Changes in Dynamic Mean Ankle Moment Arm in Unimpaired Walking Across Speeds, Ramps, and Stairs

Abstract

Understanding the natural biomechanics of walking at different speeds and activities is crucial to develop effective assistive devices for persons with lower-limb impairments. While continuous measures such as joint angle and moment are well-suited for biomimetic control of robotic systems, whole-stride summary metrics are useful for describing changes across behaviors and for designing and controlling passive and semi-active devices. Dynamic mean ankle moment arm (DMAMA) is a whole-stride measure representing the moment arm of the ground reaction impulse about the ankle joint—effectively, how “forefoot-dominated” or “hindfoot-dominated” a movement is. DMAMA was developed as a target and performance metric for semi-active devices that adjust once per stride. However, for implementation in this application, DMAMA must be characterized across various activities in unimpaired individuals. In our study, unimpaired participants walked at “slow,” “normal,” and “fast” self-selected speeds on level ground and at a normal self-selected speed while ascending and descending stairs and a 5-degree incline ramp. DMAMA measured from these activities displayed a borderline-significant negative sensitivity to walking speed, a significant positive sensitivity to ground incline, and a significant decrease when ascending stairs compared to descending. The data suggested a nonlinear relationship between DMAMA and walking speed; half of the participants had the highest average DMAMA at their “normal” speed. Our findings suggest that DMAMA varies substantially across activities, and thus, matching DMAMA could be a valuable metric to consider when designing biomimetic assistive lower-limb devices.

Introduction

Characterizing the biomechanics of unimpaired walking is important for effectively designing biomimetic assistive devices. To increase the usability of these devices, we must implement an understanding of how gait changes when walking at different speeds and while navigating over different types of surfaces. One class of such devices is semi-active prostheses, which are designed not to fully replace muscular joint actuation, but rather to adjust their passive properties for different tasks and movements. Such systems are particularly promising for lower-limb prostheses, where semi-active control over damping [1–6], stiffness [7–11], shape [12], and energy recycling [13,14] have been explored to add adaptability with reduced weight and power. But, how to tune such systems for the specific tasks persons undertake, such as walking on level ground, ramps, and stairs, remains an open question.

Various measures have been investigated as targets for tuning prostheses, such as ankle quasi-stiffness [15–18] ankle impedance [19–21], and lower-limb roll-over shapes [22–26]. These measures are continuous and vary throughout stance phase, making them well suited for fully robotic prostheses that can control the prosthetic foot dynamically throughout stance phase while bearing load [27,28]. However, as semi-active prostheses can only adjust once per stride when the foot is unloaded, a corresponding once-per-stride measure is needed. These devices are more similar to traditional passive prostheses, which respond according to their mechanical properties [29,30], but with the addition of adaptability. DMAMA is a promising candidate measure for application in semi-active prostheses [31,32]. DMAMA represents the moment arm of the ground reaction impulse about the ankle joint. As a whole-stride measure, DMAMA could be useful as a target for this once-per-stride adaptation, enabling semi-active devices to mimic overall control of the natural ankle. Previous work [32] found that DMAMA is sensitive to variations of forefoot stiffness in a variable stiffness prosthesis and is also sensitive to changes in terrain (ramps and stairs) [8]. Using the relationship between DMAMA and prosthesis stiffness, those findings can be combined to serve as a practical resource to inform terrain-adaptive stiffness adjustments. Biomimetic DMAMA targets may also be used in the design of diabetic footwear as it has been found that altering the stiffness of such footwear affects plantar pressure and can be individually optimized to increase user comfort [33,34]. However, DMAMA in unimpaired gait has only been characterized on level ground across speeds—not over different terrains. Therefore, to inform the control of novel lower-limb prostheses and orthoses, our research focuses on observing changes in this prospective control parameter—DMAMA—among unimpaired people when walking on ramps and stairs.

The external moment arm of force about the ankle is the ratio of ankle moment to ground reaction force; similarly, DMAMA is defined as the ratio of ankle moment impulse to ground reaction force impulse during the course of a whole stance phase. As seen in Eq. (1), since these impulses are integrated over stance phase, DMAMA can alternatively be calculated by dividing the mean sagittal ankle moment by the mean sagittal ground reaction force. DMAMA can also be understood as a summative measure that describes the ankle's control of the location of force interaction with the ground in a single value per stride. The possible range of DMAMA is approximately −0.15 (near the middle of the heel pad) to 0.55–0.60 (slightly past the metatarsal head) with a typical values falling between +0.25 and +0.45 (midfoot) [31]. While computationally simple, DMAMA is sensitive to walking/running speed in unimpaired individuals [31] and sensitive to ramp and stair climbing in individuals that use lower-limb prostheses [32].

