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Open Access

Peer-reviewed

Research Article

Simulations suggest walking with reduced propulsive force would not mitigate the energetic consequences of lower tendon stiffness

  • Richard E. Pimentel,

    Roles Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Writing – original draft, Writing – review & editing

    Affiliation Joint Department of Biomedical Engineering, UNC Chapel Hill and NC State University, Chapel Hill, North Carolina, United States of America

    ⨯
  • Gregory S. Sawicki,

    Roles Funding acquisition, Supervision, Writing – review & editing

    Affiliations Georgia Institute of Technology, George W. Woodruff School of Mechanical Engineering, Atlanta, Georgia, United States of America, Georgia Institute of Technology, School of Biological Sciences, Atlanta, Georgia, United States of America

    ⨯
  • Jason R. Franz

    Roles Conceptualization, Funding acquisition, Supervision, Writing – review & editing

    jrfranz@email.unc.edu

    Affiliation Joint Department of Biomedical Engineering, UNC Chapel Hill and NC State University, Chapel Hill, North Carolina, United States of America

    ⨯

Abstract

Aging elicits numerous effects that impact both musculoskeletal structure and walking function. Tendon stiffness (kT) and push-off propulsive force (FP) both impact the metabolic cost of walking and are diminished by age, yet their interaction has not been studied. We combined experimental and computational approaches to investigate whether age-related changes in function (adopting smaller FP) may be adopted to mitigate the metabolic consequences arising from changes in structure (reduced kT). We recruited 12 young adults and asked them to walk on a force-sensing treadmill while prompting them to change FP (±20% & ±40% of typical) using targeted biofeedback. In models driven by experimental data from each of those conditions, we altered the kT of personalized musculoskeletal models across a physiological range (2–8% strain) and simulated individual-muscle metabolic costs for each kT and FP combination. We found that kT and FP independently affect walking metabolic cost, increasing with higher kT or as participants deviated from their typical FP. Our results show no evidence for an interaction between kT and FP in younger adults walking at fixed speeds. We also reveal complex individual muscle responses to the kT and FP landscape. For example, although total metabolic cost increased by 5% on average with combined reductions in kT and FP, the triceps surae muscles experienced a 7% local cost reduction on average. Our simulations suggest that reducing FP during walking would not mitigate the metabolic consequences of lower kT. Wearable devices and rehabilitative strategies can focus on either kT or FP to reduce age-related increases in walking metabolic cost.

Citation: Pimentel RE, Sawicki GS, Franz JR (2023) Simulations suggest walking with reduced propulsive force would not mitigate the energetic consequences of lower tendon stiffness. PLoS ONE 18(10): e0293331. https://doi.org/10.1371/journal.pone.0293331

Editor: Charlie M. Waugh, The University of British Columbia, CANADA

Received: May 10, 2023; Accepted: October 10, 2023; Published: October 26, 2023

Copyright: © 2023 Pimentel et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: Manuscript data and processing codes are available at the GitHub repository: https://github.com/peruvianox/kT-Fp-MetCost.

Funding: JRF and GSS received funding for this study from National Institutes of Health (https://www.nih.gov/) Grant: R01AG058615. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: The authors have declared that no competing interests exist.

Introduction

Older adults consume energy roughly 10–30% faster than young adults to walk at the same speed or cover the same distance [1–4]. There are a number of morphological, biomechanical, neural and biochemical factors that may contribute to these higher metabolic costs. However, a recent narrative review implicated the potential interplay between age-related changes in series elastic tendon stiffness (a structural change) and push-off intensity (a functional change) during the propulsive phase of walking [5]. Model estimates suggest that lower tendon stiffness (kT) yields shorter muscle fascicle lengths, decreasing the economy of force generation and increasing muscle metabolic cost [6,7]. Similarly, empirical data in younger adults show that walking with diminished push-off intensity, measured via the peak anterior/propulsive component of the ground reaction force (i.e., FP), also increases the metabolic cost of walking [8]. Both of these factors (i.e., decreased kT and reduced FP) are characteristic of elderly gait and have been independently studied in the context of walking economy. However, interactions between kT and FP and any resultant effects on the metabolic cost of walking have yet to be explored.

Although some discrepancies exist in the comparative literature, most human studies show that older adults exhibit lower kT and higher maximal strain during force-matched functional tasks compared to young adults [9,10]. Most reports focus on the Achilles tendon due to its relevance to walking metabolic cost and accessibility for in vivo imaging. Age-related decreases in Achilles kT associate with lower walking performance (shorter 6-minute walk test distance) in older adults [11,12]. This supports the role of elastic energy storage and return as a vital mechanism to minimize the metabolic cost of walking [13,14]. Altered kT has direct influence on the mechanics and economy of muscle contractions which, at least for the Achilles tendon, may influence push-off behavior. When walking at the same speed, older adults display a diminished soleus muscle operating range compared to young adults [15]. Could walking with a reduced FP mitigate the metabolic penalty we pay for reduced kT?

Walking function, particularly during the push-off phase, arises from the interaction between muscle activity, muscle mechanics, and tendon elastic energy storage and return. During steady-state walking at preferred speeds, these muscle-tendon dynamics are tuned to optimize movement economy. We perform significant mechanical work during push-off–predominantly via muscle-tendon units (MTU) spanning the ankle–to propel the body forward, which exacts a metabolic cost to transition from one step to the next. Reduced FP among older adults increases walking metabolic cost by placing higher demand on more proximal leg muscles to perform mechanical work [16]. Specifically, demand for mechanical power normally accommodated by distal MTUs spanning the ankle is redistributed to more proximal MTUs spanning the hip [16,17]. This has metabolic consequences because, unlike those spanning the hip, MTUs spanning the ankle are uniquely designed for economical force production during walking with relatively shorter fascicles and longer tendons.

Although individuals can increase kT in response to mechanical stimuli from exercise[18,19], it can be challenging to quantify the role kT plays in modulating walking whole-body metabolic cost. Fortunately, musculoskeletal modeling [20–22] overcomes some of these methodological challenges. Our lab [6] and others [11,23] have used such models to reveal that decreasing kT elicits shorter muscle fiber lengths, requiring higher activations and thus higher metabolic costs to meet the task demands of walking. However, prior studies have only augmented Achilles’ kT (rather than all of the tendons in the simulated lower limb), even though there is little experimental data to suggest that age-related decreases in kT are limited to tendons spanning the ankle. Furthermore, limiting altered kT to only the Achilles tendon may disguise other compensatory muscle actions.

Our purpose was to quantify the individual and combined effects of kT and FP on walking metabolic cost in total and at the individual-muscle level. Our central motivation was to determine whether walking with reduced FP mitigates the metabolic penalty of reduced kT. However, examining larger than usual FP values is an important scientific contribution, allowing for a more comprehensive understanding of the relation between FP, kT, and walking metabolic cost. Understanding the full landscape of both decreasing and increasing FP in response to biofeedback can enhance the clinical impact toward therapeutic interventions designed to enhance FP. Therefore, we hypothesized that: 1) decreasing kT would contribute to higher metabolic costs during walking; and 2) kT and FP would significantly interact to affect the metabolic cost of walking. More specifically, we thought that reducing FP may offer a way to mitigate higher metabolic costs anticipated with decreased kT. We also explored our experimental effects on muscle activation and fiber length to probe the mechanisms underlying the kT, FP, and metabolic cost landscape. Our anticipated results are intended to provide valuable insight into the tendency of older adults to walk with smaller FP and diminished ankle push-off, and how clinicians, scientists, and engineers might design devices and interventions to overcome the burden of inefficient walking.

