Use of a powered ankle–foot prosthesis reduces the metabolic cost of uphill walking and improves leg work symmetry in people with transtibial amputations

Abstract

People with transtibial amputations (TTAs) who use a powered ankle–foot prosthesis have equivalent metabolic costs and step-to-step transition work for level-ground walking over a range of speeds compared to non-amputees. The effects of using a powered compared to passive-elastic prosthesis for sloped walking are unknown. We sought to understand how the use of passive-elastic compared to powered ankle–foot prostheses affect metabolic cost and step-to-step transition work during sloped walking. Ten people (six M, four F) with TTAs walked 1.25 m s⁻¹ at 0°, ±3°, ±6° and ±9° using their own passive-elastic prosthesis and the BiOM powered ankle–foot prosthesis, while we measured metabolic rates, kinematics and kinetics. We calculated net metabolic power, individual leg step-to-step transition work and individual leg net work symmetry. The net metabolic power was 5% lower during walking on +3° and +6° uphill slopes when subjects used the BiOM compared to their passive-elastic prosthesis (p < 0.05). The use of the BiOM compared to a passive-elastic prosthesis did not affect individual leg step-to-step transition work (p > 0.05), but did improve individual leg net work symmetry on +6° and +9° uphill slopes (p < 0.01). People with TTAs who use a powered ankle–foot prosthesis have the potential to reduce metabolic costs and increase symmetry during walking on uphill slopes.

1. Introduction

The metabolic cost of level-ground walking is predominately due to generating force to support body weight and performing work to transition body mass from step to step in non-amputees. Generating force to support body weight (primarily during single support) comprises approximately 28%, whereas performing work to redirect and accelerate the centre of mass (COM) (primarily during the step-to-step transition) comprises approximately 45% of the net metabolic power required to walk on level ground [1]. More specifically, generating horizontal propulsive force (primarily provided by the gastrocnemius and soleus) comprises approximately 50% of the net metabolic power required to walk on level ground in non-amputees [2]. Thus, the push-off work generated during the step-to-step transition is a primary determinant of the metabolic cost of walking. Additionally, over a wide range of speeds, the muscles surrounding the ankle joint provide approximately 41% of the total individual leg positive mechanical power when walking on level ground in non-amputees [3], indicating that the function provided by the muscles surrounding the ankle joint is critical to steady-state walking at different speeds and slopes. For people with impaired or no ankle function, such as people with a transtibial amputation (TTA) using passive-elastic prostheses, the biomechanical constraints of impaired or no ankle function likely explain the higher metabolic costs compared to non-amputees walking at the same speed [4–6].

Previous studies have shown that individual leg work over the entire stance phase changes when walking on uphill and downhill slopes for non-amputees [7–9]. For example, positive individual leg work increases and negative individual leg work decreases with steeper uphill slopes until the work done by each leg is almost entirely positive when walking up a +9° slope [8]. Similarly, the magnitude of negative leg work increases and positive leg work decreases with steeper downhill slopes until the work done by each leg is almost entirely negative when walking down a −9° slope [8]. Similar to individual leg work, step-to-step transition work also increases with speed and uphill slope [5,10]. Because the mechanical work performed during the step-to-step transition is a primary determinant of the metabolic cost of walking and varies with slope, biomimetic ankle–foot prostheses that attempt to emulate biological ankle work during this phase should vary as well.

