straightforward assumption that assistive moments that reduce overall muscle activations will also 457 reduce metabolic rates. We did, however, identify several cases in which the assistive moment reduced 458 agonist muscle activations to zero, without substantially increasing antagonist muscle activations, and resulted 459 in overall reduced metabolic rates, specifically with motor-based ankle plantarflexion and knee extension 460 assistance. 461 Our identified ideal motor-based plantarflexion assistive moment profiles are similar to previously reported 462 moment profiles that were found to reduce metabolic rates, but our ideal spring -based plantarflexion assistive 463 moments disagreed somewhat. At normal walking speed, the ideal motor -based plantarflexion assistive 464 moment profile was similar to those identified from human-the-loop optimization studies that aimed for 465 minimal metabolic rates (3,31). The peak in the profile we identified was near 50% of the gait cycle, agreeing 466 with other identified optimal moment trajectories (3,31). However, our simulation predicts a metabolic 467 reduction (22%) at normal walking speed, which is substantially larger than experimentally reported metabolic 468 rate reduction reported by Zhang et al. at a slightly lower speed (14% metabolic reduction at 1.25 m/s) (31). 469 We also found that with motor-based plantarflexion assistance, the metabolic reduction should be more 470 pronounced as walking speed increases, in agreement with prior studies (3,31). However, experimental 471 comparisons with spring-based assistance are more challenging, as very few studies have studied muscle 472 activation changes across walking speeds. In a study from Nuckols and Sawicki using an exoskeleton emulator 473 to mimic spring-like actuation, the optimal spring stiffness to reduce metabolic rates was similar at speeds of 474 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint 22 1.25 and 1.75 m/s (32). This finding does not align with our results, presumably because our optimal assistive 475 moment does not directly minimize metabolic rates. 476 Our findings of decreased muscle activation but increased muscle positive power during loading response with 477 knee extension assistance might explain why previous experimental studies with this aim have failed to reduce 478 metabolic rates during walking. Metabolic rate reduction with knee extension assistance has only been 479 achieved with motor-based actuation compared to wearing a powered-off exoskeleton (33,34) or in 480 challenging environments such as carrying loads while walking on an inclined surface (35). Our simulation 481 suggests that, with knee extensor assistance, the knee extensor muscle forces decrease during loading 482 response, resulting in decreased tendon strain and, thus, higher muscle fiber velocities and muscle positive 483 power, which in turn actually increased the muscle metabolic rates. Jackson et al. reported a similar finding 484 that even if muscle moment is reduced with an ankle exoskeleton, the metabolic cost can increase if the 485 muscle moment corresponds to increasing muscle positive work (7). In our study, we found little to no 486 potential benefit from knee extensor assistance, regardless of actuation mode or walking speed. 487 Spring-based and especially motor-based hip flexion assistance shows promise in reducing metabolic rates, 488 particularly at fast walking speeds. Only a few studies have evaluated the effects of hip flexion assistance with 489 powered devices (36–38). Studies of devices that reduced metabolic cost parametrized the assistive profile 490 such that it began at maximum hip extension (38) or provided a power burst during a predefined time window 491 (corresponding to 25% of the gait cycle) (37); both studies found that the optimal peak assistive moment 492 should be later than the net hip flexion moment. These assistive trajectories disagree somewhat with the 493 optimal assistive moments that we identified. We also found that the increased antagonist hip extensor 494 muscle moment during the swing phase counterintuitively reduced metabolic rate, in agreement with findings 495 reported in another simulation study (9). It is possible that this counterintuitive benefit from simulation 496 studies might not translate experimentally; it has, to the best of our knowledge, not been tested 497 experimentally. Furthermore, previous experimental studies reported a metabolic decrease of 8.8% with hip 498 flexion assistance compared to unassisted conditions (38) and 6.1% compared with a powered-off exoskeleton 499 (39), which agrees with our predictions (9% near preferred walking speed). With spring -based hip flexion 500 assistance, only two experimental studies reported metabolic rate reduction (19,40). Zhou et al. reported 7.2% 501 metabolic rate reduction at 1.5 m/s and suggested that optimal assistive is likely speed -dependent (19). We 502 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint 23 found no metabolic reduction with spring-based assistance at preferred walking speed but a small decrease 503 (4%) in fast walking. To the best of our knowledge, no previous study has evaluated the influence of hip flexion 504 assistance, neither spring- or motor-based, at different walking speeds. Our simulation supports a hypothesis 505 that hip flexion assistance from either actuation mode can potentially decrease metabolic rate as walking 506 speed increases. 