@misc{boyer_hayes_umberger_adamczyk_bean_brach_clark_clark_ferrucci_finley_et al._2023, title={Age-related changes in gait biomechanics and their impact on the metabolic cost of walking: Report from a National Institute on Aging workshop}, volume={173}, ISSN={["1873-6815"]}, DOI={10.1016/j.exger.2023.112102}, abstractNote={Changes in old age that contribute to the complex issue of an increased metabolic cost of walking (mass-specific energy cost per unit distance traveled) in older adults appear to center at least in part on changes in gait biomechanics. However, age-related changes in energy metabolism, neuromuscular function and connective tissue properties also likely contribute to this problem, of which the consequences are poor mobility and increased risk of inactivity-related disease and disability. The U.S. National Institute on Aging convened a workshop in September 2021 with an interdisciplinary group of scientists to address the gaps in research related to the mechanisms and consequences of changes in mobility in old age. The goal of the workshop was to identify promising ways to move the field forward toward improving gait performance, decreasing energy cost, and enhancing mobility for older adults. This report summarizes the workshop and brings multidisciplinary insight into the known and potential causes and consequences of age-related changes in gait biomechanics. We highlight how gait mechanics and energy cost change with aging, the potential neuromuscular mechanisms and role of connective tissue in these changes, and cutting-edge interventions and technologies that may be used to measure and improve gait and mobility in older adults. Key gaps in the literature that warrant targeted research in the future are identified and discussed.}, journal={EXPERIMENTAL GERONTOLOGY}, author={Boyer, Katherine A. and Hayes, Kate L. and Umberger, Brian R. and Adamczyk, Peter Gabriel and Bean, Jonathan F. and Brach, Jennifer S. and Clark, Brian C. and Clark, David J. and Ferrucci, Luigi and Finley, James and et al.}, year={2023}, month={Mar} }
 @article{mccain_dalman_berno_libera_lewek_sawicki_saul_2023, title={The influence of induced gait asymmetry on joint reaction forces}, volume={153}, ISSN={["1873-2380"]}, DOI={10.1016/j.jbiomech.2023.111581}, abstractNote={Chronic injury- or disease-induced joint impairments result in asymmetric gait deviations that may precipitate changes in joint loading associated with pain and osteoarthritis. Understanding the impact of gait deviations on joint reaction forces (JRFs) is challenging because of concurrent neurological and/or anatomical changes and because measuring JRFs requires medically invasive instrumented implants. Instead, we investigated the impact of joint motion limitations and induced asymmetry on JRFs by simulating data recorded as 8 unimpaired participants walked with bracing to unilaterally and bilaterally restrict ankle, knee, and simultaneous ankle + knee motion. Personalized models, calculated kinematics, and ground reaction forces (GRFs) were input into a computed muscle control tool to determine lower limb JRFs and simulated muscle activations guided by electromyography-driven timing constraints. Unilateral knee restriction increased GRF peak and loading rate ipsilaterally but peak values decreased contralaterally when compared to walking without joint restriction. GRF peak and loading rate increased with bilateral restriction compared to the contralateral limb of unilaterally restricted conditions. Despite changes in GRFs, JRFs were relatively unchanged due to reduced muscle forces during loading response. Thus, while joint restriction results in increased limb loading, reductions in muscle forces counteract changes in limb loading such that JRFs were relatively unchanged.}, journal={JOURNAL OF BIOMECHANICS}, author={McCain, Emily M. and Dalman, Morgan J. and Berno, Matthew E. and Libera, Theresa L. and Lewek, Michael D. and Sawicki, Gregory S. and Saul, Katherine R.}, year={2023}, month={May} }
 @article{mccain_libera_berno_sawicki_saul_lewek_2021, title={Isolating the energetic and mechanical consequences of imposed reductions in ankle and knee flexion during gait}, volume={18}, ISSN={["1743-0003"]}, DOI={10.1186/s12984-021-00812-8}, abstractNote={Abstract}, number={1}, journal={JOURNAL OF NEUROENGINEERING AND REHABILITATION}, author={McCain, Emily M. and Libera, Theresa L. and Berno, Matthew E. and Sawicki, Gregory S. and Saul, Katherine R. and Lewek, Michael D.}, year={2021}, month={Feb} }
 @article{shafer_philius_nuckols_mccall_young_sawicki_2021, title={Neuromechanics and Energetics of Walking With an Ankle Exoskeleton Using Neuromuscular-Model Based Control: A Parameter Study}, volume={9}, ISSN={["2296-4185"]}, DOI={10.3389/fbioe.2021.615358}, abstractNote={Powered ankle exoskeletons that apply assistive torques with optimized timing and magnitude can reduce metabolic cost by ∼10% compared to normal walking. However, finding individualized optimal control parameters is time consuming and must be done independently for different walking modes (e.g., speeds, slopes). Thus, there is a need for exoskeleton controllers that are capable of continuously adapting torque assistance in concert with changing locomotor demands. One option is to use a biologically inspired, model-based control scheme that can capture the adaptive behavior of the human plantarflexors during natural gait. Here, based on previously demonstrated success in a powered ankle-foot prosthesis, we developed an ankle exoskeleton controller that uses a neuromuscular model (NMM) comprised of a Hill type musculotendon driven by a simple positive force feedback reflex loop. To examine the effects of NMM reflex parameter settings on (i) ankle exoskeleton mechanical performance and (ii) users’ physiological response, we recruited nine healthy, young adults to walk on a treadmill at a fixed speed of 1.25 m/s while donning bilateral tethered robotic ankle exoskeletons. To quantify exoskeleton mechanics, we measured exoskeleton torque and power output across a range of NMM controller Gain (0.8–2.0) and Delay (10–40 ms) settings, as well as a High Gain/High Delay (2.0/40 ms) combination. To quantify users’ physiological response, we compared joint kinematics and kinetics, ankle muscle electromyography and metabolic rate between powered and unpowered/zero-torque conditions. Increasing NMM controller reflex Gain caused increases in average ankle exoskeleton torque and net power output, while increasing NMM controller reflex Delay caused a decrease in net ankle exoskeleton power output. Despite systematic reduction in users’ average biological ankle moment with exoskeleton mechanical assistance, we found no NMM controller Gain or Delay settings that yielded changes in metabolic rate. Post hoc analyses revealed weak association at best between exoskeleton and biological mechanics and changes in users’ metabolic rate. Instead, changes in users’ summed ankle joint muscle activity with powered assistance correlated with changes in their metabolic energy use, highlighting the potential to utilize muscle electromyography as a target for on-line optimization in next generation adaptive exoskeleton controllers.}, journal={FRONTIERS IN BIOENGINEERING AND BIOTECHNOLOGY}, author={Shafer, Benjamin A. and Philius, Sasha A. and Nuckols, Richard W. and McCall, James and Young, Aaron J. and Sawicki, Gregory S.}, year={2021}, month={Apr} }
 @article{krupenevich_beck_sawicki_franz_2021, title={Reduced Achilles Tendon Stiffness Disrupts Calf Muscle Neuromechanics in Elderly Gait}, ISSN={["1423-0003"]}, DOI={10.1159/000516910}, abstractNote={Older adults walk slower and with a higher metabolic energy expenditure than younger adults. In this review, we explore the hypothesis that age-related declines in Achilles tendon stiffness increase the metabolic cost of walking due to less economical calf muscle contractions and increased proximal joint work. This viewpoint may motivate interventions to restore ankle muscle-tendon stiffness, improve walking mechanics, and reduce metabolic cost in older adults. }, journal={GERONTOLOGY}, author={Krupenevich, Rebecca L. and Beck, Owen N. and Sawicki, Gregory S. and Franz, Jason R.}, year={2021}, month={Jul} }
