Emulating the Effective Ankle Stiffness of Commercial Prosthetic Feet Using a Robotic Prosthetic Foot Emulator

When prosthetists and prescribing physicians select a prosthetic foot for an individual with a lower limb amputation (LLA), they must integrate a variety of information to choose one that will best suit the person's abilities and functional goals. For example, clinicians use findings from the physical examination of the individual, knowledge of prosthetic foot features and biomechanics, and familiarity with specific prosthetic feet [1–5]. The hundreds of commercial foot models with varying geometries, material properties, features, and costs, make foot selection complex [3–7]. Furthermore, while there is an abundance of comparative studies aimed at evaluating individual prosthetic foot models, reviews on the topic have determined that existing scientific evidence is insufficient for establishing criteria to guide the prescription of prosthetic feet [5,8–10].

Decision-making processes for selecting a prosthetic foot rely primarily on clinician judgment [2]. Consequently, persons with LLA who receive a foot may seldom be aware of potential options or be offered a chance to participate in this aspect of their care [1,11,12]. In addition, there are often limited opportunities for them to provide experiential input into the decision by evaluating different types of prosthetic feet. Ideally, clinicians would have methods allowing people with LLA to play a more prominent role in providing input into prosthetic foot selection based on the relative impact of foot performance on outcomes that are meaningful to them [13,14].

One approach for incorporating patient experiential preference into prosthetic foot selection would be to allow patients to trial different feet. Presently, clinicians could purchase multiple feet and allow a patient to try each foot for a short period of time, returning ones that are not selected. However, this approach is often not feasible (e.g., it requires substantial time and effort for the clinical practice to manage inventory and for the clinician as many feet have different build heights that require customized adjustment for the user's prosthesis) and does not allow for immediate, back-to-back comparisons among feet. Another potential approach could be to use a robotic prosthetic foot emulator (PFE) to mimic the mechanical performance of different commercial prosthetic feet. Although there are also some limitations to this approach (e.g., cost of the system and constraining the prosthesis use to in-laboratory or in-clinic activities), use of a PFE has the potential to facilitate rapid testing of different prosthetic feet in a single session. However, assessing the feasibility of emulating commercial prosthetic foot properties using a PFE would be a necessary first step toward using a PFE to facilitate short-term trials of different feet.

A PFE enables systematic exploration of foot-ankle biomechanical variables [15–18]. Thus, a PFE could permit quick trials of multiple feet by selecting corresponding emulated mechanical property foot profiles that have been programmed into the PFE software (e.g., choosing a foot model, size, and stiffness category from a drop-down menu selection) and making straightforward hardware adjustments to the prosthesis end effector (e.g., adding mass to emulate the inertial properties of the commercial foot) while avoiding more time-consuming prosthetic adjustments between commercial prosthetic feet (e.g., adjusting the prosthesis length to accommodate feet with different build heights) [19–21]. This is relatively quick and obvious compared to switching between actual prosthetic feet, which requires changing pylon componentry and reestablishing prosthetic alignment, steps which require iteration on the part of the clinician or technician. Instead, the PFE could be configured to the user's prosthetic leg length and static alignment once and the prosthetist could focus on dynamic alignment adjustments only, as needed, between emulated prosthetic feet. A PFE has been used previously to test experimental ankle push-off foot conditions in people with LLA [15–17,22,23]. However, emulation of commercial feet is a novel undertaking, requiring first that the properties of prosthetic feet be measured and then used as input for a PFE to mimic the stance phase behavior of the feet during walking.

