Propulsion without penalty: Greater soleus force with stiffer footwear does not necessarily increase estimated soleus metabolic cost across walking speeds

Abstract

Numerous assistive devices have been designed to improve mobility by improving propulsion and reducing the metabolic cost of walking. Stiff carbon fiber insoles integrated into footwear have emerged as a potentially viable option by increasing longitudinal bending stiffness, providing additional leverage for the ankle joint musculature and increasing soleus force output. However, it remains unknown whether this increased leverage comes with a metabolic penalty at the individual muscle level, which would create a translational barrier for prescribing carbon fiber insoles as targeted interventions. We incorporated motion capture, cine B-mode ultrasound, and electromyography data (N=14) into a bioenergetic model to estimate soleus metabolic cost. Participants walked on an instrumented treadmill at 1.25, 1.75, and 2.0 m/s wearing standardized shoes containing either no carbon fiber insole (low stiffness), a 1.6 mm thick insole (medium stiffness), or a 3.2 mm thick insole (high stiffness). We found a significant main effect (p < 0.001) of walking speed, but not stiffness, for estimated soleus average metabolic power. These results indicate that increases in soleus force output while walking due to increased footwear bending stiffness do not statistically significantly alter muscle-specific metabolic cost, likely due to concomitant reductions in fascicle shortening velocity. As such, carbon fiber insoles may be a particularly useful assistive device for walking in those with ankle plantarflexion deficits.

Graphical Abstract

NEW & NOTEWORTHY:

Increasing footwear bending stiffness via carbon fiber insoles has been shown to reduce soleus fascicle shortening velocity and increase force output. Here we used a bioenergetic model to estimate the metabolic energy consumed by the soleus muscle with increasing footwear stiffness across walking speeds. Footwear stiffness did not statistically significantly alter estimated soleus muscle energy consumption at any speed, highlighting carbon fiber insoles’ capacity to increase muscle force without a clear metabolic penalty.

INTRODUCTION

Reducing the metabolic energy required to perform everyday tasks like walking is crucial goal for improving mobility and quality of life. Individuals that expend additional energy to move about the world may find it harder to perform daily activities and may then choose to move less and/or slower, resulting in a number of negative health outcomes (1–3). To combat these deleterious effects of excessive energy expenditure, numerous lower-limb active (e.g., 4) and passive exoskeletons (e.g., 5), orthotics (e.g., 6), and prostheses (e.g., 7) have been developed and implemented with the aim of reducing an individual’s metabolic cost of locomotion. Many of these devices have specifically targeted the ankle joint (e.g., 8, 9), because the ankle musculature supplies a substantial portion of the positive mechanical work necessary for gait (10) and have been estimated to consume nearly a third of the lower limb’s net metabolic energy for walking (11–13). As such, reducing the energy costs of the ankle joint musculature via assistive devices has been targeted as a viable solution for improving mobility.

Low-cost, lightweight, passive assistive devices are particularly attractive in that they are more readily accessible to a broader population and can be used without imposing physical burdens or requiring external power input. Shoe insoles made from carbon fiber may be one such low-cost and lightweight option. Carbon fiber integrated into footwear has recently become ubiquitous in elite running, based in large part on the Nike Vaporfly 4% shoe, so named as runners used ~4% less energy when running in them compared with other running footwear (14, 15). Individuals with partial foot amputation are also prescribed carbon fiber-based orthotics or protheses to increase leverage about the ankle joint and improve gait biomechanics (16). These benefits in elite athletes and those with amputation highlight the potential for low-cost, lightweight, passive assistive devices like carbon fiber insoles to serve as meaningful mobility aids.

Increasing a shoe’s longitudinal bending stiffness has been shown to alter ankle joint and muscle dynamics (6, 17, 18). In walking, stiffening footwear reduces fascicle shortening velocity of the largest ankle plantarflexor muscle, the soleus, and increases estimated soleus force output (6, 17). Slower soleus shortening velocity, in isolation, would reduce muscle metabolic cost due to the force-velocity relation of muscle (19–21). However, these benefits may be offset by increased cost due to greater muscle force output (22, 23). Therefore, it remains unclear how these carbon fiber insoles alter the metabolic energy needs of the largest ankle plantarflexor muscle in walking.

