Abstract

Walking is more difficult for transtibial prosthesis users, partly due to a lack of calf muscle function. Powered ankle prostheses can partially restore calf muscle function, specifically push-off power from the soleus. But one limitation of a powered ankle is that emulating the soleus does not restore the multi-articular function of the gastrocnemius. This missing function may explain elevated hip and knee muscle demands observed in individuals walking on powered ankles. These elevated demands can make walking more fatiguing and impact mobility. Adding an Artificial Gastrocnemius to a powered ankle might improve gait for prosthesis users by reducing the prosthesis-side hip and knee demands. This work investigates if an Artificial Gastrocnemius reduced prosthesis-side hip or knee demands for individuals walking with a powered ankle providing high levels of push-off. We performed two case series studies that examined the effects that a passive elastic Artificial Gastrocnemius has on joint moment-impulses when prosthesis users walked with a powered ankle. We found that hip moment-impulse was reduced during stance when walking with an Artificial Gastrocnemius for six of seven participants. The Artificial Gastrocnemius effects on knee kinetics were variable and subject-specific, but in general, it did not reduce the knee flexor or extensor demands. The Artificial Gastrocnemius should be further explored to determine if reduced hip demands improve mobility or the user's quality of life by increasing the distance they can walk, increasing walking economy, or leading to increased physical activity or community engagement.

1 Introduction

Walking is more difficult for transtibial prosthesis users, partly due to a lack of calf muscle function. Prosthesis users walking on passive feet face significant functional deficits including the inability to generate net positive push-off work from their prosthetic ankle-foot complex [1,2]. Positive work is typically generated when the soleus and gastrocnemius muscles plantarflex the ankle during push-off [3]. Passive prostheses, however, only store and return energy and cannot generate positive work during walking [46]. Reduced push-off work from the prosthesis-side leg is associated with increased external adduction moment and may increase risks of osteoarthritis in the intact knee [7]. Further disadvantages associated with the loss of calf muscle function include: slower self-selected walking speeds [8,9], increased metabolic cost of walking [10], and greater muscle activity in the knee extensors and flexors [4,9,11] and hip flexors [11].

Powered ankle prostheses can partially restore calf muscle function, specifically that of the soleus. Powered prostheses can normalize ankle push-off work and self-selected walking speeds in transtibial participants [5,12]. Researchers have also shown that powered prostheses can reduce peak forces and external adduction moments in the intact knee, which may reduce risks of knee osteoarthritis [13,14]. In this study, a powered prosthesis will be referred to as an Artificial Soleus because it mono-articularly plantarflexes the ankle joint, much like how the biological soleus acts about the ankle joint. Thus, the terms Artificial Soleus and powered ankle prosthesis will be used interchangeably.

Prosthesis-limb hip and knee muscle demands remain elevated when users walk and an Artificial Soleus has not restored these muscle demands down to able-bodied levels. For instance, while walking with an Artificial Soleus, prosthesis users still exhibited higher peak hip power generation and peak knee power absorption compared to the intact hip and knee [12]. These joint kinetics suggest elevated contributions from the iliopsoas (or other hip flexors). Reducing hip and knee demands to levels more consistent with able-bodied controls could make walking less strenuous for prosthesis users and promote more community participation.

There is inconsistent evidence regarding the effect an Artificial Soleus has on the metabolic cost of walking. Some studies found that an Artificial Soleus reduced the cost of walking [5,15,16] while other studies found that the push-off work from an Artificial Soleus did not significantly change metabolic cost [17,18]. Previous labs studied participants walking on an Artificial Soleus with push-off work values of biomimetic settings (which mimic the push-off work of a biological ankle, for instance, 0.08–0.09 J/kg at 1.1 m/s) and higher-powered settings (which provide more push-off work than the biological ankle, e.g., >0.09 J/kg at 1.1 m/s) [19]. The same study observed that increasing push-off work from biomimetic to higher-powered levels reduced participants' metabolic cost of walking, but reached a plateau of diminishing returns beyond 0.24 J/kg of push-off work [19]. It was suggested that this plateau occurred because the higher-powered ankle push-off created an extension moment at the knee that increased demand on the remaining knee flexor muscles. This suggestion was strengthened by another study that associated increased Artificial Soleus push-off work with increased knee flexor (biceps femoris) muscle activity [18]. These findings indicate that higher-powered push-off from an Artificial Soleus can reduce a prosthesis user's metabolic cost of walking, but may simultaneously alter or increase demands about other joints such as the knee or hip.

One limitation of an Artificial Soleus is that it does not restore the multi-articular function of the gastrocnemius muscle. The gastrocnemius creates a flexion moment at the knee and a plantarflexion moment at the ankle, as opposed to the mono-articular soleus muscle that only creates a plantarflexion moment at the ankle [20]. The gastrocnemius's multi-articular nature is beneficial as it is able to coordinate multiple joint movements and aid in transferring energy along the leg [20]. Current Artificial Soleus devices approximate the plantarflexion function of the soleus, but do not restore the knee flexion moment produced by the multi-articular gastrocnemius. In simulations, this lack of a gastrocnemius resulted in increased hip flexor demand (particularly from the iliopsoas muscle) during stance; however, a simple, elastic gastrocnemius reduced peak iliopsoas force by 50% during walking [21]. The missing multi-articular gastrocnemius function may explain the elevated hip and knee muscle demands observed in individuals walking on powered ankles. These elevated demands can make walking more fatiguing and impact the user's mobility.

Adding an Artificial Gastrocnemius to an Artificial Soleus might further improve gait for prosthesis users, for instance, by helping to reduce hip and knee demands. In doing so, muscle exertions and metabolic cost of walking might decrease and lead to increased physical activity or community engagement. In previous lab studies, Artificial Gastrocnemius devices were comprised of a knee brace or tether affixed to the user's prosthetic socket and prosthetic ankle [2225]. The different Artificial Gastrocnemius designs were actuated by motors or passive spring elements. Studies that combined an Artificial Soleus and an Artificial Gastrocnemius showed that hip and knee demands were reduced in trials where the Artificial Gastrocnemius was active compared to control trials [24,25]. Specifically, one study observed that the biological contributions to prosthesis-side hip flexion and knee flexion work and moment-impulses were reduced while using the Artificial Gastrocnemius [24]. These studies did not, however, test an Artificial Gastrocnemius with a higher-powered Artificial Soleus (with push-off work greater than biomimetic). What remains unknown is how an Artificial Gastrocnemius affects hip and knee demands when prosthesis users walk with a higher-powered Artificial Soleus.

Therefore, we aimed to answer: for individuals wearing a higher-powered Artificial Soleus, does an Artificial Gastrocnemius reduce biological hip or biological knee muscle demands of the prosthesis-side limb? We hypothesized that adding an Artificial Gastrocnemius would reduce muscle demands at the prosthesis-side hip and knee during stance. From this hypothesis, we predicted that these reduced muscle demands would be indicated by reduced hip and knee moment-impulses.

2 Methods

We performed two case series studies that examined the effects that a passive Artificial Gastrocnemius has on prosthesis-side hip and knee joint moment-impulses when prosthesis users walked with a higher-powered Artificial Soleus. We performed Case Series 1 with Artificial Soleus push-off work that was twice the value of biomimetic levels. We performed Case Series 2 with Artificial Soleus push-off work that was triple the value of biomimetic levels. As a secondary analysis, we tested a range of Artificial Gastrocnemius stiffness settings for both Case Series 1 and 2 to determine the effect on the joint moment-impulses.

Each participant attended two sessions: one familiarization session, and one data collection session at Vanderbilt University's Center for Rehabilitation Engineering and Assistive Technology. The protocol was approved by the Vanderbilt University Institutional Review Board, and all participants gave their written informed consent.

2.1 Experimental Hardware for Case Series 1 and 2.

For both sessions, participants wore their prescribed socket, a programable Artificial Soleus (Humotech Caplex PRO-001), a flexible, low-profile programable Artificial Gastrocnemius, and an upper body safety harness (attached to the ceiling via a slightly slack cable) as seen in Fig. 1. The Artificial Soleus has previously shown the ability to replicate various powered prosthetic and biological ankle dynamics during gait [26]. The Artificial Gastrocnemius has previously shown the ability to emulate a wide range of dynamics [27]. As shown in Fig. 1, a cable runs from the Artificial Gastrocnemius's actuator encoder and spans the user's knee joint and prosthetic ankle joint, mimicking the biological gastrocnemius. This configuration allows the actuator encoder to measure the change in the length of the multi-articular cable as a result of both knee and ankle angle changes. The Artificial Gastrocnemius is then able to create a spring-like tension during stance phase that is directly modulated by both the knee and ankle kinematics. Tension begins about 0.1 s after heelstrike. During swing phase, the Artificial Gastrocnemius is controlled to be lightly tensioned (nominally about 15 N). The prosthetic ankle was fitted with a pylon that was cut to match the height of the participant's prescribed prosthetic foot (as per training by a certified prosthetist).