Although various mechanical properties describe prosthetic foot behavior, foot stiffness properties have often been associated with changes in gait mechanics, prosthetic foot preference, and energy efficiency in people with LLA [24–31]. In contrast to the biological ankle-foot, the majority of commercial prosthetic feet have fixed stiffness properties determined by their material composition and shape. Across types of commercial prosthetic feet, a wide range of stiffnesses have been observed [20,32–39]. Previous studies have demonstrated the effects of forefoot stiffness, in particular, on prosthesis user gait [24,25,27,29–31]. For example, a less stiff forefoot has been correlated with improved energy storage and return [26,27,29] and increased prosthesis ankle peak push-off power and work [40,41]. However, an overly compliant prosthetic forefoot may be associated with increased intact knee loading [28,29,31] or necessitate gait compensations due to a “drop-off” effect in late stance [27]. These examples of tradeoffs illustrate the importance of matching the prosthetic foot stiffness properties to the functional abilities and goals of the prosthesis user. Given the importance of prosthetic forefoot stiffness for walking in people with LLA, we elected to emulate the effective stiffness of commercial prosthetic feet (i.e., relative to a PFE's fixed axis of rotation).

Commercial prosthetic foot stiffness properties can be measured by collecting kinematic and kinetic data of a person walking with a foot [15,42,43]. However, gait deviations and user-specific gait compensations are commonly observed in people with LLA, which could confound the measurement of foot stiffness properties due to individual factors [44,45]. In contrast, mechanical testing offers a quicker and more controlled method for collecting data on prosthetic foot properties independent of the user.

The purpose of this study was to develop a procedure by which a PFE could be configured to emulate the effective angular stiffness of commercial prosthetic forefeet in a user-independent manner. The secondary aim of this study was to assess the accuracy of these commercial prosthetic foot emulation methods. We hypothesized that the emulated effective ankle stiffness would be significantly associated with the corresponding commercial prosthetic forefeet effective ankle stiffness. Second, we hypothesized that the magnitude of difference between emulated and commercial forefoot effective ankle torque at different ankle angles would be independent of factors such as type of prosthetic foot, foot size, or expected user body weight (e.g., load).

The PFE (Caplex system; Humotech; Pittsburgh, PA) is a single-axis (one-degree-of-freedom [DoF]) robotic prosthetic foot with an actuated keel to control forefoot stance behavior in the sagittal plane (Fig. 1) [15,16]. The heel component of the PFE is a passive fiberglass composite strut that is similar to conventional prosthetic feet. The sensors include a single-axis load cell (i.e., measuring torque) and an angle encoder (i.e., measuring ankle angle position). Actuation of the forefoot about the ankle axis is accomplished using an off-board actuator unit located behind the user [16]. Accordingly, the PFE is restricted to in-laboratory use on a treadmill or similar equipment. The control unit reads data from the sensors integrated within the foot and sends motor velocity commands to the actuator unit, permitting ankle torque control during forefoot loading.

The PFE foot uses a standard four-hole male pyramid adapter on its proximal surface, allowing it to connect to a user's prosthetic socket using typical endoskeletal components. The build height of the PFE (11.3 cm (4.4 in.)) is comparable to low-profile commercial feet. The PFE end effector is designed to be used without a shoe. The PFE contains several interchangeable hardware components, including the forefoot module length, which has four possible configurations in 1 cm increments (e.g., 26–29 cm). Prosthetic feet have differing roll-over characteristics (i.e., effective foot lengths), which can be described by the dynamic progression of the center of pressure (COP) during stance phase [46,47]. Thus, the length of the PFE forefoot module for each emulated foot was configured to match the effective foot length of the corresponding commercial feet.

Prosthetic ankle torque (τ_ank) of the PFE is controlled as a function of angle (θ) (i.e., angular stiffness) [15,16], which describes the dependence of effective ankle torque on the angular progression of the pylon as the foot undergoes loading. This characterization of ankle behavior is commonly used to reproduce the stance phase mechanical performance of commercial feet [48,49]. The desired ankle torque (τ_ank,_des) is calculated based on the ankle angle position. Ankle motor command velocities are then sent from the motor driver using proportional control of torque [15]. This input allows the PFE to be responsive to user loading and walking behavior while continuously emulating the ankle torque of a commercial foot depending on the user's ankle angle position. Adjustments made in the control software interface are responsible for altering the ankle torque properties for an emulated forefoot, using reference data from the respective commercial prosthetic foot during stance phase [15]. A finite state-machine control architecture is used to dictate PFE behavior, including discrete transitions between stance and swing phases of gait.