Methods

Participants & experimental design

This study leverages previously published experimental data, and a detailed description of our experimental design and method can be found elsewhere [8,17]. The authors of this study did not have direct access to identifiable participant information. All participants provided written informed consent prior to engaging in any study activities. This study was approved by the University of North Carolina Institutional Review Board (IRB Protocol 18–0797). Between April and August of 2019, we recruited a convenience sample of 12 (8 female) healthy young adults (average ± standard deviation: age: 23.3±3.1 years; height = 1.74±0.12 m; mass = 74.7±14.3 kg). Participants walked 4 passes in a hallway with timing gates spaced 30 meters apart to determine their preferred walking speed.

We recorded a 5-minute, habitual-walking trial for each participant on an instrumented dual-belt treadmill (Bertec Corp., Columbus, Ohio, USA) at their preferred overground speed (1.37±0.15 m/s). We measured the peak anterior ground reaction force (i.e., propulsive force or FP) from the final 2 minutes of the habitual walking trial by extracting FP from stance phases using a 20-N vertical force threshold. For our FP biofeedback, we displayed the average FP from the previous 2 steps in real time on a screen in front of the participant (Fig 1A). Alongside the real-time FP, we displayed a target as a horizontal line (corresponding to the final 2-minute average FP from the habitual trial). We then familiarized each participant to our biofeedback paradigm over a 3-minute exploration trial, ensuring that each participant could readily increase and decrease FP on command prior to moving forward with the experimental protocol.

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Fig 1. Experimental design.

An overview of the (A) experimental and (B) computational methods to examine how tendon stiffness (kT) and propulsive force (FP) affect the metabolic cost of walking. In our experimental design (A), we asked participants to walk at their preferred speed while targeting specific FP using visual biofeedback. We simulated their movement in numerous musculoskeletal models at a range of kT levels (εo = 2%, 3.3% (model default), 4%, 6%, and 8%) and estimate d the metabolic cost for each condition (kT & FP). This figure is similar but not identical to a flowchart image we recently published [17].

https://doi.org/10.1371/journal.pone.0293331.g001

We used the average FP from the final 2 minutes of the habitual walking trial as each participant’s typical FP (Norm). For experimental trials, participants walked at their preferred speed for 5-minute trials while responding to biofeedback targets of their Norm FP as well as ±20% and ±40% of Norm, presented in randomized order. In between each trial, participants rested in a seated position for at least 2 minutes.

Musculoskeletal simulations

We performed musculoskeletal simulations in OpenSim [20–22] (version 4.1) to estimate individual muscle mechanics and metabolic energy costs. Using functional hip joint centers [24] and a static pose, we scaled all body segments of a gait2392 model [25] for subject-specific anthropometrics in 3 dimensions. These musculoskeletal models use Hill-type muscle models (Thelen2003Muscle) with standard equilibrium equations to simulate musculotendon dynamics [26]. Model parameters based on anthropometrics (optimal fiber length and tendon slack length) were scaled using segmental scale factors. Similar to previous modeling studies [27,28], we scaled maximum isometric force by 1.5 times default value to ensure all simulations could produce the requisite joint moments. We maintained defaults for all other model parameters. We also maintained the classic optimization function that minimizes the square of muscle activations when computing muscle dynamics.

Following standard human musculoskeletal modeling techniques (Fig 1B) described previously[17], we performed computed muscle control simulations [29] across a range of tendon strain levels (i.e., εo, tendon strain at maximum isometric force). Specifically, we simulated εo at 2%, 3.3% (model default), 4%, 6%, and 8% for all model tendons (92 in total). We changed tendon strain because we could not directly alter tendon stiffness in the musculoskeletal model. We chose these strain values because they lie within previous simulation studies [6,30], contain the expected range of tendon strain for younger and older adults [11,31,32], and, in the case of 2% εo, provides a stiffer comparison versus default (3.3% εo).

During the simulations, we probed muscle metabolic costs using the Bhargava 2004 and Umberger 2010 models [33,34], which are readily available in OpenSim. For a conservative estimate, we report the average of these two bioenergetic models. All metabolic costs presented in this study result from the musculoskeletal models, not from indirect calorimetry. Furthermore, we refer to muscle names using the standard nomenclature from the gait2392 model MTU actuators. Finally, we follow syntax from the metabolic models and report the sum of all modeled muscles as Total metabolic cost.

To follow common terminology, we use the term tendon stiffness (kT) generally throughout, rather than tendon strain (εo). We acknowledge that this complicates the narrative due to the inverse relation between stiffness and strain (2% εo = most stiff, 8% εo = least stiff). We clarify these parameters in our figures by labeling both strain (εo) and stiffness (kT) whenever possible.

Data reduction & statistics

From a selection of gait cycles over the final 2 minutes of each trial, we reduced simulation input data (motions & forces) down to one gait cycle on each side by selecting the first left and right stride from the 10-second window with the most accurate biofeedback targeting during the two minutes (as performed previously [17]). We performed a total of 600 computational simulations (i.e., 12 subjects, 5 biofeedback targets, 5 εo values, 2 strides [left & right]). We averaged metabolic cost estimates bilaterally for each condition prior to statistical analysis. Outcome variables included total and individual-muscle metabolic costs, reported on average and as a percentage of the gait cycle. We simplified muscles with multiple lines of action (i.e., glut_med1, glut_med2, glut_med3) by summing each component for the whole muscle (i.e., glut_med).

To analyze the effects on stride-average walking metabolic cost, we performed two-way repeated measure analyses of variance (ANOVA) to test for main effects of and interactions between kT and FP at whole-body and individual-muscle levels (α = 0.05). Alongside the ANOVA results, we also report partial eta squared (ɳp2) effect sizes. Similarly, to assess the effects on walking metabolic cost as a percentage of the gait cycle, we used statistical parametric mapping [35,36] to quantify main effects of kT and FP (α = 0.001). We also performed Pearson correlations to explore associations between primary variables (metabolic cost, kT, and FP) and muscle-level determinants (i.e., activation and fiber length). We performed all statistical calculations using the Pingouin and SciPy packages [37,38]. For transparency and to support open science, we provide our simulation data and processing scripts at: https://github.com/peruvianox/kT-Fp-MetCost.

Results

Total metabolic cost

We found significant main effects of kT (p<0.001, ɳp2 = 0.423, Fig 2 horizontal axis) and FP (p = 0.014, ɳp2 = 0.244, Fig 2 vertical axis) on total metabolic cost. We did not find a significant interaction between kT and FP (p = 0.162, ɳp2 = 0.111). In general, total metabolic cost increased as kT decreased (εo increased) or as FP deviated from the Norm intensity.

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Fig 2. Total average metabolic costs.

