{"paper_id":"cad07404-016c-49de-87ba-e596066772df","body_text":"1 \n \nSprings vs. motors: Ideal assistance in the lower limbs 1 \nduring walking at different speeds 2 \n 3 \nIsrael Luis1*, Maarten Afschrift2, Elena M. Gutierrez-Farewik1,3 4 \n1 KTH MoveAbility Lab, Dept. Engineering Mechanics, KTH Royal Institute of Technology, Stockholm, Sweden  5 \n2 Faculty of Behavioural and Movement Sciences, VU Amsterdam, Amsterdam, The Netherlands 6 \n3 Department of Women’s and Children’s Health, Karolinska Institutet, Stockholm, Sweden  7 \n* Corresponding author, email: ailp@kth.se 8 \n 9 \nAbstract 10 \nRecent years have witnessed breakthroughs in assistive exoskeletons; both passive and active devices have 11 \nreduced metabolic costs near preferred walking speed by assisting muscle actions. Metabolic reductions at 12 \nmultiple speeds should thus also be attainable. Musculoskeletal simulation can potentially predict the 13 \ninteraction between assistive moments, muscle-tendon mechanics, and walking energetics. In this study, we 14 \nsimulated devices’ optimal assistive moments based on minimal muscle activations during walking with 15 \nprescribed kinematics and dynamics. We used a generic musculoskeletal model with calibrated muscle -tendon 16 \nparameters and computed metabolic rates from muscle actions. We then simulated walking across multiple 17 \nspeeds and with two ideal actuation modes – motor-based and spring-based – to assist ankle plantarflexion, 18 \nknee extension, hip flexion, and hip abduction and compared computed metabolic rates. We found that both 19 \nactuation modes considerably reduced physiological joint moments but did not always reduce metabolic rates. 20 \nCompared to unassisted conditions, motor-based ankle plantarflexion and hip flexion assistance reduced 21 \nmetabolic rates, and this effect was more pronounced as walking speed increased. Spring -based hip flexion 22 \nand abduction assistance increased metabolic rates at some walking speeds despite a moderate decrease in 23 \nsome muscle activations. Both modes of knee extension assistance reduced metabolic rates to a small extent, 24 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint \n\n2 \n \neven though the actuation contributed with practically the entire net knee extension moment during stance. 25 \nMotor-based hip abduction assistance reduced metabolic rates more than spring-based assistance, though this 26 \nreduction was relatively small. Future work should experimentally validate the effects of assistive moments 27 \nand refine modeling assumptions accordingly. Our computational workflow is freely available online.  28 \n 29 \nAuthor Summary 30 \nWe used simulation to identify ideal assistance at major lower limb joints that can potentially be produced by 31 \nmotor-based or spring-based assistive devices in slow, normal, and fast walking. We found that assistance 32 \nfrom both actuation modes decreased muscle activations and net muscle moments to varying extents, 33 \ndepending on joint and walking speed, but they did not always reduce metabolic energy of muscles. Motor-34 \nbased assistance was overall more effective than spring-based assistance, and spring-based assistance at times 35 \nincreased the metabolic energy.  The largest metabolic energy reductions occurred with motor-based 36 \nplantarflexion assistance, followed by motor-based hip flexion assistance, both more notably at higher speeds. 37 \nMotor-based hip abduction assistance also reduced metabolic energy, somewhat inversely with walking speed. 38 \nSpring-based assistance was overall less effective than motor-based assistance but did reduce metabolic 39 \nenergy with plantarflexion assistance in slow walking and with hip flexion assistance in fast walking.  Knee 40 \nextension assistance, regardless of actuation mode or walking speed, had little to no influence on metabolic 41 \nenergy. Our simulation findings do not support knee extension assistance at all, nor spring -based hip flexion 42 \nassistance in slow walking or hip abduction assistance at any speed if a device goal is to reduce muscle 43 \nactivations.  44 \n 45 \nKeywords 46 \nGait exoskeletons, musculoskeletal modeling, optimal control, locomotion, assistive technology. 47 \n1. Introduction 48 \nMultiple lower limb exoskeletons have made breakthroughs in the past decade by improving walking and 49 \nrunning efficiency (1). Increasingly efficient actuators and batteries, better strategies for human -device 50 \ncontrol, and lighter structures and physical interfaces have continuously improved assistance efficiency (2). 51 \nCurrent efforts to bridge the gap between laboratory-based observations and real-world benefits focus 52 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint \n\n3 \n \nfrequently on refining methods to identify optimal assistance (3), integrating human movement intention into 53 \nexoskeleton control (4), and expanding exoskeleton use to make them suitable across multiple locomotion 54 \nmodes (5). In this regard, musculoskeletal simulations can complement these efforts by guiding hypotheses 55 \nabout muscle-device interaction and revealing causal relationships in experimental observations (6).  56 \nPrior musculoskeletal simulation studies of exoskeleton assistance have provided insights into muscle-tendon 57 \nmechanics and energetics, though simulation findings have not always agreed with experimental observations. 58 \nResearchers have, through simulations, estimated the influence of exoskeleton assistance on tendon energy 59 \nstorage and release (7), on muscle fiber operating lengths and velocities (8), and on muscle activations, all of 60 \nwhich influence muscle energetics and metabolic rates (9–11). In theory, a model-based approach can be used 61 \nto design exoskeleton controllers that result in optimal muscle dynamics and minimal energy cost. For 62 \ninstance, Franks et al. (12) used simulations with prescribed kinematics and dynamics to predict optimal multi-63 \njoint assistive moments, i.e. leading to minimal metabolic rates during walking. In subsequent experiments 64 \nwith these assistive moments, they indeed observed reduced muscle excitations and metabolic costs, but not 65 \nas much as the model predicted. Uchida et al. (11) used a similar computational approach to predict optimal 66 \nassistive moments for running; these were later evaluated experimentally by Lee et al. (13), who reported 67 \ndecreased metabolic cost, but again not as much as the model predicted. Some discrepancies between 68 \nsimulations and experiments are to be expected, as modeling approaches rely on a number of assumptions, 69 \nincluding simplified muscle control and dynamics, simplified or no user-device interaction forces, massless 70 \ndevices, and unchanged kinematics. Model-based approaches thus have potential use in informing the design 71 \nof assistive interventions, more so if they can accurately estimate muscle energetics and metabolic rates. 