Fig. 1
Depiction of the Artificial Soleus and Artificial Gastrocnemius sensing and off-board actuation hardware. The Humotech Artificial Soleus solely plantarflexes the prosthetic ankle while the Artificial Gastrocnemius, which is affixed to the thigh, flexes the participant's knee and plantarflexes the prosthetic ankle. The force plates in the treadmill allow for heelstrike and toe-off sensing to determine whether the participant is in stance or swing. The actuator encoders measure the position and extension of the Artificial Gastrocnemius during stance. This extension measurement then informs the controller how much tension to provide given the current stiffness being tested. The load cells provide feedback for independent Artificial Soleus and Artificial Gastrocnemius tension control.
Fig. 1
Depiction of the Artificial Soleus and Artificial Gastrocnemius sensing and off-board actuation hardware. The Humotech Artificial Soleus solely plantarflexes the prosthetic ankle while the Artificial Gastrocnemius, which is affixed to the thigh, flexes the participant's knee and plantarflexes the prosthetic ankle. The force plates in the treadmill allow for heelstrike and toe-off sensing to determine whether the participant is in stance or swing. The actuator encoders measure the position and extension of the Artificial Gastrocnemius during stance. This extension measurement then informs the controller how much tension to provide given the current stiffness being tested. The load cells provide feedback for independent Artificial Soleus and Artificial Gastrocnemius tension control.
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2.2 Experimental Protocol for Case Series 1.

During Case Series 1, we observed a group of unilateral, transtibial prosthesis users (N =5; male; 34 ± 8 years; 1.81 ± 0.05 m; 88.5 ± 11.9 kg) while treadmill walking with the Artificial Soleus and Artificial Gastrocnemius. The Artificial Soleus was programed to provide higher-powered push-off work of 0.16 J/kg to the prosthetic ankle over the course of each step. This higher-powered push-off work is roughly double the typical biological ankle push-off at the tested gait speed [19]. The Artificial Gastrocnemius was programed to emulate springs with stiffnesses of 0, 28, 56, and 84 N/m/kg, scaled by participant body mass. However, one participant did not illicit a consistent response from the Artificial Gastrocnemius system due to their gait pattern. Hence, they never reached steady-state walking necessary for analysis (see Sec. 2.4) and were excluded, resulting in N =4 for Case Series 1.

With the exception of one participant who returned 16 days after their first session, other participants returned within a week of session one (3 ± 2 days) for the second session where data were collected. As supplementary reference data, we observed participants walking with a passive (spring-like) Artificial Soleus without an Artificial Gastrocnemius, and walking with biomimetic Artificial Soleus providing 0.08 J/kg of net push-off work [5] with each of the Artificial Gastrocnemius stiffnesses. A summary of these reference data sets can be found in the Appendix (Tables 7 and 10). For Case Series 1, trials were conducted in randomized order; Table 1 provides a visualization of these tested conditions.

Table 1

A visualization of the different combinations of Artificial Soleus and Artificial Gastrocnemius behaviors tested during the Experimental Protocol for Case Series 1

Artificial Gastrocnemius stiffness (N/m/kg)
0285684
Prosthesis push-off work (J/kg)0.16RandRandRandRand
0.08RandRandRandRand
0Rand
Artificial Gastrocnemius stiffness (N/m/kg)
0285684
Prosthesis push-off work (J/kg)0.16RandRandRandRand
0.08RandRandRandRand
0Rand

Grayed cells indicate that the combination of behaviors was not tested in this Case Series. Trials in Case Series 1 were conducted in a randomized order.

Table 7

Change in hip moment-impulses between the lowest and highest stiffness trials with 0.08 J/kg of ankle push-off work from Case Series 1

Case Series 1 hip moment-impulse changes (0.08 J/kg push-off)
Participant0 N/m/kg (Nm*s/kg)84 N/m/kg (Nm*s/kg)Raw change (Nm*s/kg)Percent change (Nm*s/kg)
Hip moment-impulse (flexion and extension)
P10.199 ± 0.0190.177 ± 0.017−0.023−11.3%
P20.212 ± 0.0150.188 ± 0.018−0.024−11.5%
P30.250 ± 0.0180.213 ± 0.015−0.036−14.6%
P40.243 ± 0.0150.225 ± 0.016−0.018−7.3%
Group0.226 ± 0.0240.201 ± 0.022−0.025−11.1%
Hip flexion moment-impulse only
P10.146 ± 0.0190.119 ± 0.019−0.027−18.4%
P20.130 ± 0.0150.102 ± 0.014−0.028−21.7%
P30.115 ± 0.0130.079 ± 0.011−0.036−31.0%
P40.068 ± 0.0100.036 ± 0.009−0.032−46.6%
Group0.115 ± 0.0340.084 ± 0.036−0.031−27.0%
Case Series 1 hip moment-impulse changes (0.08 J/kg push-off)
Participant0 N/m/kg (Nm*s/kg)84 N/m/kg (Nm*s/kg)Raw change (Nm*s/kg)Percent change (Nm*s/kg)
Hip moment-impulse (flexion and extension)
P10.199 ± 0.0190.177 ± 0.017−0.023−11.3%
P20.212 ± 0.0150.188 ± 0.018−0.024−11.5%
P30.250 ± 0.0180.213 ± 0.015−0.036−14.6%
P40.243 ± 0.0150.225 ± 0.016−0.018−7.3%
Group0.226 ± 0.0240.201 ± 0.022−0.025−11.1%
Hip flexion moment-impulse only
P10.146 ± 0.0190.119 ± 0.019−0.027−18.4%
P20.130 ± 0.0150.102 ± 0.014−0.028−21.7%
P30.115 ± 0.0130.079 ± 0.011−0.036−31.0%
P40.068 ± 0.0100.036 ± 0.009−0.032−46.6%
Group0.115 ± 0.0340.084 ± 0.036−0.031−27.0%

Changes in only hip flexion moment-impulses are included because these were most affected by the intervention (Fig. 2(b)). Hip extension moment-impulses were not included for brevity, but can be calculated by subtracting the flexion from moment-impulses.

Table 10

Change in knee moment-impulses between the lowest and highest stiffness trials with 0.08 J/kg of ankle push-off work from Case Series 1

Case Series 1 knee moment-impulse changes (0.08 J/kg push-off)
Participant0 N/m/kg (Nm*s/kg)84 N/m/kg (Nm*s/kg)Raw change (Nm*s/kg)Percent change (Nm*s/kg)
Knee moment-impulse (flexion and extension)
P10.167 ± 0.0130.180 ± 0.015+0.013+7.5%
P20.290 ± 0.0160.297 ± 0.021+0.008+2.7%
P30.162 ± 0.0130.181 ± 0.016+0.020+12.2%
P40.101 ± 0.0150.093 ± 0.017−0.008−7.8%
Group0.180 ± 0.0790.188 ± 0.084+0.008+4.4%
Knee extension moment-impulse only
P10.148 ± 0.0130.162 ± 0.016+0.015+9.9%
P20.286 ± 0.0160.294 ± 0.022+0.008+2.7%
P30.150 ± 0.0140.172 ± 0.016+0.022+14.8%
P40.004 ± 0.0040.077 ± 0.019+0.073+1838%
Group0.147 ± 0.1150.176 ± 0.089+0.029+19.7%
Case Series 1 knee moment-impulse changes (0.08 J/kg push-off)
Participant0 N/m/kg (Nm*s/kg)84 N/m/kg (Nm*s/kg)Raw change (Nm*s/kg)Percent change (Nm*s/kg)
Knee moment-impulse (flexion and extension)
P10.167 ± 0.0130.180 ± 0.015+0.013+7.5%
P20.290 ± 0.0160.297 ± 0.021+0.008+2.7%
P30.162 ± 0.0130.181 ± 0.016+0.020+12.2%
P40.101 ± 0.0150.093 ± 0.017−0.008−7.8%
Group0.180 ± 0.0790.188 ± 0.084+0.008+4.4%
Knee extension moment-impulse only
P10.148 ± 0.0130.162 ± 0.016+0.015+9.9%
P20.286 ± 0.0160.294 ± 0.022+0.008+2.7%
P30.150 ± 0.0140.172 ± 0.016+0.022+14.8%
P40.004 ± 0.0040.077 ± 0.019+0.073+1838%
Group0.147 ± 0.1150.176 ± 0.089+0.029+19.7%

Changes in only knee extension moment-impulses are included because these were most affected by the intervention (Fig. 5(b)). Knee flexion moment-impulses were not included for brevity, but can be calculated by subtracting the extension from moment-impulses.