At a typical walking speed (1.25 m/s), our group (6, 17) demonstrated increases in whole-body metabolic cost of transport (MCoT) in a very stiff footwear condition. However, we reported a 7% reduction in whole-body MCoT when participants walked very fast when wearing these insoles (2.0 m/s) (17). Our group previously proposed that this speed-dependent effect was due to the soleus operating at a unfavorable region of its force-velocity curve at very fast walking speeds (24). As such, reducing the soleus fascicle velocity via carbon fiber insoles would be particularly beneficial, imparting a whole-body MCoT benefit that was not the case at slower walking speeds wherein the soleus operates in a perhaps more favorable region. This potential mechanism highlights the need to explore how soleus operating conditions during assistive device use contribute to its force generation capacity and metabolic energy needs across walking speeds.

Understanding how assistive devices alter the metabolic energy consumed by the largest ankle plantarflexor would provide insight into contexts in which these devices may improve mobility outcomes, thereby guiding future device design and implementation. We have demonstrated that walking with these insoles increases the ankle joint moment and estimated soleus muscle force production in younger adults (6, 17). These effects would be beneficial in those whose gait is characterized by ankle-specific deficits. For example, older adults classically present with smaller peak ankle joint moments while walking (25), perhaps due to less favorable muscle operation conditions (26). Importantly, this ankle joint moment has been identified as a limiting factor in older adults’ propulsion capacity (27). Other clinical populations, such as those with partial foot amputation, who present with decreased ankle joint moments (16) may be similarly limited in their propulsive capacity. Examining whether increasing these moments via footwear stiffening coincides with increases in muscle-specific metabolic energy expenditure would help characterize the costs and benefits of using carbon fiber insoles as assistive devices. However, current experimental methods for measuring the metabolic energy consumed during gait (i.e., indirect calorimetry), cannot parse the metabolic demands of individual muscles across tasks. Fortunately, bioenergetic models (e.g., 28–30) used primarily in computational gait simulations allow for estimation of muscle-specific metabolic energy cost using experimental muscle dynamics measures (muscle activation and fascicle length, velocity, and estimated force) and are therefore well-suited for examining how individual muscles respond to changes in task demand.

Physiologically based models have recently been used to estimate the metabolic energy demands of single joint tasks like knee flexion/extension and ankle plantar/dorsiflexion (31–33). Konno et al. (33) used a bioenergetic model to estimate whole-body metabolic rate differences captured during experimental lower-limb joint flexion/extension tasks where cycle rate (34), duty cycle (35), and fascicle length (36) were perturbed. Although these tasks are more isolated than gait, they resulted in changes to muscle activation, moment, and muscle force-velocity behavior that also occur when modulating gait speed and footwear stiffness (17). These results therefore provide confidence that these bioenergetic models can capture potential changes as a result of increased walking speed and footwear stiffness.

The present investigation aimed to explore the metabolic energy changes of the soleus muscle as a function of footwear stiffness across walking speeds. In line with the proposal of Ray & Takahashi (17) that reductions in soleus fascicle shortening velocity are particularly beneficial at very fast walking speeds, we hypothesized that increasing footwear bending stiffness would impart a soleus-specific metabolic benefit at the fastest walking speed.

MATERIALS AND METHODS

Motion capture, cine B-mode ultrasound, and electromyography data from 14 healthy younger adult participants (12M/2F, 23 ± 2.1 yrs, 177.7 ± 7.1 cm, 76.5 ± 13.0 kg) from Ray & Takahashi (17) were reanalyzed to estimate soleus-specific metabolic energy expenditure. One participant’s data from the previous study were excluded due to technical issues when collecting electromyography data. Participants gave informed consent to participate in an IRB-approved protocol (University of Nebraska Omaha, IRB # 351–16-EP) wherein they walked on a split-belt, instrumented treadmill at 1.25, 1.75, and 2.0 m/s wearing standardized shoes (Reebok RealFlex Train). At each speed, participants completed a six-minute walking trial with shoes that had either no carbon fiber insole (low stiffness), a 1.6 mm thick insole (medium stiffness), or a 3.2 mm thick insole (high stiffness). Speed and stiffness conditions order was randomized.