72 \nMost musculoskeletal modeling studies aiming to predict optimal assistive moments have focused on gait at or 73 \nnear preferred walking speed, even though daily activities encompass  a wide range of speeds and locomotion 74 \nmodes. Several studies have predicted optimal lower limb exoskeleton assistive moments near preferred 75 \nwalking speed in normal and loaded conditions, such as carrying extra weight (6)(9). Other activities, such as 76 \nwalking at various speeds or stair ascent, have been studied less (6). To the best of our knowledge, only two 77 \nmusculoskeletal-based studies have examined optimal assistance during gait at a range of speeds; Uchida et al. 78 \nexamined mechanics and energetics in young adults with ideal actuators during running at 2 and 5 m/s (11), 79 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint \n\n4 \n \nand Cseke et al., in elderly adults during walking at self-selected slow (0.86 m/s), comfortable (1.22 m/s) and 80 \nfast (1.53 m/s) speeds (10).  81 \nWhereas variable assistive torque profiles that can theoretically be provided by a motor can be expected to 82 \nreduce metabolic rates, spring-based actuation, i.e., a spring or elastic component that can store potential 83 \nenergy during elongation and then release it during shortening, can also potentially influence muscle dynamics 84 \nand gait energetics. Spring-based exoskeletons can also potentially be lighter and less cumbersome than 85 \nmotorized exoskeletons. Spring-based assistance should theoretically be effective during gait phases 86 \ncharacterized by joint power absorption followed by joint power generation , which is the case with ankle 87 \ndorsi-/plantarflexion and hip flex-/extension in pre-swing, hip ab-/adduction during midstance, and knee flex-88 \n/extension during loading response and midstance (14). Spring-based actuators have been observed 89 \nexperimentally to substantially decrease physiological joint moments, i.e., joint moments from muscle actions, 90 \nbut with negligible metabolic reduction (15). Prior musculoskeletal simulation studies have provided insights 91 \ninto the causal relationship between muscle mechanics and spring -based assistive moments near preferred 92 \nspeed (16,17) predictions have agreed with experimental observations to some degree (18,19).  Simulations 93 \nthat investigate the influence of spring-based assistance on muscle energetics can potentially inform device 94 \ndesign. 95 \nThe objectives of the study were thus to simulate how two modes of assistance, spring -based and motor-96 \nbased, at individual lower limb joints affect computed muscle dynamics and metabolic rates during walking at 97 \nvarious speeds. We hypothesized that assistive moments will reduce muscle activations and metabolic rates 98 \nand that motor-based actuation will be more efficient than spring-based actuation. Also, assisting ankle 99 \nplantarflexion with any mode of assistance will yield the largest reduction of metabolic rates compared to 100 \nunassisted conditions among all the muscle groups and at all walking speeds.    101 \n 102 \n2. Methods 103 \n2.1 Musculoskeletal simulation workflow 104 \nWe implemented a simulation workflow to estimate muscle dynamics and metabolic rates during walking 105 \nusing musculoskeletal models with calibrated muscle-tendon parameters and recorded motion. We used 106 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint \n\n5 \n \npreviously reported experimental data (20) and the OpenSim software (21) to scale a generic musculoskeletal 107 \nmodel and compute joint kinematics and dynamics. We calibrated muscle-tendon parameters in the scaled 108 \nmusculoskeletal model to better represent fiber lengths and passive angle -moment relationships (22). Then, 109 \nwe performed musculoskeletal simulations while walking with prescribed kinematics and dynamics  using 110 \ntrajectory optimization (23) (Fig. 1). 111 \n 112 \n 113 \nFig. 1.  Simulation workflow per each subject. Inverse kinematics and dynamics are computed using the 114 \nOpenSim workflow. Moment arms and muscle-tendon lengths are computed from the inverse kinematic 115 \nsolution using the Muscle Analysis tool from OpenSim. We then tuned the muscle -tendon parameters – 116 \noptimal fiber length, tendon slack length, and tendon stiffness – such that the simulated muscle fiber lengths 117 \nand excursions matched reported findings from ultrasound imaging. Next, we tuned the muscle passive force 118 \ncurves such that the simulated passive moments matched passive angle -moment joint relationships reported 119 \nin an in vivo study. Finally, we simulated walking across various speeds with no actuators and with the various 120 \nassistive actuators. 121 \n 122 \nExperimental data 123 \nExperimental motion data: marker trajectories and ground reaction force of five unimpaired (2/3 male/female, 124 \n[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 \npublication were used for this study (20). In brief, subjects walked on a treadmill at a range of walking speeds, 126 \nspecifically 55%, 70%, 85%, 100%, 115%, 130%, and 145% of their estimated preferred walking speed (PWS) . 127 \nSubjects then walked along a lab pathway and emulated different walking speeds by matching recorded 128 \ncadences from treadmill walking. Marker positions (100 Hz), based on the Conventional Gait Model with the 129 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint \n\n6 \n \nExtended-foot model (CGM 2.4) and ground reaction forces (1000 Hz) were measured using optical motion 130 \ncapture (Vicon V16, Oxford, UK) and strain gauge force platforms (AMTI, Watertown, MA, USA), respectively.  131 \nMusculoskeletal model, joint kinematics, and inverse dynamics  132 \nA generic musculoskeletal model developed by Rajagopal et al. (24) with modified hip abductor muscle paths 133 \n(25) was selected for this study. We scaled the generic model using OpenSim’s Scale Tool, which adjusted 134 \nmuscle paths, skeletal geometry, and segment inertial properties to fit anthropometric dimensions obtained 135 \nfrom a captured static calibration trial.  We adjusted the maximum isometric force of the soleus, 136 \ngastrocnemius, and tibialis anterior as per Arnold et al. (26).  137 \nMarker trajectories and ground reaction forces throughout three gait cycles per subject at low (55% PWS), 138 \nnormal (100% PWS), and fast (145% PWS) walking speeds were analyzed with inverse kinematics and inverse 139 \ndynamics using OpenSim 4.1. Marker tracking weights for inverse kinematics were selected to minimize the 140 \nerror between experimental and virtual markers. The subtalar and metatarsal joints were fixed at neutral 141 \nanatomical positions. 