2.3 Experimental Protocol for Case Series 2.

The push-off work settings for Case Series 1 were double the biomimetic levels, but only two-thirds of the work recommended by Ref. [19] to maximally reduce the metabolic cost of walking [19]. We implemented this push-off magnitude because one pilot participant indicated that any greater push-off work settings were uncomfortable. Similarly, Artificial Gastrocnemius stiffness settings for Case Series 1 were limited to moderate levels because one pilot participant indicated that higher stiffness settings were uncomfortable. After completing tests with five participants, we found that all other participants were comfortable with greater Artificial Soleus and Artificial Gastrocnemius work and stiffnesses. Therefore, we reassessed our testing parameters and increased the Artificial Soleus push-off work and the maximum stiffness of the Artificial Gastrocnemius for Case Series 2, which enabled us to more deeply probe our hypothesis.

During Case Series 2, we observed a group of unilateral, transtibial prosthesis users (N = 4; male; 38 ± 11 years; 1.78 ± 0.05 m; 79.3 ± 11.6 kg) during treadmill walking with the Artificial Soleus and Artificial Gastrocnemius. One participant was a returning prosthesis user from Case Series 1. In Case Series 2, the Artificial Soleus was programed to provide higher-powered push-off work of 0.24 J/kg to the prosthetic ankle over the course of each step. This push-off work is triple the typical biological ankle push-off and matches the metabolically-optimal push-off observed in Ref. [19]. The Artificial Gastrocnemius was programed to simulate virtual springs with stiffnesses of 0, 56, 84, 112, and 140 N/m/kg. This expands on Case Series 1 by adding two settings of greater stiffness (similar to those tested in previous literature [24]) while removing the lowest 28 N/m/kg stiffness.

With the exception of one participant who returned a month after their first session, other participants returned within a week of session one (2 ± 2 days) for the second session where data were collected. As supplementary reference data, we observed participants walking with a passive (spring-like) Artificial Soleus, and walking with biomimetic push-off of 0.09 J/kg of net push-off work with each of the Artificial Gastrocnemius stiffnesses. For Case Series 2, trials were completed by holding Artificial Soleus push-off work constant and testing every Artificial Gastrocnemius stiffness in ascending order from 0 to 140 N/m/kg. This ascending order was followed by retesting the 0 and 140 N/m/kg settings (withdrawal and reintroduction trials) to achieve an ABAB protocol, which assists with results interpretation [28]. After completing these trials with the Artificial Soleus set to 0.24 J/kg of net push-off work, the procedure was repeated for the 0.09 J/kg and 0 J/kg (passive) settings for supplementary reference data. A summary of the last two data sets can be found in the Appendix (Tables 89, 1112). Table 2 provides a visualization of these tested conditions.

Table 2

A visualization of the different combinations of Artificial Soleus and Artificial Gastrocnemius behaviors tested during the Experimental Protocol for Case Series 2

Artificial Gastrocnemius stiffness (N/m/kg)
0285684112140Repeat 0Repeat 140
Prosthesis push-off work (J/kg)0.241234567
0.09891011121314
015161718192021
Artificial Gastrocnemius stiffness (N/m/kg)
0285684112140Repeat 0Repeat 140
Prosthesis push-off work (J/kg)0.241234567
0.09891011121314
015161718192021

Grayed cells indicate that the combination of behaviors was not tested in this Case Series. Trials in Case Series 2 were conducted in the numerical order as indicated.

Table 11

Change in knee moment-impulses between the lowest and highest stiffness trials (and the repeated trials) with 0.09 J/kg of ankle push-off work from Case Series 2

Case Series 2 knee moment-impulse changes (0.09 J/kg push-off)
Participant0 N/m/kg (Nm*s/kg)140 N/m/kg (Nm*s/kg)Raw change (Nm*s/kg)Percent change (Nm*s/kg)
Knee moment-impulse (flexion and extension)
P50.151 ± 0.0170.128 ± 0.013−0.023−15.1%
P60.205 ± 0.0130.197 ± 0.017−0.008−3.8%
P70.194 ± 0.0140.192 ± 0.015−0.001−0.8%
P80.102 ± 0.0160.182 ± 0.015+0.080+78.5%
Group0.163 ± 0.0470.175 ± 0.032+0.012+7.4%
Knee extension moment-impulse only
P50.092 ± 0.0210.074 ± 0.012−0.018−19.5%
P60.180 ± 0.0120.189 ± 0.019+0.009+5.0%
P70.188 ± 0.0140.188 ± 0.015+0.000+0.0%
P80.090 ± 0.0190.175 ± 0.015+0.086+95.7%
Group0.137 ± 0.0540.157 ± 0.055+0.020+14.6%
Repeat knee moment-impulse (flexion and extension)
P50.142 ± 0.0170.132 ± 0.016−0.010−7.1%
P60.196 ± 0.0120.199 ± 0.014+0.003+1.4%
P70.185 ± 0.0130.190 ± 0.014+0.005+2.8%
P80.100 ± 0.0120.160 ± 0.017+0.060+60.4%
Group0.156 ± 0.0440.170 ± 0.030+0.014+9.0%
Repeat knee extension moment-impulse only
P50.070 ± 0.0100.076 ± 0.012+0.005+7.7%
P60.167 ± 0.0100.189 ± 0.016+0.022+13.1%
P70.180 ± 0.0140.185 ± 0.014+0.005+2.8%
P80.084 ± 0.0130.150 ± 0.018+0.066+78.8%
Group0.125 ± 0.0560.150 ± 0.053+0.025+20.0%
Case Series 2 knee moment-impulse changes (0.09 J/kg push-off)
Participant0 N/m/kg (Nm*s/kg)140 N/m/kg (Nm*s/kg)Raw change (Nm*s/kg)Percent change (Nm*s/kg)
Knee moment-impulse (flexion and extension)
P50.151 ± 0.0170.128 ± 0.013−0.023−15.1%
P60.205 ± 0.0130.197 ± 0.017−0.008−3.8%
P70.194 ± 0.0140.192 ± 0.015−0.001−0.8%
P80.102 ± 0.0160.182 ± 0.015+0.080+78.5%
Group0.163 ± 0.0470.175 ± 0.032+0.012+7.4%
Knee extension moment-impulse only
P50.092 ± 0.0210.074 ± 0.012−0.018−19.5%
P60.180 ± 0.0120.189 ± 0.019+0.009+5.0%
P70.188 ± 0.0140.188 ± 0.015+0.000+0.0%
P80.090 ± 0.0190.175 ± 0.015+0.086+95.7%
Group0.137 ± 0.0540.157 ± 0.055+0.020+14.6%
Repeat knee moment-impulse (flexion and extension)
P50.142 ± 0.0170.132 ± 0.016−0.010−7.1%
P60.196 ± 0.0120.199 ± 0.014+0.003+1.4%
P70.185 ± 0.0130.190 ± 0.014+0.005+2.8%
P80.100 ± 0.0120.160 ± 0.017+0.060+60.4%
Group0.156 ± 0.0440.170 ± 0.030+0.014+9.0%
Repeat knee extension moment-impulse only
P50.070 ± 0.0100.076 ± 0.012+0.005+7.7%
P60.167 ± 0.0100.189 ± 0.016+0.022+13.1%
P70.180 ± 0.0140.185 ± 0.014+0.005+2.8%
P80.084 ± 0.0130.150 ± 0.018+0.066+78.8%
Group0.125 ± 0.0560.150 ± 0.053+0.025+20.0%

Changes in only knee extension moment-impulses are included because these were most affected by the intervention (Fig. 5(b)). Knee flexion moment-impulses were not included for brevity, but can be calculated by subtracting the extension from moment-impulses.

