Muscle Metabolic Energy Costs While Modifying Propulsive Force Generation During Walking

We pose that an age-related increase in the metabolic cost of walking arises in part from a redistribution of joint power where muscles spanning the hip compensate for insufficient ankle push-off and smaller peak propulsive forces (FP). Young adults elicit a similar redistribution when walking with smaller FP via biofeedback. We used targeted FP biofeedback and musculoskeletal models to estimate the metabolic costs of operating lower limb muscles in young adults walking across a range of FP. Our simulations support the theory of distal-to-proximal redistribution of joint power as a determinant of increased metabolic cost in older adults during walking.


Introduction
workload from the ankle to the hip without changing total positive mechanical work, thereby emulating the walking biomechanics of older adults (Browne & Franz 2017a;Fickey et al. 2018). Thus, using this biofeedback paradigm in young adults would allow for testing how differences in the relative reliance on distal versus proximal leg muscles that typically accompany reductions in FP affect muscle metabolic cost. Additionally, a young adult demographic allows for biomechanical investigation that is independent of other age-related changes that may affect metabolism (sarcopenia, tendon compliance, mitochondrial physiology, etc.).
It is not feasible to directly measure the metabolic cost of operating individual muscles during walking. Fortunately, models of the human musculoskeletal system allow for simulation of body movements and estimation of muscle dynamics underlying those movements. Thus, our purpose was to use a targeted biofeedback paradigm and musculoskeletal simulations to estimate the metabolic costs of operating lower limb muscles in young adults walking across a range of FP. We first hypothesized that the simulated muscle metabolic energy cost of walking would increase in a manner consistent with whole-body measurements when targeting smaller or larger FP. We also hypothesized that the metabolic costs of operating proximal versus distal leg muscles would exhibit fundamentally different responses to targeting smaller and larger FP. Ultimately, we seek to provide muscle-level insight to inform movement scientists, rehabilitation engineers, and clinicians interested in understanding and mitigating age-and disease-related increases in walking metabolic cost.

Participants
We recruited 12 young adults (7 females; age=23.3±3.14 years; height=1.74±0.12 m; mass=74.7±14.3 kg, BMI=24.6±3.0 kg/m 2 , mean ± standard deviation) via word of mouth to participate in this single-visit study. All participants confirmed absence of neurologic impairments and musculoskeletal injuries in the previous 6 months. Prior to data collection, each participant provided written informed consent and the study was approved by the University of North Carolina Biomedical Sciences Institutional Review Board.

Experimental Protocol
We measured each participant's preferred over-ground walking speed via the average time from three passes down a 30-meter walkway (average preferred walking speed: 1.37±0.15 m/s). For motion capture measurements, we placed 19 retroreflective markers on the sacrum and bilateral anterior superior iliac spines, posterior superior iliac spines, lateral/medial femoral epicondyles, lateral/medial malleoli, lateral calcanei, and lateral first and fifth metatarsal heads. An additional 14 markers tracked the thighs and shanks of each participant on rigid clusters. After a static calibration trial, we located functional hip joint centers via leg circumduction tasks to improve model scaling accuracy (Cappozzo 1984;Bell et al. 1990; Piazza et al. 2001). Prior to walking measurements, participants stood still for 5 minutes to estimate standing metabolic rate (see Metabolic Measurements). Participants then completed all walking trials at their preferred speed on a force-sensing, dual-belt treadmill (Bertec Corp., Columbus, Ohio, USA), beginning with a 5-minute warm up. The average peak anterior ground reaction force from all steps taken during the final two minutes of the warm-up determined each subjects' habitual FP using a custom Matlab (MathWorks, Natick, MA, USA) script that extracted and analyzed ground reaction forces in real-time.
Subjects then participated in a visual biofeedback paradigm in which they were encouraged to push off the ground with varying vigor to target their typical walking FP (Norm) as well as ±20% and ±40% of Norm as outlined below ( Figure 1A). Using a Matlab script and visual interface described in detail previously (Browne & Franz 2017a), a monitor positioned in front of the participant simultaneously displayed the respective target FP value for each trial and the average FP from their previous 4 steps (2 right and 2 left), updated on a step-by-step basis (Browne & Franz 2017a). For all trials involving biofeedback, we normalized the scaling of each subject's FP data on the monitor to evenly distribute all target values over the ordinate range. Prior to beginning the targeting biofeedback, each participant completed an exploration period to become familiarized with increasing and decreasing their FP across the range of target values. Then, across five separate 5-minute trials, participants walked at their preferred speed and targeted each of the FP targets in randomized order. During the final two minutes of each trial, we recorded bilateral lower body kinematics using a 12-camera motion capture system (Motion Analysis Corporation, Santa Rosa, CA, USA) operating at 100 Hz and measured split-belt treadmill ground reaction forces at 1000 Hz. We filtered marker trajectories and ground reaction forces using a 4 th -order low-pass Butterworth filter with 6 and 20 Hz cutoff frequencies, respectively.