142 \nTuning of muscle-tendon parameters 143 \nWe used a computational tool to tune muscle-tendon parameters such that each subject’s muscle excitations, 144 \nfiber lengths, and passive moments best resembled experimental observations (22). The tuning was done in 145 \ntwo steps. First, we tuned optimal fiber lengths, tendon slack lengths, and tendon stiffnesses of the 146 \ngastrocnemius lateralis, gastrocnemius medialis, soleus, and vasti (lateralis, medialis, and intermedius) to 147 \nmatch muscle fiber lengths and excursions obtained from those reported in from ultrasound imaging (27,28). 148 \nThen, we tuned muscle passive force-length curves to match the reported passive moment at various ankle, 149 \nknee, and hip joint angles from an in vivo study (29). Compared to simulation with the original generic model, 150 \nthese steps result in estimated muscle excitations that better agree with observed electromyography signals 151 \n(22).  152 \nSolving muscle redundancy  153 \nOur implementation is based on the simulation framework proposed by De Groote et al. (23), which uses 154 \ndirect collocation dynamic optimization and implicitly incorporates activation and contraction dynamics. 155 \nMuscle excitations, states, and state derivatives were computed based on the assumption that the muscle 156 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint \n\n7 \n \nredundancy is solved by the optimization criterion of minimal muscle activations squared. Two other terms are 157 \npresent in the objective function to improve the feasibility and convergence of the formulation. Reserve 158 \nactuators in each degree of freedom are added to guarantee the problem’s feasibility, and their use is 159 \npenalized in the objective function. Also, a term that minimizes muscle fiber velocities is included to improve 160 \nnumerical computation (L2 regularization). The objective function is implemented as (1):  161 \nmin (𝑤𝑎 ∫ ∑ 𝑎𝑛\n2(𝑡)𝑁\n𝑛=1\n𝑡𝑓\n𝑡𝑖\n𝑑𝑡+ +𝑤𝑟 ∫ ∑ 𝑒𝑅𝑗\n2 (𝑡)𝐽\n𝑗=1\n𝑡𝑓\n𝑡𝑖\n𝑑𝑡+ 𝑤𝑣 ∫ ∑ 𝑣̃𝑛\n2(𝑡)𝑁\n𝑛=1\n𝑡𝑓\n𝑡𝑖\n𝑑𝑡)  (1) 162 \nWhere 𝑎𝑛 is muscle activation of muscle 𝑛, 𝑒𝑅𝑗 is the excitation of the reserve actuator of joint 𝑗, 𝑣̃𝑛 is the 163 \nnormalized fiber velocity of muscle 𝑛, 𝑡𝑓 and 𝑡𝑖 are the initial and final times of the gait cycle, respectively; 𝑁 164 \nand 𝐽 are the total number of muscles and joints in the musculoskeletal model, respectively; and 𝑤𝑎, 𝑤𝑟 and 165 \n𝑤𝑣 are the weights of the terms in the objective function related to the muscle activations, reserve actuators, 166 \nand fiber velocities, respectively. The sum of the moments produced by muscle-tendon and reserve actuators 167 \nequals the net joint moment obtained from inverse dynamics at each joint. This condition was implemented as 168 \na constraint in the optimization problem as in (2) 169 \n𝜏𝐼𝐷𝑗(𝑡) = 𝜏𝑀𝑈𝑆𝑗(𝑡) + 𝑒𝑅𝑗(𝑡)𝑇𝑅,      𝑗 = 1, … , 𝐽   (2) 170 \nWhere, at joint 𝑗, 𝜏𝐼𝐷𝑗 is the net joint moment, 𝜏𝑀𝑈𝑆𝑗 is the moment produced by the muscle-tendon 171 \nactuators, subsequently referred to here as “muscle moments”, and  𝑇𝑅 is the magnitude of the reserve 172 \nactuator. ((Thinking about Svein’s comments, maybe comment about inertia components in the solver?))  173 \n3.2 Determining optimal assistive moments 174 \nOptimal assistive moments were computed using scaled musculoskeletal models with tuned muscle -tendon 175 \nparameters, inverse kinematics, and inverse dynamics solutions as described above. Constraints and design 176 \nvariables were added when solving the muscle redundancy to model assistive moments at various muscle 177 \ngroups. For each mode of actuation, ideal assistive moments were added at each simulated gait cycle to assist 178 \nspecific muscle groups individually: plantarflexion, knee extension, hip flexion, and hip abduction. Per each 179 \nsubject, nine gait cycles were simulated (three gait cycles per walking speed); therefore, nine assistive 180 \nmoments per mode of actuation and muscle group were determined.  181 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint \n\n8 \n \nWhen solving the muscle redundancy, the objective function was the same as in unassisted conditions but 182 \nconstraints were added to model assistive device moment to assist muscle-tendon actuators in reproducing 183 \nthe inverse dynamics, i.e., the sum of the muscle moment, reserve actuator moment, and assistive device 184 \nmoment equals the net joint moment at each joint, as in (3) 185 \n𝜏𝐼𝐷𝑗(𝑡) = 𝜏𝑀𝑈𝑆𝑗(𝑡) + 𝑒𝑅𝑗(𝑡)𝑇𝑅 + 𝜏𝐸𝑋𝑂𝑀,𝑆𝑗\n(𝑡),     𝑗 = 1, … , 𝐽   (3) 186 \nWhere 𝜏𝐸𝑋𝑂𝑀,𝑆𝑗\nis the assistive device moment at joint 𝑗.  In this regard, the assistive moments are the optimal 187 \nsolutions to assist muscles based on minimal summed muscle activations squared.  188 \nMotor-based moment profiles 189 \nThe motor-based actuation was modeled as a unidirectional ideal moment at the corresponding degree of 190 \nfreedom in the musculoskeletal model. The assistive moment ( 𝜏𝐸𝑋𝑂𝑀(𝑡)) was implemented as a time-series 191 \ndesign variable. Its magnitude was constrained to assist the aimed muscle group explicitly. For instance, 192 \n𝜏𝐸𝑋𝑂𝑀(𝑡) < 0 for assisting ankle plantarflexion corresponds to ankle plantarflexion moment (agonist muscle 193 \ngroup) and avoids generating ankle dorsiflexion moment (antagonist muscle group). The motor-based 194 \nactuation was not constrained in its trajectory; hence, it could have any value at each point in time to assist a 195 \nmuscle group. Optimal assistive moment based on motor-based actuation was determined individually for 196 \neach subject and gait cycle.  197 \nSpring-based device parameters 198 \nThe spring-based actuator was modeled as a unidirectional torsional spring that engages and disengages in 199 \nspecific joint angles. To implement this, we introduced three design variables: engaged timing (𝑡𝑐), disengaged 200 \ntiming (𝑡𝑑), and spring stiffness (𝑘𝑟), we added a constraint to impose that the angle at which the spring 201 \nengaged and disengaged are similar as in (4) 202 \n(𝑞(𝑡𝑐) − 𝑞(𝑡𝑑))\n2\n< 0.01     (4) 203 \nWhere 𝑞(𝑡) is the joint angle corresponding to the assisted muscle group. The assistive moment was 204 \ncomputed as a product of the spring stiffness and the angle within the period that the spring is engaged as in 205 \n(5) 206 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint \n\n9 \n \n𝜏𝐸𝑋𝑂𝑆(𝑡) = 𝑘𝑟𝑞𝐸𝑋𝑂(𝑡)      (5) 207 \nWhere 𝑞𝐸𝑋𝑂(𝑡) is the joint angle displacement from the angle of engagement. This angle was modeled using 208 \nhyperbolic tangent function as in (6), (7), (8), and (9) 209 \n𝑇𝑒(𝑡) = 0.5 + 0.5 tanh(𝑏(𝑡𝑖𝑚𝑒(𝑡) − 𝑡𝑐))     (6) 210 \n𝑇𝑑(𝑡) = 0.5 + 0.5 tanh (𝑏(𝑡𝑑 − 𝑡𝑖𝑚𝑒(𝑡)))    (7) 211 \n𝑇𝑎𝑐𝑡𝑖𝑣𝑒(𝑡) = 𝑇𝑒(𝑡)𝑇𝑑(𝑡)     (8) 212 \n𝑞𝐸𝑋𝑂(𝑡) = 𝑇𝑎𝑐𝑡𝑖𝑣𝑒(𝑡)(𝑞(𝑡) − 𝑞(𝑡𝑐))     (9) 213 \nWhere 𝑇𝑒 is the start of the engaged period, 𝑇𝑑 is the start of the disengagement period, and 𝑇𝑎𝑐𝑡𝑖𝑣𝑒(𝑡) is the 214 \nperiod where spring is engaged.  215 \nWe selected 𝑤𝑎, 𝑤𝑟 and 𝑤𝑣 as 1, 1000, and 0.001; thus, the use of reserve actuators was heavily penalized, and 216 \nthe influence of fiber velocities was relatively small. Also, we selected 𝑇𝑅 as 100 Nm, and b as 1000 since it 217 \nprovided a smooth yet steep transition between null to assistive moment generation (Supplementary Fig. 1). 