## Abstract

Lower-limb amputees experience many gait impairments and limitations. Some of these impairments can be attributed to the lack of a functioning biarticular gastrocnemius (GAS) muscle. We propose a transtibial prosthesis that implements a quasi-passive spring mechanism to replicate GAS function. A prototype biarticular prosthesis (BP) was designed, built, and tested on one subject with a transtibial amputation. They walked on an instrumented treadmill with motion capture under three different biarticular spring stiffness conditions. A custom-developed OpenSim musculoskeletal model, which included the BP, was used to calculate the work performed and torque applied by the BP spring on the knee and ankle joints. The BP functioned as expected, generating forces with similar timing to GAS. Work transfer occurred from the ankle to the knee, with stiffer springs transferring more energy. Driven mostly by kinematics, the quasi-passive design of the BP consumed very low power (5.15 W average) and could lend itself well to future lightweight, low-power designs.

## Introduction

Lower limb amputation is a growing problem—the amputee population in the U.S. is approximately 2 million and is projected to reach 3.6 million by 2050 [1]. Individuals with lower-limb amputation experience secondary musculoskeletal conditions such as low back pain, contralateral knee pain, and osteoarthritis [2]. Additionally, amputees tend to experience bilateral asymmetries, which result in slower walking speeds and a higher metabolic cost of walking [3]. The purpose of this work was to design a novel prosthesis that may address these gait impairments.

Lower-limb amputees lack the function of the gastrocnemius (GAS) and other distal leg muscles that are important to normal ambulation. The GAS and soleus (SOL) are the primary ankle plantarflexors. Both muscles have distinct and important roles in healthy gait, the GAS accelerating the leg into swing during late stance phase, while the SOL accelerates the trunk forward [4]. The GAS is biarticular, causing both ankle plantarflexion and knee flexion when it contracts. GAS is active during mid- and terminal-stance, and peaks at roughly 40% of the gait cycle [5]. The lack of plantarflexor muscles has been linked to increased muscle force in the rectus femoris, biceps femoris, vastus lateralis, and iliopsoas [3,68]. Van der Krogt et al. (2012) showed that human gait is sensitive to GAS and SOL weakness [8]. In their simulations of healthy gait, they found that GAS weakness caused increased muscle activation in the biceps femoris, semimembranosus, semitendinosus, iliopsoas, gluteus medius, gluteus maximus, sartorius, and SOL [9]. They also noted that 80% weakness of both plantarflexors (GAS and SOL) resulted in a total muscle stress increase of over 200% [9]. These findings indicate the importance of the ankle plantarflexors in overall gait energetics. Additionally, the biarticular nature of the GAS allows for work transfer between the knee and ankle [10,11]. Further analysis of the work transfer can yield important insight into biarticular GAS function during gait.

In normal gait, GAS is nearly isometric in mid to late stance phase, and the force production during this portion of the gait cycle is primarily from tendon stretch [12]. Tendons are passive elastic elements in series with the muscle and as such, act as simple springs in muscle models [12,13]. Collins et al. showed that a passive clutched spring in parallel with the ankle plantarflexors could reduce SOL activation by 22% and the metabolic cost of unimpaired walking by up to 7%, which suggests that quasi-passive spring design solutions may also have the potential to reduce the effort of amputee gait [13,14].

There are a number of research groups that have designed prostheses that impact both the knee and ankle, but with some differences compared to the device described here. In preliminary work at MIT, Endo et al. added a clutched spring mechanism that spanned only the knee joint to a powered ankle transtibial prosthesis [15]. Tests with a single subject showed a decrease in overall metabolic cost compared to a passive device, though the hamstring muscle activation was elevated. This design however, uses a uniarticular spring at the knee to represent the biarticular GAS and neglects the ankle in its optimization analysis [15]. Unal et al. presented a BP design for transfemoral amputees with simulated results [16] and demonstrated the mechanical function with a nonamputee [17].

This paper presents a novel biarticular transtibial prosthesis design that has the potential to replicate GAS function in walking, using a quasi-passive clutched spring mechanism. We include a description of the device, its control system, and preliminary evaluation during treadmill ambulation.