 @article{mccain_berno_libera_lewek_sawicki_saul_2021, title={Reduced joint motion supersedes asymmetry in explaining increased metabolic demand during walking with mechanical restriction}, volume={126}, ISSN={["1873-2380"]}, DOI={10.1016/j.jbiomech.2021.110621}, abstractNote={Recent research has highlighted the complex interactions among chronic injury- or disease-induced joint limitations, walking asymmetry, and increased metabolic cost. Determining the specific metabolic impacts of asymmetry or joint impairment in clinical populations is difficult because of concurrent neurological and physiological changes. This work investigates the metabolic impact of gait asymmetry and joint restriction by unilaterally (asymmetric) and bilaterally (symmetric) restricting ankle, knee, and combined ankle and knee ranges of motion in unimpaired individuals. We calculated propulsive asymmetry, temporal asymmetry, and step-length asymmetry for an average gait cycle; metabolic rate; average positive center of mass power using the individual limbs method; and muscle effort using lower limb electromyography measurements weighted by corresponding physiological cross-sectional areas. Unilateral restriction caused propulsive and temporal asymmetry but less metabolically expensive gait than bilateral restriction. Changes in asymmetry did not correlate with changes in metabolic cost. Interestingly, bilateral restriction increased average positive center of mass power compared to unilateral restriction. Further, increased average positive center of mass power correlated with increased energy costs, suggesting asymmetric step-to-step transitions did not drive metabolic changes. The number of restricted joints reduces available degrees of freedom and may have a larger metabolic impact than gait asymmetry, as this correlated significantly with increases in metabolic rate for 7/9 participants. These results emphasize symmetry is not by definition metabolically optimal, indicate that the mechanics underlying symmetry are meaningful, and suggest that available degrees of freedom should be considered in designing future interventions.}, journal={JOURNAL OF BIOMECHANICS}, author={McCain, Emily M. and Berno, Matthew E. and Libera, Theresa L. and Lewek, Michael D. and Sawicki, Gregory S. and Saul, Katherine R.}, year={2021}, month={Sep} }
 @article{nuckols_sawicki_2020, title={Impact of elastic ankle exoskeleton stiffness on neuromechanics and energetics of human walking across multiple speeds}, volume={17}, ISSN={["1743-0003"]}, DOI={10.1186/s12984-020-00703-4}, abstractNote={Abstract}, number={1}, journal={JOURNAL OF NEUROENGINEERING AND REHABILITATION}, author={Nuckols, Richard W. and Sawicki, Gregory S.}, year={2020}, month={Jun} }
 @article{krupenevich_clark_sawicki_franz_2020, title={Older Adults Overcome Reduced Triceps Surae Structural Stiffness to Preserve Ankle Joint Quasi-Stiffness During Walking}, volume={36}, ISSN={["1543-2688"]}, DOI={10.1123/jab.2019-0340}, abstractNote={Ankle joint quasi-stiffness is an aggregate measure of the interaction between triceps surae muscle stiffness and Achilles tendon stiffness. This interaction may be altered due to age-related changes in the structural properties and functional behavior of the Achilles tendon and triceps surae muscles. The authors hypothesized that, due to a more compliant of Achilles’ tendon, older adults would exhibit lower ankle joint quasi-stiffness than young adults during walking and during isolated contractions at matched triceps surae muscle activations. The authors also hypothesized that, independent of age, triceps surae muscle stiffness and ankle joint quasi-stiffness would increase with triceps surae muscle activation. The authors used conventional gait analysis in one experiment and, in another, electromyographic biofeedback and in vivo ultrasound imaging applied during isolated contractions. The authors found no difference in ankle joint quasi-stiffness between young and older adults during walking. Conversely, this study found that (1) young and older adults modulated ankle joint quasi-stiffness via activation-dependent changes in triceps surae muscle length–tension behavior and (2) at matched activation, older adults exhibited lower ankle joint quasi-stiffness than young adults. Despite age-related reductions during isolated contractions, ankle joint quasi-stiffness was maintained in older adults during walking, which may be governed via activation-mediated increases in muscle stiffness.}, number={4}, journal={JOURNAL OF APPLIED BIOMECHANICS}, author={Krupenevich, Rebecca L. and Clark, William H. and Sawicki, Gregory S. and Franz, Jason R.}, year={2020}, month={Aug}, pages={209–216} }
 @article{lewis_williams_langley_jarvis_sawicki_olby_2019, title={Development of a Novel Gait Analysis Tool Measuring Center of Pressure for Evaluation of Canine Chronic Thoracolumbar Spinal Cord Injury}, volume={36}, ISSN={0897-7151 1557-9042}, url={http://dx.doi.org/10.1089/neu.2019.6479}, DOI={10.1089/neu.2019.6479}, abstractNote={Gait evaluation after spinal cord injury (SCI) is an important component of determining functional status. Analysis of center of pressure (COP) provides a dynamic reflection of global locomotion and postural control and has been used to quantify various gait abnormalities. We hypothesized that COP variability would be greater for SCI versus normal dogs and that COP would be able to differentiate varying injury severity. Our objective was to investigate COP, COP variability, and body weight support percentage in dogs with chronic SCI. Eleven chronically non-ambulatory dogs after acute severe thoracolumbar SCI were enrolled. COP measurements in x (right-to-left, COPx) and y (craniocaudal, COPy) directions were captured while dogs walked on a pressure-sensitive treadmill with pelvic limb sling support. Root mean square values (RMS_COPx and RMS_COPy) were calculated to assess variability in COP. Body weight support percentage was measured using a load cell. Gait also was quantified using an open field scale (OFS) and treadmill-based stepping and coordination scores (SS, RI). Mean COPx, COPy, RMS_COPx, and RMS_COPy were compared between dogs with SCI and previously evaluated healthy controls. RMS measurements and support percentage were compared with standard gait scales (OFS, SS, RI). Mean COPy was more cranial and RMS_COPx and RMS_COPy were greater in SCI versus normal dogs (p < 0.001). Support percentage moderately correlated with SS (p = 0.019; R2 = 0.47). COP analysis and body weight support measurements offer information about post-injury locomotion. Further development is needed before consideration as an outcome measure to complement validated gait analysis methods in dogs with SCI.}, number={21}, journal={Journal of Neurotrauma}, publisher={Mary Ann Liebert Inc}, author={Lewis, Melissa J. and Williams, Kimberly D. and Langley, Taylor and Jarvis, Leighanne M. and Sawicki, Gregory S. and Olby, Natasha J.}, year={2019}, month={Nov}, pages={3018–3025} }
 @article{mccain_dick_giest_nuckols_lewek_saul_sawicki_2019, title={Mechanics and energetics of post-stroke walking aided by a powered ankle exoskeleton with speed-adaptive myoelectric control}, volume={16}, ISSN={["1743-0003"]}, DOI={10.1186/s12984-019-0523-y}, abstractNote={Ankle exoskeletons offer a promising opportunity to offset mechanical deficits after stroke by applying the needed torque at the paretic ankle. Because joint torque is related to gait speed, it is important to consider the user's gait speed when determining the magnitude of assistive joint torque. We developed and tested a novel exoskeleton controller for delivering propulsive assistance which modulates exoskeleton torque magnitude based on both soleus muscle activity and walking speed. The purpose of this research is to assess the impact of the resulting exoskeleton assistance on post-stroke walking performance across a range of walking speeds.Six participants with stroke walked with and without assistance applied to a powered ankle exoskeleton on the paretic limb. Walking speed started at 60% of their comfortable overground speed and was increased each minute (n00, n01, n02, etc.). We measured lower limb joint and limb powers, metabolic cost of transport, paretic and non-paretic limb propulsion, and trailing limb angle.Exoskeleton assistance increased with walking speed, verifying the speed-adaptive nature of the controller. Both paretic ankle joint power and total limb power increased significantly with exoskeleton assistance at six walking speeds (n00, n01, n02, n03, n04, n05). Despite these joint- and limb-level benefits associated with exoskeleton assistance, no subject averaged metabolic benefits were evident when compared to the unassisted condition. Both paretic trailing limb angle and integrated anterior paretic ground reaction forces were reduced with assistance applied as compared to no assistance at four speeds (n00, n01, n02, n03).Our results suggest that despite appropriate scaling of ankle assistance by the exoskeleton controller, suboptimal limb posture limited the conversion of exoskeleton assistance into forward propulsion. Future studies could include biofeedback or verbal cues to guide users into limb configurations that encourage the conversion of mechanical power at the ankle to forward propulsion.N/A.}, journal={JOURNAL OF NEUROENGINEERING AND REHABILITATION}, author={McCain, Emily M. and Dick, Taylor J. M. and Giest, Tracy N. and Nuckols, Richard W. and Lewek, Michael D. and Saul, Katherine R. and Sawicki, Gregory S.}, year={2019}, month={May} }