Table 12

Change in knee moment-impulses between the lowest and highest stiffness trials (and the repeated trials) with the passive prosthesis settings from Case Series 2

Case Series 2 knee moment-impulse changes (0 J/kg push-off)
Participant0 N/m/kg (Nm*s/kg)140 N/m/kg (Nm*s/kg)Raw change (Nm*s/kg)Percent change (Nm*s/kg)
Knee moment-impulse (flexion and extension)
P50.164 ± 0.0190.149 ± 0.017−0.015−8.9%
P60.206 ± 0.0150.189 ± 0.014−0.017−8.4%
P70.162 ± 0.0110.153 ± 0.013−0.009−5.8%
P80.084 ± 0.0150.081 ± 0.014−0.003−3.4%
Group0.154 ± 0.0510.143 ± 0.045−0.011−7.1%
Knee extension moment-impulse only
P50.070 ± 0.0110.075 ± 0.012+0.005+6.6%
P60.146 ± 0.0110.161 ± 0.010+0.015+10.4%
P70.157 ± 0.0120.146 ± 0.014−0.011−6.8%
P80.076 ± 0.0150.071 ± 0.015−0.005−6.9%
Group0.112 ± 0.0450.113 ± 0.047+0.001+0.9%
Repeat knee moment-impulse (flexion and extension)
P50.169 ± 0.0150.147 ± 0.017−0.022−13.0%
P60.209 ± 0.0140.193 ± 0.014−0.017−8.1%
P70.152 ± 0.0110.147 ± 0.014−0.005−3.3%
P80.073 ± 0.0090.072 ± 0.010−0.001−1.5%
Group0.151 ± 0.0570.140 ± 0.050−0.011−7.3%
Repeat knee extension moment-impulse only
P50.075 ± 0.0090.074 ± 0.011−0.001−1.6%
P60.154 ± 0.0090.170 ± 0.012+0.015+10.0%
P70.145 ± 0.0110.140 ± 0.014−0.005−3.2%
P80.053 ± 0.0100.061 ± 0.011+0.008+15.8%
Group0.107 ± 0.0500.111 ± 0.052+0.004+3.7%
Case Series 2 knee moment-impulse changes (0 J/kg push-off)
Participant0 N/m/kg (Nm*s/kg)140 N/m/kg (Nm*s/kg)Raw change (Nm*s/kg)Percent change (Nm*s/kg)
Knee moment-impulse (flexion and extension)
P50.164 ± 0.0190.149 ± 0.017−0.015−8.9%
P60.206 ± 0.0150.189 ± 0.014−0.017−8.4%
P70.162 ± 0.0110.153 ± 0.013−0.009−5.8%
P80.084 ± 0.0150.081 ± 0.014−0.003−3.4%
Group0.154 ± 0.0510.143 ± 0.045−0.011−7.1%
Knee extension moment-impulse only
P50.070 ± 0.0110.075 ± 0.012+0.005+6.6%
P60.146 ± 0.0110.161 ± 0.010+0.015+10.4%
P70.157 ± 0.0120.146 ± 0.014−0.011−6.8%
P80.076 ± 0.0150.071 ± 0.015−0.005−6.9%
Group0.112 ± 0.0450.113 ± 0.047+0.001+0.9%
Repeat knee moment-impulse (flexion and extension)
P50.169 ± 0.0150.147 ± 0.017−0.022−13.0%
P60.209 ± 0.0140.193 ± 0.014−0.017−8.1%
P70.152 ± 0.0110.147 ± 0.014−0.005−3.3%
P80.073 ± 0.0090.072 ± 0.010−0.001−1.5%
Group0.151 ± 0.0570.140 ± 0.050−0.011−7.3%
Repeat knee extension moment-impulse only
P50.075 ± 0.0090.074 ± 0.011−0.001−1.6%
P60.154 ± 0.0090.170 ± 0.012+0.015+10.0%
P70.145 ± 0.0110.140 ± 0.014−0.005−3.2%
P80.053 ± 0.0100.061 ± 0.011+0.008+15.8%
Group0.107 ± 0.0500.111 ± 0.052+0.004+3.7%

Changes in only knee extension moment-impulses are included because these were most affected by the intervention (Fig. 5(b)). Knee flexion moment-impulses were not included for brevity, but can be calculated by subtracting the extension from moment-impulses.

2.4 Data Collection and Processing.

For both studies, we performed the Artificial Soleus parameter sweep by manipulating the dorsiflexion and plantarflexion torque-angle curves in the Humotech software. The Artificial Gastrocnemius stiffness sweep was performed by inputting the desired stiffness into a customized portion of the software. All walking trials were conducted on a split-belt instrumented treadmill (Bertec, Columbus, OH), with a sampling frequency of 2000 Hz. Retroreflective markers were affixed to the prosthetic foot and the participant's lower body, and their positions were recorded with the Vicon motion capture system (200 Hz; Vicon, Oxford, UK).

During the first session, participants familiarized themselves with the prosthetic ankle and Artificial Gastrocnemius hardware while walking on the treadmill at 1.1 m/s for roughly 90 min (not including breaks). Participants reported that, before familiarization, they had never walked with a powered prosthetic ankle while using an Artificial Gastrocnemius device. They walked with each of the trial settings (a combination of the different net push-off work values provided by the Artificial Soleus and Artificial Gastrocnemius stiffnesses) for three minutes, allowing them to become familiar with the different behaviors of the Artificial Soleus and Artificial Gastrocnemius emulator. Each trial was 3 min long, but only the final 90 s of data were analyzed to ensure processing of steady-state walking data.

Ground reaction force and synchronized motion capture data were filtered with a zero-phase, 4th-order, low-pass Butterworth filter with a cutoff frequency of 15 and 8 Hz, respectively. Additionally, the prosthetic ankle angle, Artificial Soleus cable tension, and Artificial Gastrocnemius actuator angle and tension were recorded. The Artificial Gastrocnemius tension data were filtered with a 1st order, low-pass Butterworth filter with a cutoff frequency of 30 Hz.

We used joint moment-impulse as a surrogate for the biological hip and biological knee muscle demands of the prosthesis-side limb during stance. We explored the moment-impulse for this study as it represents the net joint moment and the combined, sustained muscle efforts throughout the stance period. We integrated the absolute value of the joint moments with respect to stance time for each step to find the moment-impulses. We averaged across steps to find the mean moment-impulse for each combination of Artificial Gastrocnemius and Artificial Soleus. The Artificial Gastrocnemius's moment arm was measured with retroreflective markers affixed to the device, capturing its moment arm at the knee in real-time for every subject. The Artificial Gastrocnemius's contribution to the knee flexion moment was calculated using the real-time moment arm and tension measured by the device's load cell. To isolate the biological contributions to the knee moment we computationally removed the Artificial Gastrocnemius's contribution to the knee flexion moment from the internal net moment calculated in Visual3D (C-motion, Germantown, MD). The knee moment-impulse data presented in Results are calculated from the biological contributions to the net joint moment.

3 Results

3.1 Hip Joint Moment-Impulse.

Prosthesis-side hip moment-impulse was reduced during stance when walking with an Artificial Gastrocnemius for seven of eight participants (Fig. 2(a)). The change in hip moment-impulse during stance ranged from +5.1% to –27.4% across all participants (Figs. 34 and Tables 3 and 4). The hip moment-impulse reductions between the withdrawal and reintroduction trials were within 7% of the initial reductions for all participants in Case Series 2 (Fig. 4).

Fig. 2
(a) Hip moment-impulses during stance decreased in trials with the Artificial Gastrocnemius (AG) for most participants. Values for “With Artificial Gastrocnemius” column were calculated from the stiffest Artificial Gastrocnemius trial for each participant. (b) Two representative plots of hip flexion moment (hip flexion shown as positive, hip extension shown as negative) over one stride from trials with and without the Artificial Gastrocnemius. Hip moment-impulses from (a) were calculated by integrating the absolute value of the hip moments (including both extension and flexion moments) during the stance phase (highlighted region), when the Artificial Gastrocnemius was active.
Fig. 2
(a) Hip moment-impulses during stance decreased in trials with the Artificial Gastrocnemius (AG) for most participants. Values for “With Artificial Gastrocnemius” column were calculated from the stiffest Artificial Gastrocnemius trial for each participant. (b) Two representative plots of hip flexion moment (hip flexion shown as positive, hip extension shown as negative) over one stride from trials with and without the Artificial Gastrocnemius. Hip moment-impulses from (a) were calculated by integrating the absolute value of the hip moments (including both extension and flexion moments) during the stance phase (highlighted region), when the Artificial Gastrocnemius was active.
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Fig. 3
Average hip moment-impulses for Case Series 1 for each stiffness tested (magnitudes above, percent change from zero Artificial Gastrocnemius stiffness below). Participants 1, 3, and 4 exhibited reductions in moment-impulses as Artificial Gastrocnemius stiffness increased, but Participant 2 exhibited a slight increase in magnitudes.
Fig. 3
Average hip moment-impulses for Case Series 1 for each stiffness tested (magnitudes above, percent change from zero Artificial Gastrocnemius stiffness below). Participants 1, 3, and 4 exhibited reductions in moment-impulses as Artificial Gastrocnemius stiffness increased, but Participant 2 exhibited a slight increase in magnitudes.
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Fig. 4
Average hip moment-impulses from Case Series 2 for each stiffness tested (raw magnitudes on top, percent change on bottom). All participants exhibited reductions in hip moment-impulses as Artificial Gastrocnemius stiffness increased. For all participants, the hip moment-impulses decreased with the Artificial Gastrocnemius, increased when the Artificial Gastrocnemius was withdrawn (0 N/m/kg), and decreased again with the reintroduction of the Artificial Gastrocnemius (140 N/m/kg).
Fig. 4
Average hip moment-impulses from Case Series 2 for each stiffness tested (raw magnitudes on top, percent change on bottom). All participants exhibited reductions in hip moment-impulses as Artificial Gastrocnemius stiffness increased. For all participants, the hip moment-impulses decreased with the Artificial Gastrocnemius, increased when the Artificial Gastrocnemius was withdrawn (0 N/m/kg), and decreased again with the reintroduction of the Artificial Gastrocnemius (140 N/m/kg).
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Table 3