## Device Description

The BP consists of a rigid thigh cuff (COMBO ToeOFF Orthosis, Allard USA, Inc., Rockway NJ), pylon in series with a 6DOF load cell (iPecs, RTC electronics, Inc., Dexter MI) and a College Park Venture foot (College Park, Warren MI), and fits onto the participant's own prescribed socket. The BP includes a clutched spring that attaches distally and posterior to the ankle, and proximally above the knee via a spectra cable. The spring attaches such that it has a static position moment arm of approximately 15 cm at the knee and 10 cm at the ankle. It is controlled by a microcontroller to replicate GAS function (Fig. 1). Force production in the biarticular spring is controlled via kinematic events, rather than temporal control, to allow the BP to operate appropriately under a range of walking speeds (Fig. 2). The force sensor in series with the pylon detects pylon axial force to determine heel strike and signal the clutch to lock. A microcontroller locks the clutch (Ogura AMC 40, SDP S90BF9-26A06) after heel strike occurs, and disengages the clutch once both the BP spring force and the iPecs force fall below their respective thresholds. This method for clutch disengagement ensures that the spring is no longer loaded (avoiding a rapid step down in force), and that the clutch is disengaged for swing phase. A small recoil spring ensures that the spectra cable connecting the spring does not slack, and applies a consistent force of about 30 N. The clutch is ratcheted so that, when locked, the cable connecting the spring can shorten but not lengthen. The ratcheted clutch ensures that BP is controlled through kinematic events, i.e., biarticular force production begins just after minimum string length, regardless of gait speed or step-to-step variability. Exploded views of the clutch mechanism are shown in Fig. 3. BP spring forces were measured using a single axis load cell (OMEGA Engineering, Inc., Norwalk, CT) in series with the BP spring.

Fig. 1
Fig. 1
Close modal
Fig. 2
Fig. 2
Close modal
Fig. 3
Fig. 3
Close modal

## Methods

With VA Puget Sound Health Care System and University of Washington IRB approval, one individual with transtibial amputation was recruited and provided informed consent. The subject was a 55-year-old female, with a weight of 89.4 kg and height of 1.77 m. During a brief initial fitting visit, measurements and photos of the affected leg were taken so that the BP could be appropriately fitted to the individual. These measurements included: weight, thigh circumference, the height of the tibial plateau above the ground, and knee width. The thigh cuff size was selected per the manufacturer's recommendations and the upright lengths were adjusted to align the orthotic knee joint to the subject's knee joint. The polycentric knee joint from the Allard orthosis minimizes the effect of knee misalignment. The BP's Venture foot was fitted with the appropriate components based on the subject's weight, impact level, amputation level, and shoe size, per the manufacturer's specification. This participant wore the F4 foreheel, medium front bumper, medium ankle bushings, and firm rear bumper.

The data collection was limited to a session of 4 h, during which the participant walked on the BP in several configurations. Motion capture data were collected using a 12-camera Vicon system (Oxford Metrics, Oxford, UK) and an instrumented treadmill (Bertec Corp., Columbus, OH). The subject was instrumented with 74 reflective markers in a modified Plug-in Gait set. Modifications to the Plug-in Gait set included: clusters on the femur, shank, and humerus [18], tracking of the shank with markers on the tibial tuberosity and fibular head, and adding medial joint markers to the elbow, knee, and ankle. The BP would occlude several markers placed on the subject's anatomy, so we placed the following markers on the BP: thigh cluster (four markers), knee (medial + lateral markers), and fibular head. It is possible that relative motion between the BP and subject's leg could cause tracking errors. Three additional markers were placed on the BP to define the line of action of the clutched spring. The BP's modified College Park Venture foot has a defined axis of plantar-dorsiflexion at the ankle, aiding in precise marker placement. Full three-dimensional motion capture and ground reaction force data were collected, in addition to the clutch on–off signal, BP spring force, and pylon axial force.

The subject then donned the BP, and a certified prosthetist adjusted the fit of the device. Foot alignment and rear bumper preload was adjusted to suit the patient's comfort and optimize their walking gait. After a static trial was recorded (Fig. 4), we determined the subject's self-selected walking speed by having the subject walk on the treadmill at a slow speed (0.5 m/s) and then increased or decreased speed in increments of 0.1 m/s at the subject's request until they perceived the walking speed to be representative of their self-selected over ground walking speed. This speed was then used for all subsequent walking trials.

Fig. 4
Fig. 4
Close modal

The different walking conditions are summarized in Table 1. First, the participant walked on the BP in its unpowered mode. In this condition the clutch never locked, so only the passive effect of the device and recoil spring was measured. Next, the BP was powered (clutch locking occurred), and the participant walked with a low-stiffness (k = 1.85 N/mm), a medium-stiffness (k = 3.7 N/mm), and a high-stiffness (k = 10.5 N/mm) spring, consecutively. Stiffness was varied by physically changing out the spring component between walking conditions. The springs were tested in order from weakest (low-k) to strongest (high-k) to give the participant time to acclimate to the new device and the gradually larger torques that it produced across their knee and ankle. Data were collected until five successful 10 s trials were completed under each condition. Successful trials were defined as walking in steady-state, centered on the treadmill, with each foot contacting only one force plate. This required 3 to 5 min of ambulation per condition. While collecting gait data with the different spring stiffnesses, the subject was asked about their preference for one spring compared to another, and to describe their perceptions of the device. Once five successful 10 s trials were collected under each condition, the data collection session ended and the subject's prescribed prosthetic foot was replaced.

