The effects of ankle stiffness on mechanics and energetics of walking with added loads: a prosthetic emulator study

The human ankle joint has an important influence on mechanics and energetics of gait. Specifically, the role of the muscles acting at the ankle joint during normal walking is to provide body support, aid in forward propulsion, and to initiate leg swing [1]. The peak ankle joint power can be ~ 2.5 W/kg, which is greater than the maximum power produced by the knee joint and hip joint [2, 3]. Individuals with impaired ankle function (e.g., older adults, individuals who have survived a stroke) or individuals with artificial ankles (e.g., individuals with an amputation) have to compensate for the diminished ankle joint power with proximal muscles such as the hip joint [4‐8]. Thus, preserving natural ankle joint functions is important for rehabilitation and/or assistive devices since compensations via proximal muscles can often lead to an increase in metabolic cost of walking [9‐11].

One important feature of the human ankle joint is the regulation of ‘quasi-stiffness,’ which hereby will be referred to as stiffness. The human ankle stiffness is defined as the slope of the moment-angle relationship of the joint, or the ratio of the ankle moment to angular displacement [12‐14]. This stiffness can be quantified in different phases during the gait cycle [13], including when the ankle joint is dorsiflexing while applying a plantarflexion moment (i.e., dorsiflexion stiffness). There appears to be an optimal level of ankle dorsiflexion stiffness to aid the shank as it rocks over the foot, which has been supported through several studies involving prosthetic ankles. If the prosthetic ankle joint is too compliant, then the joint may not provide enough plantarflexion moment to adequately support the body upright [6, 15, 16]. On the other hand, if the prosthetic ankle joint is too stiff, there would be excessive resistance to dorsiflexion motion, which would prohibit the shank’s progression [6].

Numerous studies have shown that humans can alter ankle dorsiflexion stiffness in response to changes in mechanical demands of walking [17‐19], most likely through modulation of muscle activation. As walking speed increases or when walking uphill, the human ankle joint stiffness increases due to the plantarflexion moment increasing and the dorsiflexion angle decreasing [17, 18]. Additionally, the human ankle joint stiffness increases when individuals walk with additional load [18, 20]. Kern et al. found that the human ankle stiffness, normalized to body mass, increased by about 13% when walking with 30% additional body mass [20]. All of these studies show the human’s capacity to modulate ankle joint stiffness in response to the mechanical demand of the task. However, the functional importance of such ability to modulate stiffness is unclear. Due to the human ankle’s purported role in minimizing metabolic energy expenditure during locomotion [21], it is possible that modulating stiffness when transitioning from one locomotion task to another (e.g., normal walking to load carrying) could preserve energy expenditure across the various locomotor demands. Yet, there are currently no studies that have directly linked the ankle’s ability to modulate stiffness and their role in minimizing metabolic energy expenditure across various locomotor tasks. Such knowledge would contribute to the overall structure-function relationship of the human ankle and could also inform designs of wearable devices (e.g., prostheses) intended to emulate biological function.

Studies involving lower-limb ankle-foot prostheses have provided valuable insights on the role of stiffness in regulating metabolic energy during walking. There have been many studies done to determine what the best prosthetic ankle or foot stiffness is for lowering metabolic cost and improving gait for individuals with amputation [6, 15, 16, 22, 23]. Major et al. showed that a lower dorsiflexion ankle stiffness (relative to commercially-available prostheses) reduces the vertical ground reaction force during the loading phase of the prosthetic stance as well as the net metabolic cost [15]. Fey et al. showed that lower foot stiffness can also increase the amount of energy stored and returned, contributing to greater forward propulsion and assisting swing initiation [6]. Zelik et al. had individuals walk with three different spring stiffnesses in prosthetic feet and found that an intermediate spring stiffness had the lowest metabolic energy [24], suggesting a quadratic relationship between prosthetic stiffness and metabolic cost. While these studies indicate that the stiffness of the ankle joint or prosthetic foot plays a role in regulating metabolic energy during normal walking, the role that this stiffness has in regulating metabolic energy across different walking conditions and demands (e.g., walking with added loads) is unknown. When individuals with an amputation walk with additional loads, they have altered gait mechanics [25] and expend more metabolic energy than healthy controls [26]. Thus, determining whether a prosthesis should be able to change stiffness across different walking conditions may be important, which could warrant recent developments in micro-processor-controlled prostheses that can modulate stiffness [27, 28].