Most people with a TTA are prescribed and use a passive-elastic prosthesis. Passive-elastic energy storage and return (ESAR) prostheses are made of carbon fibre, do not have an articulating ankle joint and function as a spring by absorbing collision work during the beginning of stance and returning a portion (between 30 and 66% [11,12]) of this work at the end of stance. A passive-elastic prosthesis cannot generate net positive prosthetic ankle work de novo and therefore people with a TTA must compensate by generating positive work with more proximal muscles in their affected leg compared to the legs of non-amputees [13]. This reallocation of leg power to more proximal joints may be responsible for the 10–30% higher metabolic demand of people with a unilateral TTA using a passive-elastic prosthesis compared with non-amputees during walking at the same speed over level ground [5,10]. When people with a unilateral TTA use a passive-elastic prosthesis to walk on level ground, their step-to-step transition work is compromised such that their unaffected leg, when leading, absorbs more negative work and when trailing, generates greater positive work compared to non-amputees [5,10,14]. Further, the affected leg, when leading, absorbs less negative work, and when trailing, provides less positive work compared to non-amputees [5,10,14]. The use of a powered ankle–foot prosthesis has normalized the metabolic cost and step-to-step transition work for people with a TTA walking on level ground at a range of speeds (0.75–1.75 m s⁻¹) [5] and up a +5° slope [10] compared to non-amputees. People with a leg amputation using a passive-elastic prosthesis have an increased metabolic cost compared to non-amputees when walking on a +5° uphill slope at 1.24 m s⁻¹ [10]. In contrast with previous studies [4–6], one study found that young (average 29 years old), active service members with a TTA using a passive-elastic prosthesis had similar metabolic demands compared to non-amputees walking at the same speed on level ground [15]. While not significant, a similar study found that subjects (n = 6) who used an ESAR prosthesis had 9% higher metabolic costs compared to when they used a powered prosthesis during level-ground walking at 1.24 m s⁻¹ [10], which is in line with previous studies [16–18]. Thus, it is inconclusive whether young, fit and active people with a TTA using a passive-elastic prosthesis have higher metabolic demands compared to non-amputees walking at the same speed over level ground.

While level-ground walking has been the focus of many studies investigating the effects of using prostheses, few studies have addressed the effects of using a prosthesis to walk on uphill and downhill slopes. The effects of uphill and downhill walking on metabolic costs and joint kinetics and kinematics have been reported for healthy non-amputee adult populations [8,9] and for people with a TTA using passive prostheses [19,20]. When people with a TTA walked while using passive (both ESAR and solid-ankle cushioned heel) prostheses, they took shorter strides when walking up a +5% inclined ramp and had shorter step lengths when walking down a −5% declined ramp compared to non-amputees [20]. Shorter steps and strides could indicate reduced trailing leg positive step-to-step transition work or individual leg work asymmetry between the affected and unaffected legs. Only one study [10] has investigated both the metabolic and biomechanical effects of people with a TTA using both passive-elastic and powered prostheses to walk up a +5° inclined ramp and found that the use of the powered prosthesis provided 63% greater trailing limb step-to-step transition work. The same study [10] found that the use of the powered prosthesis resulted in 9% lower metabolic cost than the use of a passive-elastic prosthesis for subjects walking on a level treadmill. The study found that the use of the powered prosthesis produced normative step-to-step transition work on a +5° uphill slope but did not reduce metabolic cost compared to the use of a passive-elastic prosthesis [10]. However, the authors had a relatively small sample size (n = 6), and did not investigate individual leg work for multiple consecutive steps or downhill walking. Thus, it is not conclusive how the use of a passive-elastic or powered ankle–foot prosthesis affects the metabolic cost and biomechanics of walking on a range of uphill and downhill slopes.

We sought to determine how the use of a passive-elastic prosthesis and powered ankle–foot prosthesis affects the metabolic demands and individual leg work of people with a unilateral TTA during walking on uphill and downhill slopes. We hypothesized that the use of a powered compared to passive-elastic prosthesis would: (i) require less net metabolic power, (ii) result in lower unaffected leg leading step-to-step transition work, (iii) result in greater affected leg trailing step-to-step transition work, and (iv) improve individual leg work symmetry over an entire stride during walking on a range of uphill and downhill slopes.

2. Methods

2.1. Subject recruitment

Ten healthy adults with a unilateral TTA (six M, four F, mean ± s.d.: age 42 ± 11 years, height 1.70 ± 0.08 m, and mass 81.3 ± 14.7 kg) participated (table 1). All subjects provided informed consent in accordance with the Declaration of Helsinki and US Department of Veterans Affairs institutional review board (COMIRB no. 12-0553). Subjects self-reported that they were free of neurological, cardiovascular and musculoskeletal disease other than that associated with a unilateral TTA. All subjects self-reported they were at or above a K3 Medicare Functional Classification Level.