 @article{robertson_vadakkeveedu_sawicki_2017, title={A benchtop biorobotic platform for in vitro observation of muscle-tendon dynamics with parallel mechanical assistance from an elastic exoskeleton}, volume={57}, ISSN={["1873-2380"]}, DOI={10.1016/j.jbiomech.2017.03.009}, abstractNote={We present a novel biorobotic framework comprised of a biological muscle-tendon unit (MTU) mechanically coupled to a feedback controlled robotic environment simulation that mimics in vivo inertial/gravitational loading and mechanical assistance from a parallel elastic exoskeleton. Using this system, we applied select combinations of biological muscle activation (modulated with rate-coded direct neural stimulation) and parallel elastic assistance (applied via closed-loop mechanical environment simulation) hypothesized to mimic human behavior based on previously published modeling studies. These conditions resulted in constant system-level force-length dynamics (i.e., stiffness), reduced biological loads, increased muscle excursion, and constant muscle average positive power output—all consistent with laboratory experiments on intact humans during exoskeleton assisted hopping. Mechanical assistance led to reduced estimated metabolic cost and MTU apparent efficiency, but increased apparent efficiency for the MTU + Exo system as a whole. Findings from this study suggest that the increased natural resonant frequency of the artificially stiffened MTU + Exo system, along with invariant movement frequencies, may underlie observed limits on the benefits of exoskeleton assistance. Our novel approach demonstrates that it is possible to capture the salient features of human locomotion with exoskeleton assistance in an isolated muscle-tendon preparation, and introduces a powerful new tool for detailed, direct examination of how assistive devices affect muscle-level neuromechanics and energetics.}, journal={JOURNAL OF BIOMECHANICS}, author={Robertson, Benjamin D. and Vadakkeveedu, Siddarth and Sawicki, Gregory S.}, year={2017}, month={May}, pages={8–17} }
 @article{sawicki_robertson_2017, title={An In Vitro Approach for Directly Observing Muscle-Tendon Dynamics with Parallel Elastic Mechanical Assistance}, volume={15}, ISBN={["978-3-319-46668-2"]}, ISSN={["2195-3562"]}, DOI={10.1007/978-3-319-46669-9_106}, abstractNote={Lower-limb exoskeletons are a promising tool for restoring or augmenting locomotion performance. While engineering advances have led to marked improvements on the machine side of the human machine interface, fundamental aspects of the physiological response of the human user remain unknown—especially at the level of individual leg muscles. One complication is that it is difficult to make direct measurements from muscles in humans without being invasive. Here we offer a novel benchtop approach by introducing a ‘smart’ robotic interface into the framework of biological muscle-tendon work loop experiments in order to simulate the local dynamical environment muscles experience in vivo during locomotion with exoskeleton assistance. Using this framework we demonstrate that providing force in parallel with a muscle-tendon using an ‘exo-tendon’ can have unintended consequences, disrupting the ‘tuned’ spring-like mechanics of the underlying biological muscle tendon unit.}, journal={CONVERGING CLINICAL AND ENGINEERING RESEARCH ON NEUROREHABILITATION II, VOLS 1 AND 2}, author={Sawicki, Gregory S. and Robertson, Benjamin D.}, year={2017}, pages={643–647} }
 @article{blau_davis_gorney_dohse_williams_lim_pfitzner_laber_sawicki_olby_2017, title={Quantifying center of pressure variability in chondrodystrophoid dogs}, volume={226}, ISSN={1090-0233}, url={http://dx.doi.org/10.1016/j.tvjl.2017.07.001}, DOI={10.1016/j.tvjl.2017.07.001}, abstractNote={The center of pressure (COP) position reflects a combination of proprioceptive, motor and mechanical function. As such, it can be used to quantify and characterize neurologic dysfunction. The aim of this study was to describe and quantify the movement of COP and its variability in healthy chondrodystrophoid dogs while walking to provide a baseline for comparison to dogs with spinal cord injury due to acute intervertebral disc herniations. Fifteen healthy adult chondrodystrophoid dogs were walked on an instrumented treadmill that recorded the location of each dog’s COP as it walked. Center of pressure (COP) was referenced from an anatomical marker on the dogs’ back. The root mean squared (RMS) values of changes in COP location in the sagittal (y) and horizontal (x) directions were calculated to determine the range of COP variability. Three dogs would not walk on the treadmill. One dog was too small to collect interpretable data. From the remaining 11 dogs, 206 trials were analyzed. Mean RMS for change in COPx per trial was 0.0138 (standard deviation, SD 0.0047) and for COPy was 0.0185 (SD 0.0071). Walking speed but not limb length had a significant effect on COP RMS. Repeat measurements in six dogs had high test retest consistency in the x and fair consistency in the y direction. In conclusion, COP variability can be measured consistently in dogs, and a range of COP variability for normal chondrodystrophoid dogs has been determined to provide a baseline for future studies on dogs with spinal cord injury.}, journal={The Veterinary Journal}, publisher={Elsevier BV}, author={Blau, S.R. and Davis, L.M. and Gorney, A.M. and Dohse, C.S. and Williams, K.D. and Lim, J-H. and Pfitzner, W.G. and Laber, E. and Sawicki, G.S. and Olby, N.J.}, year={2017}, month={Aug}, pages={26–31} }
 @article{rosario_sutton_patek_sawicki_2017, title={The springs of time-limited bullfrog jumps and slow-preparation grasshopper leaps are tuned to their muscle dynamics}, volume={57}, journal={Integrative and Comparative Biology}, author={Rosario, M. V. and Sutton, G. P. and Patek, S. N. and Sawicki, G. S.}, year={2017}, pages={E390–390} }
 @article{sawicki_khan_2016, title={A Simple Model to Estimate Plantarflexor Muscle-Tendon Mechanics and Energetics During Walking With Elastic Ankle Exoskeletons}, volume={63}, ISSN={["1558-2531"]}, DOI={10.1109/tbme.2015.2491224}, abstractNote={Goal: A recent experiment demonstrated that when humans wear unpowered elastic ankle exoskeletons with intermediate spring stiffness, they can reduce their metabolic energy cost to walk by ~7%. Springs that are too compliant or too stiff have little benefit. The purpose of this study was to use modeling and simulation to explore the muscle-level mechanisms for the “sweet spot” in stiffness during exoskeleton assisted walking. Methods: We developed a simple lumped uniarticular musculoskeletal model of the plantarflexors operating in parallel with an elastic “exo-tendon.” Using an inverse approach with constrained kinematics and kinetics, we rapidly simulated human walking over a range of exoskeleton stiffness values and examined the underlying neuromechanics and energetics of the biological plantarflexors. Results: Stiffer ankle exoskeleton springs resulted in larger decreases in plantarflexor muscle forces, activations, and metabolic energy consumption. However, in the process of unloading the compliant biological muscle-tendon unit, the muscle fascicles experienced larger excursions that negatively impacted series elastic element recoil that is characteristic of a tuned “catapult mechanism.” Conclusion: The combination of disrupted muscle-tendon dynamics and the need to produce compensatory forces/moments to maintain overall net ankle moment invariance could explain the “sweet spot” in metabolic performance at intermediate ankle exoskeleton stiffness. Future work will aim to provide experimental evidence to support the model predictions presented here using ultrasound imaging of muscle-level dynamics during walking with elastic ankle exoskeletons. Significance: Engineers must account for the muscle-level effects of exoskeleton designs in order to achieve maximal performance objectives.}, number={5}, journal={IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING}, author={Sawicki, Gregory S. and Khan, Nabil S.}, year={2016}, month={May}, pages={914–923} }