Five commonly prescribed commercial foot models (Table 1) were selected for input to the PFE to represent a range of prosthetic feet that may be appropriate for a variety of user mobility levels. Four common foot sizes (i.e., 26–29 cm) for each prosthetic foot model were included to accommodate different users. In addition, all manufacturer-determined stiffness categories intended for user body weights between 58–115 kg (125–250 lbs) were tested for each foot model and size. Therefore, a total of 88 prosthetic feet were mechanically tested to build a library of reference data for the PFE.

Trajectory-based displacement control was used to apply uniaxial, quasi-static loads to each prosthetic foot using a 6DoF R2000 Rotopod parallel robot (Mikrolar, Inc.; Hampton, NH) with a vertically mounted loading plate on its top surface (Fig. 2). The prosthetic feet were attached to the steel frame of the R2000 and remained stationary throughout testing. Custom software was used for position control of the R2000 to load and unload the forefoot with the loading platform. Each foot was shod with its corresponding foot shell (including a Spectra sock, if applicable). A standardized, heel-height appropriate shoe in the respective size (Model MW577; New Balance; Boston, MA) was donned to mimic clinical use and to incorporate properties of footwear into the measured data since the PFE is designed to be used without a shoe. The plantar surface of the shoe was covered in a low-friction film interface to mitigate the effects of tangential shear forces and prevent over-constraining the system during testing (i.e., Shear-ban, Tamarack Habilitation Technologies; St. Paul, MN) [50].

A six-axis load cell (MC3A, AMTI; Watertown, MA) was mounted in-line with the prosthetic foot to collect force and moment data (i.e., using a 32 mm double-ended female pyramid prosthetic adapter). An 8-camera motion capture system (Vicon Motion Systems Ltd.; Centennial, CO) surrounding the R2000 s frame was used to track the motion of the foot and R2000 during testing, with respect to the load cell sensor origin local coordinate system. Reflective markers were placed on the loading platform, the prosthetic foot and shoe, and the load cell. A voltage trigger synced the load cell and motion capture system data collection.

All testing was performed at a discrete pylon progression angle (i.e., +20 deg to simulate forefoot unloading) by orienting the loading platform relative to the foot (Fig. 2). The +20 deg pylon progression orientation was determined to be the minimum angle that isolated the forefoot properties of the prosthetic foot under full simulated body weight loading conditions. The platform was displaced along a single axis in the direction of the pylon toward the mounted foot at a constant rate of 20 mm/s (i.e., the fastest possible system rate). Each foot was loaded to a threshold representative of 1.2 times the maximum manufacturer-specified user body weight for each foot (Table 1) to simulate the typical ground reaction force experienced in late stance during walking [36,51]. Each foot was loaded and entirely unloaded for six consecutive cycles. The first three loading cycles were treated as preconditioning and discarded. Data from the final three loading cycles were averaged and used to calculate effective ankle stiffness of the commercial prosthetic feet based on the COP trajectory relative to the PFE axis of rotation using custom software (matlab 2019; MathWorks, Natick) (see Supplemental Material on the ASME Digital Collection). During testing, marker position data were collected at 200 Hz and smoothed using a fourth-order Butterworth filter with a cutoff frequency of 50 Hz. Load cell force and moment data were collected at 1000 Hz and resampled at 200 Hz, and no filtering was applied to these data.