Change in hip moment-impulses during stance between the lowest and highest stiffness trials for Case Series 1

Case Series 1 hip moment-impulse changes
Participant0 N/m/kg (Nm*s/kg)84 N/m/kg (Nm*s/kg)Raw change (Nm*s/kg)Percent change (Nm*s/kg)
Hip moment-impulse (flexion and extension)
P10.215 ± 0.0260.175 ± 0.019−0.039−18.2%
P20.197 ± 0.0140.207 ± 0.013+0.010+5.1%
P30.255 ± 0.0160.217 ± 0.019−0.037−14.7%
P40.247 ± 0.0170.218 ± 0.015−0.029−11.9%
Group0.228 ± 0.0270.204 ± 0.020−0.024−10.5%
Hip flexion moment-impulse only
P10.162 ± 0.0260.118 ± 0.018−0.044−27.0%
P20.117 ± 0.0130.127 ± 0.011+0.010+8.3%
P30.130 ± 0.0160.093 ± 0.013−0.037−28.4%
P40.051 ± 0.0110.038 ± 0.010−0.013−24.6%
Group0.115 ± 0.0470.094 ± 0.040−0.021−18.3%
Case Series 1 hip moment-impulse changes
Participant0 N/m/kg (Nm*s/kg)84 N/m/kg (Nm*s/kg)Raw change (Nm*s/kg)Percent change (Nm*s/kg)
Hip moment-impulse (flexion and extension)
P10.215 ± 0.0260.175 ± 0.019−0.039−18.2%
P20.197 ± 0.0140.207 ± 0.013+0.010+5.1%
P30.255 ± 0.0160.217 ± 0.019−0.037−14.7%
P40.247 ± 0.0170.218 ± 0.015−0.029−11.9%
Group0.228 ± 0.0270.204 ± 0.020−0.024−10.5%
Hip flexion moment-impulse only
P10.162 ± 0.0260.118 ± 0.018−0.044−27.0%
P20.117 ± 0.0130.127 ± 0.011+0.010+8.3%
P30.130 ± 0.0160.093 ± 0.013−0.037−28.4%
P40.051 ± 0.0110.038 ± 0.010−0.013−24.6%
Group0.115 ± 0.0470.094 ± 0.040−0.021−18.3%

Changes in only hip flexion moment-impulses are included because these were most affected by the intervention (Fig. 2(b)). Hip extension moment-impulses were not included for brevity, but can be calculated by subtracting the flexion from the hip moment-impulses.

Table 4

Change in hip moment-impulses during stance between the lowest and highest stiffness trials (and the repeated trials) for Case Series 2

Case Series 2 hip moment-impulse changes
Participant0 N/m/kg (Nm*s/kg)140 N/m/kg (Nm*s/kg)Raw change (Nm*s/kg)Percent change (Nm*s/kg)
Hip moment-impulse (flexion and extension)
P50.217 ± 0.0220.165 ± 0.019−0.052−23.9%
P60.243 ± 0.0180.189 ± 0.022−0.055−22.5%
P70.230 ± 0.0190.207 ± 0.019−0.022−9.8%
P80.318 ± 0.0110.297 ± 0.014−0.021−6.6%
Group0.252 ± 0.0450.214 ± 0.058−0.038−15.1%
Hip flexion moment-impulse only
P50.150 ± 0.0190.082 ± 0.019−0.068−45.7%
P60.150 ± 0.0160.064 ± 0.010−0.086−57.5%
P70.097 ± 0.0130.070 ± 0.012−0.027−27.8%
P80.051 ± 0.0080.060 ± 0.008+0.009+18.1%
Group0.112 ± 0.0480.069 ± 0.009−0.043−38.4%
Repeat hip moment-impulse (flexion and extension)
P50.232 ± 0.0210.168 ± 0.021−0.064−27.4%
P60.239 ± 0.0160.201 ± 0.019−0.038−15.9%
P70.243 ± 0.0160.216 ± 0.020−0.026−10.9%
P80.298 ± 0.0130.295 ± 0.013−0.003−1.1%
Group0.253 ± 0.0310.220 ± 0.054−0.033−13%
Repeat hip flexion moment-impulse only
P50.147 ± 0.0190.080 ± 0.019−0.068−46.0%
P60.131 ± 0.0140.069 ± 0.009−0.061−47.0%
P70.108 ± 0.0150.074 ± 0.013−0.034−31.5%
P80.082 ± 0.0120.074 ± 0.006−0.008−9.3%
Group0.117 ± 0.0280.074 ± 0.004−0.043−36.8%
Case Series 2 hip moment-impulse changes
Participant0 N/m/kg (Nm*s/kg)140 N/m/kg (Nm*s/kg)Raw change (Nm*s/kg)Percent change (Nm*s/kg)
Hip moment-impulse (flexion and extension)
P50.217 ± 0.0220.165 ± 0.019−0.052−23.9%
P60.243 ± 0.0180.189 ± 0.022−0.055−22.5%
P70.230 ± 0.0190.207 ± 0.019−0.022−9.8%
P80.318 ± 0.0110.297 ± 0.014−0.021−6.6%
Group0.252 ± 0.0450.214 ± 0.058−0.038−15.1%
Hip flexion moment-impulse only
P50.150 ± 0.0190.082 ± 0.019−0.068−45.7%
P60.150 ± 0.0160.064 ± 0.010−0.086−57.5%
P70.097 ± 0.0130.070 ± 0.012−0.027−27.8%
P80.051 ± 0.0080.060 ± 0.008+0.009+18.1%
Group0.112 ± 0.0480.069 ± 0.009−0.043−38.4%
Repeat hip moment-impulse (flexion and extension)
P50.232 ± 0.0210.168 ± 0.021−0.064−27.4%
P60.239 ± 0.0160.201 ± 0.019−0.038−15.9%
P70.243 ± 0.0160.216 ± 0.020−0.026−10.9%
P80.298 ± 0.0130.295 ± 0.013−0.003−1.1%
Group0.253 ± 0.0310.220 ± 0.054−0.033−13%
Repeat hip flexion moment-impulse only
P50.147 ± 0.0190.080 ± 0.019−0.068−46.0%
P60.131 ± 0.0140.069 ± 0.009−0.061−47.0%
P70.108 ± 0.0150.074 ± 0.013−0.034−31.5%
P80.082 ± 0.0120.074 ± 0.006−0.008−9.3%
Group0.117 ± 0.0280.074 ± 0.004−0.043−36.8%

Changes in only hip flexion moment-impulses are included because these were most affected by the intervention (Fig. 2(b)). Hip extension moment-impulses were not included for brevity, but can be calculated by subtracting the flexion from hip moment-impulses.

Moment-impulse changes were most prominent during mid- and late-stance when the hip moment was in flexion (Fig. 2(b)). Hip flexion moment-impulse was reduced when walking with an Artificial Gastrocnemius for six of eight participants; the change in hip flexion moment-impulse ranged from +8.3% to −57.5% (Tables 3 and 4).

3.2 Knee Joint Moment-Impulse.

Prosthesis-side knee moment-impulse was reduced when walking with an Artificial Gastrocnemius for three of eight participants (Fig. 5(a)). The change in knee moment-impulse during stance ranged from +23.3% to −33.6% across all participants (Figs. 6 and 7 and Tables 5 and 6). The moment-impulse changes between the withdrawal and reintroduction trials were inconsistent with the initial changes for three of four participants in Case Series 2 (Fig. 7). For example, Participant 5 exhibited increased moment-impulse during the first trial with the stiffest Artificial Gastrocnemius, but then exhibited a reduction between the withdrawal and reintroduction trials (Fig. 7). The inverse is true for Participants 6 and 7 where they first exhibited reductions, then exhibited increases (Fig. 7).