Table 1.

Subject anthropometrics with the powered (BiOM) and elastic storage and return (ESAR) prostheses, and ESAR prosthetic foot models.

sex	height (m)	mass with BiOM (kg)	mass with ESAR (kg)	ESAR foot model
F	1.66	59.5	58.0	Freedom Innovations Renegade
F	1.66	65.3	61.7	Ottobock Triton IC60
F	1.68	69.4	68.5	Össur Pro-flex XC
M	1.75	72.1	70.3	Freedom Innovations Renegade
M	1.71	78.0	77.0	Össur Vari-flex
F	1.71	84.1	81.8	Össur Vari-flex XC
M	1.82	89.4	88.9	College Park Soleus
M	1.85	96.2	95.3	Össur Proflex
M	1.83	97.1	95.5	Ability Dynamics Rush 81
M	1.82	102.3	100.2	Ability Dynamics Rush 87
AVG (s.d.)	1.70 (0.08)	81.3 (14.72)	79.7 (14.98)	—

2.2. Experimental protocol

2.2.1. Tuning of the powered prosthesis

First, a certified prosthetist from BionX Medical Technologies aligned the powered prosthesis (BiOM T2, BionX Medical Technologies, Inc., Bedford, MA, USA) to each subject. We then placed reflective markers on subjects' lower limbs over joint centres and with clusters of at least four markers over each segment. We placed reflective markers on the shoe at the approximate locations of the prosthetic foot first and fifth metatarsal heads, posterior calcaneus, and medial and lateral malleoli according to the positions on the unaffected leg. We placed malleoli markers for the powered prosthesis on the encoder, which coincided with the centre of rotation in the sagittal plane (figure 1). We placed malleoli markers for the passive-elastic prosthesis on the medial and lateral edges of the carbon fibre prosthesis at the most dorsal point of the keel. Subjects then walked 1.25 m s⁻¹ on a dual-belt force-measuring treadmill (Bertec Corp., Columbus, OH, USA) for at least 45 s per trial on slopes of 0°, ±3°, ±6° and ±9°, while we simultaneously measured kinematics at 100 Hz (Vicon, Oxford, UK) and ground reaction forces (GRFs) from each leg at 1000 Hz.

Figure 1.

‘Malleolus’ marker placement on the encoder/centre of rotation for the BiOM powered prosthesis. (Online version in colour.)

To objectively tune the powered prosthesis at each slope, we calculated prosthetic ankle angles, moments, powers and work normalized to subject mass with the prosthesis during each 45 s trial using Visual 3D (C-Motion, Germantown, MD, USA) and compared these data with averages from 20 non-amputees walking at the same speed and slope on the same equipment [21]. We then iteratively tuned the powered prosthesis for each slope using a tablet with software provided by the manufacturer (BionX Medical Technologies). The BiOM was tuned until prosthetic ankle range of motion, peak moment, peak power and net work were equivalent to the values from the unaffected ankle and/or non-amputee averages within two standard deviations of the mean measured from the kinematics and GRFs (figure 2).

Figure 2.

Results of iteratively tuning the BiOM for subjects walking at 1.25 m s⁻¹ compared to non-amputees (black) (a) ankle range of motion, (b) peak ankle moment, (c) peak ankle power and (d) net ankle work (mean ± s.e.). BiOM prosthetic ankle data collected at the end of the tuning day (white) and on the final day of the protocol (grey). Data collected on day 6 were used for analyses.