The purpose of this study was to determine how net metabolic energy cost was affected by ankle stiffness while walking with different mechanical demands (i.e., with and without additional load). Walking with an additional load directly increases metabolic cost [29]. As a proof of concept, this study involved individuals with a simulated amputation by using an immobilizer boot with the prosthesis, which has been used in various other studies [24, 30‐33] (Fig. 1). We used a robotic prosthetic emulator, which simulated an elastic prosthesis with a range of ankle joint stiffnesses around a typical human ankle stiffness value during walking with and without additional loads [14, 18, 20, 34]. We hypothesized that the lowest stiffness would minimize metabolic cost for walking without added load. We also hypothesized that the stiffness that minimized metabolic cost during the load carriage would be greater compared to the no load conditions, since the human ankle increases its stiffness when walking with added load [18, 20]. Furthermore, we hypothesized that the lowest stiffness would maximize prosthetic positive ankle-foot work and minimize ipsilateral hip positive work. Lastly, we hypothesized that maximizing prosthetic ankle-foot work and minimizing ipsilateral positive hip work would require a greater prosthesis stiffness during the load carrying conditions than in the no load conditions. The findings of this research could help uncover the importance of the human ankle’s ability to modulate joint stiffness across locomotor tasks, and could also inform how prostheses should change ankle stiffness based on walking demands.

We used a robotic prosthetic emulator to simulate various ankle joint stiffnesses above and below a typical human ankle stiffness during different mechanical demands (e.g., with and without additional load). This experimental approach allowed us to vary the ankle joint stiffness while keeping every other parameter (e.g., foot length, mass, shape) constant on the device. We tested the hypothesis that the lowest stiffness would minimize metabolic cost for normal walking (no added load), and the stiffness that minimized metabolic cost during load carriage would be greater compared to the no load conditions. However, contrary to our hypothesis, the highest stiffness, out of the range tested, minimized metabolic energy for both walking conditions. We found no significant interaction between stiffness and load on metabolic energy cost.

One potential reason why our hypothesis was not supported is that we focused solely on the stiffness of the ankle joint and did not take into consideration other joints within the foot. The joints within the human foot are important and play a role in how the ankle-foot complex behaves during walking [46‐51]. A study by Kern et al. found that the human midtarsal joint (i.e., arch) stiffness is about 2.5 times greater than the ankle joint, and both the midtarsal joint and ankle joint increase in stiffness when carrying additional loads [20]. Therefore, a higher stiffness might have been needed to minimize metabolic cost in order to incorporate the role of the midtarsal joint. A recent study involving an articulated toe and ankle prosthesis found that varying the toe joint stiffness affected whole-body mechanics just as much, if not more, than varying ankle joint stiffness [52]. The prosthesis used in our study did not have any articulations besides the ankle. Thus, in the absence of compliance within the foot arch or toes, the ankle stiffness may need to be stiffer than the typical human ankle stiffness in order to incorporate the functions of the foot structures as well.

The range of stiffness we tested could have influenced why the metabolic energy was minimized at the highest stiffness for both conditions. The range of input stiffness tested was from 0.0928 Nm/deg/kg to 0.1392 Nm/deg/kg, which is around the typical human ankle stiffness for normal walking, as well as walking with additional load [14, 18, 20, 34]. The actual stiffness range was larger since the experimentally-derived stiffness was not exactly the same as the prescribed input stiffness. It is possible that the range tested might have been too narrow to determine a different optimal stiffness for both load conditions. In comparison, Major et al. found that there was an 8% decrease in metabolic energy from their highest prosthetic stiffness (approximately 200% of our highest stiffness) to their lowest stiffness (approximately 80% of our lowest stiffness) in individuals with an amputation [15]. However, they did not test any stiffness values in the middle of the range, therefore it cannot be determined if there is a linear trend between the two points or if there is another trend that would appear if more values were tested.

From each participant’s highest stiffness to their lowest input stiffness, metabolic cost decreased by about 0.11 W/kg for the no load condition, or 3.2%, and 0.10 W/kg for the additional load conditions, or 2.57%. This difference would equate to the metabolic cost of transport of 0.01 J/Nm, which is less than the reported minimal detectable difference (0.022 J/Nm) using a portable metabolic system [53]. The study mentioned above was not using a prosthesis, which can influence the results of the minimal detectable difference. While the non-portable metabolic system we used for our study could be more accurate than the portable system, it is still likely that the difference in metabolic cost within the range of ankle stiffness we tested is relatively small. If the stiffness range tested was wider, it is possible that we could have seen a greater decrease in metabolic cost. Since there was a slight reduction in metabolic cost, we also wanted to see how participants’ perception of the difficulty of the condition related to this reduction.