We show how average total metabolic cost varies across kT (horizontal axis) and FP intensity (vertical axis). This heatmap is color coded for the reference metabolic cost (default kT and Norm FP intensity) to be displayed in white, with higher costs in red and lower costs in blue. We found significant ANOVA main effects separately for kT (horizontal arrow) and FP (vertical arrow), but no interaction (no diagonal arrow) between them.

https://doi.org/10.1371/journal.pone.0293331.g002

When viewed across the gait cycle (Fig 3), we found that kT and FP affect instantaneous metabolic cost differently across various phases of the gait cycle. We found significant main effects of kT (εo) during early stance (10–16% gait cycle), late stance (48–52% and 55–60% gait cycle) and late swing (92–100% gait cycle). Alternatively, we found significant main effects of FP during mid-to-late stance (~25–32% and 40–45% gait cycle) and mid-to-terminal swing (72–80% and 97–100% gait cycle). In general, the effects of kT and FP on total metabolic cost occurred at different times of the gait cycle, not simultaneously. Although we found no interaction between kT and FP for total metabolic cost on average, we observed a few interactions during early stance and push-off (Fig 3).

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Fig 3. Total instantaneous metabolic costs.

We show instantaneous, whole-body metabolic cost as a percentage of the gait cycle, across both kT (left minor axes) and FP (right major axis). The average metabolic cost at default kT and Norm FP is normalized to white. We display higher costs in red, and lower costs in blue, with the color intensity profiles even between the two. At the top of the figure, we show periods with significant main effects for kT (or εo) and FP. The black horizontal bars indicate a significant repeated measures ANOVA main effect via statistical parameter mapping.

https://doi.org/10.1371/journal.pone.0293331.g003

Individual muscle metabolic costs

Table 1 shows the metabolic costs for all modeled muscles, ranked in order of energy consumption, and how their consumption varied as a function of kT and FP. Ten different muscles contributed >4% (>2% unilateral) to total metabolic cost. The three highest energy-consuming muscles (glut_med, rec_fem, and soleus) each contributed >8% (>4% unilateral).

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Table 1. Muscle metabolic costs.

https://doi.org/10.1371/journal.pone.0293331.t001

Fig 4 graphically summarizes the effects of kT and FP for the top 12 most costly muscles, which accounted for 70.8% (35.4% unilateral) of the total metabolic cost at default kT and Norm FP. Eight of top 12 individual-muscle contributors to total metabolic cost showed a main effect of kT (horizontal arrows), including all three muscles spanning the ankle and three out of the five muscles spanning the knee. Nine of the top 12 contributors to total metabolic cost showed a main effect of FP (vertical arrows), including six of the seven muscles spanning the hip (all but rec_fem). Finally, five of the top 12 most energy-consuming muscles showed an interaction effect (diagonal arrows), including all three muscles spanning the ankle.

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Fig 4. Individual muscle average metabolic costs.

Individual muscle metabolic costs respond uniquely across kT and FP. In this figure, we show the top 12 lower-body muscles that contribute to walking metabolic cost (Table 1). We oriented the heatmaps with proximal musculature (hip) towards the top, and distal musculature (ankle) towards the bottom. Like Fig 2, we normalized each heatmap for the default kT and FP values (3.3% and Norm, respectively) to be shown in white, with higher costs in red and lower costs in blue. Within each heatmap, we show significant ANOVA main effects via horizontal, vertical, and diagonal arrows indicating significant effects for kT, and FP, and interaction, respectively.

https://doi.org/10.1371/journal.pone.0293331.g004

Fig 5 shows how the individual muscle metabolic costs vary across the gait cycle. We see interaction effects at the individual-muscle level during specific instances of the gait cycle (gray shaded regions along the top bar). For example, on average, we found significant interactions between kT and FP for soleus, glut_max, tib_ant, and med_gas (Table 1). We can see these interactions during early-to-mid stance for glut_max (Fig 5C); early stance, push-off, and late swing for soleus (Fig 5J); intermittently throughout stance phase for med_gas (Fig 5K); and push-off for tib_ant (Fig 5L).

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Fig 5. Individual muscle instantaneous metabolic costs.

Timing and intensity of individual-muscle metabolic costs change when varying kT and FP. In this figure, we show 12 lower-body muscles as in Fig 4, now including instantaneous metabolic cost across the gait cycle. These heatmaps are designed similar to the whole-body costs in Fig 3, with kT on the left minor vertical axis, FP on the right vertical major axis, and relative time (% GC) on the horizontal axis. We show significant ANOVA main effects from instantaneous statistical parametric mapping using blocks (εo and FP) and shaded regions (interactions) along the top bar.

https://doi.org/10.1371/journal.pone.0293331.g005

Individual muscle fiber lengths and activation levels

We found a significant association between metabolic cost and mean activation (Fig 6A) but not for normalized mean fiber length (Fig 6B). FP had a mixed influence on the relationship between activation and fiber length (Fig 6C), whereas kT (strain) showed a strong tendency for shorter fiber lengths and higher activations (Fig 6D, downward & rightward shift from blue [most stiff] to pink [least stiff]).

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Fig 6. Activation, fiber length, and metabolic costs.

These scatterplots show general associations between the underlying muscle-tendon dynamics of activation and fiber length and their influence on the relationships between metabolic cost, FP, and kT. Each circle represents the subject-average outcome at a given activation, fiber length, metabolic cost, FP, and kT for the top dozen individual-muscle contributors to metabolic cost (also shown in Figs 4 and 5). We found a significant association between metabolic cost and mean activation (A) but not for normalized mean fiber length (B). FP (C) seemed to have more mixed influence on the relationship between activation and fiber length, whereas kT (strain, D) showed a strong effect for shorter fiber lengths and higher activations (downward & rightward shift from blue (most stiff) to pink (least stiff)).

https://doi.org/10.1371/journal.pone.0293331.g006

For additional context and transparency behind our simulations, we provide supplementary figures showing the simulated activation levels (S1 and S3 Figs) and fiber lengths (S2 and S4 Figs) for total and individual-muscle metabolic costs. We also show the average activation levels and normalized fiber lengths at default kT and Norm FP for these muscles in S1 and S2 Tables. On average across the gait cycle, the top dozen energy-consuming muscles (bolded muscle names) tended to have higher activation levels (higher ranks in S1 Table) and shorter fiber lengths (lower ranks in S2 Table) compared with the rest of the musculature.

We conclude our results by providing additional data on the triceps surae musculature (S5 Fig) and on lower-body sagittal plane kinematics across the biofeedback conditions (S6 Fig). S5 Fig summarizes comparisons between the three triceps surae muscles, as lat_gas was not a member of the top 12 contributors to metabolic cost. The cost landscape for lat_gas largely aligned with that of med_gas but with smaller metabolic costs. In terms of kinematics, we found that reducing FP tended to decrease sagittal plane hip, knee, and ankle joint ranges of motion (S6 Fig). Conversely, increasing FP tended to increase ankle extension near push-off (~60% gait cycle).

Discussion

A hybrid of experimental and computational approaches allowed us to investigate whether age-related changes in function (adopting smaller FP) affected the metabolic consequences arising from those in structure (having lower kT). This combined experiment yielded simulated instantaneous metabolic costs, providing the ability to identify muscle level responses across two of the predominant aging-related factors that contribute to increased walking metabolic cost.