2.2.2. Metabolic data collection

Each subject had approximately 6 h of acclimation using the powered prosthesis during tuning, which occurred on two different days prior to measuring metabolic rates. We did not change tuning parameters for the powered prosthesis after the tuning days. After acclimation, subjects walked 1.25 m s⁻¹ for 5 min at each of seven slopes (0°, ±3°, ±6°, ±9°) on two separate days that were at least 22 h apart while we measured their rates of oxygen consumption and carbon dioxide production via indirect calorimetry (ParvoMedics, Salt Lake City, UT, USA). Prior to metabolic trials, we calibrated the indirect calorimetry system with known gases and volumes (3 l) at five different flow rates. On one day, subjects used their own passive-elastic prosthesis and on another day, subjects used the powered prosthesis. The order of days was randomized. We averaged metabolic rates from the last 2 min of each 5 min trial and calculated metabolic power using a standard equation [22]. We calculated net metabolic power by subtracting the metabolic power required for standing quietly from the power required for each walking condition and normalized to subject body mass including the appropriate prosthesis. Metabolic testing sessions were at the same time of day, subjects fasted for at least 2 h prior to metabolic data collection and trial order was randomized to mitigate any potential day-to-day variability or order effects.

2.2.3. Kinetic and kinematic data collection

Subjects used the powered prosthesis for approximately 12 h over four different days before we collected kinetic and kinematic data for analyses. We used the same tuning parameters for the powered prosthesis that were established from the tuning days. Subjects walked 1.25 m s⁻¹ on a dual-belt force-measuring treadmill (Bertec Corp., Columbus, OH, USA) on slopes of 0°, ±3°, ±6° and ±9° using their own passive-elastic prosthesis and the powered prosthesis while we simultaneously measured kinematics at 100 Hz using the same marker placement as described above and GRFs at 1000 Hz. We filtered GRF data using a fourth-order recursive Butterworth filter with a 30 Hz cut-off and filtered kinematic data using a sixth-order recursive Butterworth filter with a 7 Hz cut-off. We used a perpendicular GRF threshold of 20 N to determine ground contact. We averaged at least five strides (heel-strike to heel-strike of the same foot) for each subject at each condition and calculated an ensemble average of all 10 subjects.

We determined the external mechanical power from each individual leg. First, we calculated the acceleration of the CoM (a) with respect to time (t):

2.1

2.2

2.3

where medio-lateral (ML), parallel (parallel) and perpendicular (perp) GRF components were calculated relative to the treadmill, m is the body mass including the appropriate prosthesis, and the treadmill slope. Then we calculated the COM velocity (v) as the integral of acceleration with respect to time:

2.4

We determined integration constants (v_o) for perpendicular (v_perp) and medio-lateral (v_ML) velocities by assuming the average v over a stride equalled zero and determined v_o for parallel velocity (v_parallel) by assuming the average v over a stride equalled the treadmill velocity. We calculated the external mechanical power performed by each individual leg (P_leg) on the COM as the sum of the products of the GRFs and COM velocities (v_com) in the medio-lateral, parallel and perpendicular planes:

2.5

We calculated individual leg net work as the integral of leg power over an entire stride. We defined symmetry—and will refer to it throughout—as the ratio of the affected leg net work divided by the unaffected leg net work; perfect symmetry equals 1.0 [23]. Similar to previous studies [5,10], we determined step-to-step transition work as the integral of individual leg power during double support when the unaffected leg was leading and the affected leg was trailing.

2.2.4. Statistical analyses

We performed repeated-measures ANOVAs to determine the main effects of prosthetic foot, slope and the interaction of foot and slope on net metabolic power and individual leg step-to-step transition work with a significance level of 0.05. We used post hoc paired independent t-tests to determine differences in net metabolic power and individual leg step-to-step transition work between prostheses at each slope with a significance level of 0.05 (R-Studio, Boston MA, USA).

3. Results

When tuning the powered prosthesis for each subject at each slope, we matched non-amputee net ankle work within two standard deviations of the mean at all slopes (figure 2). For the remaining parameters, we tuned the powered prosthesis to match the unaffected ankle joint range of motion, peak moment and peak power within two standard deviations of the mean. After the tuning days, we implemented the same tuning parameters for the powered prosthesis throughout the protocol. On the final day of the protocol when we collected kinematic and kinetic data, the tuning settings established from the first 2 days’ tuning trials resulted in prosthetic ankle biomechanics that matched non-amputee ankle net work within two standard deviations of the mean (figure 2). Similarly, the tuning settings resulted in prosthetic ankle range of motion that matched the unaffected leg ankle joint within one standard deviation of the mean for all slopes, peak ankle moment within two standard deviations of the mean for all slopes and peak ankle power within two standard deviations of the mean on level and all uphill slopes.