A quadratic Bezier curve was fit to each foot's data to convert experimentally derived effective ankle torque-angle data into a continuous function of effective ankle stiffness representing an emulated “foot profile” for each commercial foot (i.e., model, size, stiffness category) (see Supplemental Material on the ASME Digital Collection). A Bezier curve is a multivalued, parametric function that follows the shape of a defining polygon. The convex hull property of Bezier curves makes them well-suited for smoothing trajectories in nonlinear robotic control systems [52–56]. In this study, the Bezier curve parameters permitted a continuous function of nonlinear ankle torque-angle data for robotic control of the PFE. A quadratic Bezier curve relies on three control points (i.e., P₀, P₁, and P₂). The control points were determined according to the following constraints: P₀ was defined at the minimum load and neutral (i.e., zero) ankle angle, P₂ was defined at peak load and peak dorsiflexion angle, and P₁ determined the concavity of the Bezier function and was defined at a perpendicular distance from the bisection of P₀ and P₂ and was adjusted to match the radius of nonlinear curvature (via the shape parameter). Increasing the shape parameter expanded the width of the polygon and, therefore, the concavity of the Bezier curve. Least-squares were used to optimize the fit of the Bezier curve to each foot's experimental effective ankle torque-angle data (see Supplemental Material). The set of Bezier curve parameters that provided the best fit to the commercial data of each foot (i.e., minimal residual error) were kept and applied within the PFE's finite state-machine controller to determine the effective ankle torque behavior of the emulated foot profiles [15].

The mechanical testing procedures described above were repeated using the PFE programmed to emulate the individual commercial feet to determine the correlation between emulated feet and the respective commercial prosthetic feet. Twenty of the 88 total emulated prosthetic feet were selected for validation testing. Feet in the validation subset included all five types of commercial feet in two sizes (i.e., 26 and 27 cm). Additionally, within each foot type and size combination, two stiffness categories were selected based on different example user body weights (i.e., 79.4 kg and 90.7 kg, or 175 and 200 lbs). These feet and stiffness categories were chosen to reflect a range of PFE hardware and software configurations, as well as to evaluate the effect of possible sources of error (e.g., foot size) on the accuracy of the emulations.

The PFE was attached in-line with the load cell using the same prosthetic adapter and aligned neutrally in all planes using the same techniques as the commercial feet. Per design, the PFE was not tested with footwear. In addition, the same low-friction film used in testing commercial feet was attached to the plantar surface of the PFE to mitigate shear forces imposed between the force plate and the tread of the PFE to avoid over-constraining the system. In preparation for each emulated foot test, the PFE was configured with the appropriate forefoot length. The respective Bezier curve reference data were then selected within the software, and the PFE motors were enabled with the controller.

The same testing equipment (i.e., R2000 and loading platform, MC3A load cell, and 8-camera Vicon motion capture system) used during commercial foot testing were used for emulated foot testing. Reflective markers were placed in the same locations on the loading platform and the load cell. The locations of reflective markers on the PFE were intended to be similar to the commercial feet, though they differed slightly based on the absence of a shoe. All testing was performed at the same +20 deg pylon progression angle by orienting the R2000 loading platform relative to the PFE (Fig. 2(c)).

Linear mixed-effects regression was used to assess the association between emulated foot effective ankle torque and commercial foot effective ankle torque at a given ankle angle position, with prosthetic foot modeled as a random effect (see Supplemental Material on the ASME Digital Collection). Likelihood ratio tests were carried out to assess the mean correlation between emulated and commercial feet ankle torque. Results were summarized as the slope of change across±standard error (SE), 95% confidence intervals (CI), and marginal R-squares (R²). Approximate effect sizes were computed for each coefficient by dividing the coefficient by the product of the standard error and square root of the total sample size. All analyses were carried out using R 4.0.2 [57] and packages lme4, lmertest, and emmeans.