 @article{huang_crouch_liu_sawicki_wang_2016, title={A cyber expert system for auto-tuning powered prosthesis impedance control parameters}, volume={44}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84944521097&partnerID=MN8TOARS}, DOI={10.1007/s10439-015-1464-7}, abstractNote={Typically impedance control parameters (e.g., stiffness and damping) in powered lower limb prostheses are fine-tuned by human experts (HMEs), which is time and resource intensive. Automated tuning procedures would make powered prostheses more practical for clinical use. In this study, we developed a novel cyber expert system (CES) that encoded HME tuning decisions as computer rules to auto-tune control parameters for a powered knee (passive ankle) prosthesis. The tuning performance of CES was preliminarily quantified on two able-bodied subjects and two transfemoral amputees. After CES and HME tuning, we observed normative prosthetic knee kinematics and improved or slightly improved gait symmetry and step width within each subject. Compared to HME, the CES tuning procedure required less time and no human intervention. Hence, using CES for auto-tuning prosthesis control was a sound concept, promising to enhance the practical value of powered prosthetic legs. However, the tuning goals of CES might not fully capture those of the HME. This was because we observed that HME tuning reduced trunk sway, while CES sometimes led to slightly increased trunk motion. Additional research is still needed to identify more appropriate tuning objectives for powered prosthetic legs to improve amputees' walking function.}, number={5}, journal={Annals of Biomedical Engineering}, author={Huang, He and Crouch, D. L. and Liu, M. and Sawicki, G. S. and Wang, D.}, year={2016}, pages={1613–1624} }
 @article{takahashi_gross_werkhoven_piazza_sawicki_2016, title={Adding Stiffness to the Foot Modulates Soleus Force-Velocity Behaviour during Human Walking}, volume={6}, ISSN={["2045-2322"]}, DOI={10.1038/srep29870}, abstractNote={Abstract}, journal={SCIENTIFIC REPORTS}, author={Takahashi, Kota Z. and Gross, Michael T. and Werkhoven, Herman and Piazza, Stephen J. and Sawicki, Gregory S.}, year={2016}, month={Jul} }
 @article{danos_holt_sawicki_azizi_2016, title={Modeling age-related changes in muscle-tendon dynamics during cyclical contractions in the rat gastrocnemius}, volume={121}, ISSN={["1522-1601"]}, DOI={10.1152/japplphysiol.00396.2016}, abstractNote={ Efficient muscle-tendon performance during cyclical tasks is dependent on both active and passive mechanical tissue properties. Here we examine whether age-related changes in the properties of muscle-tendon units (MTUs) compromise their ability to do work and utilize elastic energy storage. We empirically quantified passive and active properties of the medial gastrocnemius muscle and material properties of the Achilles tendon in young (∼6 mo) and old (∼32 mo) rats. We then used these properties in computer simulations of a Hill-type muscle model operating in series with a Hookean spring. The modeled MTU was driven through sinusoidal length changes and activated at a phase that optimized muscle-tendon tuning to assess the relative contributions of active and passive elements to the force and work in each cycle. In physiologically realistic simulations where young and old MTUs started at similar passive forces and developed similar active forces, the capacity of old MTUs to store elastic energy and produce positive work was compromised. These results suggest that the observed increase in the metabolic cost of locomotion with aging may be in part due to the recruitment of additional muscles to compensate for the reduced work at the primary MTU. Furthermore, the age-related increases in passive stiffness coupled with a reduced active force capacity in the muscle can lead to shifts in the force-length and force-velocity operating range that may significantly impact mechanical and metabolic performance. Our study emphasizes the importance of the interplay between muscle and tendon mechanical properties in shaping MTU performance during cyclical contractions. }, number={4}, journal={JOURNAL OF APPLIED PHYSIOLOGY}, author={Danos, Nicole and Holt, Natalie C. and Sawicki, Gregory S. and Azizi, Emanuel}, year={2016}, month={Oct}, pages={1004–1012} }
 @article{rosario_sutton_patek_sawicki_2016, title={Muscle-spring dynamics in time-limited, elastic movements}, volume={283}, ISSN={["1471-2954"]}, DOI={10.1098/rspb.2016.1561}, abstractNote={Muscle contractions that load in-series springs with slow speed over a long duration do maximal work and store the most elastic energy. However, time constraints, such as those experienced during escape and predation behaviours, may prevent animals from achieving maximal force capacity from their muscles during spring-loading. Here, we ask whether animals that have limited time for elastic energy storage operate with springs that are tuned to submaximal force production. To answer this question, we used a dynamic model of a muscle–spring system undergoing a fixed-end contraction, with parameters from a time-limited spring-loader (bullfrog:Lithobates catesbeiana) and a non-time-limited spring-loader (grasshopper:Schistocerca gregaria). We found that when muscles have less time to contract, stored elastic energy is maximized with lower spring stiffness (quantified as spring constant). The spring stiffness measured in bullfrog tendons permitted less elastic energy storage than was predicted by a modelled, maximal muscle contraction. However, when muscle contractions were modelled using biologically relevant loading times for bullfrog jumps (50 ms), tendon stiffness actually maximized elastic energy storage. In contrast, grasshoppers, which are not time limited, exhibited spring stiffness that maximized elastic energy storage when modelled with a maximal muscle contraction. These findings demonstrate the significance of evolutionary variation in tendon and apodeme properties to realistic jumping contexts as well as the importance of considering the effect of muscle dynamics and behavioural constraints on energy storage in muscle–spring systems.}, number={1838}, journal={PROCEEDINGS OF THE ROYAL SOCIETY B-BIOLOGICAL SCIENCES}, author={Rosario, M. V. and Sutton, G. P. and Patek, S. N. and Sawicki, G. S.}, year={2016}, month={Sep} }
 @article{takahashi_lewek_sawicki_2015, title={A neuromechanics-based powered ankle exoskeleton to assist walking post-stroke: a feasibility study}, volume={12}, ISSN={["1743-0003"]}, DOI={10.1186/s12984-015-0015-7}, abstractNote={In persons post-stroke, diminished ankle joint function can contribute to inadequate gait propulsion. To target paretic ankle impairments, we developed a neuromechanics-based powered ankle exoskeleton. Specifically, this exoskeleton supplies plantarflexion assistance that is proportional to the user's paretic soleus electromyography (EMG) amplitude only during a phase of gait when the stance limb is subjected to an anteriorly directed ground reaction force (GRF). The purpose of this feasibility study was to examine the short-term effects of the powered ankle exoskeleton on the mechanics and energetics of gait.Five subjects with stroke walked with a powered ankle exoskeleton on the paretic limb for three 5 minute sessions. We analyzed the peak paretic ankle plantarflexion moment, paretic ankle positive work, symmetry of GRF propulsion impulse, and net metabolic power.The exoskeleton increased the paretic plantarflexion moment by 16% during the powered walking trials relative to unassisted walking condition (p < .05). Despite this enhanced paretic ankle moment, there was no significant increase in paretic ankle positive work, or changes in any other mechanical variables with the powered assistance. The exoskeleton assistance appeared to reduce the net metabolic power gradually with each 5 minute repetition, though no statistical significance was found. In three of the subjects, the paretic soleus activation during the propulsion phase of stance was reduced during the powered assistance compared to unassisted walking (35% reduction in the integrated EMG amplitude during the third powered session).This feasibility study demonstrated that the exoskeleton can enhance paretic ankle moment. Future studies with greater sample size and prolonged sessions are warranted to evaluate the effects of the powered ankle exoskeleton on overall gait outcomes in persons post-stroke.}, journal={JOURNAL OF NEUROENGINEERING AND REHABILITATION}, author={Takahashi, Kota Z. and Lewek, Michael D. and Sawicki, Gregory S.}, year={2015}, month={Feb} }