Fig. 5
(a) Knee moment-impulses exhibited minimal changes with the Artificial Gastrocnemius (AG). (b) Two representative plots of biological contributions to knee moment (knee extension shown as positive, knee flexion shown as negative) over a stride from trials with and without the Artificial Gastrocnemius. Additionally, a third representative plot of the total knee moment with the Artificial Gastrocnemius (the sum of the biological contributions and the Artificial Gastrocnemius contributions) is shown for reference. Knee moment-impulses from (a) were calculated by integrating the absolute value of the knee moment during the stance phase (as highlighted), when the Artificial Gastrocnemius was active.
Fig. 5
(a) Knee moment-impulses exhibited minimal changes with the Artificial Gastrocnemius (AG). (b) Two representative plots of biological contributions to knee moment (knee extension shown as positive, knee flexion shown as negative) over a stride from trials with and without the Artificial Gastrocnemius. Additionally, a third representative plot of the total knee moment with the Artificial Gastrocnemius (the sum of the biological contributions and the Artificial Gastrocnemius contributions) is shown for reference. Knee moment-impulses from (a) were calculated by integrating the absolute value of the knee moment during the stance phase (as highlighted), when the Artificial Gastrocnemius was active.
Close modal
Fig. 6
Average knee moment-impulses for Case Series 1 for each stiffness tested (raw magnitudes on top, percent change on bottom). All participants exhibited an increase in knee moment-impulse magnitudes as Artificial Gastrocnemius stiffness increased.
Fig. 6
Average knee moment-impulses for Case Series 1 for each stiffness tested (raw magnitudes on top, percent change on bottom). All participants exhibited an increase in knee moment-impulse magnitudes as Artificial Gastrocnemius stiffness increased.
Close modal
Fig. 7
Average knee moment-impulses from Case Series 2 for each stiffness tested (raw magnitudes on top, percent change on bottom). Changes in knee moment-impulses varied greatly by participant and by stiffness tested. Participant 7 exhibited decreases in knee moment-impulse as Artificial Gastrocnemius stiffness increased, but these decreases persisted even when the Artificial Gastrocnemius was withdrawn.
Fig. 7
Average knee moment-impulses from Case Series 2 for each stiffness tested (raw magnitudes on top, percent change on bottom). Changes in knee moment-impulses varied greatly by participant and by stiffness tested. Participant 7 exhibited decreases in knee moment-impulse as Artificial Gastrocnemius stiffness increased, but these decreases persisted even when the Artificial Gastrocnemius was withdrawn.
Close modal
Table 5

Change in knee moment-impulses between the lowest and highest stiffness trials for Case Series 1

Case Series 1 knee moment-impulse changes
Participant0 N/m/kg (Nm*s/kg)84 N/m/kg (Nm*s/kg)Raw change (Nm*s/kg)Percent change (Nm*s/kg)
Knee moment-impulse (flexion and extension)
P10.172 ± 0.0190.178 ± 0.016+0.006+3.3%
P20.308 ± 0.0220.317 ± 0.019+0.009+2.9%
P30.148 ± 0.0230.161 ± 0.019+0.013+8.6%
P40.078 ± 0.0140.096 ± 0.015+0.018+23.3%
Group0.176 ± 0.0960.188 ± 0.093+0.012+6.8%
Knee extension moment-impulse only
P10.155 ± 0.0180.168 ± 0.016+0.013+8.7%
P20.305 ± 0.0220.313 ± 0.019+0.008+2.6%
P30.139 ± 0.0240.152 ± 0.020+0.014+9.8%
P40.061 ± 0.0160.078 ± 0.016+0.017+27.0%
Group0.165 ± 0.1020.178 ± 0.098+0.013+7.9%
Case Series 1 knee moment-impulse changes
Participant0 N/m/kg (Nm*s/kg)84 N/m/kg (Nm*s/kg)Raw change (Nm*s/kg)Percent change (Nm*s/kg)
Knee moment-impulse (flexion and extension)
P10.172 ± 0.0190.178 ± 0.016+0.006+3.3%
P20.308 ± 0.0220.317 ± 0.019+0.009+2.9%
P30.148 ± 0.0230.161 ± 0.019+0.013+8.6%
P40.078 ± 0.0140.096 ± 0.015+0.018+23.3%
Group0.176 ± 0.0960.188 ± 0.093+0.012+6.8%
Knee extension moment-impulse only
P10.155 ± 0.0180.168 ± 0.016+0.013+8.7%
P20.305 ± 0.0220.313 ± 0.019+0.008+2.6%
P30.139 ± 0.0240.152 ± 0.020+0.014+9.8%
P40.061 ± 0.0160.078 ± 0.016+0.017+27.0%
Group0.165 ± 0.1020.178 ± 0.098+0.013+7.9%

Changes in only knee extension moment-impulses are included because these were most affected by the intervention (Fig. 5(b)). Knee flexion moment-impulses were not included for brevity, but can be calculated by subtracting the extension from moment-impulses.

Table 6

Change in knee moment-impulses between the lowest and highest stiffness trials (and the repeated trials) for Case Series 2

Case Series 2 knee moment-impulse changes
Participant0 N/m/kg (Nm*s/kg)140 N/m/kg (Nm*s/kg)Raw change (Nm*s/kg)Percent change (Nm*s/kg)
Knee moment-impulse (flexion and extension)
P50.184 ± 0.0160.193 ± 0.019+0.008+4.4%
P60.219 ± 0.0140.213 ± 0.021−0.007−3.0%
P70.270 ± 0.0180.240 ± 0.017−0.030−11.0%
P80.133 ± 0.0190.123 ± 0.023−0.010−7.8%
Group0.202 ± 0.0580.192 ± 0.050−0.010−5%
Knee extension moment-impulse only
P50.174 ± 0.0170.181 ± 0.018+0.007+4.1%
P60.210 ± 0.0150.205 ± 0.022−0.005−2.4%
P70.266 ± 0.0180.236 ± 0.018−0.031−11.6%
P80.117 ± 0.0190.110 ± 0.023−0.007−6.0%
Group0.192 ± 0.0630.183 ± 0.053−0.009−4.7%
Repeat knee moment-impulse (flexion and extension)
P50.176 ± 0.0180.166 ± 0.019−0.010−5.9%
P60.227 ± 0.0140.229 ± 0.023+0.002+0.9%
P70.227 ± 0.0140.232 ± 0.019+0.004+1.8%
P80.148 ± 0.0180.098 ± 0.013−0.050−33.6%
Group0.195 ± 0.0390.181 ± 0.063−0.014−7.2%
Repeat knee extension moment-impulse only
P50.158 ± 0.0170.152 ± 0.019−0.006−3.8%
P60.212 ± 0.0150.225 ± 0.024+0.013+6.3%
P70.224 ± 0.0150.227 ± 0.020+0.003+1.4%
P80.139 ± 0.0190.084 ± 0.014−0.055−39.3%
Group0.183 ± 0.0410.172 ± 0.068−0.011 ± 0.030−6%
Case Series 2 knee moment-impulse changes
Participant0 N/m/kg (Nm*s/kg)140 N/m/kg (Nm*s/kg)Raw change (Nm*s/kg)Percent change (Nm*s/kg)
Knee moment-impulse (flexion and extension)
P50.184 ± 0.0160.193 ± 0.019+0.008+4.4%
P60.219 ± 0.0140.213 ± 0.021−0.007−3.0%
P70.270 ± 0.0180.240 ± 0.017−0.030−11.0%
P80.133 ± 0.0190.123 ± 0.023−0.010−7.8%
Group0.202 ± 0.0580.192 ± 0.050−0.010−5%
Knee extension moment-impulse only
P50.174 ± 0.0170.181 ± 0.018+0.007+4.1%
P60.210 ± 0.0150.205 ± 0.022−0.005−2.4%
P70.266 ± 0.0180.236 ± 0.018−0.031−11.6%
P80.117 ± 0.0190.110 ± 0.023−0.007−6.0%
Group0.192 ± 0.0630.183 ± 0.053−0.009−4.7%
Repeat knee moment-impulse (flexion and extension)
P50.176 ± 0.0180.166 ± 0.019−0.010−5.9%
P60.227 ± 0.0140.229 ± 0.023+0.002+0.9%
P70.227 ± 0.0140.232 ± 0.019+0.004+1.8%
P80.148 ± 0.0180.098 ± 0.013−0.050−33.6%
Group0.195 ± 0.0390.181 ± 0.063−0.014−7.2%
Repeat knee extension moment-impulse only
P50.158 ± 0.0170.152 ± 0.019−0.006−3.8%
P60.212 ± 0.0150.225 ± 0.024+0.013+6.3%
P70.224 ± 0.0150.227 ± 0.020+0.003+1.4%
P80.139 ± 0.0190.084 ± 0.014−0.055−39.3%
Group0.183 ± 0.0410.172 ± 0.068−0.011 ± 0.030−6%

Changes in only knee extension moment-impulses are included because these were most affected by the intervention (Fig. 5(b)). Knee flexion moment-impulses were not included for brevity, but can be calculated by subtracting the extension from moment-impulses.