218 \nOptimal assistive moment based on spring-based actuation was determined individually for each subject and 219 \ngait cycle. 220 \n3.3 Metabolic rate computation  221 \nFor each subject/gait cycle, each speed, and each device, the metabolic rate of each muscle was computed 222 \nbased on the muscle excitations, states, and state derivatives obtained from our optimization routine using a 223 \nmetabolic energy model proposed by Bhargava et al. (30), which we previously reported to agree with 224 \nrecorded metabolic rates obtained from spiroergonometry (20). In brief, muscle metabolic rate is computed as 225 \nin (10) 226 \n𝐸̇𝑛(𝑡) = 𝑊̇ 𝐶𝐸𝑛(𝑡) + 𝐻̇ 𝑛(𝑡)     (10) 227 \nWhere 𝐸̇𝑛, 𝑊̇ 𝐶𝐸𝑛 and 𝐻̇ 𝑛 are the metabolic rate, contractile element work rate, and heat rate, respectively, of 228 \nmuscle 𝑛. The contractile element work rate, also called muscle power, is computed as in (11)  229 \n𝑊̇ 𝐶𝐸𝑛(𝑡) = 𝐹𝐶𝐸𝑛(𝑡) 𝑉𝐶𝐸𝑛(𝑡)    (11) 230 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint \n\n10 \n \nWhere 𝐹𝐶𝐸𝑛 and 𝑉𝐶𝐸𝑛 are the muscle force and fiber velocity, respectively, of muscle 𝑛. The heat rate depends 231 \non muscle mass, muscle activations, fiber velocities, and a function that approximates the size principle of 232 \nmotor recruitment, explained in detail by Bhargava et al. (30). The original formulation did not explicitly 233 \naddress negative metabolic rates, which are possible during eccentric contractions if muscle negative power 234 \nexceeds the heat rate. As a negative metabolic rate is physiologically questionable, we adjusted it in such cases 235 \nby updating the heat rate and re-computing the metabolic rate as in (12) and (13) 236 \n𝐻̇ 𝑛,𝑚𝑜𝑑(𝑡) = −𝑊̇ 𝐶𝐸𝑛(𝑡) − 𝐻̇ 𝑛(𝑡),     𝐸̇𝑛(𝑡) < 0  (12) 237 \n𝐸̇𝑛(𝑡) = 𝑊̇ 𝐶𝐸𝑛(𝑡) + 𝐻̇ 𝑛,𝑚𝑜𝑑(𝑡)     (13) 238 \nThe metabolic rates for one leg (𝐸̇𝐿) is computed as the sum of all the individual muscle metabolic rates as in 239 \n(14) 240 \n𝐸̇𝐿(𝑡) = ∑ 𝐸̇𝑛(𝑡)𝑁\n𝑛=1        (14) 241 \nF. Data and statistical analysis 242 \nWe evaluated the change of muscle activations, physiological joint moments, and metabolic rates between 243 \nunassisted and assisted with two actuation modes during walking across speeds.  Muscle activations were the 244 \nsum of all the muscle activations in one leg obtained from solving the muscle redundancy and divided by the 245 \nnumber of muscles. Net muscle moments are defined here as the net joint moments minus the assistive 246 \nmoments (3). Net muscle moments for agonists (plantarflexion, knee extension, hip flexion, and hip abduction) 247 \nand antagonists (dorsiflexion, knee flexion, hip extension, and hip adduction) were computed in 248 \ncorrespondence to the muscle group assisted, e.g., with ideal plantarflexion assistive moments, plantarflexion 249 \nand dorsiflexion net muscle moments were presented. Metabolic rates were the sum of all the muscle 250 \nmetabolic rates in one leg (13). Average muscle activations, agonist and antagonist net muscle moment, and 251 \nmetabolic rates in unassisted and assisted conditions over each gait cycle were computed as the integral of its 252 \ncorresponding time-series divided by the gait cycle duration as in (15) 253 \n𝑋̅ =\n1\n𝑡𝑓−𝑡𝑖\n∫ 𝑋\n𝑡𝑓\n𝑡𝑖\n𝑑𝑡    (15) 254 \nWhere 𝑋̅ are the average values of the muscle activations, agonist and antagonist net muscle moment, and 255 \nmetabolic rates over a gait cycle. To facilitate comparison, we computed the change ( ∆) in the average muscle 256 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint \n\n11 \n \nactivations, net muscle moment, and metabolic rates for each gait cycle between unassisted and assisted 257 \nconditions, and presented it as a percentage of that value in unassisted conditions as in (16)  258 \n∆ =\n𝑋̅𝑢𝑛𝑎𝑠𝑠𝑖𝑠𝑡𝑒𝑑−𝑋̅𝑎𝑠𝑠𝑖𝑠𝑡𝑒𝑑\n𝑋̅𝑢𝑛𝑎𝑠𝑠𝑖𝑠𝑡𝑒𝑑\n 𝑥 100%     (16) 259 \nWhere 𝑋̅𝑢𝑛𝑎𝑠𝑠𝑖𝑠𝑡𝑒𝑑 and 𝑋̅𝑎𝑠𝑠𝑖𝑠𝑡𝑒𝑑 are the average values of the muscle activations, agonist and antagonist net 260 \nmuscle moment, and metabolic rates over the gait cycle in unassisted and assisted conditions, respectively.  For 261 \neach walking speed, we computed the average values for all subjects and gait cycles and presented the change 262 \nin average metabolic rates vs. change in average muscle activations, as well as the time -series of muscle 263 \nactivations, agonist and antagonist net muscle moment, and metabolic rates between unassisted and assisted 264 \nwalking at slow (55% PWS), normal (100% PWS), and fast walking speeds (145% PWS). In addition, to 265 \ncomplement the description of the estimated muscle-tendon mechanics and energetics, we presented the 266 \nactivations, work rates (obtained from (11)), and metabolic rates of individual muscles for unassisted and 267 \nassisted conditions at normal walking speed in the supplementary material (average values among all subjects 268 \nand gait cycles).  269 \n 270 \n3. Results 271 \n3.1. Influence of assistive moments on relative muscle activations and metabolic rates  272 \nCompared to unassisted conditions, with either actuation mode, relative muscle activation changes varied, 273 \ndepending on the joint and muscle group assisted and with walking speed (Fig. 2). With motor -based 274 \nactuation, muscle activation reduced most overall with hip flexion assistance at a high walking speed; this 275 \nchange decreased with decreasing walking speeds.  The next highest muscle activation reduction was observed 276 \nwith hip abduction assistance, which, in contrast to hip flexion assistance, was proportionally higher as walking 277 \nspeed decreased. Muscle activations were reduced moderately with plantarflexion assistance, with a small 278 \nrelation to walking speed. Muscle activations were nearly unchanged with knee extension assistance at any 279 \nwalking speed.  280 \nWith spring-based actuation, relative muscle activations were nearly with identical trends as with motor -based 281 \nactuation, though all proportionally lower, with one major contrast, that muscle activation changes with 282 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint \n\n12 \n \nplantarflexion assistance were inversely proportional to walking speed, and were practically zero at fast 283 \nwalking speed.  284 \nWhile relative muscle activation changes were largely proportional to relative metabolic rate changes, they did 285 \nnot always translate to reduced metabolic cost; spring-based assistance actually resulted in 2-4% higher 286 \nmetabolic rates, most notably with hip flexion assistance at slow and normal speeds and with hip abduction 287 \nassistance at fast speed. The largest reduction (average ca. 7%) of relative metabolic rate with spring -based 288 \nactuation resulted from ankle plantarflexion assistance at slow speed, followed ca. 5% reduction with hip 289 \nflexion reduction at fast speed. 