Soleus metabolic rate was estimated using experimentally derived fascicle length, velocity, force, work, muscle activation, and estimated muscle mass. Soleus fascicles were imaged via cine B-mode ultrasonography using a 60 mm linear probe (Telemed LV7.5/60/128Z-2, Lithuania) placed over the lateral gastrocnemius. Fascicle length was approximated using an open-source, semi-automated tracking algorithm (37) and was differentiated with respect to time to estimate fascicle velocity. Given that experiments to determine an optimal fascicle length were not carried out for the present data, we turned to previous investigations of fascicle lengths referenced to an experimentally derived optimal length. Rubenson et al. (38) found that, on average, participant’s fascicle length during shod walking at preferred speeds were 90% of the optimal fascicle length at heel-strike and shortened to about 70% of this length near toe-off. Therefore, optimal fascicle length was set as the length at heel-strike during the low stiffness, 1.25 m/s condition divided by 0.9. This resulted in a range of mean fascicle lengths between ~73–98% of their optimal length across conditions. Rubenson et al. (38) concluded that soleus fascicle lengths were conserved to the ascending region of the force-length curve, therefore we feel that this approach accurately captures fascicle lengths as a proportion of optimal fascicle length. Force along the soleus fascicles (hereafter referred to as ‘soleus fascicle force’) was estimated in Ray & Takahashi (17) by first computing (Eq.1) Achilles tendon force ($F_{\mathit{\text{AT}}}$) from the resultant ankle joint moment ($M_{\mathit{\text{ankle}}})$ and estimated participant-specific Achilles tendon moment arm ($r_{\mathit{\text{AT}}};$ 39)

$$F_{\mathit{\text{AT}}}=M_{\mathit{\text{ankle}}}*{r_{\mathit{\text{AT}}}}^{-1}$$ [Eq. 1]

Participant-specific Achilles tendon moment arm as a function of ankle joint angle were estimated using the horizontal distance from the lateral malleolus to the posterior aspect of the Achilles tendon (6, 17) and regression equations (39). Achilles tendon force was then partitioned into the soleus component (0.56) based on triceps surae muscle cross-sectional area proportions (40) and the ultrasound-measured fascicle pennation angle (θ; Eq. 2)

$$F_{\mathit{\text{soleus}}\mathit{\text{fascicles}}}=F_{\mathit{\text{AT}}}*0.56*{\mathit{\text{cos}}\left(\theta \right)}^{-1}$$ [Eq. 2]

Fascicle power (i.e., power along the muscle fascicles) was computed as the dot product of fascicle force and fascicle velocity, and fascicle work was computed as the time integral of fascicle power. Soleus muscle activation was normalized with respect to the highest voltage from the low stiffness, 2.0 m/s condition, given that this condition displayed the highest mean voltage peak across participants (17). During 2.0 m/s walking, soleus activation is ~70% of that during maximum voluntary contractions (41). Therefore, all values were normalized such that the highest voltage in the low stiffness, 2.0 m/s condition was set to 0.7. Statistical conclusions were not altered when activation values were instead normalized to 0.5 or 1.0 in the low stiffness, 2.00 m/s walking condition, indicating that the present results are not sensitive to this parameter choice (see Supplemental Fig. S1 and Supplemental Table S1; 10.5281/zenodo.15658852). Soleus muscle mass was estimated as the product of soleus volume and density (Eq. 3). Lower-limb muscle mass was first computed as a function of participant body mass and height using regression equations established by Handsfield et al. (42). This mass was then multiplied by a density ($\rho$) of 1059.7 kg/m³ (43) and by soleus volume as a proportion of total lower-limb muscle volume (0.062) from MRI (42) (Eq. 3).

$$\mathit{\text{soleus}}\mathit{\text{mass}}=\left(47\times m\times h+1285\right)*\rho *0.062$$ [Eq. 3]

Where m represents body mass and h represents height.

Soleus fascicle length, velocity, force, work, activation, and mass were input into the bioenergetic models of Umberger et al. (28), Bhargava et al. (29), Lichtwark & Wilson (44), and Umberger (45). Mathematical formulations of each model can be found in the corresponding publications. In general, these models compute muscle the metabolic power ($\dot{E}$) by summing the heat due to muscle activation and maintenance (${\dot{h}}_{\mathit{\text{act}}/\mathit{\text{maint}}})$, the heat due to muscle shortening and lengthening (${\dot{h}}_{\mathit{\text{shorten}}/\mathit{\text{lengthen}}})$, and the rate of mechanical work (i.e., power) performed by the contractile element ($\dot{W}$)

$$\dot{E}={\dot{h}}_{\mathit{\text{act}}/\mathit{\text{maint}}}+{\dot{h}}_{\mathit{\text{shorten}}/\mathit{\text{lengthen}}}+\dot{W}$$ [Eq. 4]

Here, the total muscle metabolic power is restricted from dropping below 1 W per kilogram estimated muscle mass to approximate muscle metabolic cost during rest-like conditions (46). For simplicity, the results presented here are from the model of Umberger (45), as it is widely used in OpenSim (47) and is based on data from mammalian muscle. However, soleus metabolic power estimates were very consistent across models (all model-by-model correlation coefficients were above r = 0.92, Supplemental Table S3; 10.5281/zenodo.15658852), and statistical conclusions were not sensitive to the chosen model (see Supplemental Fig. S2 and Supplemental Table S2; 10.5281/zenodo.15658852).

