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K3 Promoter™ Prosthetic Foot Reduces the Metabolic Cost of Walking for Unilateral Transtibial Amputees

Grabowski, Alena M. PhD; Rifkin, Jerome MSME; Kram, Rodger PhD

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JPO Journal of Prosthetics and Orthotics: April 2010 - Volume 22 - Issue 2 - p 113-120
doi: 10.1097/JPO.0b013e3181cca79c
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People with a unilateral, transtibial amputation generally require 20%–30% more metabolic energy to walk at the same speeds as people without an amputation.1–3 This heightened metabolic energy demand can lead to premature fatigue and reduced walking speeds compared with nonamputees. Unilateral amputees may require greater metabolic energy due to the adoption of highly asymmetrical gait patterns.4–8 Kinetic gait asymmetries, such as greater joint loading of the intact leg,6 may also increase the risk of degenerative joint disease, osteoarthritis, and lower back pain in amputees.9–13 Therefore, a prosthesis that both reduces metabolic energy demand and improves gait symmetry would provide enormous benefits for amputees.

To date, no elastic storage and return (ESAR) prostheses have shown substantial improvements in metabolic energy demand, preferred walking speed, or gait symmetry.3,4,14 However, the use of ESAR prostheses has led to improved perceptions of comfort and mobility for amputees. ESAR prostheses store mechanical energy during the first half of the stance phase of walking, but release less than half of the mechanical energy normally generated by the soleus and gastrocnemius muscles during the second half of stance.8,15,16 Transtibial amputees typically overcome this power deficit by aggressively using their hamstring muscles to extend the hip during early to midstance phases of walking.7 This heightened muscle activity creates an excessive flexion moment about the knee that must be controlled and counteracted by increased contraction of the knee extensor muscles.7,15 If elastic energy can be more effectively stored in and returned from a prosthetic foot, these collateral muscle actions could be obviated. Thus, better energy return from a prosthetic ankle may allow transtibial amputees to experience more symmetrical gait patterns and improved metabolic economy during walking.

A simple inverted pendulum has been widely used in previous research to model stance phase biomechanics during walking, where the body is represented by a point mass and the leg by a rigid strut.17–19 In this model, the primary mode of mechanical energy exchange during walking is due to the body arcing over the stance leg, where the center of mass' kinetic energy is converted into gravitational potential energy during the first half of stance, and then gravitational potential energy is converted back into kinetic energy during the second half of the stance phase. However, the energy returned from the foot and ankle during the later part of stance is important for minimizing step-to-step transition work20 and for propelling the leg forward into the swing phase.16,21–23 Typical ESAR prostheses emulate this elastic energy storage and return with a spring. However, if the ESAR spring stiffness is inadequate for the walking speed or terrain, the prosthesis can greatly disrupt walking gait and disable center of mass energy exchange.

Typical ESAR prostheses are comprised of a leaf spring with nonlinear stiffness and do not have an ankle or metarsal-phalangeal (MTP) joint. Generally, these nonjointed prostheses are stiff during tibial progression, requiring a high level of loading before they begin bending, and then become less stiff after the initial bending period. This “loading lag” correlates with the “dead spot” that many amputees complain of during walking. In contrast, the muscles that act at the biological human ankle generate only modest torque during tibial progression and then become more stiff during midstance through toe-off.24 During walking, the biological ankle and subtalar joints work in concert in the sagittal plane, stabilize the tibia, and control the abduction/adduction motion during the stance phase of the gait cycle. Thus, these biological joints can accommodate terrain irregularities and ensure a smooth stable gait.25–27