290 \nMotor-based assistance always caused a decrease in metabolic rates, wherein the highest relative reduction 291 \n(average ca. 24%) was observed with ankle plantarflexion assistance at fast speed, followed by ankle 292 \nplantarflexion assistance at lower speeds (22% at normal and 16% at slow speeds) then by hip flexion 293 \nassistance (15%) at high walking speed. Hip flexion assistance at low speed had practically no effect on 294 \nmetabolic rate change, nor did knee extension assistance at any speed.  295 \nAnalyses of the influence of ideal assistive moments at each joint are described in more detail in the next 296 \nsection.  297 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint \n\n13 \n \n 298 \n 299 \nFig. 2.  Change in metabolic rates vs. reduction of muscle activations, shown as % of unassisted conditions, at 300 \nslow, normal, and fast walking speeds with motor-based and spring-based assistance. The values shown are 301 \naverage  1 standard deviation among all subjects and gait cycles.   302 \n 303 \n3.2. Ankle plantarflexion assistance 304 \nThe computed ideal motor-based plantarflexion assistance contributed with more than half of the net ankle 305 \nplantarflexion moment, and only increased slightly in magnitude with increasing speed; the net plantarflexion 306 \nmuscle moment was reduced by approximately 60% at all speeds (Fig. 3), while the net dorsiflexor muscle 307 \nmoment increased by up to 4%. With motor-based assistance, the total metabolic rate peak at all speeds was 308 \nreduced near terminal stance and pre-swing phases. Overall, these differences resulted in a 16% reduction in 309 \noverall metabolic rate in slow walking and a 24% reduction in fast walking. Soleus activation was nearly 310 \nDecrease \nIncrease \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint \n\n14 \n \nentirely reduced with motor-based plantarflexion assistance, and, to a lower extent, gastrocnemius activation 311 \n(Supplementary Fig. 2). The gastrocnemius still generated a moment during midstance, contributing to the 312 \nankle plantarflexion and knee flexion moments. Tibialis anterior activation remains nearly the same compared 313 \nto unassisted conditions during mid-stance.  314 \nIdeal spring-based plantarflexion assistance contributed with more overall moments in slow walking than in 315 \nnormal or fast walking; the plantarflexor muscle moment was reduced by more than half (55%) in slow 316 \nwalking, by 43% in normal and 27% in fast walking. With spring-based assistance, the total metabolic rate peak 317 \nwas reduced by 7% in slow walking, 2% in normal, and 1% in fast walking.  The peak ankle dorsiflexion angle, 318 \nwhich sets the assistive moment peak, occurs earlier in the gait cycle as walking speed increases; the spring 319 \ncan thus not maximally assist the muscle plantarflexor moment peak at pre -swing to the same extent as 320 \nmotor-based actuation can. During terminal stance, soleus and gastrocnemius activations were reduced with 321 \nspring-based assistance, but tibialis anterior activations were increased. Muscle fiber velocities increased in 322 \nthe soleus and gastrocnemius during push-off, and, as a result, muscle positive power increased 323 \n(supplementary Fig. 2 and 3), resulting in increased total metabolic rate peak at all speeds even though the 324 \naverage metabolic rate over the gait cycle decreased (supplementary Fig. 4).  325 \nFig. 3.  Assistive device moments [first column], net muscle moments [second column], muscle activations 326 \n[third column], and metabolic rates [fourth column] in unassisted conditions and with motor -based and spring-327 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint \n\n15 \n \nbased assistance during slow (upper row), normal (middle row), and fast (lower row) walking speed, shown as 328 \naverage values among all subjects and gait cycles. Positive moment refers to ankle plantarflexion, and negative 329 \nto ankle dorsiflexion. Change in ankle plantarflexion (𝛥𝜏𝑃) and ankle dorsiflexion (ΔτD) moments, muscle 330 \nactivations (Δa), and metabolic rates (ΔE), shown as % of unassisted conditions, are presented. 331 \n 332 \n3.3. Knee extensor assistance 333 \nIdeal motor-based knee extensor assistance was only effectual in loading response and early midstance, where 334 \nit contributed with nearly all knee extensor moments at all walking speeds (Fig. 4). The assistive moment 335 \nresulted in a net muscle moment decrease of 47-50% at all speeds. The assistive moment resulted in a slightly 336 \nincreased knee flexion moment just after initial contact, more so at high walking speed. With assistance, 337 \nduring loading response, vasti activations decreased, but muscle power increased (supplementary Fig. 2 and 338 \n3); knee extension assistance resulted in decreased vasti tendon force, which decreased tendon strain and 339 \nthus increased fiber velocities. As a result, both muscle negative power during loading response and muscle 340 \npositive power in early midstance increased. Consequently, metabolic rates from vasti dynamics decreased in 341 \nloading response and increased slightly in early midstance (supplementary Fig. 4). Overall, the motor -based 342 \nassistance resulted in a 2-3% metabolic rate reduction at all walking speeds.  343 \nIdeal spring-based knee extensor assistance was likewise only effectual in loading response and early 344 \nmidstance, to practically the same degree as motor-based assistance. It resulted in similar reductions in muscle 345 \nactivations, net muscle moments, and metabolic energy rates, yet to a somewhat lower magnitude; with 346 \nassistance, the total metabolic rate was reduced by approximately 2% at all speeds.  347 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint \n\n16 \n \n 348 \nFig. 4.  Assistive device moments [first column], net muscle moments [second column], muscle activations 349 \n[third column], and metabolic rates [fourth column] in unassisted conditions and with motor -based and spring-350 \nbased assistance during slow (upper row), normal (middle row), and fast (lower row) walking speed, shown as 351 \naverage values among all subjects and gait cycles. Positive moment refers to knee extension, and negative to 352 \nknee flexion. Change in knee extension (𝛥𝜏𝐸) and knee flexion (ΔτF) moments, muscle activations (Δa), and 353 \nmetabolic rates (ΔE), shown as % of unassisted conditions, are presented. 