Table 1

Description of walking test conditions

ConditionDescription
BP: recoilWalking at self-selected speed, wearing BP with just the recoil spring active (no clutch locking)
BP: low-kWalking at self-selected speed, wearing BP with low stiffness spring
BP: medium-kWalking at self-selected speed, wearing BP with medium stiffness spring
BP: high-kWalking at self-selected speed, wearing BP with high stiffness spring
ConditionDescription
BP: recoilWalking at self-selected speed, wearing BP with just the recoil spring active (no clutch locking)
BP: low-kWalking at self-selected speed, wearing BP with low stiffness spring
BP: medium-kWalking at self-selected speed, wearing BP with medium stiffness spring
BP: high-kWalking at self-selected speed, wearing BP with high stiffness spring
The motion and ground reaction force data was processed in Vicon, then opensim [19] was used for further analysis. A subject-specific model was created in the Scale Tool using the static trials and a generic model [20] with modified mass and inertial properties to match a transtibial amputee.2opensim's Inverse Kinematics and Inverse Dynamics tools were used to compute joint angles and joint torques [19]. For the trials in which the subject wore the BP, inverse dynamics was performed twice: once with the ground reaction forces applied, and once where both the ground reaction forces and the measured BP spring forces were applied. Net torque is determined in the first inverse dynamics result; it is defined as the summed total moment at a joint, which would include both the BP spring and muscle forces. The difference in joint torques between these two sets of inverse dynamics calculations is considered the joint torque applied by the BP spring. Peak BP spring ankle plantarflexion torque and peak BP spring knee flexion torque were calculated, and reported as a percentage of the peak net torque at the joint for each gait cycle. Additionally, the work that the BP spring did on the knee or ankle was calculated as the sum of the BP spring torque, $τBP$, times the change in angle, $θ$, for each time-step
$W= ∑i=n1n2−1τBP,i*(θi+1−θi)$
(1)

Because the BP spring was only active for a fraction of the gait cycle, BP work calculations were limited to the time window when the clutch was locked, represented by $n1$ and $n2$ in Eq. (1).

## Results

One female subject walked on the BP at a self-selected walking speed of 0.5 m/s, and chose to lightly use the handrail at all times. The handrail was not instrumented, and its use may have had a small effect on kinetic results. Results from the analysis of her gait include the mechanical function of the device, BP contribution to net joint torque, work at the knee and ankle, and affected-limb joint kinematics and kinetics.

### Device Mechanical Function.

The BP functioned mechanically as expected, producing torques at both the knee and ankle joints over approximately the same window of the gait cycle (GC) as estimates of GAS force production [5] (Fig. 5). The peak BP spring force occurred at 39% GC, which is close to the estimated GAS peak at 40% GC [5]. The clutch locked shortly after heel strike, at 13% GC and spring force production began shortly after, at approximately 15% GC (Fig. 5). Device function is insensitive to the timing of locking the clutch because the BP spring will not start producing force until the minimum distance between the proximal and distal attachment points is reached, which occurs closer to 20% of the gait cycle. Thus, for proper BP function, the clutch can be locked anytime between heel strike and minimum biarticular distance near 20% of the gait cycle. After the minimum distance is reached, the BP spring is stretched and produces force as the distance between the proximal and distal attachments is increased with typical gait kinematics. Due to normal knee and ankle kinematics, the BP spring force naturally falls to zero before toe off (61% GC).

Fig. 5
Fig. 5
Close modal

### Biarticular Prosthesis Contribution to Knee and Ankle Torque.

Figure 6 shows the contribution of the BP spring torque to the net joint torque at the ankle and knee. As spring stiffness increased, the BP spring contributed more torque at both the knee and ankle joints. The BP spring torque contribution is much larger at the knee than at the ankle. The medium-k and high-k spring resulted in a larger peak BP spring torque than the peak net knee torque, suggesting that the higher spring stiffnesses may have too large an effect for this user. The step-to-step variation in net knee joint torque was much higher than at the ankle. The recoil spring alone showed nearly 10% of the peak joint torque at the knee.

Fig. 6
Fig. 6
Close modal

### Work Transfer.

The average work that the BP spring performed over a gait cycle on the ankle and knee is presented in Fig. 7. In each condition, BP ankle work was negative, and BP knee work was positive. This indicates that the ankle did work on the spring, and the spring did work on the knee, resulting in a net energy transfer from the ankle to the knee. BP ankle work increased in magnitude as spring stiffness increased. BP knee work was largest in the medium-k spring condition, and the high-k spring showed the highest variability at the knee.