We found a main effect of prosthetic foot type and slope on net metabolic power (p < 0.005) but found no main effect of the interaction of prosthetic foot type and slope (p = 0.72). The use of the powered prosthesis resulted in 5% lower net metabolic power at +3° and +6° compared with the use of a passive-elastic prosthesis (p = 0.021 and p = 0.013, respectively, figure 3 and table 2). At +9°, net metabolic power trended lower with the use of the powered compared to passive-elastic prosthesis (13%, p = 0.155), but only two subjects were able to complete the 5 min metabolic trial with primarily oxidative metabolism (RER < 1.0) using their passive-elastic prosthesis and only three using the powered prosthesis. Similarly, at +6°, only six subjects were able to complete the trial using their passive-elastic prosthesis and seven were able to complete the trial using the powered prosthesis with primarily oxidative metabolism.

Figure 3.

Net metabolic power (mean ± s.e.) of subjects with a TTA walking 1.25 m s⁻¹ on slopes of −9° to +9° with the BiOM powered ankle–foot (white) and passive-elastic ESAR (grey) prostheses. *Significant difference between BiOM and ESAR.

Table 2.

Net metabolic power (W kg⁻¹) for all subjects walking 1.25 m s⁻¹ using the BiOM powered prosthesis and their own passive-elastic ESAR prosthesis at each slope.

slope (°)	foot	Sub01	Sub02	Sub03	Sub04	Sub05	Sub06	Sub07	Sub08	Sub09	Sub10	AVG (s.e.)
+9	BiOM	9.06	—	—	—	—	—	9.28	8.53	—	—	8.96 (0.22)
	ESAR	—	—	—	—	—	—	10.33	10.27	—	—	10.30 (0.03)
+6	BiOM	6.65	—	7.84	6.78	—	7.58	6.63	5.94	—	8.08	7.07 (0.29)*
	ESAR	7.38	—	—	7.78	—	7.46	7.29	7.28	—	7.38	7.43 (0.07)
+3	BiOM	4.33	4.95	4.92	4.44	4.63	4.83	4.83	3.61	4.97	5.28	4.68 (0.15)*
	ESAR	4.40	6.00	5.42	4.79	4.72	4.53	4.98	4.52	5.25	4.40	4.90 (0.16)
0	BiOM	3.60	3.63	2.65	2.66	2.01	2.51	3.02	2.59	3.00	3.00	2.87 (0.16)
	ESAR	2.56	3.23	3.32	2.96	2.85	3.05	2.81	2.40	2.82	2.56	2.86 (0.09)
−3	BiOM	2.11	2.87	2.92	2.58	1.47	1.89	1.73	1.15	1.99	2.04	2.07 (0.18)
	ESAR	1.58	2.00	2.67	1.42	1.90	1.65	2.10	1.56	1.84	1.58	1.83 (0.12)
−6	BiOM	2.26	2.57	3.60	1.61	1.69	1.74	1.88	1.06	2.15	2.24	2.08 (0.22)
	ESAR	1.88	2.04	3.82	1.67	1.86	1.87	1.89	1.34	1.80	1.88	2.01 (0.21)
−9	BiOM	2.98	3.42	5.85	2.18	1.94	2.63	2.61	1.51	2.40	2.60	2.81 (0.38)
	ESAR	2.81	2.64	5.68	2.96	2.61	2.67	2.81	1.37	2.18	2.81	2.85 (0.35)

*Significant difference between BiOM and ESAR prostheses.