In this study, we evaluate a recently developed prosthetic foot (K3 Promoter™, Tensegrity Prosthetics Inc., Louisville, CO) (Figure 1) that has a nonlinear loading response that qualitatively emulates the loading response of a biological ankle. In addition, the K3 Promoter has midfoot and MTP joints that are comprised of rigid segments made from lightweight metals assembled with steel cables, elastomeric urethane, and glass-fiber and Teflon filled nylon. The midfoot joint of the K3 Promoter is designed to emulate the functional ranges of motion of biological ankle and subtalar joints and can accommodate a 5% off camber incline with a very small resultant inversion/eversion moment. Moreover, the midfoot joint has little resistance to dorsiflexion rotation within the first half of stance, but it becomes progressively stiffer as the shank rotates over the foot, so that the end of the single-stance phase is smooth, rather than exhibiting an abrupt cessation of motion. This robust behavior is accomplished by using an elastic tension member made from urethane overmolded around steel cables and a steel anchor, which allows the joint to be “tuned” to accommodate different body weights and activity levels. By carefully choosing the geometry and materials, the midfoot joint can be designed and fabricated to exhibit a specific dynamic joint torque curve. Similarly, the MTP joint of the K3 Promoter has three rotational degrees of freedom, and a notably larger range of motion about the dorsiflexion/plantarflexion axis.

Figure 1.:
K3 Promoter™ prosthetic foot. Unlike conventional ESAR prosthetic feet, the K3 Promoter includes midfoot and metatarsal-phalangeal (MTP) joints that emulate the loading response of a biological ankle.

The K3 Promoter's midfoot joint is specifically designed to emulate the torque response curve of a biological human ankle at slow to moderate walking speeds. Because of the K3 Promoter's specific nonlinear torque response, this prosthetic foot requires less mechanical energy to move compared with a conventional ESAR prosthesis. Thus, we hypothesized that amputees would require less oxygen to walk at slow and moderate speeds while using the K3 Promoter compared with using an ESAR prosthetic foot. We also hypothesized that unilateral, transtibial amputees using the K3 Promoter foot would exhibit improved kinematic and kinetic gait symmetry during walking when compared with using a conventional ESAR prosthetic foot. Stance phase timing and peak ground reaction forces (GRFs) provide quantifiable and standard metrics that allow us to determine whether the unaffected and affected legs are symmetrical, thus we used the ratios of affected to unaffected leg contact times, swing times, and stride frequencies to compare kinematic symmetry. We used peak vertical and horizontal GRFs to compare kinetic symmetry between prostheses.


We measured metabolic cost and GRFs across a range of walking speeds in four otherwise healthy adult male unilateral transtibial amputees (mean body mass 78.19 kg [SD 8.68], age 38–39 yr) while they used the K3 Promoter prosthesis and their own ESAR prosthesis. Subject 1 used a Seattle Lightfoot, subject 2 used a DP Advantage 2, subject 3 used an Ossur Variflex, and subject 4 used a College Park Trustep ESAR prosthetic foot. All subjects were volunteers and independent functional community ambulators (Medicare level K3 or above) who did not use additional assistive devices such as canes or walkers. The cause of amputation was traumatic in nature for three subjects and congenital for one subject. In all subjects, the date of amputation was at least 2 years before the date of initial testing. Before participating, all subjects gave informed written consent according to the University of Colorado Human Research Committee approved protocol.


Before beginning the walking trials with the K3 Promoter, we conducted a bench test to adjust the midfoot and MTP joints, so that they emulated a biological ankle's loading response at slow walking speeds (Figure 2). We deliberately placed the attachment points for each spring, allowed for changes in lever arm distance with joint motion, and fabricated variable stiffness springs that produced the desired nonlinear loading characteristics based on each subject's body mass and activity level. Examples of bench test data are shown for custom fabricated urethane springs (70 Shore D and 90 Shore A) in Figure 3. Subjects 1–3 used a soft urethane spring, and subject 4 used a hard urethane spring in the K3 Promoter.

Figure 2.:
Bench test apparatus used to determine and tune the loading response of the midfoot joint of the K3 Promoter™.
Figure 3.:
Loading response of the midfoot joint from a bench test. The Hard Urethane (70 Shore D) shown by the thick line shows a much stiffer response than the Soft Urethane (90 Shore A) shown by the thin line.


Each subject completed three laboratory sessions. During the first session, subjects used their own ESAR prosthetic foot. Then, before the second session, each subject was fitted and aligned with a K3 Promoter foot by a certified prosthetist. The fitting and alignment met the approval of the subject, prosthetist, and the scientific team. Within 3 days of the fitting, subjects completed a second laboratory session with the new prosthetic foot. After the second session, each subject took the K3 Promoter foot home and used it exclusively for their activities of daily living for at least 21 consecutive days before they completed their third and final laboratory session.