Fig. 7
Fig. 7
Close modal

### Joint Kinematics.

Average lower-limb kinematics for the amputated limb are shown in Fig. 8. All BP spring conditions showed similar kinematic and kinetic results. As spring stiffness increased, there was a trend of decreasing knee extension and increasing hip flexion in late stance.

Fig. 8
Fig. 8
Close modal

## Discussion

The BP functioned reliably and as expected. The quasi-passive clutched spring design delivered torques up to 0.22 N·m/kg at the ankle and 0.38 N·m/kg at the knee (19.6 N·m and 33.6 N·m, respectively). The quasi-passive design uses relatively low power to achieve these forces. The clutch used 8.7 W only when locked, and the microprocessor used a constant 0.5 W. This results in an average power consumption of 5.15 W, which is a fraction of other powered devices [21].

Preliminary results show promising trends in BP torque contribution and BP spring work. BP torque contribution increases with spring stiffness, despite slight variations in kinematics at the knee and hip. The medium-k and high-k springs generated a larger knee flexion moment than the peak net flexion moment, which indicates that knee extensors were active and working against the BP springs. The BP spring design has a large knee moment arm, and this can be modified in future device designs to reduce this effect. The BP did negative work at the ankle and positive work at the knee, which indicates a net energy transfer from the ankle to the knee. Since GAS contributes substantial power to toe off, we hypothesized that the spring would transfer work from the knee to the ankle. Further study is needed to understand the direction of work transfer, and the role of biarticular components at the knee and ankle.

In the high-k condition, the BP spring produced the highest torque (Fig. 6), but did less work at the knee than in the medium-k condition (Fig. 7). This can be attributed to the difference in knee kinematics between walking conditions, as the high-k condition showed the least angle change during late stance (Fig. 8). Since work is the integral of torque times change in angle (Eq. (1)), this fairly constant knee flexion results in lower work values, despite the higher torque.

The current design of the device has a much larger moment arm at the knee than at the ankle, which does not match GAS anatomy [20]. This has created a larger torque effect at the knee than at the ankle, and potentially caused both the ankle-to-knee work transfer direction (Fig. 7) and the variation in knee kinematics during late stance phase (Fig. 8). The reduced late-stance knee extension trend is a deviation from nonamputee walking, which is likely undesirable as it requires higher knee extensor torques and reduced BP knee work at higher spring stiffness. Future work will focus on altering parameters such as the knee and ankle moment arms and BP spring stiffness to improve work transfer and optimize BP torque contribution to the ankle and knee.

This device contributes a coupled knee and ankle torque through the clutched-spring, as GAS does in nonamputee gait. Compared to traditional passive transtibial prostheses, the BP design is substantially different because it provides assistive knee torque. In contrast, commercially available transtibial prostheses are all uniarticular in nature. Optimizing and coupling the knee and ankle torques may decrease gait asymmetries and reduce the difficulty of amputee gait. When asked about spring preference, the participant preferred the high-k spring when walking. While walking on the treadmill with the high-k spring, she said, “I feel more help in lifting my heel at the end of my stride,” and that “It feels like I'm walking normal.” It is difficult to compare the BP outcomes to other transtibial prostheses that impact both the knee and ankle, as all are still in early development. Qualitative subject feedback indicates that stiffer springs made walking feel more natural, which may correspond to a similar reduction in effort.

Further work is necessary to delineate the effects of the device on gait kinematics and kinetics, and to develop the design. Optimization of the moment arms at the ankle and knee as well as the BP spring stiffness for each subject may allow the BP to improve gait outcomes beyond what was found with the tested device. It remains unclear how additional participants would walk with the BP, and if their spring preferences would be the same as this participant. Furthermore, as most amputees have been without a functioning GAS for years, we believe training may be necessary for users to get the most benefit from the device. Additionally, the current iteration of the BP is heavy and restricting, and these issues will need resolution in future designs, as it has been shown that adding weight to a prosthesis, even proximally, can negatively affect metabolics [22].

## Conclusions

The results from this test offer insights into device operation and may shed light on paths to future device optimization. Our next steps will be to continue to study the BP with additional prosthesis users and examine other outcome measures. The quasi-passive design has the potential to efficiently replicate GAS function for individuals with transtibial amputation, which may reduce their walking effort and improve quality of life.

## Acknowledgment

This work was supported in part by the Department of Veterans Affairs Research Rehabilitation and Development grants RX002130, A9243C, and RX002357. In addition, Krista Sanchez and Ava Segal provided valuable assistance with data collection and processing procedures. Some conference travel funds were provided by University of Washington's Graduate & Professional Student Services (GPSS).

## Funding Data

• Department of Veterans Affairs Rehabilitation Research and Development (Grant Nos. RX002130, A9243C, and RX002357; Funder ID: 10.13039/100000738).

• University of Washington's Graduate & Professional Student Services (GPSS; Funder ID: 10.13039/100007812).

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