Metabolic Measurements
For this study, we repurposed metabolic measurements from a previously published study using methods therein described in detail (Pieper et al. In Revision). Briefly, expired oxygen and carbon dioxide were sampled on a breath-by-breath basis via COSMED K5 wearable metabolic system (COSMED, Rome, Italy). To estimate standing and walking metabolic rates, we averaged expired gases over the final two minutes of the 5-minute standing condition and each 5-minute walking condition, respectively. We used standardized regression equations (Brockway 1987) to estimate whole-body metabolic power from oxygen consumption and carbon dioxide production, subtracted standing from walking to calculate net metabolic power, and finally normalized outcomes by body mass (W/kg).

Inclusion of Trunk Kinematics
Our original walking data was derived from another study (Pieper et al. In Revision) and did not include trunk marker trajectories; however, the reliability of musculoskeletal simulations improves when including trunk kinematics for center of mass estimates and dynamic consistency. Thus, we opted to record and benchmark normal pelvis and trunk marker trajectories (adding sternal notch and bilateral acromion processes) in three additional participants walking at 1.2 m/s. We then used the resultant average kinematics to create a virtual trunk segment for each participant in our primary experiment. Specifically, we synchronized the measurements using timenormalized walking motions and defined virtual trunk marker locations as position vectors in the pelvis coordinate system. We scaled the position vector magnitudes to each participant's average leg length to account for inter-individual differences in subject stature. Supplementary Figure S1 shows the profiles of virtual trunk kinematics across all subjects and conditions.

Musculoskeletal Modeling and Simulation
We performed all musculoskeletal modeling and bioenergetic simulations using filtered marker trajectories and ground reaction forces in OpenSim (version 4.0) (Delp et al. 2007;Seth et al. 2018) and the gait2392 musculoskeletal model ( Figure 1B). We preserved all default muscle parameters, except maximum isometric force, which was set to 1.5 times default for all models (in accordance with OpenSim documentation, and similarly performed by other groups (Arnold et al. 2013)). Subject-specific models were scaled using a combination of anatomical, functional, and virtual markers that aligned with the local coordinate axes of each body segment. We locked the subtalar and metatarsal-phalangeal joints at 0° for all simulations because our marker set was insufficient to yield those kinematics (Rajagopal et al. 2016).
We analyzed the first left and right strides from the 10-second window with the most accurate biofeedback performance (i.e., steps where their actual FP closely matched the target) for each walking condition and subject. From these two strides, inverse kinematics determined segment kinematics that minimized the sum of the square marker trajectory error. Then, we iteratively applied a residual reduction algorithm to identify model segment mass distributions and joint kinematics consistent with measured ground reaction forces. We updated model segment masses after the first iteration and used kinematics from the second iteration to ensure dynamic consistency. After residual reductions, we used computed muscle control without constraints to determine the lower limb muscle activations necessary to drive the scaled model to match the recorded kinematics.
Finally, we determined our primary outcome measure (muscle metabolic power) using two different muscle metabolic cost models (i.e., "probes") readily available within OpenSim (Umberger et al. 2003;Bhargava et al. 2004;Umberger 2010). Our purpose was not to objectively compare the models' efficacy; rather, we included two models with checks for consistency to build confidence in our model predictions. Each model estimated metabolic power for each individual muscle actuator as a function of heat rate (activation, shortening/lengthening, force maintenance, basal) and mechanical work rate (Umberger et al. 2003;Bhargava et al. 2004;Umberger 2010). It is not within the scope of this paper to discuss these models in detail. Nevertheless, each was governed by time-dependent variables that included, for each individual muscle actuator, its excitation and activation, relative % of fast versus slow twitch muscle fibers, contractile velocity, force-generating capacity, mass, and optimal fiber length.