Bland–Altman Limits of Agreement were computed and Bland–Altman plots were created to visualize the extent of agreement between emulated and commercial foot measured torque further (see Supplemental Material) [58,59]. The limits of agreement were defined as the mean differences between conditions (i.e., mean bias)±the square root of total variance, with consideration for repeated measurements within each foot. The differences between corresponding pairs of measurements were plotted on the y-axis, and the means of corresponding pairs of measurements were plotted on the x-axis. All analyses were carried out using R 4.0.2 [57], and packages redres, lme4, and blandaltmanleh.

Linear mixed-effects regression was also used to assess the difference between emulated and commercial feet and to evaluate what factors predicted the magnitude of the difference between emulated and commercial feet (see Supplemental Material on the ASME Digital Collection). Effective ankle torque differences between the commercial forefeet and respective emulated foot were calculated across the loading range. Ankle angle position was treated as a fixed effect in the model to determine whether the agreement between emulated and commercial foot angular stiffness differed based on the region of the ankle torque-angle curve. Likelihood ratio tests were carried out to assess if the mean difference in ankle torque between emulated and commercial feet differed from zero and to test for variability in slopes across foot types, sizes, or intended user body weight. Results were summarized as the slope of change across±standard error (SE), 95% CI, and marginal R-squares (R²). All analyses were carried out using R 4.0.2 [57], and packages lme4, lmertest, and emmeans.

All 88 commercial prosthetic feet exhibited nonlinear stiffness behavior during forefoot loading and unloading and a range of effective ankle angular stiffness was observed across the different commercial feet (Fig. 3). For example, some feet had substantially lower overall effective ankle stiffness (as demonstrated by more displacement under similar loads or less steep slopes in the ankle torque curves). There was a general increase in angular stiffness across manufacturer stiffness categories for all feet (i.e., feet from higher categories had stiffer forefeet).

Least-squares optimization of the Bezier curve control points to minimize the root-mean-square error (RMSE) in the parameterization resulted in all Bezier curves having R² values greater than 0.99 (Fig. 4). On average, the R² of the Bezier curves compared to the plotted commercial foot stiffness data were 0.998±0.001 across all foot types, foot sizes, and user body weights.

The mean difference in effective ankle stiffness between emulated and commercial prosthetic feet was –0.76±1.73 Nm/deg (–1.0±2.5%) across all ankle angles for all foot types, foot sizes, and stiffness categories (Fig. 5, Table 2). Across types of prosthetic feet, the range of differences in effective ankle stiffness between emulated and commercial feet was –1.75 ± 2.07 Nm/deg (i.e., for the Walk-tek) to +0.32 ± 1.39 N·m/deg (i.e., for the AllPro). A negative difference (i.e., commercial-emulated) indicated the commercial foot effective ankle stiffness had a smaller magnitude, on average, than the respective emulated foot at a given ankle angle.

Commercial foot effective ankle torque was significantly correlated with emulated foot effective ankle torque (p <0.001) (Table 1 available in the Supplemental Materials on the ASME Digital Collection). For each 1 N·m increase in commercial foot ankle torque, there was an estimated increase of 0.96 N·m in emulated foot ankle torque, holding all else constant. Ankle angle was also significantly correlated with emulated foot effective ankle torque (p <0.001) (Supp. Table 1). For each standard deviation (SD) increase in ankle angle (with higher values representing greater dorsiflexion), there was an increase of 3.04 N·m emulated foot ankle torque, holding all else constant, demonstrating greater ankle torque under greater forefoot deflection. Furthermore, the two-way interaction was significant, indicating that the relationship between commercial and emulated effective ankle torque depends on the ankle angle position during loading. To understand the nature of this interaction, model-implied values were computed for five levels of ankle angle position (–2 SD, –1 SD, mean, +1 SD, and +2 SD) across a range of commercial ankle torque values (0–120 N·m). As shown in Fig. 6, the interaction was disordinal, with the least amount of difference between emulated and commercial ankle torque near the midrange of ankle torque (approximately 60 N·m, on average). Larger magnitude differences were observed near the extreme ends of ankle torque (near zero and peak torque) but in equal and opposite directions depending on the ankle angle.