Our data support our first hypothesis, that decreasing kT increases the metabolic cost of walking for total costs as well as nearly all individual muscles. Our second hypothesis was more nuanced. We reject our second hypothesis at the whole-body level, as total metabolic cost only increased as kT and FP decreased (rightward and downward shift in Fig 2). However, certain muscles did display cost savings when emulating age-related changes (lower kT and reduced FP). In particular, the triceps surae muscles are a primary determinant of FP generation and exhibited a rightward and downward shift (S5A–S5C Fig). For example, if we compare the default condition (Norm FP and 3.3% εo) with a reasonable aging shift (i.e., -20% FP and 6% εo) we see a 4.6% increase in total metabolic cost (Fig 2) as well as a 7% cost reduction for the triceps surae (4.4%, 6.8%, and 9.9% reductions for the soleus, med_gas, and lat_gas, respectively, Figs 4 & S5). Thus, these simulations suggest that older adults may adopt a strategy with local reductions in metabolic cost, but with increased costs when summed at the whole-body level.

We found no interaction at the whole-body level between kT and FP on metabolic cost using simulations of walking at a constant speed in young adults. Rather, kT and FP each independently affect walking metabolic cost, with no evidence that walking with smaller FP may be adopted to mitigate the metabolic consequences arising from reduced kT.

By exploring individual muscle contributions to total metabolic cost, we show unique inter-muscular responses to alterations in kT and FP. In the following sections, we further interpret these cumulative results from young adults walking across a range of FP intensities in the context of characteristic changes in structure and gait function in older adults. These findings highlight the importance of structural components (kT) and functional behavior (FP) as determinants of walking economy.

Effects of simulated changes in tendon stiffness

It is well documented that kT decreases with age and physical inactivity. Lower kT associates with worse walking performance [11,12] generally via two mechanisms: directly via changes in tendon elastic energy storage, return, and MTU power generation, and indirectly by compelling shorter muscle lengths. For example, altering gastrocnemius and solus reference tendon strain in silico from 3–11% yields vastly different tendon and muscle lengths during stance, and thus the timing and magnitudes of tendon and muscle power [6]. Our main premise is that operating a less-stiff tendon elicits shorter muscle lengths to compensate for greater tendon elongation for a given force output and MTU length [6]. These effects presume higher excitations at a metabolic penalty or may sufficiently alter musculotendon dynamics to alter muscle activation timing.

In a similar study to ours, increasing Achilles tendon stiffness did not significantly decrease walking energy cost in older adults [23]. Biological ranges of kT incorporate the local cost minima of walking [23,39]. We generally interpret reduced kT as pathophysiological change that would benefit from intervention. However, as a potential alternative interpretation, older adults likely participate in less physical activity, and thus their lower stiffness may be a physiological adaptation to optimize metabolic cost for their daily activities [10].

Altering only the Achilles kT in older and younger adults yields relatively small effects (~1.5% change from baseline) on whole-body metabolic cost across a range of walking speeds [23]. Although the Achilles tendon and triceps surae musculature may be most impacted by changing kT, we cannot assume that only the Achilles tendon would be affected by altered kT. Thus, we allowed for uniform changes in kT across all MTUs in our musculoskeletal models. In doing so, we found a rather large effect size for kT (ɳp2 = 0.423, explaining ~42% of the variance in metabolic cost) [40]. When considering Norm FP alone, reducing kT (increasing εo up to 8%) yielded a 5% increase in metabolic cost on average (10.2 W/kg at 3.3% εo vs. 10.8 W/kg at 8% εo). Our findings agree well with the literature that reducing kT increases the metabolic cost of walking [6,30].

We can see instantaneous effects of kT on total metabolic cost particularly during the beginning of the push-off phase (i.e., around 50% of the gait cycle, Fig 3). At that instant, simulations with lower kT (i.e., 6–8% εo) showed an earlier increase in metabolic cost than those with higher kT (i.e., 2–4% εo). Breaking this down to individual muscles, this kT effect on metabolic cost arises from ankle extensors (i.e., soleus and med_gas) and hip flexors (i.e., psoas and iliacus). We also saw main effects of kT on activation for med_gas (S3K Fig) and on fiber length for all four muscles (S4A, S4B, S4J and S4K Fig). Operating against their least stiff tendons, the soleus and med_gas showed large metabolic effects of kT, functioned at shorter fiber lengths, and did not lengthen much during mid-stance phase (10–50% gait cycle). Conversely, operating against their stiffest tendons, these same muscles exhibit lengthening behavior during mid stance, and function at longer fiber lengths during push off. If timed appropriately, tendons with lower stiffness may exploit tendon elongation to store spring potential energy for powering forceful activities (such as FP) later. Indeed, med_gas MTUs with the less-stiff tendons exhibit bursts of higher costs at the beginning of push-off (~40% gait cycle), but dramatic cost savings later in push-off (50–60% gait cycle, Fig 5K). For a clearer distinction of these fiber length differences, please refer to S7 Fig.

Qualitatively looking at muscle dynamics, kT also seemed to show a direct impact on mean activation and fiber length demonstrating a clear shift towards shorter fiber lengths and higher activations (Fig 6D). Our walking simulations and metabolic outcomes are consistent with the majority of outcomes from other studies, finding that individual muscle actions and metabolic cost during walking are highly sensitive to changes in kT [18,23,39,41].

The large effects of kT on metabolic cost may arise because it impacts not only the force-length, but also the force-velocity relation of muscle. For force-length, a less-stiff tendon would compel shorter muscle operating ranges when MTU length is constrained (as it was in this study). Shorter muscles generate less force, thus requiring a higher activation at a given submaximal force output, yielding higher metabolic costs. For force-velocity, a less-stiff tendon would elongate more when transmitting a specific force. In MTU-shortening activity, this would require the muscle to shorten more rapidly, requiring higher activations and thus, higher costs.

Effects of changing propulsive force

In this study, we used FP as our proxy for functional changes, due to its strong association with walking speed [42,43] and hallmark decline among older adults [44–47]. We recently discovered empirical evidence that a diminished FP increases metabolic cost, explained via the distal-to-proximal redistribution of muscle workload [16]. Not surprisingly, walking with larger FP at a fixed speed, at least among younger adults, also increases measured walking metabolic cost. Our whole-body bioenergetic predictions support these earlier measurements.

Interestingly, we did not see an effect of FP on total metabolic cost during push-off phase (50–60% gait cycle, Fig 3). Similar studies that increased/decreased propulsion found increases in neuromuscular drive to the ankle extensors [48,49]. In agreement with the literature, we do see individual muscle effects (for metabolic cost, activation, and fiber length) during this phase for the hip flexors (psoas and ilacus), hip abductor (glut_med), and ankle extensors (soleus and med_gas). These individual muscle outcomes reveal the compensatory costs of walking with altered FP. For example, walking with greater FP exacts higher ankle extensor metabolic costs. Conversely, walking with a diminished FP requires the hip flexors to compensate with higher metabolic costs to drive hip flexion. As a particularly interesting outcome, glut_med (a hip abductor), operated at higher costs when walking with larger FP (Figs 4D and 5D). We suggest this may relate to an increased need for hip stability while transmitting larger forces from the ankle extensors to the body’s center of mass [50].