We used the same trial order for each session. Subjects first stood quietly, and then walked at 0.75, 1.00, 1.25, and 1.50 m/s on a dual-belt treadmill28–30 with a force plate (AMTI Inc., Watertown, MA) mounted under one of the treadmills. Each trial was approximately 9 minutes long with at least 5 minutes rest between trials. During the first 7 minutes of each trial, we collected metabolic and force data as subjects walked with the force plate under their right foot. Then during the final 2 minutes of each trial, after stopping the treadmill briefly, we reversed the direction of the treadmill belts and captured the forces under the left foot.


We measured rates of oxygen consumption and carbon dioxide production using an open-circuit respirometry system (Physio-Dyne Instruments, Quogue, NY). We calculated steady-state rates of oxygen consumption and carbon dioxide production as the average of the rates during minutes 4–6 of each trial. Then, we calculated the net rate of oxygen consumption by subtracting the average rate of oxygen consumption during standing from the gross rate during walking. Respiratory exchange ratios were <1.0 during all trials, indicating that metabolic energy was supplied primarily by oxidative metabolism.


Between minutes 4 and 5 of each trial, we collected 30 seconds of GRF data at 1000 Hz from the subject's right leg. After minute 7 of each trial, we stopped both treadmills, had the subject turn around and walk in the other direction for at least 1 minute, and then recorded 30 seconds of GRF data at 1000 Hz from the subject's left leg. By using a custom Matlab (Mathworks, Natick, MA) program, we filtered the raw GRF data using a fourth-order zero-pass Butterworth filter with a cutoff frequency of 15 Hz and calculated the following kinematic and kinetic parameters from 20 steps per leg per trial: contact time, leg swing time, stride frequency, peak vertical GRF, and peak horizontal GRFs. Next, we compared these parameters by calculating the ratio between affected and unaffected legs and used this ratio as a measure of symmetry (i.e., 1.0 = perfect symmetry).


We administered an exit survey after the final experimental session to obtain subjective evaluations of the K3 Promoter. The survey included 15 questions that addressed subjects' perceptions of stability, comfort, weight, and adaptability to changes in terrain and velocity.


We used repeated measures analysis of variances to compare gross rates of oxygen consumption, kinematic stride variables, and kinetic stride variables between prosthetic conditions. Because of the low number of subjects, we chose to use p ≤ 0.10 as a criterion for statistical significance. These p values likely indicate clinical significance, but further research with a larger sample size is warranted. One subject was not able to walk at the fastest speed; therefore, our results reflect four subjects for all but the 1.5 m/s walking trial, where n = 3.


We found that when subjects walked while using an ESAR prosthetic foot, their rates of oxygen consumption were 30%–40% greater than those of persons with intact limbs31 (Figure 4). During the initial session while using the K3 Promoter™ (session 2), subjects' gross rates of oxygen consumption were not significantly different at any of the measured walking speeds compared with using their ESAR prosthetic foot. However, after using the K3 Promoter for an accommodation period of at least 21 days, subjects' rates of oxygen consumption were lower while walking compared with using the ESAR prosthetic foot (Figure 4). Thus, all of the K3 Promoter data that we present are from the final experimental session (after accommodation).

Figure 4.:
A, Gross rates of oxygen consumption (V̇o2) over a range of walking speeds while using an elastic storage and return (ESAR) prosthesis (filled squares) and the K3 Promoter™ prosthesis (filled circles). While using an ESAR prosthesis, amputees' gross rates of oxygen consumption were 30%–40% greater than young, healthy, nonamputees from Martin et al, 1992 (filled triangles). While using the K3 Promoter™, amputees' rates of oxygen consumption were significantly lower compared with using an ESAR prosthesis at speeds of 0.75 and 1.0 meter/second. On average, gross rate of oxygen consumption was 9.6, 9.8, 7.0, and 4.8% lower at walking speeds of 0.75, 1.0, 1.25, and 1.5 meter/second, respectively. Asterisks indicate a significant difference between prosthetic feet (p < 0.10). B, The greatest percentage reductions in gross rate of oxygen consumption for individual subjects occurred at different walking speeds. Gross rates of oxygen consumption were 14.4, 13.2, 15.9, and 13.1% lower at speeds of 0.75, 1.0, 0.75, and 1.25 meter/second for subjects 1, 2, 3, and 4, respectively. Subjects 1–3 used a soft urethane spring and subject 4 used a hard urethane spring in the K3 Promoter™. The K3 Promoter™ data are from the final experimental session.