Average rates of energy change were computed as the time integral of the energy or heat rate divided by the stride time. The average soleus metabolic power as well as each component of the bioenergetic model (fascicle power, heat rate due to activation and maintenance, and heat rate due to shortening and lengthening, and total heat rate calculated as the sum of the two heat components) was expressed with respect to total body mass [W/kg].

Statistical differences in soleus average metabolic power and each component of the bioenergetic model were assessed parametrically or non-parametrically using two-way (stiffness, speed – both within-subjects factors) repeated measures analysis of variance (α = 0.05). Normality was assessed using the D’Agostino-Pearson K² test (48), and constant variance was assessed using Bartlett’s test. Non-parametric analysis of variance was employed if either the normality or constant variance test was statistically significant using a probability density function generated from 10,000 unique permutations of the data (49). In the presence of a statistically significant interaction effect, one-way, repeated measures analysis of variance was used to test for a main effect of speed at each stiffness and vice versa. Post-hoc pairwise comparisons in the presence of statistically significant main effects were conducted with a Bonferroni-corrected α of 0.017. Statistical tests were performed using spm1d (v0.4.8; 50) in MATLAB (v2023b; Natick, Massachusetts).

RESULTS

Total average metabolic power, as well as that for each of the bioenergetic model components (fascicle power, activation and maintenance heat rate, and shortening and lengthening heat rate) demonstrated peaks during the push-off phase of gait (Figure 1). Average soleus metabolic power (F(2, 26) = 154.65, p < 0.001), fascicle power (F(2, 26) = 30.12; p < 0.001), and activation and maintenance heat rate (F(2, 26) = 173.52; p < 0.001) demonstrated main effects of walking speed (Figures 2 and 3). There was no main effect of footwear stiffness on the average metabolic power (F(2, 26) = 1.23; p = 0.305), fascicle power (F(2, 26) = 0.04; p = 0.965), or the activation and maintenance heat rate (F(2, 26) = 1.78; p = 0.188). There was a statistically significant footwear stiffness × speed interaction effect for the average shortening and lengthening heat rate (F(2, 26) = 4.03; p = 0.006). One-way repeated measures analysis of variance indicated main effects of speed at each footwear stiffness (Low Stiffness: F(2, 26) = 55.45; p < 0.001); Medium Stiffness: F(2, 26) = 62.06; p < 0.001; High Stiffness: F(2,26) = 63.94; p < 0.001) and main effects of footwear stiffness in the 1.25 m/s (F(2, 26) = 5.36; p = 0.006) and 2.0 m/s (F(2, 26) = 8.54; p = 0.002) walking speed conditions.

Figure 1.

Mean time-series of the total soleus metabolic power, fascicle power, heat rate due to activation and maintenance, and heat rate due to shortening and lengthening. Time-series are time-normalized to a given stride and expressed relative to participant (N=14) body mass. Increased footwear stiffness is represented by darkening line color and each color (blue, green, and red) and line style (dot dash, dash, and solid) represent a different walking speed (1.25 m/s, 1.75 m/s, and 2.0 m/s, respectively).

Figure 2.

Soleus average metabolic power. Values are expressed with respect to participant (N=14) body mass with increasing footwear stiffness (darker colors) and walking speed (each represented by a different color). Horizontal bars and asterisks (*) represent pair-wise differences between walking speeds (p < 0.017).

Figure 3.

Soleus metabolic energy model components with respect to participant (N=14) body mass. The total heat rate is the sum of heat rate due to activation and maintenance and heat rate due to shortening and lengthening. Values are expressed as average rates of energy change. Darker colors represent increasing footwear stiffness, and each color (blue, green, and red) represents a different walking speed (1.25 m/s, 1.75 m/s, and 2.0 m/s, respectively). Horizontal bars and (*) or (^) represent pair-wise differences between walking speeds or footwear stiffnesses, respectively (p < 0.017).