We found that the participants’ perception of the difficulty of the condition was predicted by the interaction of load and stiffness (Additional file 9: Figure S9). Therefore, individuals did not perceive differences for the different stiffness values during the no additional load conditions, but they perceived that it was more unnatural to walk with increasing stiffness at the additional load conditions. This is the reverse of what was observed metabolically since their metabolic energy decreased as the stiffness increased for the additional load conditions. A previous study using a hip exoskeleton saw that participants did not always prefer the condition that was the most metabolically beneficial [54, 55]. Additionally, we performed a one-way repeated measures ANOVA to determine the relationship of order of trials with added mass on perception to determine if individuals perceived the later conditions as more difficult (i.e., potential fatigue effect). We found that there were no significant differences (p = 0.246), suggesting that subjects did not perceive later conditions as more difficult than others.

There was a great amount of variability between participants in terms of which condition minimized their metabolic energy expenditure. For each loading condition, we fit a quadratic regression to metabolic cost as a function of ankle stiffness and found the minimum of the curve, which was the stiffness that minimized metabolic cost within the range of stiffness tested. The average stiffness that minimized metabolic cost for the no load condition was 0.1166 ± 0.0247 Nm/deg/kg, and the average for the additional load condition was 0.1300 ± 0.0259 Nm/deg/kg. While the average stiffness that minimized metabolic cost increased with the additional load condition, the variability of each value was large in that one standard deviation is approximately 50% of the original range of stiffness tested in this study. This suggests that the stiffness that minimized metabolic cost might be better quantified on a per individual basis, since there is no single stiffness value that will minimize energy expenditure for all participants. A similar high participant to participant variability has been seen in exoskeletons and optimal timing profiles [55]. An approach like the ‘human in the loop’ optimization may be needed in order to find participant-specific parameters that will optimize the metabolic cost of walking, or any other variables, as seen in exoskeleton studies [56, 57]. The prosthesis that we used in this experiment is able to change stiffness on a step-to-step basis, therefore, it could be used with the “human in the loop” approach to vary stiffness until a metabolic minimum for each subject is reached. Such an iterative approach may be better suited to find a beneficial stiffness setting that accounts for the variability among individuals.

In partial support of our hypothesis, the lowest stiffness had the greatest amount of ankle-foot work for the no load conditions. Previous studies have seen similar trends where increasing prosthesis ankle joint stiffness decreases the amount of positive work in prosthetic devices [6, 16, 23, 24]. However, the stiffness condition that maximized prosthetic ankle-foot positive work did not correspond to the stiffness that minimized metabolic energy consumption. Instead, the stiffness that minimized prosthetic positive work (i.e., highest stiffness) corresponded to the stiffness that minimized metabolic cost. Ankle-foot work decreased by about 0.036 J/kg from the subject’s lowest stiffness to the highest stiffness, but this decrease only amounted to about a 3% decrease in metabolic cost. Previous studies that have modulated the amount of ankle work may suggest that a greater change in work may be needed to see a large change in metabolic energy [24, 31, 58]. Contrary to our findings, Caputo et al. used a powered prosthesis and found that for a work decrease of about 0.03 J/kg, there would be an increase of about 0.148 W/kg in metabolic cost [31]. Zelik et al. had about a 4.6 J difference in ankle push-off work (0.06 J/kg for a 75 kg person) from their lowest to highest stiffness but found no statistical significance between the metabolic cost at these two stiffness values [24]. The metabolic cost did decrease by about 7 to 8% from the highest to the medium stiffness, which had about a 2.6 J difference in push off work (0.035 J/kg for a 75 kg person) [24]. In a study with a commercially-available powered prosthesis, the prosthetist-chosen power setting was a mean ankle work of 0.11 ± 0.06 J/kg, but the best power setting for decreasing metabolic cost (by about 8.8% ± 4.6%) was 0.24 ± 0.07 J/kg [58]. Therefore, our differences in ankle-foot work between stiffness conditions may not have been large enough to influence the metabolic cost.

At the ipsilateral hip joint, our original hypothesis was that the lowest stiffness would minimize hip positive work, and a higher stiffness would minimize hip work when carrying additional loads. Our statistical model found that hip positive work did not significantly change between stiffness conditions for the no load condition. We found an interaction of both stiffness and load, as well as stiffness squared and load, which indicates that ipsilateral hip positive work varies as a function of both variables. Therefore, our hypothesis was partially supported, since the highest stiffness minimized hip positive work at the 30% load condition. This is important since many individuals with amputation experience an increase in metabolic cost, which can at least partly be attributed to their increase in hip positive work [9‐11]. Upon further analysis, we found that both prosthetic ankle-foot positive work (p < 0.001) and ipsilateral hip positive work (p < 0.001) were significant predictors of metabolic cost (adjusted R² = 0.7765). The equation was: \( {\dot{\mathrm{E}}}_{met}=1.92+2.55\bullet {W}_{IPS\_ HIP}+4.30\bullet {W}_{PRO\_ ANK\_ FT} \). Therefore, as both the ankle-foot positive work and the ipsilateral hip positive work decreased, the metabolic cost decreased.