 @article{mahon_farris_sawicki_lewek_2015, title={Individual limb mechanical analysis of gait following stroke}, volume={48}, ISSN={["1873-2380"]}, DOI={10.1016/j.jbiomech.2015.02.006}, abstractNote={The step-to-step transition of walking requires significant mechanical and metabolic energy to redirect the center of mass. Inter-limb mechanical asymmetries during the step-to-step transition may increase overall energy demands and require compensation during single-support. The purpose of this study was to compare individual limb mechanical gait asymmetries during the step-to-step transitions, single-support and over a complete stride between two groups of individuals following stroke stratified by gait speed (≥0.8 m/s or <0.8 m/s). Twenty-six individuals with chronic stroke walked on an instrumented treadmill to collect ground reaction force data. Using the individual limbs method, mechanical power produced on the center of mass was calculated during the trailing double-support, leading double-support, and single-support phases of a stride, as well as over a complete stride. Robust inter-limb asymmetries in mechanical power existed during walking after stroke; for both groups, the non-paretic limb produced significantly more positive net mechanical power than the paretic limb during all phases of a stride and over a complete stride. Interestingly, no differences in inter-limb mechanical power asymmetry were noted between groups based on walking speed, during any phase or over a complete stride. Paretic propulsion, however, was different between speed-based groups. The fact that paretic propulsion (calculated from anterior–posterior forces) is different between groups, but our measure of mechanical work (calculated from all three directions) is not, suggests that limb power output may be dominated by vertical components, which are required for upright support.}, number={6}, journal={JOURNAL OF BIOMECHANICS}, author={Mahon, Caitlin E. and Farris, Dominic J. and Sawicki, Gregory S. and Lewek, Michael D.}, year={2015}, month={Apr}, pages={984–989} }
 @article{robertson_farris_sawicki_2015, title={More is not always better: Modeling the effects of elastic exoskeleton compliance on underlying ankle muscle-tendon dynamics (vol 9, 046018, 2014)}, volume={10}, number={1}, journal={Bioinspiration & Biomimetics}, author={Robertson, B. D. and Farris, D. J. and Sawicki, G. S.}, year={2015} }
 @article{sawicki_sheppard_roberts_2015, title={Power amplification in an isolated muscle-tendon unit is load dependent}, volume={218}, ISSN={["1477-9145"]}, DOI={10.1242/jeb.126235}, abstractNote={During rapid movements, tendons can act like springs, temporarily storing work done by muscles and then releasing it to power body movements. For some activities, like frog jumping, energy is released from tendon much more rapidly than it is stored, thus amplifying muscle power output. The period during which energy is loaded into tendon by muscle work may be aided by a catch mechanism that restricts motion, but theoretical studies indicate that power can be amplified in a muscle-tendon-load system even in the absence of a catch. To explore the limits of power amplification with and without a catch, we studied the using bullfrog plantaris muscle-tendon during in vitro contractions. A novel servomotor controller allowed us to measure muscle-tendon unit (MTU) mechanical behavior during contractions against a variety of simulated inertial-gravitational loads, ranging from zero to 1X the peak isometric force of the muscle. Power output of the MTU system was load dependent, and power amplification occurred only at intermediate loads, reaching ∼1.3X the peak isotonic power output of the muscle. With a simulated anatomical catch mechanism in place, the highest power amplification occurred at the lowest loads, with a maximum amplification of more than 4X peak isotonic muscle power. At higher loads, the benefits of a catch for MTU performance diminished sharply, suggesting that power amplification >2.5X may come at the expense of net mechanical work delivered to the load.}, number={22}, journal={JOURNAL OF EXPERIMENTAL BIOLOGY}, author={Sawicki, Gregory S. and Sheppard, Peter and Roberts, Thomas J.}, year={2015}, month={Nov}, pages={3700–3709} }
 @article{collins_wiggin_sawicki_2015, title={Reducing the energy cost of human walking using an unpowered exoskeleton}, volume={522}, ISSN={["1476-4687"]}, DOI={10.1038/nature14288}, abstractNote={With efficiencies derived from evolution, growth and learning, humans are very well-tuned for locomotion1. Metabolic energy used during walking can be partly replaced by power input from an exoskeleton2, but is it possible to reduce metabolic rate without providing an additional energy source? This would require an improvement in the efficiency of the human–machine system as a whole, and would be remarkable given the apparent optimality of human gait. Here we show that the metabolic rate of human walking can be reduced by an unpowered ankle exoskeleton. We built a lightweight elastic device that acts in parallel with the user's calf muscles, off-loading muscle force and thereby reducing the metabolic energy consumed in contractions. The device uses a mechanical clutch to hold a spring as it is stretched and relaxed by ankle movements when the foot is on the ground, helping to fulfil one function of the calf muscles and Achilles tendon. Unlike muscles, however, the clutch sustains force passively. The exoskeleton consumes no chemical or electrical energy and delivers no net positive mechanical work, yet reduces the metabolic cost of walking by 7.2 ± 2.6% for healthy human users under natural conditions, comparable to savings with powered devices. Improving upon walking economy in this way is analogous to altering the structure of the body such that it is more energy-effective at walking. While strong natural pressures have already shaped human locomotion, improvements in efficiency are still possible. Much remains to be learned about this seemingly simple behaviour. The attachment of a simple, unpowered, mechanical exoskeleton to the foot and ankle results in a net saving of 7% of the metabolic energy expended in human walking. Walking is the most commonplace of activities, yet we know remarkably little about it and no robot has yet reproduced the grace and poise of a human walk. Steven Collins et al. now show that the attachment of a simple mechanical exoskeleton to the foot and ankle results in a 7% reduction of the metabolic energy expended in walking. This work shows that net energy input is not a fundamental requirement for reducing the metabolic cost of human walking, and that reducing calf muscle forces — while also fulfilling normal ankle functions and minimizing penalties associated with added mass or restricted motions — can be beneficial.}, number={7555}, journal={NATURE}, author={Collins, Steven H. and Wiggin, M. Bruce and Sawicki, Gregory S.}, year={2015}, month={Jun}, pages={212-+} }