Moment-impulse changes were most prominent during mid- and late-stance when the knee moment was in extension (Fig. 5(b)). Knee extension moment-impulse was reduced when walking with an Artificial Gastrocnemius for three of eight participants; the change in extension moment-impulse ranged from +27.0% to −39.3% (Tables 5 and 6).

4 Discussion

Hip flexor demands decreased for prosthesis users when walking with the Artificial Gastrocnemius. These results support our prediction that the Artificial Gastrocnemius coupled with higher-powered push-off work would reduce the user's prosthesis-side hip flexor demands, as evidenced by reductions in hip moment-impulse (Figs. 3 and 4). Most participants reported that the Artificial Gastrocnemius made walking easier for them. Participants 5, 6, and 7 all exhibited substantial hip flexor reductions, of −46%, −57.5%, and −28%, respectively, and these participants stated that the Artificial Gastrocnemius: “reduced attention necessary to walk”, made it so their prosthesis-side “leg needs to work less hard”, and gave them a “more natural response while walking” with the higher-powered ankle prosthesis. Conversely, Participant 8, who exhibited a hip flexor increase of 18% with the intervention (Table 4), slightly preferred the trials without the Artificial Gastrocnemius. Hence, the subject-specific feedback seemed to corroborate the objective hip kinetics results.

The hip flexor demand reductions are qualitatively consistent with previous studies. A similar study (N =2) was performed using a biomimetic-powered ankle and an Artificial Gastrocnemius comprised of a rotational spring at the knee [24] which was roughly equivalent to 130–160 N/m/kg of linear stiffness with our Artificial Gastrocnemius. The previous study observed hip flexor demand reductions of −26% and −14%, similar to the results we observed for comparable settings (i.e., the hip flexor reductions with the biomimetic Artificial Soleus settings displayed in Appendix Table 8). When coupled with higher push-off work, the same Artificial Gastrocnemius produced even greater reductions, up to −56%, in hip flexor demand (Table 4). Following this trend, an Artificial Gastrocnemius may be increasingly beneficial when higher-powered prostheses are used.

Table 8

Change in hip moment-impulses between the lowest and highest stiffness trials (and the repeated trials) with 0.09 J/kg of ankle push-off work from Case Series 2

Case Series 2 hip moment-impulse changes (0.09 J/kg push-off)
Participant0 N/m/kg (Nm*s/kg)140 N/m/kg (Nm*s/kg)Raw change (Nm*s/kg)Percent change (Nm*s/kg)
Hip moment-impulse (flexion and extension)
P50.225 ± 0.0240.191 ± 0.015−0.034−15.0%
P60.236 ± 0.0150.222 ± 0.016−0.014−6.0%
P70.248 ± 0.0170.209 ± 0.016−0.038−15.5%
P80.301 ± 0.0120.282 ± 0.010−0.019−6.2%
Group0.252 ± 0.0330.226 ± 0.039−0.026−10.3%
Hip flexion moment-impulse only
P50.138 ± 0.0170.087 ± 0.013−0.051−36.8%
P60.134 ± 0.0150.141 ± 0.015+0.007+5.2%
P70.108 ± 0.0140.097 ± 0.011−0.012−10.7%
P80.095 ± 0.0090.095 ± 0.007+0.000+0.2%
Group0.119 ± 0.0210.105 ± 0.024−0.014−11.8%
Repeat hip moment-impulse (flexion and extension)
P50.225 ± 0.0200.195 ± 0.018−0.030−13.3%
P60.297 ± 0.0150.213 ± 0.014−0.084−28.4%
P70.247 ± 0.0190.239 ± 0.017−0.008−3.4%
P80.405 ± 0.0160.310 ± 0.016−0.095−23.4%
Group0.294 ± 0.0800.239 ± 0.051−0.055−18.7%
Repeat hip flexion moment-impulse only
P50.118 ± 0.0170.086 ± 0.015−0.032−27.4%
P60.221 ± 0.0130.130 ± 0.014−0.091−41.0%
P70.126 ± 0.0110.107 ± 0.012−0.019−15.4%
P80.028 ± 0.0040.116 ± 0.009+0.088+311.1%
Group0.123 ± 0.0790.110 ± 0.019−0.013−10.6%
Case Series 2 hip moment-impulse changes (0.09 J/kg push-off)
Participant0 N/m/kg (Nm*s/kg)140 N/m/kg (Nm*s/kg)Raw change (Nm*s/kg)Percent change (Nm*s/kg)
Hip moment-impulse (flexion and extension)
P50.225 ± 0.0240.191 ± 0.015−0.034−15.0%
P60.236 ± 0.0150.222 ± 0.016−0.014−6.0%
P70.248 ± 0.0170.209 ± 0.016−0.038−15.5%
P80.301 ± 0.0120.282 ± 0.010−0.019−6.2%
Group0.252 ± 0.0330.226 ± 0.039−0.026−10.3%
Hip flexion moment-impulse only
P50.138 ± 0.0170.087 ± 0.013−0.051−36.8%
P60.134 ± 0.0150.141 ± 0.015+0.007+5.2%
P70.108 ± 0.0140.097 ± 0.011−0.012−10.7%
P80.095 ± 0.0090.095 ± 0.007+0.000+0.2%
Group0.119 ± 0.0210.105 ± 0.024−0.014−11.8%
Repeat hip moment-impulse (flexion and extension)
P50.225 ± 0.0200.195 ± 0.018−0.030−13.3%
P60.297 ± 0.0150.213 ± 0.014−0.084−28.4%
P70.247 ± 0.0190.239 ± 0.017−0.008−3.4%
P80.405 ± 0.0160.310 ± 0.016−0.095−23.4%
Group0.294 ± 0.0800.239 ± 0.051−0.055−18.7%
Repeat hip flexion moment-impulse only
P50.118 ± 0.0170.086 ± 0.015−0.032−27.4%
P60.221 ± 0.0130.130 ± 0.014−0.091−41.0%
P70.126 ± 0.0110.107 ± 0.012−0.019−15.4%
P80.028 ± 0.0040.116 ± 0.009+0.088+311.1%
Group0.123 ± 0.0790.110 ± 0.019−0.013−10.6%

Changes in only hip flexion moment-impulses are included because these were most affected by the intervention (Fig. 2(b)). Hip extension moment-impulses were not included for brevity, but can be calculated by subtracting the flexion from moment-impulses. Participant 8 exhibited a normal flexion moment-impulse relative to others for their repeat “140 N/m/kg” trial. Their flexion moment-impulse for the repeat “0 N/m/kg” trial was uncharacteristically low and resulted in a +311.1% change.

Reductions to hip flexor demands when using an Artificial Gastrocnemius could potentially increase users' quality of life. A previous study observed transfemoral prosthesis users walking with a hip exoskeleton that reduced hip flexor demands to a similar degree to the Artificial Gastrocnemius. With the hip exoskeleton, participants (N =6; 4 male, 2 female; 33.8 ± 9.8 years) averaged a 15.6% reduction in metabolic cost of walking [29]. Two prior studies also observed the clinical effects of a hip exoskeleton on non-prosthesis user populations. The first study found that participants with neurological disorders (stroke, Parkinson's disease, multiple sclerosis, cervical and lumbar stenosis) walked 15% further with less exhaustion while using the device [30]. The second study found that older participants (N =8; male; 63.5 ± 5.9 years) exhibited a 4% reduction in metabolic cost while walking with the hip exoskeleton [31]. With reduced hip flexor demands from an Artificial Gastrocnemius, transtibial prosthesis users might also be able to walk longer distances with less exhaustion and less energy consumption.

Neither knee flexor nor extensor muscle demands decreased consistently for prosthesis users when walking with the Artificial Gastrocnemius. Seven of eight participants did not exhibit repeatable reductions in knee flexor or extensor demands, as evidenced by inconsistent changes in knee moment-impulse (Figs. 6 and 7). All four participants of Case Series 1 exhibited increases in knee extensor demands (Table 5). Only one of four participants from Case Series 2 exhibited a decrease in knee moment-impulse for both the original and reintroduction trials (Table 6). In contrast, a previous study (N =2) found knee flexor demands decreased with an Artificial Gastrocnemius [24], though it is hard to compare or interpret differences given the small sample size. In our study, the hypothesis that the Artificial Gastrocnemius would reduce the user's prosthesis-side knee demands was not supported.