We found a main effect of prosthetic foot type and slope (p < 0.05) but not their interaction (p = 0.15) on individual leg step-to-step transition work for the affected leg trailing (figure 4). We found a main effect of slope (p < 0.001) but not prosthetic foot type or their interaction (p > 0.05) on individual leg step-to-step transition work for the unaffected leg leading (figure 4). However, in post hoc t-tests at each slope, we found no difference in affected leg trailing or unaffected leg leading step-to-step transition work (p > 0.05, figure 4). We found a main effect of slope (p < 0.001) and the interaction of prosthetic foot type and slope (p < 0.05) but no main effect of prosthetic foot type (p = 0.10) on individual leg net work symmetry. Specifically, the use of the powered prosthesis improved individual leg net work symmetry by 212% (from 0.26 with passive-elastic to 0.81 with powered) at +6° and 180% at +9° (from 0.33 with passive-elastic to 0.93 with powered) compared to the use of the passive-elastic prosthesis (p < 0.01, figure 5).

Figure 4.

Positive affected leg (AL) trailing step-to-step transition work (mean ± s.e., J kg⁻¹, top) and negative unaffected leg (UL) step-to-step transition work (±s.e., J kg⁻¹, top) for subjects with a TTA walking 1.25 m s⁻¹ on slopes of −9° to +9° with the BiOM powered ankle–foot (white) and passive-elastic ESAR (grey) ankle–foot prostheses. There were no significant differences between prostheses.

Figure 5.

Net leg work (positive work + negative work = net work) symmetry (AL/UL) over an entire stride for subjects with a TTA walking 1.25 m s⁻¹ on slopes of −9° to +9° with the BiOM powered ankle–foot (white) and passive-elastic ESAR (grey) ankle–foot prostheses. 1.0 indicates perfect symmetry. *Significant difference between BiOM and ESAR prostheses.

4. Discussion

In partial support of our first hypothesis, we found that subjects with a unilateral TTA using the powered ankle–foot prosthesis significantly reduced net metabolic power at +3° and +6° and net metabolic power trended lower at +9° compared to using their own passive-elastic prosthesis. In contrast with the results of Herr & Grabowski [5], we did not find significant differences in metabolic power when subjects used the powered compared to passive-elastic prosthesis for walking on level ground. This could be due to differences in the powered prosthetic tuning strategy, and/or the relative mass of the prosthesis compared to the user's body mass in each study. We tuned the powered prosthesis for each slope by measuring prosthetic ankle biomechanics and comparing these metrics to biological ankle biomechanics of non-amputees using the same motion capture system rather than using data provided by the prosthesis (such as in Herr & Grabowski [5]) or relying on a clinician to tune the device (as was done in Russell-Esposito et al. [10]). We adjusted 10 tuning settings in the powered prosthesis to change the prosthetic ankle kinematics and kinetics realized by each subject. Changes to the tuning settings adjust the response of the prosthetic control strategy, but do not guarantee specific kinematics and kinetics because each subject responds differently to the tuning changes. Specifically, the powered prosthesis uses prosthetic ankle angle, angular velocity and torque to determine the state space control and appropriate prosthetic ankle response throughout the gait cycle; though no studies have systematically varied tuning parameters and investigated the effects on the metabolic demand and biomechanics of walking [24–26]. Furthermore, though we matched biological ankle biomechanics (ankle range of motion, peak ankle moment, peak ankle power and net ankle work) with the powered prosthesis during tuning in accordance with the manufacturer recommendations (within ±2 s.d. of biological ankle average values) and kept these tuning settings consistent throughout the protocol, there were changes in prosthetic ankle biomechanics during the final testing session due to the user's response, which likely influenced our results. Additionally, tuning in accordance with the manufacturer recommendations does not guarantee normalization of leg biomechanics or metabolic cost.

Additionally, the average mass of our subjects was 81.3 kg, whereas in Herr & Grabowski [5], subjects had an average mass of 98.5 kg and in the Russell-Esposito et al. [10], subjects had an average mass of 92.7 kg. The recommended body mass for use of the powered prosthesis by people with a TTA is 80 kg; however, we included some subjects who were lighter than 80 kg to increase the generalizability of our results. We performed a post hoc analysis and found that if we had excluded subjects lighter than 80 kg in the present study, our conclusions would have been the same; there were no additional significant differences when analysing the results from subjects greater than 80 kg compared to using all subjects' data. While Mattes et al. [27] found that adding mass to a passive-elastic prosthesis—until the total mass and inertia matched the intact limb, similar to the powered prosthesis [5]—resulted in greater gross metabolic power of approximately 21 W per 1 kg added, it is unclear how the combination of prosthetic ankle power and added distal mass relative to the residual limb changes metabolic demand.