Our protocol prompted changes in FP using targeted biofeedback which changed lower body kinematics (S6 Fig). Because even minor changes in joint kinematics can influence tendon length (and therefore strain) [51], we would infer the inverse is also true (where minor changes in tendon strain can influence joint kinematics). This inverse relationship is supported in part by differing joint kinematics between younger and older adults during walking [52]. Because there is no way to control for all experimental variables (kT, FP, simulated metabolic cost, and effects of aging) in this study, we note that joint kinematics did change in response to FP, but were constrained across the kT simulations.

Interactions between propulsive force and tendon stiffness

Although we did not find an interaction between kT and FP for total metabolic cost on average (Fig 2), we did see periods of significant interactions across the gait cycle (Fig 3) occurring during early stance (~5–20%) and push off (~55%). Because the instantaneous total metabolic costs in Fig 3 are comprised of bilateral data, the periods of significant interaction (5–10% and 55–60% gait cycle) may arise from the bilateral nature of gait, with both distal and proximal muscles contributing to the interactions across both time periods. As total metabolic cost is the sum from individual muscles, we discuss the individual muscles likely to explain these interactions.

Of the 5 muscles with a significant kT and FP interaction on average (Fig 4), glut_max and vas_lat likely explain those during early stance. The cost profile for glut_max during early stance (5–10%) exhibited higher metabolic costs for both lower FP (major vertical axis) and lower kT (minor vertical axis, Fig 5C). The higher costs due to lower FP aligns with the well-documented redistribution of muscle work from the ankle to the hip [16]. The effect of kT likely arises from the relative fiber length differences imposed by tendon constraints. During this concentric activity of glut_max (S4C Fig), some of the MTU shortening is lost via tendon elongation, requiring glut_max to contract more to overcome the tendon lengthening, and thus requiring higher costs (Fig 5C).

In an eccentric example, vas_lat consumes more energy with higher kT (Fig 5F) during eccentric activity during early-to-mid stance (15–20% gait cycle, S3F and S4F Figs). Vas_lat muscle fibers attached to less-stiff tendons (higher εo) may maintain relatively similar lengths as the compliant tendons uptake changes in length. Whereas, when attached to stiff tendons, vas_lat muscle fibers must elongate to account for the length change (see white/green areas in the minor axis of S4F Fig at 15–20% gait cycle, particularly visible for Norm and +40% FP conditions). This eccentric activity is more costly than isometric activity, exhibiting one aspect of the kT−FP interaction.

Of the final 3 muscles that experienced significant interactions on average (Fig 4J–4L), soleus and tib_ant demonstrated instantaneous interactions near the end of push-off (55–60% gait cycle, Fig 5J and 5L). The soleus showed lower costs with reduced FP as well as lower costs with lower kT (higher εo). The lower metabolic costs with reduced FP is straightforward and aligns with lower soleus activation (S3J Fig). The lower metabolic cost at lower kT likely arises from elastic recoil of the Achille’s tendon providing some MTU-shortening this late into push-off. The interaction between kT and FP for the soleus also aligns with interaction timing for total metabolic cost (Fig 3). Interestingly, med_gas did not share the instantaneous kT and FP interaction with the soleus during push-off, even though there were independent significant effects for kT and FP separately (Fig 5).

Relevance to precision rehabilitation

The triceps surae musculature (soleus, med_gas, and lat_gas) provides a significant portion of the work and power for gait by generating FP. Neuromuscular adaptations conserve energy on an individual-muscle or muscle-group level. We found that neuromuscular responses to minimize activation (i.e., reducing FP in response to biofeedback) may successfully mitigate costs for the triceps surae muscles (S5 Fig), but do not necessarily reduce total energy costs (Fig 2) due to compensatory neuromuscular responses in other muscles (Fig 4).

Our results show that kT and FP do not interact in their effects on the metabolic cost of walking–at least in young adults. While this is a novel finding, it is most relevant when placed in the context of walking among older adults. Specifically, our data suggest that smaller observed Fp in older adults would not be an effective mitigation strategy to conserve total energy costs energy to counteract lower kT. A logical extension of that interpretation is that interventions designed to reduce the metabolic cost of walking in older adults are not subject to a trade-off and can independently address either or both reduced kT and diminished FP.

We envision several viable options for solutions that could address the metabolic consequences of reduced kT and diminished FP. For example, plyometric training may help increase kT [19,53] and biofeedback-based gait retraining may help improve FP [54]. Thus far, training strategies to reduce the metabolic cost of walking among older adults have been generally unsuccessful, primarily because they focused on increasing muscle strength, rather than kT [55].

Opportunities remain to simultaneously address the metabolic consequences of both reduced kT and diminished FP. For example, ankle exoskeletons could be designed to augment ankle joint stiffness and provide supplemental FP with potential to reduce the metabolic cost of walking [41,56]. In addition, exoskeletons that can provide chronic (i.e. employable over weeks to months) wearable powered assistance or resistance on-demand could be used to interleave phases of on-line gait retraining to improve volitional Fp with phases of scheduled resistance to increase muscle strength and tendon stiffness [57]. Ultimately, this stresses that holistic design, iterative functional testing, and personalized prescriptions may be needed to implement effective wearable devices or rehabilitative therapies to combat walking inefficiency and deteriorating functional ability to maintain overall health in our aging population.

Limitations

First, it is very time consuming (weeks of plyometric training or immobilization) to conduct a study to alter kT in human subjects. Furthermore, prospective tendon overloading or underloading protocols cannot isolate adaptations only to the tendon as the associated musculature will also be affected. Thus, we relied on the combination of experimental procedures and targeted modeling approach to explore the metabolic cost-kT-FP landscape. A noted by others [58], simulations cannot exactly replicate the motions and forces a participant may produce at both the specified kT and FP. Thus, our experiments may not offer exactly the appropriate constraints for estimating changes in muscle dynamics of actual participants with altered kT. We only changed tendon strain (ε) in this study in attempt to address the independent effects of kT. Yet, that single variable is unlikely to fully characterize age-related changes in musculotendon dynamics. Future studies may also alter other tendon properties within the Thelen2003 muscle model (such as tendon slack length or MTU passive shape factor) or utilize other musculotendon models that have a higher resolution for adjusting tendon parameters (i.e., Millard2012).

Second, our discoveries are, by design, inferred from data-driven musculoskeletal simulations rather than via direct empirical measures. Our simulations reported high and potentially implausible metabolic costs at the beginning of the gait cycle, relatively early in each simulation’s run time. We suspect these outcomes are simulation artifacts rather than reliable predictions. Activation simulations must compute muscle state initial values (length, force, activation) when simulating a movement. Although we applied our simulation 0.05 s before the start of each gait cycle (larger than the recommended 0.03 s), muscle states may not have fully reached equilibrium, particularly at low stiffnesses. For this reason, we opted not to discuss or interpret any findings during very early stance phase (<5% gait cycle). Additionally, like most forward dynamic simulations, our musculoskeletal dynamics and metabolic cost outcomes depend on optimization algorithms with objective functions that seek to minimize the muscle activation squared. Although these simulation methods are supported by experimental evidence [29,59], human neuromechanics may not always align with their outcomes.

Third, we designed our biofeedback paradigm to prompt changes in FP while at a constant speed, which also resulted in changes in stride length [8]. We did not characterize the effects of stride length specifically in this study. However, because older adults exhibit reduced stride length [60] as well as FP, we contend that the outcomes reported here are relevant to our target population. We have previously quantified and discussed at length these interactions between FP and stride length and their potential impact on metabolic cost [17,54].