The Artificial Gastrocnemius's failure to reduce knee flexor demands is counter to the previous literature. We expected the biological knee flexor demands to increase with the higher-powered push-off work [18,19]. The Artificial Gastrocnemius's flexion was intended to offload demands from the knee flexors. But the biological knee flexor demand did not increase with the higher-powered push-off work; instead, the knee exhibited an extension moment. Comparing trials from the passive prosthesis setting (Appendix Table 12), the biomimetic setting (Appendix Table 11), and the higher-powered setting (Table 6), we see that knee extensor demand increased with ankle push-off work, as indicated by the increased extension moment-impulses. The biological knee moments remained in extension when walking with the Artificial Gastrocnemius (Fig. 5(b)). Thus, the Artificial Gastrocnemius did not reduce knee muscle demands as expected; in fact, it exerted a flexion moment counter to the dominant extension moment from the user's muscles.

The Artificial Gastrocnemius's failure to reduce knee flexor demands may have been caused by the kinematic change adopted by users when walking with the higher push-off power. To generate the increased push-off work, the higher-powered prosthesis dorsiflexes earlier in stance relative to passive and biomimetic prostheses. We observed increased knee flexion for each participant when the higher-powered prosthesis performed this dorsiflexion. As a result, the user's leg was in a more crouched configuration relative to the straighter, slightly bent configuration we observed in the lower-powered push-off trials. Next, the higher-powered prosthesis provides a sustained plantarflexion moment (to provide a burst of push-off) at the end of stance. Since the knee is more flexed, the muscles likely produce a greater knee extension moment to stabilize the user's knee and keep it from buckling under the increased push-off. This knee stabilization may also be allowing for the burst of push-off power to accelerate the user's center of mass. Further research might illuminate the biomechanical effects of higher-powered prostheses and their effect on power transfer and knee joint dynamics.

Key limitations of the current study include a short acclimation period and an indirect outcome metric. Firstly, a single day of familiarization before testing would only reflect a portion of the potential long-term benefits of using an Artificial Gastrocnemius. There is potential for greater benefits to be gained if users were able to incorporate the Artificial Gastrocnemius into their daily walking habits. Continued familiarization with the Artificial Soleus would also likely affect these long-term benefits as the user becomes more accustomed to walking with a powered prosthesis. Reflecting on the varied effects on the knee kinetics, future work could explore how sensitive the knee moment-impulses are to different Artificial Soleus behaviors. Secondly, the joint moment-impulse is not a direct measurement of the muscle demand as it does not capture antagonistic muscle demands due to cocontraction. We chose to use joint moment-impulse because it captures the net moment resulting from the hip and knee flexor and extensor muscle groups. Alternative measures like electromyography (EMG) were challenging as key musculature was covered by the powered prosthesis and Artificial Gastrocnemius hardware, making it difficult to place a surface EMG on the skin or collect reliable signals without artifacts. Furthermore, EMG has its own limitations as it is a measure of activation and not muscle force or power. The joint moment-impulse, however, is calculable from motion capture and GRF data, two reliable methods that were not made challenging by the experiment hardware. Finally, due to the small sample size and the case series nature of the study, we did not perform any statistical analysis of the data.

5 Conclusion

The addition of an Artificial Gastrocnemius to a higher-powered ankle prosthesis decreased the hip flexor muscle demands for most users, as evidenced by reductions in hip moment-impulses while walking. Most participants also indicated that, with the intervention, walking felt easier and more natural. But, the addition of an Artificial Gastrocnemius did not decrease the knee flexor or extensor muscle demands for most users, as evidenced by inconsistent changes in knee moment-impulse. The Artificial Gastrocnemius should be further explored to determine if reduced hip demands improve mobility or the user's quality of life, for instance, by increasing the distance they can walk, decreasing the energy spent while walking, or leading to increased physical activity or community engagement.

Acknowledgment

We gratefully acknowledge Ryan Mott, Carl Curran, Richard Ha, and Joshua Caputo for their technical support in troubleshooting the Humotech hardware and software. We would also like to thank Gerasimos Bastas for his insights regarding experimental design for prosthesis users.

Funding Data

  • National Science Foundation (NSF) (Grant No. 1705714; Funder ID: 10.13039/100000001).

  • NSF Graduate Research Fellowship Program (GRFP) (Grant No. 1937963; Funder ID: 10.13039/100000082).

Data Availability Statement

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

Appendix

The following tables (Tables 712) are reference data for the hip and knee joint moment-impulses of participants walking with the ankle in a passive mode (0 J/kg of ankle push-off work) or in a biomimetic mode (0.08 J/kg for Case Series 1 and 0.09 J/kg for Case Series 2). These data show how the hip and knee moment-impulses changed as ankle push-off work increased and as the Artificial Gastrocnemius was introduced.

Table 9

Change in hip moment-impulses between the lowest and highest stiffness trials (and the repeated trials) with the passive prosthesis settings from Case Series 2

Case Series 2 hip moment-impulse changes (0 J/kg push-off)
Participant0 N/m/kg (Nm*s/kg)140 N/m/kg (Nm*s/kg)Raw change (Nm*s/kg)Percent change (Nm*s/kg)
Hip moment-impulse (flexion and extension)
P50.203 ± 0.0190.187 ± 0.014−0.016−8.1%
P60.291 ± 0.0140.216 ± 0.019−0.075−25.8%
P70.259 ± 0.0180.255 ± 0.020−0.005−1.8%
P80.298 ± 0.0190.259 ± 0.011−0.039−13.1%
Group0.263 ± 0.0430.229 ± 0.034−0.034−12.9%
Hip flexion moment-impulse only
P50.099 ± 0.0170.077 ± 0.011−0.022−22.6%
P60.202 ± 0.0120.131 ± 0.017−0.071−35.2%
P70.129 ± 0.0100.110 ± 0.013−0.019−15.0%
P80.121 ± 0.0120.092 ± 0.011−0.029−24.0%
Group0.138 ± 0.0440.102 ± 0.023−0.036−26.1%
Repeat hip moment-impulse (flexion and extension)
P50.227 ± 0.0150.191 ± 0.014−0.037−16.1%
P60.277 ± 0.0190.214 ± 0.016−0.063−22.8%
P70.266 ± 0.0150.252 ± 0.019−0.013−5.0%
P80.303 ± 0.0120.270 ± 0.010−0.033−10.9%
Group0.268 ± 0.0310.232 ± 0.036−0.036−13.4%
Repeat hip flexion moment-impulse only
P50.119 ± 0.0130.075 ± 0.010−0.044−37.2%
P60.198 ± 0.0160.130 ± 0.014−0.067−34.0%
P70.128 ± 0.0120.109 ± 0.013−0.019−14.8%
P80.136 ± 0.0090.104 ± 0.008−0.032−23.6%
Group0.145 ± 0.0360.105 ± 0.023−0.040−27.6%
Case Series 2 hip moment-impulse changes (0 J/kg push-off)
Participant0 N/m/kg (Nm*s/kg)140 N/m/kg (Nm*s/kg)Raw change (Nm*s/kg)Percent change (Nm*s/kg)
Hip moment-impulse (flexion and extension)
P50.203 ± 0.0190.187 ± 0.014−0.016−8.1%
P60.291 ± 0.0140.216 ± 0.019−0.075−25.8%
P70.259 ± 0.0180.255 ± 0.020−0.005−1.8%
P80.298 ± 0.0190.259 ± 0.011−0.039−13.1%
Group0.263 ± 0.0430.229 ± 0.034−0.034−12.9%
Hip flexion moment-impulse only
P50.099 ± 0.0170.077 ± 0.011−0.022−22.6%
P60.202 ± 0.0120.131 ± 0.017−0.071−35.2%
P70.129 ± 0.0100.110 ± 0.013−0.019−15.0%
P80.121 ± 0.0120.092 ± 0.011−0.029−24.0%
Group0.138 ± 0.0440.102 ± 0.023−0.036−26.1%
Repeat hip moment-impulse (flexion and extension)
P50.227 ± 0.0150.191 ± 0.014−0.037−16.1%
P60.277 ± 0.0190.214 ± 0.016−0.063−22.8%
P70.266 ± 0.0150.252 ± 0.019−0.013−5.0%
P80.303 ± 0.0120.270 ± 0.010−0.033−10.9%
Group0.268 ± 0.0310.232 ± 0.036−0.036−13.4%
Repeat hip flexion moment-impulse only
P50.119 ± 0.0130.075 ± 0.010−0.044−37.2%
P60.198 ± 0.0160.130 ± 0.014−0.067−34.0%
P70.128 ± 0.0120.109 ± 0.013−0.019−14.8%
P80.136 ± 0.0090.104 ± 0.008−0.032−23.6%
Group0.145 ± 0.0360.105 ± 0.023−0.040−27.6%

Changes in only hip flexion moment-impulses are included because these were most affected by the intervention (Fig. 2(b)). Hip extension moment-impulses were not included for brevity, but can be calculated by subtracting the flexion from moment-impulses.

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