Changes in DMAMA are conceptually related to different goals a person may have in coordinating movement, and/or the ground contact conditions under their foot. The original DMAMA study [31] observed a shift to the forefoot in running as there was a discrete jump in DMAMA values that resulted from the walking to running transition. When walking, higher speeds led to lower DMAMA values (more rearfoot). In our study on ramp walking with a prosthesis [32], walking downhill led to a more rearfoot DMAMA and walking uphill led to an increased, more forefoot, DMAMA, which was interpreted as a reflection of the mechanical interaction of a compliant device with a flat surface at different angles. In the case of natural ankles, we expect the body to choose DMAMA for some benefit or to achieve some goal, such as adding power or maintaining a margin of safety.

The purpose of this study was to analyze DMAMA in persons without amputation walking over level ground at different speeds as well as up and down ramps and stairs, to inform the design of future biomimetic assistive devices. We hypothesized that when increasing walking speed DMAMA would decrease, as observed in prior work [31]. When walking down ramps, we hypothesized a decreased, more rearfoot DMAMA due to prior observations of a direct relationship between ramp direction and ankle plantarflexor moment during stance phase [35–37]—e.g., descending a ramp results in decreased ankle plantarflexor moment. When walking up ramps, we hypothesized an increased DMAMA as more ankle power is needed to go uphill [38], requiring a larger ankle moment. On stairs, we hypothesized that DMAMA would reflect ankle torques biasing the body toward acceleration uphill (away from a dangerous fall): thus, we hypothesized an increased (more forefoot) DMAMA in stair descent and decreased (more rearfoot) DMAMA in stair ascent.

Methods

Participants.

For this study, we used data from a prior study of unimpaired walking over level ground, ramps and stairs. Ten unimpaired adults (age: 28±6 years; mass: 71±16 kg; foot length: 29±2 cm; mean±SD) provided written informed consent to participate according to approved procedures. All participants were free from orthopedic problems by self-report and visual observation. The study was granted ethical approval by the Jesse Brown VA Medical Center IRB Committee (IRB#1155354).

To determine whether this dataset was adequately powered for our proposed investigation, we performed a posthoc power analysis. Data from the original paper that reported DMAMA at different walking speeds [31] (10 participants) were used evaluate the expected number of subjects needed in a new dataset to observe changes in DMAMA. Effect size was computed on a repeated-measures basis by dividing the mean change in DMAMA from the lowest (1 m/s) to the highest (2 m/s) walking speeds by the standard deviation thereof. The effect size was −0.98, which resulted in an estimated sample size of 9 participants using Lehr's one-sample formula [39] (which assumes 80% power for a two-tailed t-test and critical α = 0.05). In addition, we performed a simulation-based power analysis using the mixedpower package in R [40,41] to estimate the number of samples needed to achieve 80% power using a linear-mixed effects model (DMAMA as the dependent variable, speed as fixed effect, and participant as the random effect). This analysis was chosen as it mirrors the statistical approach suggested in the current study. Using a t-value of 2 (critical α = 0.05), sample sizes greater than five resulted in a simulated power greater than 80%. Based on the findings of both analyses, we determined that the existing dataset of 10 participants was sufficient.

Experimental Protocol.

Participants were instructed to complete seven different activities: walking at three self-selected walking speeds over level ground (“normal” speed, N-LG; “fast,” F-LG; and “slow,” S-LG); down a five-degree ramp (DR), up a five-degree ramp (UR), down stairs (DS), and up stairs (US). When providing instructions for the different walking speeds, the “normal” speed was described as a typical walking speed, “walking down the sidewalk but not exercising.” The “slow” speed was instructed as “strolling, similar to window shopping” and “fast” was instructed as “briskly walking, similar to trying to catch a bus but without breaking into a jog/run.” All participants completed at least 7 trials in each activity, except for participant 10 whose stair trials were excluded due to faulty data. Foot length was measured using calipers, longitudinally from the heel to the toe of the foot, shod.

Data Collection Methods.