Bland–Altman analysis was conducted to quantify the agreement between the emulated and commercial foot effective ankle torque measurements (see Supplemental Material). Diagnostic plots were evaluated for violation of normality assumptions. A mean bias of 0.76 N·m/deg in ankle stiffness between the commercial and emulated device conditions was observed. The 95% CI for estimated limits of agreement was –3.12 to +3.67 N·m. Bland–Altman plots were created for each prosthetic foot to complement the numerical results, displaying the between-device differences in ankle torque against the mean ankle torque to visualize the spread between emulated and commercial foot properties (Fig. 7).

Ankle angle was significantly correlated with differences in ankle torque measurements between devices (p <0.001) (Supp. Table 2). In contrast, none of the prosthetic foot-level predictors (i.e., foot type, foot size, intended user body weight) were significantly associated with differences between emulated and commercial angular stiffnesses.

The purpose of this study was to develop and validate a procedure by which a PFE could be configured to mimic the effective ankle angular stiffness of commercial prosthetic forefeet. Overall, the methods presented in this study led to an accurate (within <5%) estimation of commercial prosthetic effective ankle stiffness using the PFE at a pylon progression angle representative of late stance phase (i.e., +20 deg).

The Bezier curves provided an effective method for parameterizing the experimental effective ankle torque-angle data from each commercial prosthetic foot into continuous functions for input to the PFE. The use of least-squares optimization to fit the Bezier curve functions to commercial foot data minimized the RMSE to improve fit of a representative polynomial, similar to optimization methods used in previous studies of ankle stiffness [27,49,60,61]. For example, Adamczyk et al. [49] estimated angular stiffness of prosthetic feet using a linear representative model and reported an R² value of 0.95 with an RMSE of 4.1 N·m/deg between estimated and observed values [49]. In contrast, use of nonlinear Bezier curves in this study resulted in R² values exceeding 0.99 for the angular stiffness data from all tested commercial prosthetic feet and the RMSE was reduced to 0.52 N·m/deg. However, the Bezier curve fitting methods used in this study had limitations. For example, optimizing the Bezier curves based on RMSE values did permit errors in the data fit across the loading range so long as they were counterbalanced. Additionally, the Bezier curve functions defined in this study were quadratic, which constrained the DoF available to optimize each curve. Specifically, the location of P₁ (i.e., where the shape parameter is applied) was dependent on the location of the other two points since it was restricted to the midpoint between P₀ and P₂. In this study, the position of P₀ was allowed to vary within a limited range to improve the alignment of P₁ with respect to the commercial foot data. It was expected that slight differences between the minimum point of the Bezier curve and the true zero ankle torque would likely be imperceptible to the user because it occurs at torque values near zero. However, future parameterization efforts may benefit from defining additional DoF (e.g., using more control points to define a Bezier polygon) to improve the curve fit for nonlinear commercial prosthetic foot data without compromising the position of P₀ (Fig. 8).

Using the Bezier curve functions as emulated prosthetic foot profiles, this study revealed close agreement in effective ankle stiffness between the emulated feet and the respective commercial prosthetic feet. Emulated foot effective ankle torque was significantly correlated with effective ankle torque of the corresponding commercial feet across ankle angles (p <0.001). On average, the emulated feet slightly overestimated effective ankle stiffness (i.e., by 0.76 N·m/deg) compared to the commercial feet. This ankle stiffness difference corresponded to a 1% difference in effective ankle stiffness between emulated and commercial feet, which is substantially smaller in percentage than the difference in prosthetic foot angular stiffness between predicted and observed values in a previous study (i.e., 5.4%) [49]. The Bland–Altman Limits of Agreement for emulated effective ankle torque relative to that of commercial feet in this study were –3.12 to +3.67 N·m, within 95% confidence [58,62]. These limits are centered around zero and substantially smaller than the total range of observed effective ankle torque values (e.g., 0–100 N·m). These findings support the accuracy of the emulated effective ankle stiffness. It is important to note that the calculated limits of agreement are estimates; thus, different commercial prosthetic feet may produce other limits. Furthermore, the limits of agreement must be compared with respect to clinically relevant differences in the outcome. There is evidence that the threshold for detecting a change in ankle angular stiffness properties is 7.7±1.3% (with 75% accuracy) for people with LLA walking with an experimental prosthetic foot [63]. Therefore, it can be reasonably assumed that a difference of 1% between the emulated and commercial forefoot is unlikely to be perceptible to the user. Importantly, the slight offset in effective angular stiffness between emulated and commercial feet was consistent across types, sizes, and intended user body weights of feet. Together, these findings support the accuracy of the emulated effective ankle angular stiffness relative to that of commercial feet.