Data Reduction and Statistical Analysis
We integrated individual muscle metabolic powers over select phases of the gait cycle (i.e., leading limb double support, single support, trailing limb double support, swing phase, and whole stride) which were calculated from instances where the vertical ground reaction force crossed a threshold of 20 N. In addition, we normalized all metabolic outcomes by body mass and total stride time to estimate metabolic power per unit second of walking. We categorized joint-level metabolic powers as those associated with operating the hip, knee, and ankle joints during each gait cycle phase by summing individual muscle metabolic powers for actuators spanning each respective joint. We partitioned biarticular muscles into their respective joints using the ratio of their sagittal plane moment arms in a standing position (Miller 2014). Finally, we averaged individual muscle metabolic outcomes bilaterally for subsequent statistical analysis.
Pearson correlations tested for associations between measured and model-predicted metabolic powers. One-way repeated measures analyses of variance (ANOVA) tested for main effects of biofeedback condition on joint-level metabolic powers within each gait cycle phase of interest. When a significant main effect was found, Fisher's least significant difference (LSD) post-hoc tests identified pairwise differences compared to Norm. One-dimensional statistical parametric mapping (SPM, http://www.spm1d.org/, (Pataky 2012)) identified regions of the gait cycle over which individual muscle metabolic powers during targeted biofeedback conditions differed from Norm (repeated measures ANOVA with LSD post-hoc tests). We performed correlations and ANOVAs in Matlab, and calculated SPM using Python. We used a critical alpha value of 0.05 to define significance of ANOVAs. We additionally report effect sizes of partial eta square (ղp 2 ) for the variance associated with main effect across biofeedback conditions as well as Cohen's d for effect size pairwise comparisons between a specific condition versus Norm.

Empirical Measurements versus Model Predictions
Compared to walking normally, measured net metabolic power increased by an average of 58% and 47% when targeting -40% and +40% FP, respectively (Figure 2A, p<0.001, ղp 2 =0.350). Total model-predicted metabolic power followed a similar trend ( Figure 2B-C) and positively correlated with empirical measurements (Umberger: r 2 =0.309, p<0.001; Bhargava: r 2 =0.342, p<0.001, Figure 2E-F). These two metabolic models were strongly correlated with each other (r 2 =0.981, p<0.001, Figure 2D) and displayed similar stride-averaged profiles ( Figure 2G). Given the high level of consistency between model predictions ( Figure 2E, F, G), we opted to use the Umberger model for subsequent joint-and muscle-level analysis. Figure 3 summarizes model-predicted metabolic power integrated across periods of interest for all muscles (A) and summed for muscle actuators spanning the hip (B), knee (C), and ankle (D) joints. Due to the many statistical comparisons for the joint-level analysis, please reference Table 1 where we document the statistical outcomes of all comparisons. Here, we report only mean pairwise differences for brevity. When targeting 40% smaller FP, metabolic power across the entire stride increased in total (+0.79 W/kg) due to increases at the hip (+0.29 W/kg) and knee (+0.22 W/kg). These increases were mainly attributed to increased power consumed during leading leg double support at the hip (+0.16 W/kg) and during leg swing in total (+0.42 W/kg) and at the knee (+0.11 W/kg). Also, when targeting 40% smaller FP, ankle metabolic power increased during single support (+0.07 W/kg) but decreased during trailing limb double support (-0.15 W/kg), resulting in no change over the entire stride.

Joint-Level Model Predictions
When targeting 40% larger FP, metabolic power across the entire stride increased in total (+0.90 W/kg) due to increases at the hip (+0.20 W/kg), knee (+0.11 W/kg), and ankle (+0.10 W/kg). These increases over the entire stride were primarily due to higher metabolic power during single support across all lower limb joints (hip: +0.13 W/kg, knee: +0.13 W/kg, ankle: +0.09 W/kg). We found no differences in metabolic power during swing phase when targeting 40% larger FP. However, when targeting 20% larger FP, swing phase metabolic power increased in total (+0.11 W/kg) and at the hip (+0.08 W/kg). Finally, there was a reduction in metabolic cost during leading limb double support when targeting +20% FP in total (-0.14 W/kg) and at the hip (-0.05 W/kg) and knee (-0.04 W/kg), which were the only significant reductions in metabolic cost across all conditions. Figure 4 shows the metabolic power estimated for 21 lower body muscles that contribute most to total model-predicted metabolic power during walking and the results of our statistical parametric mapping. Although there were several instances containing within-subject condition main effects, only a handful of significant pairwise differences arose and nearly all were for the 40% smaller FP condition. Specifically, when targeting 40% smaller FP, we observed the following changes in metabolic power (organized from distal to proximal): soleus consumed less during push-off; biceps femoris (long head) and semimembranosus consumed more during early single support; the vastii muscles consumed less during weight acceptance and more during mid-swing; and the gluteus medius and maximus both consumed less during push-off and more during late swing/early stance. When targeting 20% smaller FP, we found that the vastus medialis and intermedius consumed more metabolic power during mid-swing. Finally, when targeting 40% larger FP, the adductor longus consumed less metabolic power during early single support.