The addition of prosthetic ankle push-off work alone does not necessarily reduce the metabolic cost of walking on level ground for people with a TTA [28]. This could be because the ankle–foot prosthesis does not span the knee joint and thus replicates the function of the uni-articular soleus rather than the biarticular gastrocnemius. In experimental studies of non-amputees that measured muscle activation of the plantar-flexors during level-ground walking, ankle push-off work was primarily due to medial gastrocnemius activation, while the soleus played a small role [2,29]. Similarly, when young (average 26 years) and old (average 72 years) healthy adults walked on slopes of −9° to+9°, they activated their medial gastrocnemius more than their soleus, and older adults exhibited lower medial gastrocnemius activity compared to young adults when walking on uphill slopes of +3° and +6° [29], which likely contributed to the reduced ankle push-off work measured in older compared to young adults [30]. Therefore, it is possible that a powered ankle–foot prosthesis that only replaces the function of the uni-articular soleus is incapable of fully replicating biological ankle function in walking, which could increase the relative metabolic cost of walking on slopes.

Our second hypothesis that the use of the powered compared to passive-elastic prosthesis would result in reduced unaffected leg leading step-to-step transition work was unsupported. Similarly, we refute our third hypothesis that the use of the powered prosthesis would increase affected leg trailing step-to-step transition work compared to the use of a passive-elastic prosthesis. While powered prosthetic ankle net work was significantly greater at all slopes during tuning than passive-elastic prosthetic ankle net work and we tuned the powered prosthesis to match unaffected ankle biomechanics, this increase in ankle net work did not result in corresponding increases in the individual leg step-to-step transition work calculated via the individual limbs method when walking with a powered compared to passive-elastic prosthesis [31]. We collected data for our analyses during the final test session to ensure subjects had acclimated to using the powered prosthesis. It is possible that maintaining the same tuning strategy through the experimental protocol results in inconsistent or worse performance from the powered prosthesis. Future studies should investigate if or how tuning settings should be changed with acclimation time and the corresponding effects on metabolic cost, individual leg work and prosthetic ankle biomechanics. Furthermore, subjects, when using the powered prosthesis, could have changed their muscle recruitment strategies or increased muscle co-activation during walking so that metabolic cost changed [32,33], but step-to-step transition work did not. Future studies should determine how walking while using a passive-elastic or powered ankle–foot prosthesis affects muscle activation.

Our level-ground step-to-step transition work results are contradictory to the findings of Herr & Grabowski [5] and Russell-Esposito et al. [10]. Both of these studies found that the use of a powered compared to a passive-elastic prosthesis increased the affected leg trailing step-to-step transition work for individuals with a TTA walking on level ground. Herr & Grabowski [5] also found that unaffected leg leading work was reduced, but Russell-Esposito et al. [10] found no difference in unaffected leg leading work with the use of the powered prosthesis compared to a passive-elastic prosthesis on level ground. On an uphill slope of +5°, Russell-Esposito et al. [10] found a non-significant (p = 0.144) 53% increase in affected leg trailing step-to-step transition work when subjects with a TTA used a powered compared to passive-elastic prosthesis. The differences between our level-ground walking results and those of Herr & Grabowski [5] or Russell-Esposito et al. [10] could be due to the aforementioned powered prosthetic tuning, the powered prosthetic model or the method of data collection. The prosthetic model used in the present study was the commercially available BiOM T2 and the prosthetic model used in Herr & Grabowski [5] was a prototype developed prior to commercialization. Thus, it is possible that some changes in the control algorithm exist between the two prosthetic models. Further, our GRF data were collected over at least five consecutive strides on an instrumented treadmill, whereas kinetic data from Herr & Grabowski [5] and Russell-Esposito et al. [10] were collected on force plates mounted in a walkway. Finally, we used the individual limbs method to calculate individual leg work. This method underestimates the total work done by the joints because it does not account for simultaneous positive and negative work done at different joints [34].