354 \n 355 \n3.4. Hip flexor assistance 356 \nIdeal motor-based hip flexor assistance was effectual largely in terminal stance and preswing , increasing with 357 \nwalking speed, and mid- to late swing (Fig. 5) and to a very small amount immediately after initial contact. The 358 \nassistive moment resulted in substantially decreased hip flexion muscle moment, ranging from 66% reduction 359 \nat slow and 80% at fast walking speeds, mostly observed in terminal stance and preswing, but also increased 360 \nhip extensor muscle moment in mid- to late swing. The increase in hip extensor muscle moment was relatively 361 \nsimilar at all speeds but led to a particularly remarkable 168% increase in net hip extensor muscle moment in 362 \nslow walking, during which the extensor moment was negligible without assistance. The increase in hip 363 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint \n\n17 \n \nextension muscle moment reflects a trade-off between decreased activations in the hip flexion muscle group 364 \n(see psoas in supplementary Fig. 2) at the expense of slightly increased activations in other muscle groups (see 365 \nbiceps femoris long head and vastus lateralis in supplementary Fig. 2). As a result, with assistance, metabolic 366 \nrates were reduced during terminal stance and pre-swing but increased during early to mid-swing. Overall, 367 \nwith motor-based hip flexor assistance, the total metabolic rate decreased by 15% in fast walking, 9% in 368 \nnormal and 1% in slow walking. Without assistance, the vasti were most active during loading response and 369 \nmid-stance, but with motor-based assistance, the vasti were also active during mid-swing, likely as antagonists 370 \nfor the increased biceps femoris long head activation. This activation pattern resulted in increased vasti force 371 \nand power during the swing phase (supplementary Fig. 3), which caused vasti negative power during initial 372 \nswing and positive power during mid-swing. As muscle positive power is associated with higher metabolic 373 \nrates, motor-based assistance resulted in slightly increased metabolic rates during mid-swing.   374 \nIdeal spring-based hip flexor assistance was only effectual during terminal stance and preswing, as it is set by 375 \nspring engagement as the hip extends during mid-stance and disengagement as the hip flexes in early swing 376 \n(Fig. 5). With assistance, the hip flexor muscle moment was greatly reduced during this phase; the net hip 377 \nflexor muscle moment was reduced by 64 in slow and 69-70% in faster walking. However, its engagement 378 \nduring midstance, which accommodated energy storage during hip extension, resulted in increased hip 379 \nextensor muscle during midstance. With assistance, the gluteus maximum and semimembranosus activations 380 \nincreased in midstance, and vasti activation increased in initial swing (Supplementary Fig. 2), resulting in higher 381 \nmuscle positive power and, thereby, metabolic rates during the mid- to terminal stance. In contrast, the 382 \nincreased vasti activation corresponded to higher muscle negative power, which did not increase metabolic 383 \nrates (supplementary Fig. 3 and 4). Overall, with spring-based hip flexor assistance, the total metabolic rate 384 \ndecreased only during fast walking (4%) but increased by 2-4% in normal and slow walking.   385 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint \n\n18 \n \nFig. 5.  Assistive device moments [first column], net muscle moments [second column], muscle activations 386 \n[third column], and metabolic rates [fourth column] in unassisted conditions and with motor -based and spring-387 \nbased assistance during slow (upper row), normal (middle row), and fast (lower row) walking speed, shown as 388 \naverage values among all subjects and gait cycles. Positive moment refers to hip extension, and negative to hip 389 \nflexion. Change in hip extension (𝛥𝜏𝐸) and hip flexion (ΔτF) moments, muscle activations (Δa), and metabolic 390 \nrates (ΔE), shown as % of unassisted conditions, are presented. 391 \n 392 \n3.5. Hip abduction assistance 393 \nIdeal motor-based hip abduction assistance was effectual throughout nearly the entire stance phase, 394 \naccounting for the majority of net hip abduction moment, reducing the hip abductor muscle moment by more 395 \nthan 70% at all walking speeds and more at slower speeds (Fig. 6). The assistive moment peaked at 396 \napproximately 20 and 50% of the gait cycle. Whereas the first assistive peak reduced the net muscle hip 397 \nabduction moments and hip abductor muscle activations, the second peak increased the net hip adduction 398 \nmoment and adductor muscle activations (Supplementary Fig. 2), with correspondingly higher hip adductor 399 \nmuscle positive power and metabolic rates (supplementary Fig. 3 and 4). Overall, with motor -based hip 400 \nabduction assistance, the total metabolic rate decreased by 7-8% in normal and fast walking and by 5% in slow 401 \nwalking.  402 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint \n\n19 \n \nIdeal spring-based hip abduction assistance was likewise effectual during nearly the entire stance phase. With 403 \nspring-based assistance, the hip abductor muscle moment decreased by approximately 60% at all walking 404 \nspeeds.  However, the overall metabolic rate was nearly unchanged; with assistance, the metabolic rate 405 \ndecreased by 2% in slow walking, was unchanged in normal walking, and increased by 2% in fast walking.  The 406 \nspring-based assistance had a less pronounced peak in terminal stance than motor -based assistance, as it was 407 \nset by the hip adduction angle, and a hip abductor muscle moment was still required in this phase, though 408 \nlower than without assistance.  Similar to motor-based assistance, spring-based assistance involved a trade-off 409 \nbetween decreased hip abductor muscle activation and increased hip adductor muscle activation 410 \n(supplementary Fig. 2). This trade-off was, however, even less effective in reducing activations and metabolic 411 \nrates than the motor-based assistance. While metabolic rates decreased in gluteus medialis and minimus, and 412 \ntensor fasciae latae with spring-based assistance, they did not decrease as much as with motor -based 413 \nassistance. Also, metabolic rates in the gluteus maximum during mid-stance were higher with spring-based 414 \nthan with motor-based assistance.  415 \n 416 \nFig. 6.  Assistive device moments [first column], net muscle moments [second column], muscle activations 417 \n[third column], and metabolic rates [fourth column] in unassisted conditions and with motor -based and spring-418 \nbased assistance during slow (upper row), normal (middle row), and fast (lower row) walking speed, shown as 419 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint \n\n20 \n \naverage values among all subjects and gait cycles. Positive moment refers to hip abduction, and negative to hip 420 \nadduction. Change in hip abduction (𝛥𝜏𝐵) and hip adduction (ΔτD) moments, muscle activations (Δa), and 421 \nmetabolic rates (ΔE), shown as % of unassisted conditions, are presented. 422 \n 423 \n4. Discussion 424 \nIn this simulation study, ideal assistive moments were identified, defined as those that reduced the squared 425 \nsum of muscle activations. The assistive moment profiles in a motor -based actuator could have a variable 426 \nprofile, but those with the spring-based actuators were constrained by joint kinematics.  The ideal assistive 427 \nmoments in both actuator modes substantially decreased net muscle moments, i.e., the net joint moment 428 \nminus the assistive moment.  