Step Kinematics
To provide context for our metabolic outcomes, Table 2 displays timing information for gait cycle periods of interest. Participants took longer (shorter) steps when target larger (smaller) than normal FP, respectively. In relative terms (i.e., % stride), participants spent more time in single support and leg swing and less time in double support when targeting larger FP.

Discussion
This study sought to provide new insight into the biomechanical basis for reduced walking economy due to age and gait pathology, and thereby inform movement scientists, rehabilitation engineers, and clinicians interested in mitigating those changes to improve independence. We accept our first hypothesis that model-predicted metabolic costs increased in a manner consistent with those measured across conditions via indirect calorimetry. We also accept our second hypothesis that proximal and distal leg muscles would exhibit different responses when targeting smaller and larger than normal FP. Ultimately, our experimental manipulations and musculoskeletal simulations provide a muscle-level roadmap for better understanding the metabolic consequences of walking with: (i) smaller than normal FP, common in aging and gait pathology, and (ii) larger than normal FP, a therapeutic milestone for gait retraining or wearable assistive devices. More immediately, our results provide convincing evidence to suggest that a distal-to-proximal redistribution of muscle workload during walking may exact a significant metabolic penalty.
In In this study, our model predictions explained approximately one-third of the variance in empirical measurements across a relatively broad combination of walking conditions. When averaged across conditions, our estimates agreed quite well with measured values in absolute terms. However, we note two explanations for the variance unaccounted for across conditions. Specifically, our models tended to overestimate net metabolic power during normal walking while underestimating the sensitivity therein to prescribed changes in FP. Moving forward, we anticipate refining our predictions based on higher fidelity measurements (i.e., including trunk, subtalar, and metatarsal-phalangeal joint kinematics) and improved simulation specificity (i.e., personalized "tuning" of muscle-tendon architecture (Handsfield et al. 2014) and material properties (Uchida et al. 2016;Orselli et al. 2017)). Nevertheless, because we were able to estimate changes in whole-body metabolic cost consistent with those measured, we have confidence in using musculoskeletal modeling to answer questions related to the metabolic consequences of altered muscular demand across the lower limbs during walking.
As context for our discussion of metabolic outcomes, we do note variations in step kinematics between FP conditions (Table 2) Because the purpose of our study was to assess the metabolic costs of walking while controlling for speed, we cannot rule out the interaction between step length/duration and walking dynamics that govern our model estimates. However, we also know from our prior work that although both change simultaneously in response to our biofeedback paradigm, modifying FP is not biomechanically equivalent to modifying step lengths (Browne & Franz 2017a). Hereafter, we consider metabolic costs at the joint-and muscle-level foremost as those due to changes in FP, but also in the context of these changes in gait event timing.

Targeting smaller than normal FP
Reduced ankle power generation during push-off, characteristic of aging and many gait pathologies and associated with reduced FP, requires compensatory increases in hip mechanical output. In prior studies, this compensation has manifested as an increased demand on leading limb hip extensors to accelerate the body forward and upward ( Our results provide evidence that such compensations have metabolic consequences. First, as expected for walking with reduced push-off intensity, we found that targeting smaller FP yielded lower metabolic costs of operating muscles spanning the ankle during trailing limb double support. More proximally, we found that increases in the metabolic cost of walking with smaller FP were well-explained by muscles spanning the hip during early stancenamely, the gluteus maximus and the biarticular hamstrings. We did not find a significant increase in metabolic cost at the hip during late stance when targeting smaller FP. However, at the individual muscle level, we did find higher metabolic costs of operating the psoas and iliacus during late stance. This outcome is consistent with increased demands for swing initiation, with metabolic consequences continuing into mid-swing, where we found a large increase in metabolic cost for all four quadriceps muscles. We interpret this increase to suggest that insufficient ankle power output exacts a metabolic penalty requiring additional effort for leg swing and knee extension in preparation for each subsequent foot strike. Together, these data provide an individual muscle roadmap to explain how the distal-to-proximal redistribution increases the metabolic cost of walking. While walking with 40% smaller FP, we were surprised to find an increased metabolic cost of operating muscles spanning the ankle during single support. This increased utilization of ankle extensor muscles during single support may be due to a shift in the relative timing of the anterior GRF, which rose and peaked sooner for this biofeedback condition relative to normal walking (data not reported). At the individual muscle level, we were also surprised to find a reduced metabolic cost of operating the gluteus medius and minimus during push-off when targeting 40% smaller than normal FP. The gluteus medius and minimus are generally considered important during swing for regulating foot placement to preserve lateral stability. However, some authors have recently suggested that push-off intensity and lateral balance are inextricably connected (Kim & Collins 2015;Reimann et al. 2018). Our results are consistent with those conclusions and implicate the gluteus medius (and to a lesser extent, gluteus minimus) in providing hip stability that is proportional to push-off intensity, likely allowing for effective force transmission to the center of mass.