We also did a few secondary analyses to analyze the other joints to see if their behavior was influencing the net metabolic power outcomes. For the additional load conditions, the contralateral ankle-foot had more positive work in the higher stiffness conditions compared to the lower stiffness (Fig. 6), suggesting that it could be compensating for the reduced positive work of the prosthesis. The contralateral ankle-foot positive work did not significantly vary with stiffness for the no additional load conditions, which agrees with a previous study looking at prosthetic stiffness [24]. The ipsilateral and contralateral hip had similar behaviors, and they both varied as a function of both interaction terms.

This study had a few limitations. The prescribed prosthetic ankle stiffness was determined by approximating a single linear slope during the dorsiflexion phase based on the moment-angle relationship of human ankles [20]. A study by Shamaei et al. found that the human ankle is less stiff at the beginning of dorsiflexion compared to the end of the phase [13]. Thus, our prescribed ankle stiffness likely has a stiffer joint compared to the human ankle during early phases of dorsiflexion, which could explain the increase in ankle plantarflexion moment during the early stance phase compared to the contralateral ankle (Fig. 3). Additionally, most participants were inexperienced with walking with this prosthesis and the participants’ familiarity with load carriage was not assessed. To minimize the potential contributions of learning effects, we had each participant complete two training days before the testing day, which has been shown to be a sufficient amount of training with exoskeletons [59, 60]. A paired t-test was done for each condition between the first and second day, and the condition with 0% load, and the med-high stiffness value was significantly different (p = 0.0448). However, all other conditions were not significantly different (p ≥ 0.14) (Additional file 10: Figure S10). When the same paired t-test was done for each condition between the second and third day, all conditions were not significantly different between the 2 days (p ≥ 0.11). This may suggest that the trends between metabolic cost were similar between the second and third day and no additional changes in metabolic cost happened due to learning.

Another limitation is the generalizability of these findings. The participant recruitment was limited in that there were two sizes of lift shoes used, and there was a specific weight limit for the prosthesis. Because of these criteria, we had a restricted range of participants based on shoe size and body mass. While this increases the internal validity of the study, the findings of our study are less generalizable. In addition, using a simulator boot with the prosthesis makes these results less generalizable to individuals with amputation. There have been a variety of studies that have used emulator or simulator boots [24, 31, 33, 52]. Some studies have shown similar results between healthy controls and individuals with amputation [24], while others have shown differing results [24, 31, 35]. It is currently unclear whether the findings of our study could translate to individuals with amputation, and our findings should be verified in individuals with amputation before informing the design of prosthesis. Having healthy controls walk on simulator boots with the prosthesis helps to eliminate the amputation-specific variability including residual limb length, amputation type, amputation surgery and socket interface as well as the common comorbidities with amputations such as residual limb pain, osteoarthritic pain and scoliosis [24, 52]. Additionally, using simulator boots can show how healthy humans adapt to different toe and ankle properties [52]. The added mass of the simulator boot and added leg length can influence the results. The average metabolic cost for our study while walking with this emulator without additional load was 3.3 W/kg. Another study using a similar prosthetic emulator found that the average metabolic cost of healthy individuals walking with this emulator was 3.6 W/kg, while these same individuals had an average metabolic cost of 2.7 ± 0.37 W/kg while walking with their normal shoes [31]. This suggests that walking with this emulator could increase metabolic cost. However, our experimental protocol was a within-subjects design so the effect should be approximately the same for each condition when comparing between the conditions for each participant.

The purpose of this study was to understand the importance of changing ankle stiffness during different locomotor tasks. While human ankle’s ability to modulate joint stiffness is well documented [14, 17, 18, 20], our study found that the magnitude of changes in human ankle stiffness seen between normal (no load) walking and load carriage conditions [18, 20] likely leads to a small change in metabolic cost. Such findings may indicate that the functional importance of human ankle’s ability to modulate stiffness may involve factors besides minimizing metabolic cost across various locomotion tasks, such as maximizing stability or reducing fall risks.

Our study revealed that a stiffness higher than the typical human ankle can decrease metabolic energy at both normal walking and walking with additional loads. Additionally, we found no significant interaction between stiffness and load carriage on metabolic cost, which may suggest the modulating ankle stiffness comparable to levels of how the human ankle modulates stiffness is not likely to have a metabolic benefit. Future studies looking at a wider stiffness range or using human-in-the-loop optimization can be done to further solidify if there is an ‘optimal’ stiffness that can be determined when individuals walk under various mechanical demands.