We found that across walking speeds of 0.75–1.5 m/s, amputees' average net rates of oxygen consumption were 4%–12% lower while using the K3 Promoter compared with using their own conventional ESAR prosthesis (Figure 4A). At slow to moderate walking speeds of 0.75 and 1.00 m/s, average gross rates of oxygen consumption were significantly lower while our four subjects used the K3 Promoter (p = 0.059 and 0.045, respectively). Each subject's individual gross rates of oxygen consumption while walking with the K3 Promoter and their own ESAR prosthetic foot at walking speeds of 0.75–1.50 m/s are shown in Figure 4B. The most substantial metabolic improvements for each subject were attained at different walking speeds. The greatest individual reduction in gross rate of oxygen consumption was 15.9% for subject 3 walking at 0.75 m/s while using the K3 Promoter.

Subjects retained essentially the same stride kinematics while walking using the K3 Promoter compared with their ESAR prosthesis. Thus, there were very few significant differences in kinematics (Table 1). While using the K3 Promoter, subjects walked with significantly longer leg swing times for their affected limb at 1.00 and 1.50 m/s and significantly longer contact times for their unaffected leg at 1.25 m/s. Kinematic symmetry was also independent of the prosthesis used, with the exception of a significantly greater asymmetry in contact time and leg swing time at 1.25 m/s while using the K3 Promoter (Table 1). In general, contact time was shorter, and leg swing time was longer for the affected compared with the unaffected leg. For example, while walking at 1.00 m/s, the ratio of affected to unaffected leg values for contact time and swing time were 0.96 and 1.11 for the ESAR foot and 0.95 and 1.13 for the K3 Promoter, respectively.

Table 1:
Kinematic stride variables

In general, peak vertical GRFs were greater in both the unaffected and affected legs when subjects used the K3 Promoter compared with their ESAR prosthesis (Figure 5, Table 2). An example of the vertical and horizontal GRF traces for 20 steps from one subject is shown in Figure 6. At 0.75 and 1.0 m/s, the first peak vertical GRF was significantly greater in the unaffected leg while using the K3 Promoter compared with the ESAR prosthesis. At 0.75, 1.25, and 1.50 m/s, the second peak vertical GRF was significantly greater in the affected leg while using the K3 Promoter compared with the ESAR prosthesis. The symmetry between unaffected and affected legs for the first peak vertical GRF was not significantly different between prostheses. The symmetry for the second peak vertical GRF was significantly better at 1.25 m/s and worse at 0.75 m/s while using the K3 Promoter compared with the ESAR prosthesis.

Figure 5.:
Initial peak (1st peak) and propulsive peak (2nd peak) vertical ground reaction force (GRF) across walking speed for unaffected (filled symbols) and affected (open symbols) legs while using the elastic storage and return (squares) or K3 Promoter™ (circles) prostheses. Values are means. Error bars represent standard deviations. The K3 Promoter data are from the final experimental session.
Table 2:
Kinetic stride variables
Figure 6.:
Characteristic vertical and horizontal ground reaction force traces at each walking speed from a subject weighing 904.5 N. Each set of traces represents 20 steps from both affected and unaffected legs while the subject used his elastic storage and return (ESAR) prosthesis and the K3 Promoter™ (K3 Pro) prosthesis. The K3 Promoter data are from the final experimental session.

Peak braking and propulsive horizontal GRFs were nearly the same between prostheses, with significantly lower peak braking forces for the unaffected leg at 0.75 and 1.50 m/s and lower peak propulsive forces for the affected leg at 1.00 and 1.50 m/s in the K3 Promoter compared with the ESAR prosthesis (Figure 7, Table 2). Both types of prostheses showed greater horizontal peak GRF asymmetries at faster walking speed. The only significant difference in peak horizontal GRF was a greater asymmetry in the peak propulsive force at 1.50 m/s while using the K3 Promoter.