Our fourth and final hypothesis that individual leg net work symmetry over a stride would improve with the use of the powered compared to passive-elastic prosthesis was supported at +6° and +9°. The improved symmetry with the use of the powered versus passive-elastic prosthesis at these uphill slopes was most likely due to the inability of the passive-elastic prosthesis to generate net positive power and provide it to the user during push-off. Because walking at a steady speed up a slope requires an increase in external mechanical work done on the COM compared to walking on level ground, the compensation strategy used by individuals with an amputation using a passive-elastic prosthesis (i.e. the unaffected leg and hip joint of the affected leg increase positive power output [13]) may no longer be sufficient to maintain constant external mechanical work in the affected leg, which would result in greater individual leg net work asymmetry [14]. People with a TTA exhibit increased prosthetic ankle net and positive work with the use of a powered compared to passive-elastic prosthesis over a range of uphill and downhill slopes, but no change in knee or hip positive, negative or net work [35]. Thus, it is possible that the uni-articular nature (replacing the function of the biological soleus rather than the biological gastrocnemius) of the commercially available powered prosthesis results in insufficient work transferred to the body's COM.

In the present study, we calculated external mechanical work done on the COM, but internal work (work done with respect to the COM, such as limb swing) may also change with the use of the powered compared to passive-elastic prosthesis when walking uphill and downhill [36]. Because the external mechanical work done at each joint in both limbs changes with the use of a powered compared to passive-elastic prosthesis [35], the compensation strategy adopted by people using a passive-elastic prosthesis to walk on level ground (again, the increase in positive power output from the unaffected leg and affected leg hip joint [13]) is not reduced or eliminated when using a commercially available powered ankle–foot prosthesis over a range of slopes. To improve upon current biomimetic prosthetic device design, future studies should investigate the interactions between metabolic and mechanical tasks over a range of slopes. With this information, devices could be developed that provide adequate joint work and power and thus could normalize metabolic power and individual leg biomechanics during walking over a range of speeds and slopes, potentially increasing functional mobility and quality of life [4,37].

5. Conclusion

When people with a TTA use a powered compared to passive-elastic prosthesis, they require less net metabolic power to walk uphill at +3° and +6°. There was also a trend for net metabolic power to be lower when people with a TTA use a powered compared to passive-elastic prosthesis to walk at +9°. After tuning the powered prosthesis to match biological ankle biomechanics, the use of the powered compared passive-elastic prosthesis improved leg net work symmetry at uphill slopes of +6° and+9°. The use of such a prosthesis that decreases the metabolic cost of uphill walking and improves leg symmetry has the potential to improve mobility and quality of life for people with a TTA.

Though net work at the prosthetic ankle was significantly greater when using the powered compared to passive-elastic prosthesis, individual leg step-to-step transition work was not different. This could be due to the uni-articular nature of the powered ankle–foot prosthesis (it does not span the knee joint) or a reduction in the mechanical energy transferred to the residual limb from the powered prosthesis via the limb–socket interface. In order to design more effective biomimetic ankle–foot prostheses, future studies should determine the effects of using powered and passive-elastic prostheses that are both biarticular and uni-articular on joint work and metabolic cost for people with a unilateral TTA walking on uphill and downhill slopes.

Ethics

All subjects gave their written informed consent prior to participating in this study according to a protocol approved by the US Department of Veteran Affairs' Human Subjects Institutional Review Board (Colorado Multiple Institutional Review Board protocol no. 12-0553) and in accordance with the principles expressed in the Declaration of Helsinki.

Data accessibility

The authors confirm that all data underlying the findings are fully available without restriction. All relevant data are within the paper.

Authors' contributions

J.R.M. collected all data, carried out data analysis and drafted the manuscript. A.M.G. conceived of the study, designed the study, reviewed and edited the manuscript.

Competing interests

We declare we have no competing interests.

Funding

This study was funded by a Department of Veterans Affairs award to A.M.G., no. CDA2 A7972-W.