507 Our findings indicate little to no potential for hip abduction assistance to substantially reduce metabolic rates. 508 Only one recent pilot experimental study has evaluated metabolic rates with hip abduction assistance (41). 509 Kim et al. found that human-in-the-loop optimization with a motor-based actuation did not reduce metabolic 510 rates. They attributed this finding to the role of the hip abductors during walking, which stabilizes the hip and 511 maintains balance, and suggested that minimizing their muscle activity may not be an advantageous strategy 512 for metabolic rate reduction. Our findings likewise suggest that, as speed varies, preserving balance remains 513 the dominant objective of hip abductor activation, as metabolic rate changes are inversely proportional to 514 speed. 515 The two major limitations of our study are 1) the assumption that motion patterns in unassisted and assisted 516 conditions are unchanged, which is a dilemma in all musculoskeletal simulations with constrained kinematics, 517 and 2) the optimal assistive moments defined with the objective function in the muscle redundancy solver that 518 seeks the task-specific exoskeleton moments that minimize the sum of squared muscle activations. The 519 assumption of unchanged kinematics might be reasonable in spring -based devices at the ankle (18) and hip 520 (19), as they can be made lightweight and reasonably comfortable. With powered ankle and hip assistive 521 devices, despite evidence suggesting that joint angles and net joint moments might be preserved (36,42), 522 human-device adaptation is complex and more likely to alter the user’s motor control strategy and, thereby, 523 joint kinematics and moments (43). Regarding the second limitation, we formulated the optimization problem 524 to solve muscle redundancy and to identify optimal assistive moments using the same objective function, 525 specifically minimal muscle activation. We assumed the paradigm that human walking is achieved by minimal 526 muscle activations, and that metabolic efficiency is driven by this neuromuscular strategy. As such the assistive 527 moments in our simulation represent the optimal for minimal muscle activations, but we demonstrated that 528 minimal activations and metabolic rates are not necessarily aligned. Our findings warrant further simulation 529 studies that identify assistive moments with optimization goals other than minimal activations, ideally with 530 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint 24 goals of minimal metabolic cost. In this regard, it might be beneficial to explicitly incorporate the goal of the 531 assistive moment separately from the objective function to solve muscle redundancy. This can theoretically be 532 achieved by adopting a bilevel optimization scheme as proposed by Nguyen et al. (44), in which a low level 533 optimization problem might deal with solving muscle redundancy, while a upper level problem searches for 534 optimal assistance with a task criterion e.g., maximal walking stability or minimal metabolic cost. Furthermore, 535 forward dynamics simulation studies with assistive devices have great potential to predict musculoskeletal 536 skeletal dynamics and to explicitly formulate the goals with assistive devices. 537 538 5. Data availability 539 Experimental data to replicate this study, such as subject anthropometrics, marker trajectories, and ground 540 reaction forces are available in the following repository: https://figshare.com/s/1caa0e14c79426cb12cc 541 542 6. Code availability 543 The scripts for simulating exoskeleton assistance with tuned muscle-tendon parameters and computing 544 metabolic rates based on the metabolic energy models are available in the following repository : 545 https://github.com/israelluis/Exoskeletons_ExperimentGuidedCalibration 546 547 7. Author contributions 548 Israel Luis: Conceptualization, Software, Formal analysis, Writing – Original Draft Preparation. Maarten 549 Afschrift: Software, Formal analysis and Writing - Review & Editing. Elena M. Gutierrez-Farewik: Formal 550 analysis, Writing - Review & Editing and Supervision. 551 552 8. Competing interests 553 The authors declare no competing interests. 554 555 9. Materials & Correspondence 556 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint 25 Correspondence and requests for materials should be addressed to Israel Luis. 557 558 10. Acknowledgment 559 Authors acknowledge the funding sources provided by the Swedish Research Council (nr 2018 -00750) and 560 Promobilia Foundation (nr 18200). 561 562 11. Bibliography 563 1. Sawicki GS, Beck ON, Kang I, Young AJ. The exoskeleton expansion: Improving walking and running 564 economy. J Neuroeng Rehabil. 2020;17(1):1–9. 565 2. Young AJ, Ferris DP. State-of-the-art and Future Directions for Robotic Lower Limb Exoskeletons. IEEE 566 Transactions on Neural Systems and Rehabilitation Engineering. 2016;PP(99):1 –1. 567 3. Slade P, Kochenderfer MJ, Delp SL, Collins SH. 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