Targeting larger than normal FP
The goal of many rehabilitation paradigms and wearable assistive devices is to restore power output during push-off. In the absence of such intervention, biofeedback that encourages increased push-off intensity shows promise to reverse the characteristic redistribution of joint power generation due to age (Lewis & Ferris 2008;Browne & Franz 2017a). Knowing the individual-muscle metabolic response to enhanced push-off intensity would allow scientists and clinicians to design better rehabilitation therapies for individualized prescription with translational potential to elicit more youthful and efficient gait biomechanics. Although our young adult population are not representative of those that would require such intervention, our data provide an important reference for future bioenergetic modeling studies in the target populations.
Our simulations reveal an increased metabolic cost of operating muscles spanning the hip, knee, and ankle when targeting larger than normal FPa response that manifested most during single support. At the hip, this metabolic penalty is explained primarily by increases for the gluteus medius and maximus during early single support and the hamstrings during midstance. Those changes may arise from larger than normal braking forces during early stance and larger acceleration of the center of mass during midstance, respectively. We predict that these metabolic changes would be mitigated if walking speed was permitted to increase in response to larger propulsive forces. This methodological design may also explain why we found no increase in the metabolic cost of muscles spanning the ankle during trailing limb double support when targeted larger than normal FP. Although this outcome is surprising, it is consistent with recent ultrasound imaging data alluding to a potentially counterproductive trade-off between increased activation and shorter operating lengths on force transmission from the calf muscles during push-off (Browne & Franz In Revision).
In contrast to effects when targeting 40% larger FP, and despite higher whole-body metabolic cost on average, targeting a more modest 20% increase in FP resulted in lower metabolic costs to operate muscles spanning the hip and knee during leading limb double support. Here, the hamstring muscles appear to consume lower average metabolic cost during early stance compared to Norm. Thereafter, these reductions are overcome by increased costs during single support and leg swing. This suggests it may be theoretically possible to reduce metabolic costs of operating individual leg muscles to values lower than predicted for normal walking. Although at odds with generally accepted theories regarding energy optimization in walking (Browne & Franz 2017b), such a conclusion at the individual muscle level may allude to patterns of inter-muscular coordination that are outside the scope of this study but warrant further investigation.
Compared to walking with smaller FP, changes in the metabolic costs of operating individual leg muscles are much more evenly allocated when walking with larger FP. It is difficult to predict whether to expect the same outcome in older adults or people with gait pathology in response to interventions designed to restore FP. However, our results suggest that such interventions should consider not only the metabolic consequences of local (e.g., ankle) assistance to increase FP, but also any resultant compensation at other joints. Moving forward, we envision rehabilitative programs and assistive technologies that are informed by and objectively evaluated via individual muscle metabolic responses derived via the bioenergetic simulations used in this study.

Limitations
We first acknowledge other factors that contribute to increased metabolic cost of walking in older adults. These may include changes in trunk flexion ( However, because our participants were not older adults, future work will need to test the sensitivity of these simulations to variations in model parameters. Another limitation we recognize is that we did not measure kinematics for the subtalar or metatarsal-phalangeal joints or the upper body. To overcome part of this limitation, we used trunk kinematics averaged from another cohort in our simulations. For transparency, our appendix documents these methodological considerations in more detail. Finally, participants walked at a fixed speed despite biofeedback-induced changes in FP. This led to differences in stride frequency known to affect metabolic cost (Donelan et al. 2002;Kuo et al. 2005;Soo & Donelan 2010) and likely to confound our results in ways described earlier.