Figure 7.:
Peak horizontal braking and propulsive ground reaction force (GRF) across walking speed for unaffected (filled symbols) and affected (open symbols) legs while using the elastic storage and return (squares) or K3 Promoter™ (circles) prosthesis. Values are means. Error bars represent standard deviations. The K3 Promoter data are from the final experimental session.


Our metabolic data support our first hypothesis. We found that unilateral transtibial amputees significantly reduced their metabolic cost during slow and moderate speed walking while using the K3 Promoter compared with using an ESAR prosthesis. By enabling amputees to reduce metabolic energy demand during walking, the K3 Promoter prosthesis shows promise to improve overall function in amputees by reducing fatigue. This prosthesis could be especially useful for rehabilitation in older or ill individuals with a compromised cardiovascular capacity.

We did not find any significant improvements in kinematic timing symmetry, and only one improvement in kinetic symmetry at one speed while subjects used the K3 Promoter. Thus our data do not support our second hypothesis that unilateral transtibial amputees would have improved kinematic and kinetic gait symmetry during walking while using the K3 Promoter prosthetic foot when compared with using a conventional ESAR prosthetic foot. Amputees may have felt more confident using the K3 Promoter prosthesis and thereby increased weight acceptance on each leg,32–34 shown by greater peak vertical GRFs in both legs across all walking speeds (Table 2). However, the mechanism by which amputees decreased their metabolic cost remains uncertain. It is plausible that kinetic and kinematic variability decreased while wearing the K3 Promoter, and if so, this may have reduced metabolic cost. The exit survey results indicated that all of our subjects rated the K3 Promoter as offering better stability while walking. This improvement in stability could have decreased muscle co-contraction and changed muscle recruitment. Future work is needed to determine how the K3 Promoter affects stability and how muscle activity changes while wearing the K3 Promoter.

The K3 Promoter has a unique and novel passive-elastic design that includes joints with biomimetic ranges of motion. Previous studies have shown that elastic energy is important and may be a fundamental component of walking.23,35 More effective storage and return of elastic energy would presumably reduce the work performed by the leg muscles during step-to-step transitions, which would reduce an amputee's metabolic cost of walking. Future research is, thus, desired to determine the individual leg work for the unaffected and affected legs during walking while using different passive-elastic prostheses. Passive prostheses are advantageous in that they are typically low cost, reliable, lightweight, and do not require external power. However, unlike biological human ankles, the components of passive prostheses do not generate power. Therefore, biomimetic prosthetic designs may need to include a power source at the ankle joint to further reduce metabolic cost at faster walking speeds and to more accurately emulate biological gait.36

Although our kinetic measurements did not show notable differences between any of the three experimental sessions, metabolic benefits were apparent during the third experimental session. After 3 days of accommodation to the K3 Promoter prosthesis (session 2), we found no significant differences in metabolic cost between the ESAR and K3 Promoter prosthetic feet. However, after 21 days of accommodation to the K3 Promoter (session 3), our subjects had significant reductions in metabolic cost. Thus, we suggest that when evaluating a new prosthesis, an accommodation period longer than 3 days may be necessary to show changes in the metabolic cost of walking.

We have presented preliminary data on the K3 Promoter from four unilateral, traumatic and congenital, and transtibial amputees; thus, our conclusions and statistical power are limited. In future work, we plan to collect additional data from a larger and more diverse group of subjects that may include bilateral amputees and subjects whose cause of amputation is vascular. We believe that the K3 Promoter has the potential to dramatically improve walking metabolism in a diabetic population because of the limitations in cardiovascular capacity experienced by this population.


The K3 Promoter significantly reduced the metabolic cost of walking at slow and moderate speeds compared with conventional ESAR prostheses. This metabolic reduction is likely due to the inclusion of a spring with biomimetic ankle stiffness and the inclusion of midfoot and metatarsal-phalangeal joints. The K3 Promoter did not improve kinematic and kinetic gait symmetry compared with ESAR prostheses. However, a prosthesis that provides a more symmetrical gait may not necessarily decrease the metabolic cost of walking.37


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biomechanics; gait symmetry; locomotion; prosthesis

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