Whereas motor-based assistance always reduced total metabolic rates to some 429 \nextent, varying among joints and speeds, spring-based assistance did not always reduce metabolic rates. The 430 \nmost notable reductions in metabolic rates resulted from motor-based plantarflexion assistance, followed by 431 \nmotor-based hip flexion assistance, both more effective at higher speeds. Motor -based hip abduction 432 \nassistance also reduced metabolic rate, interestingly inversely with walking speed. Spring -based hip flexion 433 \nassistance at slow and normal speeds and hip abduction assistance at normal and fast speeds reduced muscle 434 \nactivations to some extent, but these reductions did not translate to reduced metabolic rates; rates were 435 \nunchanged or even increased slightly. Knee extension assistance, regardless of actuation mode or walking 436 \nspeed, had little to no effect on metabolic rates, even though it was able to contribute to a majority of the net 437 \nextensor moment in loading response.  438 \nOur findings indicate that an assistive strategy based on minimal muscle activations does not translate to a 439 \ndecreased metabolic rate. Assistive devices are generally designed to support motion, which might involve 440 \nreducing net muscle moment, activations, and metabolic rates (2). The optimal assistive moments in our 441 \nsimulations decreased the overall sum of muscle activation, which in turn reduced muscle forces and, thus, net 442 \nmuscle moment in the assisted muscle groups, though occasionally increasing demand on antagonist muscles. 443 \nReduction of metabolic rates was, however, more difficult to achieve. Metabolic energy models estimate 444 \nmuscle energy rates based on heat dissipation and muscle power. Heat dissipation is the sum of various 445 \nsubcomponents that depend on fiber velocities, such as the shortening and lengthening heat rates and the 446 \nactivation and maintenance heat rates  (30). All components are related to muscle activations. As such, 447 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint \n\n21 \n \nmetabolic rate is diminished if heat dissipation and muscle power are zero, which only happens when muscle 448 \nactivations are zero. However, assistive moments that submaximally reduce muscle activations, i.e. lower but 449 \nnon-zero activations, can result in higher metabolic rates if the muscle positive power  increase outweighs the 450 \nheat dissipation decrease. We observed two instances in which this was the case, both with spring -based 451 \nassistance: With plantarflexion assistance during preswing, and with knee extension assistance during mid -452 \nstance, wherein lower activation was associated with higher fiber velocity in the assisted muscles, which 453 \nincreased muscle positive power, and thereby metabolic rates. In several cases, assistive moment resulted in 454 \nincreased demand, and thus muscle positive power and metabolic rates, in antagonist muscles, for instance, 455 \nwith hip flexion assistance during mid-swing and with hip abduction assistance during loading response. It is 456 \nnot a straightforward assumption that assistive moments that reduce overall muscle activations will also 457 \nreduce metabolic rates. We did, however, identify several cases in which the assistive moment reduced 458 \nagonist muscle activations to zero, without substantially increasing antagonist muscle activations, and resulted 459 \nin overall reduced metabolic rates, specifically with motor-based ankle plantarflexion and knee extension 460 \nassistance. 461 \nOur identified ideal motor-based plantarflexion assistive moment profiles are similar to previously reported 462 \nmoment profiles that were found to reduce metabolic rates, but our ideal spring -based plantarflexion assistive 463 \nmoments disagreed somewhat. At normal walking speed, the ideal motor -based plantarflexion assistive 464 \nmoment profile was similar to those identified from human-the-loop optimization studies that aimed for 465 \nminimal metabolic rates (3,31). The peak in the profile we identified was near 50% of the gait cycle, agreeing 466 \nwith other identified optimal moment trajectories (3,31). However, our simulation predicts a metabolic 467 \nreduction (22%) at normal walking speed, which is substantially larger than experimentally reported metabolic 468 \nrate reduction reported by Zhang et al. at a slightly lower speed (14% metabolic reduction at 1.25 m/s)  (31). 469 \nWe also found that with motor-based plantarflexion assistance, the metabolic reduction should be more 470 \npronounced as walking speed increases, in agreement with prior studies (3,31). However, experimental 471 \ncomparisons with spring-based assistance are more challenging, as very few studies have studied muscle 472 \nactivation changes across walking speeds. In a study from Nuckols and Sawicki using an exoskeleton emulator 473 \nto mimic spring-like actuation, the optimal spring stiffness to reduce metabolic rates was similar at speeds of 474 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint \n\n22 \n \n1.25 and 1.75 m/s (32). This finding does not align with our results, presumably because our optimal assistive 475 \nmoment does not directly minimize metabolic rates. 476 \nOur findings of decreased muscle activation but increased muscle positive power during loading response with 477 \nknee extension assistance might explain why previous experimental studies with this aim have failed to reduce 478 \nmetabolic rates during walking. Metabolic rate reduction with knee extension assistance has only been 479 \nachieved with motor-based actuation compared to wearing a powered-off exoskeleton (33,34) or in 480 \nchallenging environments such as carrying loads while walking on an inclined surface (35). Our simulation 481 \nsuggests that, with knee extensor assistance, the knee extensor muscle forces decrease during loading 482 \nresponse, resulting in decreased tendon strain and, thus, higher muscle fiber velocities and muscle positive 483 \npower, which in turn actually increased the muscle metabolic rates. Jackson et al. reported a similar finding 484 \nthat even if muscle moment is reduced with an ankle exoskeleton, the metabolic cost can increase if the 485 \nmuscle moment corresponds to increasing muscle positive work (7). In our study, we found little to no 486 \npotential benefit from knee extensor assistance, regardless of actuation mode or walking speed.  