Conclusion

We combined computational and experimental analyses to answer the following question with clinically important implications: “Does walking with reduced FP mitigate the metabolic penalty of reduced kT?” In an experimental paradigm designed for young adults to emulate older adult walking via targeted FP biofeedback across various simulated kT levels, the answer is “no”. Walking metabolic cost is elevated both with reduced kT or with any deviation in FP and we observed no trade-off that could enable functional adaptations to overcome altered structural properties of the musculoskeletal system. However, even though total metabolic cost increased by 5% on average with moderate reductions in kT and FP, the triceps surae muscles did experience 7% local cost reductions on average. Although kT and FP may need to be quantified individually, they need not be addressed separately, as wearable devices and rehabilitative strategies could be designed to simultaneously address one or both these key factors driving metabolic cost.

Supporting information

S1 Fig. Muscle average activation levels.

We show individual-muscle activation levels as a function of both kT and FP. ANOVA main effects are shown via arrows (horizontal, vertical, & diagonal) similar to Figs 2 & 4. Eleven of the 12 highest energy consuming muscles showed significant effects in activation level for kT (all but glut_med, panel D). Five of the 12 most costly muscles showed significant effects in activation level for FP. Three out of the 12 muscles displayed significant interactions between kT and FP for activation level. These data correspond with S1 Table.

https://doi.org/10.1371/journal.pone.0293331.s001

(TIF)

S2 Fig. Muscle average fiber lengths.

We show individual-muscle fiber lengths as a function of both kT and FP. The fiber lengths of all 12 of the costliest muscles were significantly impacted by kT. Additionally, 8 of these top 12 had significant effects for FP, while 7/12 showed significant interaction effects. These data correspond with S2 Table.

https://doi.org/10.1371/journal.pone.0293331.s002

(TIF)

S3 Fig. Muscle instantaneous activation levels.

The instantaneous activation levels for highest consuming muscles highly aligned with the instantaneous metabolic costs (Fig 5).

https://doi.org/10.1371/journal.pone.0293331.s003

(TIF)

S4 Fig. Muscle instantaneous fiber lengths.

Viewing the instantaneous muscle fiber lengths, we see changes across the experimental conditions for both kT and FP. These showcase underlying changes in muscle actions as a result from the altered kT and FP. Large effects occur in the distal musculature, particularly for the solues, med_gas, and tib_ant (J, K, & L).

https://doi.org/10.1371/journal.pone.0293331.s004

(TIF)

S5 Fig. Triceps surae metabolic costs.

Due to their large influence on ankle moment and thus FP, we highlight the triceps surae metabolic cost on average (A-C) and across the gait cycle (D-F). One can see a high similarity between med_gas and lat_gas across FP and kT experimental conditions. This view of all three triceps surae muscles is inaccessible in other figures due to the small relative metabolic cost of lat_gas.

https://doi.org/10.1371/journal.pone.0293331.s005

(TIF)

S6 Fig. Lower body kinematics.

We show the influence of the FP biofeedback conditions on sagittal plane kinematics for the hip (A), knee (B), and ankle (C). Subject-averaged curves are surrounded by shading of ±1 standard deviation. We also calculated one-way repeated measures analysis of variance on the influence of FP condition on joint angles across the gait cycle using SPM. Like our other figures, a black bar at the top of each panel denotes a significant main effect for that instance of the gait cycle (1% increments). In general, reducing FP resulted in smaller dynamic ranges across all lower body joints.

https://doi.org/10.1371/journal.pone.0293331.s006

(TIF)

S7 Fig. Triceps surae impact of tendon stiffness on muscle dynamics.

To show the effects of kT on muscle length more clearly, this figure focusses on the soleus (A) and med_gas (B) muscles for the Norm FP condition. Both subplots show the average relative muscle fiber length with shaded ±1 standard deviation across the gait cycle for the least stiff (8% εo, blue solid line) and most stiff (2% εo, red dashed line) conditions. We remind readers that kinematics (and thus MTU lengths) are constrained for all simulations. Comparing the two kT extrema, we see a clear reduction in operating range for the 8% εo condition across both muscles, implying that the more compliant tendon would elongate and recoil more in contribution to MTU length changes. Conversely, a stiffer tendon is unlikely to experience as much length change, requiring its respective muscle to undergo more shortening and lengthening. Indeed, in the least-stiff condition, the med_gas (B) acts nearly isometrically during mid-stance (20–50% gait cycle).

https://doi.org/10.1371/journal.pone.0293331.s007

(TIF)

S1 Table. We show the average activation level for all modeled muscles, averaged across the gait cycle.

We display how these individual muscles respond to changes in FP, kT, and interaction by reporting the ANOVA main effect (p-value) and effect size (ɳp2). Bolded muscle names indicate the top 12 consumers of metabolic cost, highlighted in Figs 4 & 5.

https://doi.org/10.1371/journal.pone.0293331.s008

(DOCX)

S2 Table. We show the average normalized fiber length for all modeled muscles, averaged across the gait cycle.

We display how these individual muscles respond to changes in FP, kT, and interaction by reporting the ANOVA main effect (p-value) and effect size (ɳp2). Bolded muscle names indicate the top 12 consumers of metabolic cost, highlighted in Figs 4 & 5.

https://doi.org/10.1371/journal.pone.0293331.s009

(DOCX)

Acknowledgments

We would like to thank the University of North Carolina at Chapel Hill and the Research Computing group for providing computational resources and support that have contributed to these research results. We acknowledge Noah Pieper, Sidney Baudendistal, Gabriela Diaz, and Rebecca Krupenevich for collecting the data that enabled this simulation study.