Post-hoc comparisons of total soleus average metabolic power indicated statistically significant increases with increasing walking speed (mean ± SD: 1.25 m/s: 0.25 ± 0.04 W/kg; 1.75 m/s: 0.32 ± 0.05 W/kg; 2.00 m/s: 0.35 ± 0.06 W/kg; all comparisons p < 0.001; Figure 2). Average fascicle power increased with faster walking (mean ± SD: 1.25 m/s: 0.12 ± 0.05 W/kg; 1.75 m/s: 0.15 ± 0.05 W/kg; 2.00 m/s: 0.16 ± 0.06 W/kg; p < 0.001 for 1.25 vs 1.75 m/s and 1.25 vs. 2.0 m/s; p = 0.0128 for 1.75 vs 2.0 m/s). The average activation and maintenance heat rate was also statistically significantly greater with faster walking speed (mean ± SD: 1.25 m/s: 0.15 ± 0.02 W/kg; 1.75 m/s: 0.18 ± 0.02 W/kg; 2.00 m/s: 0.20 ± 0.03 W/kg; p < 0.001 for all comparisons) (Figure 3). The average shortening and lengthening heat rate showed statistically significant pairwise differences between the Low (0.00066 ± 0.0004 W/kg) and Medium (0.0017 ± 0.0007) stiffness conditions and Low and High (0.0026 ± 0.0096) stiffness conditions at 1.25 m/s (p = 0.001 and 0.0018, respectively) and 2.0 m/s (p = 0.002 and 0.004, respectively) (Figure 3).

DISCUSSION

This investigation examined whether increased footwear stiffness altered the metabolic energy needs of the soleus muscle across a range of walking speeds. Walking at faster speeds increased the estimated average metabolic power of the soleus muscle and that of each of the model components. Contrary to our hypothesis, increasing footwear stiffness did not result in a statistically significant main effect or stiffness × speed interaction on soleus average metabolic power. Across speeds, the average metabolic power decreased (albeit not statistically significantly) from 0.31 W/kg to 0.30 W/kg with increasing stiffness. The current findings combined with our prior study (17) suggest that reduced soleus fascicle shortening velocity and increased force output together result in similar estimated metabolic costs when walking with increased footwear stiffness, likely due to consistent muscle activation. The increase in ankle plantarflexor muscle force output without a statistically significant change in estimated muscle-specific metabolic cost highlights the potential benefit of carbon fiber insoles for those with targeted ankle plantarflexion deficits, providing propulsion without penalty.

Walking with increased footwear bending stiffness via carbon fiber insoles has a speed dependent effect on whole-body MCoT (17). Specifically, our group showed that the stiffest condition increased whole-body MCoT at 1.25 m/s but decreased it at 2.0 m/s (17). We previously proposed that this may be because the soleus fascicle dynamics become metabolically unfavorable at these very fast walking speeds (17). Farris & Sawicki (24) put forward similar notions, specifically that the walk-to-run transition likely occurs because ankle plantarflexor dynamics become unfavorable at very fast walking speeds. However, while the average soleus metabolic power indeed increased with faster walking, the present modeling results suggest that increased footwear bending stiffness does not demonstrate a speed dependent effect on soleus metabolic cost.

We have previously demonstrated that the soleus fascicle shortening velocity is reduced and estimated soleus fascicle force is increased with increasing foot stiffness (6, 17). Reducing muscle shortening velocity, holding all else equal, reduces the metabolic energy needs of a muscle (51), since the muscle produces less heat (19) and can produce more force per unit activation at slower shortening velocities (52). However, our data also showed that reducing the soleus shortening velocity did not impart a reduction in muscle activation. Given that the heat due to activation and maintenance was the largest contributor to the estimated muscle metabolic cost here (Figure 3), the lack of reduction in muscle activation helps explain the lack of statistically significant effect of increased footwear stiffness on average soleus metabolic power. These results are in line with those of Beck et al. (53) and Cigoja et al. (18), that suggest that using carbon fiber insoles may not alter triceps surae active muscle volume or estimated muscle metabolic energy consumption during running. Future assistive devices that aim to alter metabolic cost via reductions in triceps surae shortening velocity must therefore balance how these devices will alter muscle activation and force output as well (54).

Although the present analysis did not demonstrate a statistically significant reduction in estimated soleus metabolic cost with increased footwear stiffness, carbon fiber insoles may serve as an attractive assistive device for those with ankle plantarflexion deficits. We previously demonstrated that the estimated average and peak soleus forces increased at each speed when participants walked with these insoles, as did the peak ankle joint moment (17). That these increases in force and moment occurred concurrently with a non-statistically significant change in estimated soleus metabolic cost (Figure 2) may be a crucial effect for individuals with ankle plantarflexion deficits. For example, ankle joint moment has been demonstrated as a factor limiting older adult gait propulsion (27), and individuals with partial foot amputation walk with substantially reduced ankle plantarflexion moment and power on the affected side compared with those without amputation (16). If these devices can assist older adults and other populations in improving ankle joint kinetics without a muscle-specific metabolic penalty, they may be particularly useful as a mobility aid.