487 \nSpring-based and especially motor-based hip flexion assistance shows promise in reducing metabolic rates, 488 \nparticularly at fast walking speeds. Only a few studies have evaluated the effects of hip flexion assistance with 489 \npowered devices (36–38). Studies of devices that reduced metabolic cost parametrized the assistive profile 490 \nsuch that it began at maximum hip extension (38) or provided a power burst during a predefined time window 491 \n(corresponding to 25% of the gait cycle) (37); both studies found that the optimal peak assistive moment 492 \nshould be later than the net hip flexion moment. These assistive trajectories disagree somewhat with the 493 \noptimal assistive moments that we identified. We also found that the increased antagonist hip extensor 494 \nmuscle moment during the swing phase counterintuitively reduced metabolic rate, in agreement with findings 495 \nreported in another simulation study (9). It is possible that this counterintuitive benefit from simulation 496 \nstudies might not translate experimentally; it has, to the best of our knowledge, not been tested 497 \nexperimentally. Furthermore, previous experimental studies reported a metabolic decrease of 8.8% with hip 498 \nflexion assistance compared to unassisted conditions (38) and 6.1% compared with a powered-off exoskeleton 499 \n(39), which agrees with our predictions (9% near preferred walking speed). With spring -based hip flexion 500 \nassistance, only two experimental studies reported metabolic rate reduction (19,40). Zhou et al. reported 7.2% 501 \nmetabolic rate reduction at 1.5 m/s and suggested that optimal assistive is likely speed -dependent (19). We 502 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint \n\n23 \n \nfound no metabolic reduction with spring-based assistance at preferred walking speed but a small decrease 503 \n(4%) in fast walking. To the best of our knowledge, no previous study has evaluated the influence of hip flexion 504 \nassistance, neither spring- or motor-based, at different walking speeds. Our simulation supports a hypothesis 505 \nthat hip flexion assistance from either actuation mode can potentially decrease metabolic rate as walking 506 \nspeed increases. 507 \nOur findings indicate little to no potential for hip abduction assistance to substantially reduce metabolic rates. 508 \nOnly one recent pilot experimental study has evaluated metabolic rates with hip abduction assistance (41). 509 \nKim et al. found that human-in-the-loop optimization with a motor-based actuation did not reduce metabolic 510 \nrates. They attributed this finding to the role of the hip abductors during walking, which stabilizes the hip and 511 \nmaintains balance, and suggested that minimizing their muscle activity may not be an advantageous strategy 512 \nfor metabolic rate reduction. Our findings likewise suggest that, as speed varies, preserving balance remains 513 \nthe dominant objective of hip abductor activation, as metabolic rate changes are inversely proportional to 514 \nspeed.  515 \nThe two major limitations of our study are 1) the assumption that motion patterns in unassisted and assisted 516 \nconditions are unchanged, which is a dilemma in all musculoskeletal simulations with constrained kinematics, 517 \nand 2) the optimal assistive moments defined with the objective function in the muscle redundancy solver that 518 \nseeks the task-specific exoskeleton moments that minimize the sum of squared muscle activations. The 519 \nassumption of unchanged kinematics might be reasonable in spring -based devices at the ankle (18) and hip 520 \n(19), as they can be made lightweight and reasonably comfortable. With powered ankle and hip assistive 521 \ndevices, despite evidence suggesting that joint angles and net joint moments might be preserved  (36,42), 522 \nhuman-device adaptation is complex and more likely to alter the user’s motor control strategy and, thereby, 523 \njoint kinematics and moments (43). Regarding the second limitation, we formulated the optimization problem 524 \nto solve muscle redundancy and to identify optimal assistive moments using the same objective function, 525 \nspecifically minimal muscle activation. We assumed the paradigm that human walking is achieved by minimal 526 \nmuscle activations, and that metabolic efficiency is driven by this neuromuscular strategy. As such the assistive 527 \nmoments in our simulation represent the optimal for minimal muscle activations, but we demonstrated that 528 \nminimal activations and metabolic rates are not necessarily aligned. Our findings warrant further simulation 529 \nstudies that identify assistive moments with optimization goals other than minimal activations, ideally with 530 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint \n\n24 \n \ngoals of minimal metabolic cost. In this regard, it might be beneficial to explicitly incorporate the goal of the 531 \nassistive moment separately from the objective function to solve muscle redundancy.  This can theoretically be 532 \nachieved by adopting a bilevel optimization scheme as proposed by Nguyen et al. (44), in which a low level 533 \noptimization problem might deal with solving muscle redundancy, while a upper level problem searches for 534 \noptimal assistance with a task criterion e.g., maximal walking stability or minimal metabolic cost. Furthermore, 535 \nforward dynamics simulation studies with assistive devices have great potential to predict musculoskeletal 536 \nskeletal dynamics and to explicitly formulate the goals with assistive devices.  537 \n 538 \n5. Data availability  539 \nExperimental data to replicate this study, such as subject anthropometrics, marker trajectories, and ground 540 \nreaction forces are available in the following repository: https://figshare.com/s/1caa0e14c79426cb12cc 541 \n 542 \n6. Code availability 543 \nThe scripts for simulating exoskeleton assistance with tuned muscle-tendon parameters and computing 544 \nmetabolic rates based on the metabolic energy models are available in the following repository : 545 \nhttps://github.com/israelluis/Exoskeletons_ExperimentGuidedCalibration 546 \n 547 \n7. Author contributions 548 \nIsrael Luis: Conceptualization, Software, Formal analysis, Writing – Original Draft Preparation. Maarten 549 \nAfschrift: Software, Formal analysis and Writing - Review & Editing. Elena M. Gutierrez-Farewik: Formal 550 \nanalysis, Writing - Review & Editing and Supervision. 551 \n 552 \n8. Competing interests 553 \nThe authors declare no competing interests. 554 \n 555 \n9. Materials & Correspondence 556 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint \n\n25 \n \nCorrespondence and requests for materials should be addressed to Israel Luis. 557 \n 558 \n10. Acknowledgment 559 \nAuthors acknowledge the funding sources provided by the Swedish Research Council (nr 2018 -00750) and 560 \nPromobilia Foundation (nr 18200). 561 \n 562 \n11. Bibliography  563 \n1. Sawicki GS, Beck ON, Kang I, Young AJ. The exoskeleton expansion: Improving walking and running 564 \neconomy. J Neuroeng Rehabil. 2020;17(1):1–9.  565 \n2. Young AJ, Ferris DP. State-of-the-art and Future Directions for Robotic Lower Limb Exoskeletons. IEEE 566 \nTransactions on Neural Systems and Rehabilitation Engineering. 2016;PP(99):1 –1.  567 \n3. 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It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 22, 2024. ; https://doi.org/10.1101/2024.01.18.576164doi: bioRxiv preprint","source_license":"CC-BY-4.0","license_restricted":false}