References

  1. 1. Ortega J. D. and Farley C. T., “Individual limb work does not explain the greater metabolic cost of walking in elderly adults,” J. Appl. Physiol., vol. 102, no. 6, pp. 2266–2273, Jun. 2007, pmid:17363623
  2. 2. Peterson D. S. and Martin P. E., “Effects of age and walking speed on coactivation and cost of walking in healthy adults,” Gait Posture, vol. 31, no. 3, pp. 355–359, Mar. 2010, pmid:20106666
  3. 3. Mian O. S., Thom J. M., Ardigò L. P., Narici M. V., and Minetti A. E., “Metabolic cost, mechanical work, and efficiency during walking in young and older men,” Acta Physiol., vol. 186, no. 2, pp. 127–139, 2006, pmid:16497190
  4. 4. Ortega J. D., Fehlman L. A., and Farley C. T., “Effects of aging and arm swing on the metabolic cost of stability in human walking,” J. Biomech., vol. 41, pp. 3303–3308, 2008, pmid:18814873
  5. 5. Krupenevich R. L., Beck O. N., Sawicki G. S., and Franz J. R., “Reduced Achilles Tendon Stiffness Disrupts Calf Muscle Neuromechanics in Elderly Gait,” Gerontology, pp. 1–11, Jul. 2021, pmid:34274923
  6. 6. Orselli M. I. V., Franz J. R., and Thelen D. G., “The effects of Achilles tendon compliance on triceps surae mechanics and energetics in walking,” J. Biomech., vol. 60, pp. 227–231, 2017, pmid:28728791
  7. 7. Beck O. N., Trejo L. H., Schroeder J. N., Franz J. R., and Sawicki G. S., “Shorter muscle fascicle operating lengths increase the metabolic cost of cyclic force production,” J. Appl. Physiol., vol. 133, no. 3, pp. 524–533, Sep. 2022, pmid:35834625
  8. 8. Pieper N. L., Baudendistel S. T., Hass C. J., Diaz G. B., Krupenevich R. L., and Franz J. R., “The metabolic and mechanical consequences of altered propulsive force generation in walking,” J. Biomech., vol. 122, 2021, pmid:33933865
  9. 9. Onambele G. L., Narici M. V., and Maganaris C. N., “Calf muscle-tendon properties and postural balance in old age,” J. Appl. Physiol., vol. 100, no. 6, pp. 2048–2056, 2006, pmid:16455811
  10. 10. Stenroth L., Peltonen J., Cronin N. J., Sipilä S., and Finni T., “Age-related differences in Achilles tendon properties and triceps surae muscle architecture in vivo,” J. Appl. Physiol., vol. 113, no. 10, pp. 1537–1544, Nov. 2012, pmid:23042907
  11. 11. Delabastita T., Bogaerts S., and Vanwanseele B., “Age-Related Changes in Achilles Tendon Stiffness and Impact on Functional Activities: A Systematic Review and Meta-Analysis,” J. Aging Phys. Act., vol. 27, no. 1, pp. 116–127, 2018, pmid:29722592
  12. 12. Stenroth L. et al., “Plantarflexor Muscle–Tendon Properties are Associated With Mobility in Healthy Older Adults,” J. Gerontol. Ser. A, vol. 70, no. 8, pp. 996–1002, Aug. 2015, pmid:25733719
  13. 13. Fukunaga T., Kubo K., Kawakami Y., Fukashiro S., Kanehisa H., and Maganaris C. N., “In vivo behaviour of human muscle tendon during walking,” Proc. R. Soc. Lond. B Biol. Sci., vol. 268, no. 1464, pp. 229–233, Feb. 2001, pmid:11217891
  14. 14. Sawicki G. S., Lewis C. L., and Ferris D. P., “It pays to have a spring in your step,” Exerc. Sport Sci. Rev., vol. 37, no. 3, pp. 130–138, Jul. 2009, pmid:19550204
  15. 15. Panizzolo F. A., Green D. J., Lloyd D. G., Maiorana A. J., and Rubenson J., “Soleus fascicle length changes are conserved between young and old adults at their preferred walking speed,” Gait Posture, vol. 38, no. 4, pp. 764–769, Sep. 2013, pmid:23642629
  16. 16. DeVita P. and Hortobagyi T., “Age causes a redistribution of joint torques and powers during gait,” J. Appl. Physiol., vol. 88, no. 5, pp. 1804–1811, May 2000, pmid:10797145
  17. 17. Pimentel R. E., Pieper N. L., Clark W. H., and Franz J. R., “Muscle metabolic energy costs while modifying propulsive force generation during walking,” Comput. Methods Biomech. Biomed. Engin., vol. 24, no. 0, pp. 1552–1565, Mar. 2021, pmid:33749464
  18. 18. Albracht K. and Arampatzis A., “Exercise-induced changes in triceps surae tendon stiffness and muscle strength affect running economy in humans,” Eur. J. Appl. Physiol., vol. 113, no. 6, pp. 1605–1615, Jun. 2013, pmid:23328797
  19. 19. Epro G. et al., “The Achilles tendon is mechanosensitive in older adults: Adaptations following 14 weeks versus 1.5 years of cyclic strain exercise,” J. Exp. Biol., vol. 220, no. 6, pp. 1008–1018, 2017, pmid:28298464
  20. 20. Dembia C. L., Bianco N. A., Falisse A., Hicks J. L., and Delp S. L., “OpenSim Moco: Musculoskeletal optimal control,” PLOS Comput. Biol., vol. 16, no. 12, p. e1008493, Dec. 2020, pmid:33370252
  21. 21. Seth A. et al., “OpenSim: Simulating musculoskeletal dynamics and neuromuscular control to study human and animal movement,” 2018, pmid:30048444
  22. 22. Delp S. L. et al., “OpenSim: Open-source software to create and analyze dynamic simulations of movement,” IEEE Trans. Biomed. Eng., vol. 54, no. 11, pp. 1940–1950, 2007, pmid:18018689
  23. 23. Delabastita T., De Groote F., and Vanwanseele B., “Achilles tendon stiffness minimizes the energy cost in simulations of walking in older but not in young adults,” Physiology, preprint, Feb. 2020.
  24. 24. Piazza S. J., Okita N., and Cavanagh P. R., “Accuracy of the functional method of hip joint center location: Effects of limited motion and varied implementation,” J. Biomech., vol. 34, no. 7, pp. 967–973, 2001, pmid:11410180
  25. 25. Delp S. L., Loan J. P., Hoy M. G., Zajac F. E., Topp E. L., and Rosen J. M., “An Interactive Graphics-Based Model of the Lower Extremity to Study Orthopaedic Surgical Procedures,” IEEE Trans. Biomed. Eng., vol. 37, no. 8, pp. 757–767, 1990, pmid:2210784
  26. 26. Thelen D. G., “Adjustment of muscle mechanics model parameters to simulate dynamic contractions in older adults,” J. Biomech. Eng., vol. 125, no. 1, pp. 70–77, 2003, pmid:12661198
  27. 27. Clark W. H., Pimentel R. E., and Franz J. R., “Imaging and Simulation of Inter-muscular Differences in Triceps Surae Contributions to Forward Propulsion During Walking,” Ann. Biomed. Eng., vol. 49, no. 2, pp. 703–715, Feb. 2021, pmid:32897456
  28. 28. Arnold E. M., Hamner S. R., Seth A., Millard M., and Delp S. L., “How muscle fiber lengths and velocities affect muscle force generation as humans walk and run at different speeds,” J. Exp. Biol., vol. 216, no. 11, pp. 2150–2160, 2013, pmid:23470656
  29. 29. Thelen D. G. and Anderson F. C., “Using computed muscle control to generate forward dynamic simulations of human walking from experimental data,” J. Biomech., vol. 39, no. 6, pp. 1107–1115, 2006, pmid:16023125
  30. 30. Uchida T. K., Hicks J. L., Dembia C. L., and Delp S. L., “Stretching Your Energetic Budget: How Tendon Compliance Affects the Metabolic Cost of Running,” 2016, pmid:26930416