 @article{farris_hampton_lewek_sawicki_2015, title={Revisiting the mechanics and energetics of walking in individuals with chronic hemiparesis following stroke: from individual limbs to lower limb joints}, volume={12}, ISSN={["1743-0003"]}, DOI={10.1186/s12984-015-0012-x}, abstractNote={Previous reports of the mechanics and energetics of post-stroke hemiparetic walking have either not combined estimates of mechanical and metabolic energy or computed external mechanical work based on the limited combined limbs method. Here we present a comparison of the mechanics and energetics of hemiparetic and unimpaired walking at a matched speed.Mechanical work done on the body centre of mass (COM) was computed by the individual limbs method and work done at individual leg joints was computed with an inverse dynamics analysis. Both estimates were converted to average powers and related to simultaneous estimates of net metabolic power, determined via indirect calorimetry. Efficiency of positive work was calculated as the ratio of average positive mechanical power [Formula: see text] to net metabolic power.Total [Formula: see text] was 20% greater for the hemiparetic group (H) than for the unimpaired control group (C) (0.49 vs. 0.41 W · kg(-1)). The greater [Formula: see text] was partly attributed to the paretic limb of hemiparetic walkers not providing appropriately timed push-off [Formula: see text] in the step-to-step transition. This led to compensatory non-paretic limb hip and knee [Formula: see text] which resulted in greater total mechanical work. Efficiency of positive work was not different between H and C.Increased work, not decreased efficiency, explains the greater metabolic cost of hemiparetic walking post-stroke. Our results highlighted the need to target improving paretic ankle push-off via therapy or assistive technology in order to reduce the metabolic cost of hemiparetic walking.}, journal={JOURNAL OF NEUROENGINEERING AND REHABILITATION}, author={Farris, Dominic James and Hampton, Austin and Lewek, Michael D. and Sawicki, Gregory S.}, year={2015}, month={Feb} }
 @article{zelik_takahashi_sawicki_2015, title={Six degree-of-freedom analysis of hip, knee, ankle and foot provides updated understanding of biomechanical work during human walking}, volume={218}, ISSN={["1477-9145"]}, DOI={10.1242/jeb.115451}, abstractNote={ABSTRACT}, number={6}, journal={JOURNAL OF EXPERIMENTAL BIOLOGY}, author={Zelik, Karl E. and Takahashi, Kota Z. and Sawicki, Gregory S.}, year={2015}, month={Mar}, pages={876–886} }
 @article{sawicki_robertson_azizi_roberts_2015, title={Timing matters: tuning the mechanics of a muscle-tendon unit by adjusting stimulation phase during cyclic contractions}, volume={218}, ISSN={["1477-9145"]}, DOI={10.1242/jeb.121673}, abstractNote={A growing body of research on the mechanics and energetics of terrestrial locomotion has demonstrated that elastic elements acting in series with contracting muscle are critical components of sustained, stable, and efficient gait. Far fewer studies have examined how the nervous system modulates muscle-tendon interaction dynamics to optimize ‘tuning’ or meet varying locomotor demands. To explore the fundamental neuromechanical rules that govern the interactions between series elastic (SEE) and contractile (CE) elements within a compliant muscle-tendon unit (MTU), we used a novel work loop approach that included implanted sonomicrometry crystals along muscle fascicles. This enabled us to de-couple CE and SEE length trajectories when cyclic strain patterns were applied to an isolated plantaris MTU from the bullfrog (Lithobates catesbeianus). Using this approach, we demonstrate that the onset timing of muscle stimulation (i.e., stimulation phase) that involves a symmetrical MTU stretch-shorten cycle during active force production, results in net zero mechanical power output, and maximal decoupling of CE and MTU length trajectories. We found it difficult to ‘tune’ the muscle-tendon system for strut-like isometric force production by adjusting stimulation phase only, as the zero power output condition involved significant positive and negative mechanical work by the CE. A simple neural mechanism- adjusting muscle stimulation phase- could shift a MTU from performing net zero to net positive (energy producing) or net negative (energy absorbing) mechanical work under conditions of changing locomotor demand. Finally, we show that modifications to the classical work loop paradigm better represent in vivo muscle-tendon function during locomotion.}, number={19}, journal={JOURNAL OF EXPERIMENTAL BIOLOGY}, author={Sawicki, Gregory S. and Robertson, Benjamin D. and Azizi, Emanuel and Roberts, Thomas J.}, year={2015}, month={Oct}, pages={3150–3159} }
 @article{robertson_sawicki_2014, title={Exploiting elasticity: Modeling the influence of neural control on mechanics and energetics of ankle muscle-tendons during human hopping}, volume={353}, ISSN={["1095-8541"]}, DOI={10.1016/j.jtbi.2014.03.010}, abstractNote={We present a simplified Hill-type model of the human triceps surae-Achilles tendon complex working on a gravitational-inertial load during cyclic contractions (i.e. vertical hopping). Our goal was to determine the role that neural control plays in governing muscle, or contractile element (CE), and tendon, or series elastic element (SEE), mechanics and energetics within a compliant muscle-tendon unit (MTU). We constructed a 2D parameter space consisting of many combinations of stimulation frequency and magnitude (i.e. neural control strategies). We compared the performance of each control strategy by evaluating peak force and average positive mechanical power output for the system (MTU) and its respective components (CE, SEE), force-length (F-L) and -velocity (F-V) operating point of the CE during active force production, average metabolic rate for the CE, and both MTU and CE apparent efficiency. Our results suggest that frequency of stimulation plays a primary role in governing whole-MTU mechanics. These include the phasing of both activation and peak force relative to minimum MTU length, average positive power, and apparent efficiency. Stimulation amplitude was primarily responsible for governing average metabolic rate and within MTU mechanics, including peak force generation and elastic energy storage and return in the SEE. Frequency and amplitude of stimulation both played integral roles in determining CE F-L operating point, with both higher frequency and amplitude generally corresponding to lower CE strains, reduced injury risk, and elimination of the need for passive force generation in the CE parallel elastic element (PEE).}, journal={JOURNAL OF THEORETICAL BIOLOGY}, author={Robertson, Benjamin D. and Sawicki, Gregory S.}, year={2014}, month={Jul}, pages={121–132} }
 @article{robertson_farris_sawicki_2014, title={More is not always better: modeling the effects of elastic exoskeleton compliance on underlying ankle muscle-tendon dynamics}, volume={9}, ISSN={["1748-3190"]}, DOI={10.1088/1748-3182/9/4/046018}, abstractNote={Development of robotic exoskeletons to assist/enhance human locomotor performance involves lengthy prototyping, testing, and analysis. This process is further convoluted by variability in limb/body morphology and preferred gait patterns between individuals. In an attempt to expedite this process, and establish a physiological basis for actuator prescription, we developed a simple, predictive model of human neuromechanical adaptation to a passive elastic exoskeleton applied at the ankle joint during a functional task. We modeled the human triceps surae–Achilles tendon muscle tendon unit (MTU) as a single Hill-type muscle, or contractile element (CE), and series tendon, or series elastic element (SEE). This modeled system was placed under gravitational load and underwent cyclic stimulation at a regular frequency (i.e. hopping) with and without exoskeleton (Exo) assistance. We explored the effect that both Exo stiffness k Exo ?> and muscle activation A stim ?> had on combined MTU and Exo (MTU + Exo), MTU, and CE/SEE mechanics and energetics. Model accuracy was verified via qualitative and quantitative comparisons between modeled and prior experimental outcomes. We demonstrated that reduced A stim ?> can be traded for increased k Exo ?> to maintain consistent MTU + Exo mechanics (i.e. average positive power P ¯ mech + ?> output) from an unassisted condition (i.e. k Exo = 0 kN · m − 1 ?> ). For these regions of parameter space, our model predicted a reduction in MTU force, SEE energy cycling, and metabolic rate P ¯ met ?> , as well as constant CE P ¯ mech + ?> output compared to unassisted conditions. This agreed with previous experimental observations, demonstrating our model’s predictive ability. Model predictions also provided insight into mechanisms of metabolic cost minimization, and/or enhanced mechanical performance, and we concluded that both of these outcomes cannot be achieved simultaneously, and that one must come at the detriment of the other in a spring-assisted compliant MTU.}, number={4}, journal={BIOINSPIRATION & BIOMIMETICS}, author={Robertson, Benjamin D. and Farris, Dominic J. and Sawicki, Gregory S.}, year={2014}, month={Dec} }