It should be noted, however, that populations with ankle-specific deficits typically walk at or below a speed wherein healthy younger adults experienced an increase in MCoT in the stiffest footwear condition (16, 17, 55). If the effect of increasing footwear stiffness on MCoT depends exclusively on speed, populations that tend to walk slower may similarly experience a whole-body metabolic penalty. However, we contend that improving ankle joint and muscle dynamics in populations where they are deficient at baseline may instead lead to a whole-body MCoT reduction. This prediction should be examined experimentally in the future.

Limitations in the present approach must be considered. There may be errors in estimates of in vivo soleus fascicle force and thereby work that affect the present results. These estimates rely on partitioning the ankle joint moment into the triceps surae force components based on their relative physiological cross-sectional area (40) and participant-specific Achilles tendon moment arms. This approach ignores the contribution from other ankle plantarflexor muscles and the potential influence of coactivation. Here, each of the lateral and medial gastrocnemii, tibialis anterior, and soleus increased their activation in similar proportions with increased walking speed and there was no main effect of footwear stiffness on any muscle’s integrated activation (17), therefore inappropriate force sharing assumptions based on cross-sectional area are unlikely to explain the present trends between walking speed and footwear stiffness conditions. Previously used indirect measures of participant-specific Achilles tendon moment arm as a function of ankle angle were used here (6, 17, 39). More direct measurements of this moment arm, however, indicate that simple, kinematic scaling may be incomplete (56), since the Achilles tendon moment arm is also load dependent (57). Walking speed increased estimated Achilles tendon force in the data of Ray & Takahashi (17), which may have increased the Achilles tendon moment arm values (57), subsequently altering soleus fascicle work estimates.

There are multiple options for muscle bioenergetics models in the literature (e.g., 28–30, 44, 45). The main difference in these models is their treatment of muscle mechanical power during muscle lengthening, which is not agreed upon in the literature (the reader is directed to the discussions in Miller (11) and Uchida et al. (46)). Soleus fascicles undergo both shortening and lengthening during a stride (26, 58, 59). However, the force and work performed by the soleus muscle is almost exclusively constrained to the stance phase, wherein the muscle is primarily isometric or shortening (17, 24, 60). Furthermore, the metabolic cost of performing concentric work far exceeds that of eccentric work (61), thus dominating energy estimates. It is therefore not surprising that the present statistical conclusions regarding estimated soleus muscle metabolic energy expenditure during walking were not sensitive to the chosen bioenergetics model (see Supplemental Fig. S2, Supplemental Tables S2 and S3; 10.5281/zenodo.15658852).

Finally, there may also be limitations in the use of bioenergetic models to estimate soleus metabolic cost. For example, the results of the present study would be in error if these models do not adequately capture the metabolic cost changes with increasing task demand (e.g., increased walking speed). Investigations using tasks that isolate a given muscle across different intensity levels thereby resulting in differences in whole-body metabolic cost (e.g., dynamometer studies like Beck et al. (36) and Swinnen et al. (51)) offer valuable data for comparisons between model-estimated and experimentally measured differences. Konno et al. (33) recently performed such an analysis. They concluded that while absolute metabolic cost variables may be in error, trends across experimental conditions were captured using a computational bioenergetic model similar to the model used here.

Our previous studies indicate that increasing footwear stiffness via carbon fiber insoles results in greater soleus force output during walking. We add here that increasing this stiffness does not statistically significantly alter the metabolic energy consumed by the soleus muscle across multiple walking speeds. Together, these effects may be beneficial for those with ankle plantarflexor force deficits (e.g., older adults), in that force capacity can be enhanced without a muscle-specific metabolic penalty.

SUPPLEMENTAL MATERIAL

Supplemental Fig. S1: 10.5281/zenodo.15658852

Supplemental Table S1: 10.5281/zenodo.15658852

Supplemental Fig. S2: 10.5281/zenodo.15658852

Supplemental Table S2: 10.5281/zenodo.15658852

Supplemental Table S3: 10.5281/zenodo.15658852

DATA AVAILABILITY

Source data to reproduce the figures in this manuscript have been uploaded to Zenodo: 10.5281/zenodo.15658852.