Although the variance was small, commercial foot effective ankle torque alone accounted for more than 99% of the existing variance between commercial and emulated effective ankle stiffness before controlling for other variables. However, the interaction between commercial foot torque and ankle angle was also significant, suggesting that the correlations between emulated and commercial feet varied depending on how dorsiflexed the foot was under load. Examining this disordinal interaction revealed that differences in torque did not uniformly increase or decrease with ankle angle position but had a more nuanced relationship (Fig. 6). The largest differences were exhibited in opposite directions and at the extremes in ankle angle, while differences near the middle of the angle and torque ranges were smallest. Examinations of the Bland–Altman plots were consistent with this interaction effect, with larger mean differences observed at effective ankle torque extremes for all prosthetic feet. Given that the emulated feet are based on Bezier curves fit using least-squares optimization, as noted above, the nature of the curve fitting process (i.e., minimizing total RMSE) may explain this disordinal interaction. For instance, least-squares methods permit larger error values near the curve ends as long as the overall difference is balanced in the opposite direction across the range of ankle angles. The results in agreement demonstrated in this study reflect a particular PFE configuration (i.e., hardware and software control logic). Future research should include refining both PFE hardware and control schemes as next steps in assessing the feasibility of using a PFE with prosthesis users.

Mechanical testing requires making decisions regarding multiple variables, which may affect the resulting measurements of prosthetic foot stiffness properties. For instance, in this study, testing was limited to a single pylon progression angle to collect effective ankle stiffness data on commercial prosthetic feet. This 20 deg pylon orientation was selected to isolate the forefoot properties of commercial prosthetic feet because the PFE only actuates the forefoot section. Further, this pylon progression angle is consistent with published testing guidelines and previous mechanical testing studies [44,51]. While loading feet at a single pylon progression angle is not congruent with physiological loading during gait, standardized mechanical testing protocols ensure consistency across prosthetic foot models and permit direct comparison between feet irrespective of individual gait patterns or deviations.

Commercial foot effective ankle stiffness measured at a single pylon progression angle also may not be representative of stiffness at other stance phase pylon progression angles. Stiffness measurements taken at a 20 deg orientation correspond to late stance properties and likely underestimate the stiffness of prosthetic feet at smaller pylon progression angles. For example, at progression angles nearer midstance, the COP does not have such a large radius to impart deflection of the forefoot under load since both the heel and forefoot are undergoing loading. These changes in angular stiffness across stance phase (i.e., stiffer behavior observed in midstance compared to late stance) have been observed in previous mechanical testing studies of commercial prosthetic feet [36,44]. Thus, future mechanical testing to characterize effective ankle stiffness of prosthetic feet could ideally include loading and unloading across stance phase pylon progression angles. Additionally, future development of PFEs would benefit from including actuation of the heel component to permit emulation of ankle stiffness across the entire stance phase and incorporating prosthetic foot properties in multiple planes (i.e., coronal and transverse, in addition to sagittal).