 @article{farris_hicks_delp_sawicki_2014, title={Musculoskeletal modelling deconstructs the paradoxical effects of elastic ankle exoskeletons on plantar-flexor mechanics and energetics during hopping}, volume={217}, ISSN={["1477-9145"]}, DOI={10.1242/jeb.107656}, abstractNote={Abstract}, number={22}, journal={JOURNAL OF EXPERIMENTAL BIOLOGY}, author={Farris, Dominic James and Hicks, Jennifer L. and Delp, Scott L. and Sawicki, Gregory S.}, year={2014}, month={Nov}, pages={4018–4028} }
 @article{farris_robertson_sawicki_2013, title={Elastic ankle exoskeletons reduce soleus muscle force but not work in human hopping}, volume={115}, ISSN={["1522-1601"]}, DOI={10.1152/japplphysiol.00253.2013}, abstractNote={Inspired by elastic energy storage and return in tendons of human leg muscle-tendon units (MTU), exoskeletons often place a spring in parallel with an MTU to assist the MTU. However, this might perturb the normally efficient MTU mechanics and actually increase active muscle mechanical work. This study tested the effects of elastic parallel assistance on MTU mechanics. Participants hopped with and without spring-loaded ankle exoskeletons that assisted plantar flexion. An inverse dynamics analysis, combined with in vivo ultrasound imaging of soleus fascicles and surface electromyography, was used to determine muscle-tendon mechanics and activations. Whole body net metabolic power was obtained from indirect calorimetry. When hopping with spring-loaded exoskeletons, soleus activation was reduced (30–70%) and so was the magnitude of soleus force (peak force reduced by 30%) and the average rate of soleus force generation (by 50%). Although forces were lower, average positive fascicle power remained unchanged, owing to increased fascicle excursion (+4–5 mm). Net metabolic power was reduced with exoskeleton assistance (19%). These findings highlighted that parallel assistance to a muscle with appreciable series elasticity may have some negative consequences, and that the metabolic cost associated with generating force may be more pronounced than the cost of doing work for these muscles.}, number={5}, journal={JOURNAL OF APPLIED PHYSIOLOGY}, author={Farris, Dominic James and Robertson, Benjamin D. and Sawicki, Gregory S.}, year={2013}, month={Sep}, pages={579–585} }
 @article{shamaei_sawicki_dollar_2013, title={Estimation of Quasi-Stiffness and Propulsive Work of the Human Ankle in the Stance Phase of Walking}, volume={8}, ISSN={["1932-6203"]}, DOI={10.1371/journal.pone.0059935}, abstractNote={Characterizing the quasi-stiffness and work of lower extremity joints is critical for evaluating human locomotion and designing assistive devices such as prostheses and orthoses intended to emulate the biological behavior of human legs. This work aims to establish statistical models that allow us to predict the ankle quasi-stiffness and net mechanical work for adults walking on level ground. During the stance phase of walking, the ankle joint propels the body through three distinctive phases of nearly constant stiffness known as the quasi-stiffness of each phase. Using a generic equation for the ankle moment obtained through an inverse dynamics analysis, we identify key independent parameters needed to predict ankle quasi-stiffness and propulsive work and also the functional form of each correlation. These parameters include gait speed, ankle excursion, and subject height and weight. Based on the identified form of the correlation and key variables, we applied linear regression on experimental walking data for 216 gait trials across 26 subjects (speeds from 0.75–2.63 m/s) to obtain statistical models of varying complexity. The most general forms of the statistical models include all the key parameters and have an R2 of 75% to 81% in the prediction of the ankle quasi-stiffnesses and propulsive work. The most specific models include only subject height and weight and could predict the ankle quasi-stiffnesses and work for optimal walking speed with average error of 13% to 30%. We discuss how these models provide a useful framework and foundation for designing subject- and gait-specific prosthetic and exoskeletal devices designed to emulate biological ankle function during level ground walking.}, number={3}, journal={PLOS ONE}, author={Shamaei, Kamran and Sawicki, Gregory S. and Dollar, Aaron M.}, year={2013}, month={Mar} }
 @article{shamaei_sawicki_dollar_2013, title={Estimation of Quasi-Stiffness of the Human Hip in the Stance Phase of Walking}, volume={8}, ISSN={["1932-6203"]}, DOI={10.1371/journal.pone.0081841}, abstractNote={This work presents a framework for selection of subject-specific quasi-stiffness of hip orthoses and exoskeletons, and other devices that are intended to emulate the biological performance of this joint during walking. The hip joint exhibits linear moment-angular excursion behavior in both the extension and flexion stages of the resilient loading-unloading phase that consists of terminal stance and initial swing phases. Here, we establish statistical models that can closely estimate the slope of linear fits to the moment-angle graph of the hip in this phase, termed as the quasi-stiffness of the hip. Employing an inverse dynamics analysis, we identify a series of parameters that can capture the nearly linear hip quasi-stiffnesses in the resilient loading phase. We then employ regression analysis on experimental moment-angle data of 216 gait trials across 26 human adults walking over a wide range of gait speeds (0.75–2.63 m/s) to obtain a set of general-form statistical models that estimate the hip quasi-stiffnesses using body weight and height, gait speed, and hip excursion. We show that the general-form models can closely estimate the hip quasi-stiffness in the extension (R2 = 92%) and flexion portions (R2 = 89%) of the resilient loading phase of the gait. We further simplify the general-form models and present a set of stature-based models that can estimate the hip quasi-stiffness for the preferred gait speed using only body weight and height with an average error of 27% for the extension stage and 37% for the flexion stage.}, number={12}, journal={PLOS ONE}, author={Shamaei, Kamran and Sawicki, Gregory S. and Dollar, Aaron M.}, year={2013}, month={Dec} }
 @article{shamaei_sawicki_dollar_2013, title={Estimation of Quasi-Stiffness of the Human Knee in the Stance Phase of Walking}, volume={8}, ISSN={["1932-6203"]}, DOI={10.1371/journal.pone.0059993}, abstractNote={Biomechanical data characterizing the quasi-stiffness of lower-limb joints during human locomotion is limited. Understanding joint stiffness is critical for evaluating gait function and designing devices such as prostheses and orthoses intended to emulate biological properties of human legs. The knee joint moment-angle relationship is approximately linear in the flexion and extension stages of stance, exhibiting nearly constant stiffnesses, known as the quasi-stiffnesses of each stage. Using a generalized inverse dynamics analysis approach, we identify the key independent variables needed to predict knee quasi-stiffness during walking, including gait speed, knee excursion, and subject height and weight. Then, based on the identified key variables, we used experimental walking data for 136 conditions (speeds of 0.75–2.63 m/s) across 14 subjects to obtain best fit linear regressions for a set of general models, which were further simplified for the optimal gait speed. We found R2 > 86% for the most general models of knee quasi-stiffnesses for the flexion and extension stages of stance. With only subject height and weight, we could predict knee quasi-stiffness for preferred walking speed with average error of 9% with only one outlier. These results provide a useful framework and foundation for selecting subject-specific stiffness for prosthetic and exoskeletal devices designed to emulate biological knee function during walking.}, number={3}, journal={PLOS ONE}, author={Shamaei, Kamran and Sawicki, Gregory S. and Dollar, Aaron M.}, year={2013}, month={Mar} }