  31. 31. Kharazi M., Bohm S., Theodorakis C., Mersmann F., and Arampatzis A., “Quantifying mechanical loading and elastic strain energy of the human Achilles tendon during walking and running,” Sci. Rep., vol. 11, no. 1, Art. no. 1, Mar. 2021, pmid:33712639
  32. 32. Waugh C. M., Blazevich A. J., Fath F., and Korff T., “Age-related changes in mechanical properties of the Achilles tendon,” J. Anat., vol. 220, no. 2, pp. 144–155, 2012, pmid:22150089
  33. 33. Umberger B. R., “Stance and swing phase costs in human walking,” J. R. Soc. Interface, vol. 7, no. 50, pp. 1329–1340, 2010, pmid:20356877
  34. 34. Bhargava L. J., Pandy M. G., and Anderson F. C., “A phenomenological model for estimating metabolic energy consumption in muscle contraction,” J. Biomech., vol. 37, no. 1, pp. 81–88, 2004, pmid:14672571
  35. 35. Pataky T. C., “One-dimensional statistical parametric mapping in Python,” Comput. Methods Biomech. Biomed. Engin., vol. 15, no. 3, pp. 295–301, Mar. 2012, pmid:21756121
  36. 36. Pataky T. C., Vanrenterghem J., and Robinson M. A., “Zero- vs. one-dimensional, parametric vs. non-parametric, and confidence interval vs. hypothesis testing procedures in one-dimensional biomechanical trajectory analysis,” J. Biomech., vol. 48, no. 7, pp. 1277–1285, 2015, pmid:25817475
  37. 37. Vallat R., “Pingouin: statistics in Python,” J. Open Source Softw., vol. 3, no. 31, p. 1026, Nov. 2018,
  38. 38. Virtanen P. et al., “SciPy 1.0: fundamental algorithms for scientific computing in Python,” Nat. Methods, vol. 17, no. 3, Art. no. 3, Mar. 2020, pmid:32015543
  39. 39. Lichtwark G. A. and Wilson A. M., “Optimal muscle fascicle length and tendon stiffness for maximising gastrocnemius efficiency during human walking and running,” J. Theor. Biol., vol. 252, no. 4, pp. 662–673, Jun. 2008, pmid:18374362
  40. 40. Richardson J. T. E., “Eta squared and partial eta squared as measures of effect size in educational research,” Educ. Res. Rev., vol. 6, no. 2, pp. 135–147, 2011,
  41. 41. Nuckols R. W., Dick T. J. M., Beck O. N., and Sawicki G. S., “Ultrasound imaging links soleus muscle neuromechanics and energetics during human walking with elastic ankle exoskeletons,” Sci. Rep., vol. 10, no. 1, Art. no. 1, Feb. 2020, pmid:32109239
  42. 42. Pimentel R. E., Feldman J. N., Lewek M. D., and Franz J. R., “Quantifying mechanical and metabolic interdependence between speed and propulsive force during walking,” Front. Sports Act. Living, vol. 4, 2022, Accessed: Sep. 09, 2022. [Online]. Available: https://www.frontiersin.org/articles/10.3389/fspor.2022.942498. pmid:36157906
  43. 43. Hsiao H. Y., Zabielski T. M., Palmer J. A., Higginson J. S., and Binder-Macleod S. A., “Evaluation of measurements of propulsion used to reflect changes in walking speed in individuals poststroke,” J. Biomech., vol. 49, no. 16, pp. 4107–4112, 2016, pmid:27756571
  44. 44. Franz J. R., “The Age-Associated Reduction in Propulsive Power Generation in Walking,” Exerc. Sport Sci. Rev., vol. 44, no. 4, pp. 129–136, 2016, pmid:27433977
  45. 45. Conway K. A. and Franz J. R., “Increasing the Propulsive Demands of Walking to Their Maximum Elucidates Functionally Limiting Impairments in Older Adult Gait,” J. Aging Phys. Act., vol. 28, no. 1, pp. 1–8, Feb. 2020, pmid:31141428
  46. 46. Buddhadev H. H., Smiley A. L., and Martin P. E., “Effects of age, speed, and step length on lower extremity net joint moments and powers during walking,” Hum. Mov. Sci., vol. 71, p. 102611, Jun. 2020, pmid:32452428
  47. 47. Melzer I., Krasovsky T., Oddsson L. I. E., and Liebermann D. G., “Age-related differences in lower-limb force–time relation during the push-off in rapid voluntary stepping,” Clin. Biomech., vol. 25, no. 10, pp. 989–994, Dec. 2010, pmid:20724044
  48. 48. Gottschall J. S. and Kram R., “Energy cost and muscular activity required for propulsion during walking,” J. Appl. Physiol., vol. 94, no. 5, pp. 1766–1772, May 2003, pmid:12506042
  49. 49. Browne M. G. and Franz J. R., “The independent effects of speed and propulsive force on joint power generation in walking,” J. Biomech., vol. 55, pp. 48–55, Apr. 2017, pmid:28262285
  50. 50. Zelik K. E., Huang T.-W. P., Adamczyk P. G., and Kuo A. D., “The role of series ankle elasticity in bipedal walking,” J. Theor. Biol., vol. 346, pp. 75–85, Apr. 2014, pmid:24365635
  51. 51. Arampatzis A., Monte G. D., and Karamanidis K., “Effect of joint rotation correction when measuring elongation of the gastrocnemius medialis tendon and aponeurosis,” J. Electromyogr. Kinesiol., vol. 18, no. 3, pp. 503–508, Jun. 2008, pmid:17254800
  52. 52. Boyer K. A., Johnson R. T., Banks J. J., Jewell C., and Hafer J. F., “Systematic review and meta-analysis of gait mechanics in young and older adults,” Exp. Gerontol., vol. 95, no. September, pp. 63–70, 2017, pmid:28499954
  53. 53. Reeves N. D., “Adaptation of the tendon to mechanical usage,” J Musculoskelet Neuronal Interact, vol. 6, no. 2, pp. 174–180, 2006. pmid:16849829
  54. 54. Browne M. G. and Franz J. R., “More push from your push-off: Joint-level modifications to modulate propulsive forces in old age,” PLoS ONE, vol. 13, no. 8, pp. 1–14, 2018, pmid:30089143
  55. 55. Mian O. S., Thom J. M., Ardigò L. P., Morse C. I., Narici M. V., and Minetti A. E., “Effect of a 12-month physical conditioning programme on the metabolic cost of walking in healthy older adults,” Eur. J. Appl. Physiol., vol. 100, no. 5, pp. 499–505, Jul. 2007, pmid:16463043
  56. 56. Collins S. H., Bruce Wiggin M., and Sawicki G. S., “Reducing the energy cost of human walking using an unpowered exoskeleton,” Nature, vol. 522, no. 7555, pp. 212–215, Jun. 2015, pmid:25830889
  57. 57. Conner B. C. and Lerner Z. F., “Improving Ankle Muscle Recruitment via Plantar Pressure Biofeedback during Robot Resisted Gait Training in Cerebral Palsy,” in 2022 International Conference on Rehabilitation Robotics (ICORR), Jul. 2022, pp. 1–6. pmid:36176108
  58. 58. Dembia C. L., Silder A., Uchida T. K., Hicks J. L., and Delp S. L., “Simulating ideal assistive devices to reduce the metabolic cost of walking with heavy loads,” PLOS ONE, vol. 12, no. 7, p. e0180320, Jul. 2017, pmid:28700630
  59. 59. Thelen D. G., Anderson F. C., and Delp S. L., “Generating dynamic simulations of movement using computed muscle control,” J. Biomech., vol. 36, no. 3, pp. 321–328, Mar. 2003, pmid:12594980
  60. 60. Judge J. O., Davis R. B., and Ounpuu S., “Step Length Reductions in Advanced Age: The Role of Ankle and Hip Kinetics,” J. Gerontol. A. Biol. Sci. Med. Sci., vol. 51A, no. 6, pp. M303–M312, 1996, pmid:8914503