Another choice to be made with mechanical testing methods is the use of either force- or position-control when collecting data. In this study, we used position-control, however, force-control methods are common in previous studies [38,39,44,51]. Position-control has the potential limitation of stiffness behavior being influenced by the maximum load. Future work should explore how force-control methods compare for collecting commercial foot effective ankle stiffness data to program a PFE.

Another mechanical testing procedural decision that needs to be made is the choice of whether or not to test feet shod. The prosthetic feet in this study were tested within their respective cosmetic foot shell and shod with standardized heel-height appropriate walking shoes. Thus, the mechanical properties measured in this study include the interaction with the footwear. This decision was purposeful to mimic intended clinical use (i.e., feet are designed for use inside a shoe) since the PFE is not used with a shoe. The same shoe was used within feet of the same foot size and the same model shoe in different sizes was used across foot sizes. Therefore, the relative offset between measured stiffness of commercial prosthetic feet was considered negligible across foot models for a given user since they were collected with the same shoe. However, the effective ankle stiffness used to program the PFE in this study may not generalize to different types of shoes that a person with LLA might prefer to use with their prosthetic foot in practice (e.g., shoes with less heel height or more rigid soles) [44].

Finally, while the results of this study only generalize to populations of commercial prosthetic feet similar to those used in this study, the tested feet were selected to represent a range of commonly used prosthetic foot technology (e.g., flexible feel, energy-storage and release, extended keel). Additional types of prosthetic feet should be tested in the future to expand the library of commercial feet available for emulation, including those feet with properties designed to vary across stance phase using hydraulic or microprocessor technologies.

The methods used to compare the effective ankle angular stiffness of emulated and commercial feet relied on replicating the original mechanical testing setup as a means of validation. Although we demonstrated high accuracy of emulation under these mechanical testing conditions, it is unclear whether emulation accuracy would remain consistent across clinical use scenarios (e.g., throughout the gait cycle while a person with LLA is walking). Therefore, additional testing is needed to assess the correlation between emulated and commercial feet when users are walking with a PFE. Furthermore, future studies capturing the user's perceptions of the experience walking with emulated feet compared to commercial feet, in a blinded fashion, would inform aspects of emulation and the feasibility of using a PFE to quickly trial different prosthetic feet for people with LLA.

We developed a procedure by which a PFE was configured to mimic the effective ankle stiffness of commercial prosthetic forefeet in a user-independent manner. We used mechanical testing procedures to collect data on five types of commercial prosthetic feet across a range of foot sizes and user body weights. The Bezier curve functions we defined provided an effective method for parameterizing the respective experimental commercial foot data and enabled input to the PFE. Configuring the PFE to mimic a subset of corresponding commercial prosthetic feet and replicating the mechanical testing procedures revealed close agreement in effective ankle torque-angle data between the emulated and commercial feet under replicated testing procedures. While future research is needed to expand mechanical testing, assess user-based comparisons of emulated and commercial prosthetic feet (e.g., self-reported and biomechanical measures), and compare the potential use of a short term foot trials using the PFE compared to commercial feet, the findings from this study suggest that commercial prosthetic foot properties can be effectively mimicked by a PFE. This study is an important first step toward assessing the feasibility of using a PFE to facilitate rapid trials of different feet as part of prosthetic foot prescription.

The authors wish to thank Anne Turner for her assistance in collecting the data included in this paper. Opinions, interpretations, conclusions, and recommendations are those of the author and are not necessarily endorsed by the Department of Defense (DoD). The U.S. Army Medical Research Acquisition Activity is the awarding and administering acquisition office.

• Seattle Institute for Biomedical and Clinical Research supported by the Office of the Assistant Secretary of Defense for Health Affairs, through the Orthotics and Prosthetics Outcomes Research Program (OPORP) (Congressionally Directed Medical Research Programs) (PI: Morgenroth) (Award No. W81XWH-16-1-0569; Funder ID: 10.13039/100000090).