 @article{richards_sawicki_2012, title={Elastic recoil can either amplify or attenuate muscle-tendon power, depending on inertial vs. fluid dynamic loading}, volume={313}, ISSN={["0022-5193"]}, DOI={10.1016/j.jtbi.2012.07.033}, abstractNote={Frog jumps exceed muscle power limits. To achieve this, a muscle may store elastic energy in tendon before it is released rapidly, producing 'power amplification' as tendon recoil assists the muscle to accelerate the load. Do the musculoskeletal modifications conferring power amplification help or hinder frog swimming? We used a Hill-type mathematical model of a muscle-tendon (MT) with contractile element (CE) and series elastic element (SEE) properties of frogs. We varied limb masses from 0.3 to 30 g, foot-fin areas from 0.005 to 50 cm(2) and effective mechanical advantage (EMA=in-lever/out-lever) from 0.025 to 0.1. 'Optimal' conditions produced power amplification of ~19% greater than the CE limit. Yet, other conditions caused ~80% reduction of MT power (power attenuation) due to SEE recoil absorbing power from (rather than adding to) the CE. The tendency for elastic recoil to cause power amplification vs. attenuation was load dependent: low fluid drag loads, high limb mass and EMA=0.1 caused power amplification whereas high drag, low mass and low EMA (=0.025) caused attenuation. Power amplification emerged when: (1) CE shortening velocity is 1/3V(max), (2) elastic energy storage is neither too high nor too low, and (3). peak inertial-drag force ratio ≥ ~1.5. Excessive elastic energy storage delayed the timing of recoil, causing power attenuation. Thus our model predicts that for fluid loads, the benefit from a compliant tendon is modest, and when the system is 'poorly tuned' (i.e., inappropriate EMA), MT power attenuation can be severe.}, journal={JOURNAL OF THEORETICAL BIOLOGY}, author={Richards, Christopher T. and Sawicki, Gregory S.}, year={2012}, month={Nov}, pages={68–78} }
 @article{farris_sawicki_2012, title={Human medial gastrocnemius force-velocity behavior shifts with locomotion speed and gait}, volume={109}, ISSN={["1091-6490"]}, DOI={10.1073/pnas.1107972109}, abstractNote={
            Humans walk and run over a wide range of speeds with remarkable efficiency. For steady locomotion, moving at different speeds requires the muscle–tendon units of the leg to modulate the amount of mechanical power the limb absorbs and outputs in each step. How individual muscles adapt their behavior to modulate limb power output has been examined using computer simulation and animal models, but has not been studied in vivo in humans. In this study, we used a combination of ultrasound imaging and motion analysis to examine how medial gastrocnemius (MG) muscle–tendon unit behavior is adjusted to meet the varying mechanical demands of different locomotor speeds during walking and running in humans. The results highlighted key differences in MG fascicle-shortening velocity with both locomotor speed and gait. Fascicle-shortening velocity at the time of peak muscle force production increased with walking speed, impairing the ability of the muscle to produce high peak forces. Switching to a running gait at 2.0 m⋅s
            −1
            caused fascicle shortening at the time of peak force production to shift to much slower velocities. This velocity shift facilitated a large increase in peak muscle force and an increase in MG power output. MG fascicle velocity may be a key factor that limits the speeds humans choose to walk at, and may explain the transition from walking to running. This finding is consistent with previous modeling studies.
          }, number={3}, journal={PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA}, author={Farris, Dominic James and Sawicki, Gregory S.}, year={2012}, month={Jan}, pages={977–982} }
 @article{wutzke_sawicki_lewek_2012, title={The influence of a unilateral fixed ankle on metabolic and mechanical demands during walking in unimpaired young adults}, volume={45}, ISSN={["0021-9290"]}, DOI={10.1016/j.jbiomech.2012.06.035}, abstractNote={The plantarflexors provide a major source of propulsion during walking. When mechanical power generation from the plantarflexor muscles is limited, other joints may compensate to maintain a consistent walking velocity, but likely at increased metabolic cost. The purpose of this study was to determine how a unilateral reduction in ankle plantarflexor power influences the redistribution of mechanical power generation within and across limbs and the associated change in the metabolic cost of walking. Twelve unimpaired young adults walked with an ankle brace on the dominant limb at 1.2m/s on a dual-belt instrumented treadmill. Lower extremity kinematics and kinetics as well as gas exchange data were collected in two conditions: (1) with the brace unlocked (FREE) and (2) with the brace locked (FIXED). The brace significantly reduced ankle plantarflexion excursion by 12.96±3.60° (p<0.001) and peak ankle mechanical power by 1.03±0.51W/kg (p<0.001) in the FIXED versus FREE condition. Consequently, metabolic power (W/kg) of walking in the FIXED condition increased by 7.4% compared to the FREE condition (p=0.03). Increased bilateral hip mechanical power generation was observed in the FIXED condition (p<0.001). These results suggest that walking with reduced ankle power increases metabolic demand due to the redistribution of mechanical power generation from highly efficient ankle muscle-tendons to less efficient hip muscle-tendons. A within and across limb redistribution of mechanical workload represents a potential mechanism for increased metabolic demand in pathological populations with plantarflexion deficits or those that walk with an ankle-foot orthosis that restricts range of motion.}, number={14}, journal={JOURNAL OF BIOMECHANICS}, author={Wutzke, Clinton J. and Sawicki, Gregory S. and Lewek, Michael D.}, year={2012}, month={Sep}, pages={2405–2410} }
 @article{farris_sawicki_2012, title={The mechanics and energetics of human walking and running: a joint level perspective}, volume={9}, ISSN={["1742-5662"]}, DOI={10.1098/rsif.2011.0182}, abstractNote={Humans walk and run at a range of speeds. While steady locomotion at a given speed requires no net mechanical work, moving faster does demand both more positive and negative mechanical work per stride. Is this increased demand met by increasing power output at all lower limb joints or just some of them? Does running rely on different joints for power output than walking? How does this contribute to the metabolic cost of locomotion? This study examined the effects of walking and running speed on lower limb joint mechanics and metabolic cost of transport in humans. Kinematic and kinetic data for 10 participants were collected for a range of walking (0.75, 1.25, 1.75, 2.0 m s−1) and running (2.0, 2.25, 2.75, 3.25 m s−1) speeds. Net metabolic power was measured by indirect calorimetry. Within each gait, there was no difference in the proportion of power contributed by each joint (hip, knee, ankle) to total power across speeds. Changing from walking to running resulted in a significant (p= 0.02) shift in power production from the hip to the ankle which may explain the higher efficiency of running at speeds above 2.0 m s−1and shed light on a potential mechanism behind the walk–run transition.}, number={66}, journal={JOURNAL OF THE ROYAL SOCIETY INTERFACE}, author={Farris, Dominic James and Sawicki, Gregory S.}, year={2012}, month={Jan}, pages={110–118} }
 @inproceedings{robertson_sawicki_2011, title={Influence of parallel spring-loaded exoskeleton on ankle muscle-tendon dynamics during simulated human hopping}, DOI={10.1109/iembs.2011.6090109}, abstractNote={Robotic assistance for rehabilitation and enhancement of human locomotion has become a major goal of biomedical engineers in recent years. While significant progress to this end has been made in the fields of neural interfacing and control systems, little has been done to examine the effects of mechanical assistance on the biomechanics of underlying muscle-tendon systems. Here, we model the effects of mechanical assistance via a passive spring acting in parallel with the triceps surae-Achilles tendon complex during cyclic hopping in humans. We examine system dynamics over a range of biological muscle activation and exoskeleton spring stiffness. We find that, in most cases, uniform cyclic mechanical power production of the coupled system is achieved. Furthermore, unassisted power production can be reproduced throughout parameter space by trading off decreases in muscle activation with increases in ankle exoskeleton spring stiffness. In addition, we show that as mechanical assistance increases the biological muscle-tendon unit becomes less ‘tuned’ resulting in higher mechanical power output from active components of muscle despite large reductions in required force output.}, booktitle={2011 Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC)}, author={Robertson, B. D. and Sawicki, G. S.}, year={2011}, pages={583–586} }