Conclusion
This study provides individual muscle-level insight into the metabolic consequences of walking with less and more vigorous push-off during walking. We first conclude that walking with insufficient push-off intensity places higher mechanical demand on muscles spanning the hip which in turn increases the metabolic cost of walking. This suggests that a distal-to-proximal redistribution of muscle demand during walking may independently contribute to higher metabolic costs in older adults and those with gait pathology. We also conclude that a fundamentally different and more evenly-allocated pattern of increased muscular demand explains higher metabolic energy costs when targeting larger propulsive forces. More generally, our simulations provide an initial benchmark for the metabolic consequences of altered propulsive force generation during walking that can inform strategies to improve walking economy in those with deficits in push-off intensity. Finding ways to preserve or restore ankle power generation, via rehabilitation, assistive technologies, or other means, appears central not only to improve walking performance, but also to improve walking economy. Table 1: Statistics for repeated measures ANOVA and LSD post-hoc pairwise tests corresponding to Figure 3. Conditions with significant p-values are bolded. We do not report pairwise differences for joint-level metabolic costs with insignificant ANOVA main effect (rows with missing data). ղp 2 Table 2: Gait cycle periods of interest for each biofeedback condition in absolute (s) and relative (%) time. These periods were calculated over 10 strides in the window of best biofeedback targeting performance (i.e., best matching the -40%, -20%, etc. of FP). Bolded values indicate significant post-hoc pairwise difference versus Norm. These are the periods over which the jointlevel metabolic costs were integrated in Figure 3. Stride time is defined as 100% of the gait cycle, thus we omit these data and run post hoc analyses using duration. SD: standard deviation across participant means, s: seconds, %: percent of gait cycle   Participants pushed off the ground with varying vigor to target -40%, -20%, +20%, +40%, and their typical (Norm) propulsive force (FP) in a walking biofeedback paradigm with 5minute trials per condition. Participant anthropometrics, marker trajectories, and ground reaction forces from the final 2 minutes of each trial defined musculoskeletal modeling simulations. We simulated the first left and right full stride from the 10 second window with the most accurate biofeedback targeting performance. From these simulations, we ultimately determined the metabolic power required from each lower body muscle to drive the scaled model and match the measured movements.

Figure 2:
For each biofeedback condition, we display the walking metabolic power empirically measured using indirect calorimetry (A) and simulated from two different musculoskeletal metabolic models (B, C). The models produced nearly identical results (D) that correlated moderately with empirically-measured metabolic power (E, F), explaining about 1/3 rd of the variance. Musculoskeletal modeling of metabolic power allows researchers to estimate the metabolic power required for lower body muscles to drive a simulation of each participant's individual walking pattern. This allows for comparison across the FP biofeedback conditions at specific instances of the gait cycle (G). Given the high similarity of the two models, we opted to use the Umberger model for our metabolic cost estimates and statistical comparisons. . Metabolic powers were integrated over: the entire stride, leading limb double support, single limb support, trailing limb double support, and swing phase. Asterisks show significant LSD post hoc pairwise differences versus Norm in the presence of a significant ANOVA main effect. On the right, we also display instantaneous net metabolic power across the gait cycle.

Figure 4:
We plot the metabolic powers across the gait cycle for the 21 highest power-consuming muscles of the lower limb for each biofeedback condition. Gray shaded regions show periods with a significant repeated measures ANOVA main effect for biofeedback condition using statistical parametric mapping. Colored blocks identify any LSD post hoc pairwise differences for that respective colored condition versus Norm. OpenSim muscles with multiple lines of action (gluteus minimus/medius/maximus and adductor magnus) were summed for simplicity. segment dimensions and coordinate axes, thus errors during the model scaling process may carry forward into future model estimates.
Even with these limitations, we were able to demonstrate typical ranges of kinematics (even for the trunk), realistic muscle activation levels, and stable muscle forces across the gait cycle. To mitigate the effect of any simulation outliers, we averaged each pair of left and rightsided trials together when analyzing our primary outcome measuremuscle metabolic power. Finally, when reporting our metabolic costs, we present the individual data points for each gait cycle period of interest so that our readers may consider the results on an individual-subject level alongside the averages or boxplots for the group or condition. We believe this analysis can make a significant contribution to the field to understand individual muscle metabolic costs while walking across a range of FP, however we suggest that future investigations address the limitations we mention above.