Kinematics was collected using a 12-camera motion capture system (Motion Analysis Corporation, Santa Rosa, CA). Ground reaction forces were recorded using 6 AMTI (Advanced Mechanical Technology Inc., Watertown, MA) force platforms embedded in the level walkway. To capture ramp and stair GRFs, a ramp pedestal or staircase was bolted to two of the aforementioned force plates via threaded holes. The stairway had three steps, with the last step forming a part of the top platform. Stair geometry information was translated to visual3d (C-Motion, Inc., Germantown, MD) to generate center of pressure in the correct position with respect to the participant's foot. Markers were placed on the participants according to a modified Helen Hayes marker set [42]. For this analysis, we used only lower body markers, specifically the sacral and lateral/medial malleolus markers. The ankle center was defined as the midpoint between the medial and lateral malleolus markers and used to calculate ankle moment. Data were collected at a rate of 120 Hz.

Data Analysis.

We used visual3d software to filter the kinetic and kinematic data, determine foot contact with force plates, calculate ground reaction force/moment, calculate ankle moment, and export data to Matlab (The Mathworks, Natick, MA). When filtering the data, we used a bidirectional second-order (fourth order overall) low-pass Butterworth at 25 Hz (kinetic) and 6 Hz (kinematic). We used a custom script to determine heel contact (HC) and toe-off (TO) from kinetic data and calculated DMAMA during stance phase according to Eq. (1), where $M$ is the sagittal ankle moment (plantarflexor positive), and $F$ is the sagittal ground reaction force (anteroposterior and vertical lab frame components) [31]

$$\mathrm{DMAMA}=\hspace{0.17em}\frac{{\int }_{HC}^{TO}M\hspace{0.17em}dt}{\Vert {\int }_{HC}^{TO}F\hspace{0.17em}dt\Vert }=\hspace{0.17em}\frac{\overline{M}}{\overline{F}}$$ (1)

Dynamic mean ankle moment arm values (natively calculated in meters) were normalized as a fraction of participant foot length. The resulting DMAMA distance can be measured from ankle to toe, where any negative values would represent a DMAMA posterior to the ankle. Walking speed was determined by dividing the distance traveled by the sacral marker during each motion capture trial by the time elapsed.

Statistical Analysis.

Prior to statistical analysis, we computed the mean DMAMA from seven clean strides in each condition for every participant. We fit a linear mixed-effects model (LMM) [43] across each of the independent variables of walking speed, ramp incline, and stair direction. In the level ground walking conditions, the instructions given to participants were categorical (e.g., “walk normal/slower/faster”); however, the LMM was fit to the measured walking speed in order to obtain an actionable biomimetic target that can control a device that operates in the continuous domain. A similar approach was taken with ramp incline, where the fixed effects were set as the incline of the ramp: −5 deg (DR) and +5 deg (UR). Therefore, walking speed and ramp incline were considered continuous variables, while stair conditions were maintained as categorical and encoded numerically as −1 (down) and +1 (up) (see Table 1). We chose to employ an LMM as our statistical model to account for intersubject variability, as individuals commonly have a different baseline DMAMA and different increments of self-selected speed. In the LMM, we included DMAMA (mean of the seven strides in each condition per participant) as the dependent variable, the activities as the fixed effects, and the participant (ID) as a random effect. We define the sensitivity of DMAMA to each fixed effect as the regression coefficient from this LMM. P-values were computed via the Satterthwaite approximation. Critical $\alpha$ was set to 0.05. To quantify the variance explained by both the fixed and random effects, the conditional R² (R²c) was calculated based on the definition by Nakagawa et al. [44]. All variables were verified for normality using residual plots, histograms, and Q-Q plots. Mean DMAMA and standard deviation across participants, prior to averaging, were also computed (Table 1). DMAMA as a function of participant height and mass is included in Supplemental Materials Section B on the ASME Digital Collection. Statistical analysis was performed using R Statistical Software 4.2.1 [45] and the linear mixed-effects model was fit using the “lme4” package [43].

Table 1.

DMAMA (in units of foot length) mean and standard deviation for all activities

Activity	N	Mean±SD	Categorical value
Level ground (N-LG)	70	0.232 ± 0.026	—
Slow level ground (S-LG)	70	0.233 ± 0.034	—
Fast level ground (F-LG)	70	0.216 ± 0.025	—
Down ramp (DR)	70	0.232 ± 0.027	—
Up ramp (UR)	70	0.249 ± 0.026	—
Down stairs (DS)	63	0.352 ± 0.055	−1
Up stairs (US)	63	0.261 ± 0.076	+1

In addition, in Supplemental Materials Section A, we performed mixed-effects ANOVA tests with categorical fixed effects. If the ANOVA p-value was found to be significant ( $\alpha$ = 0.05), we calculated posthoc p-values that were Tukey adjusted. Table A-1 available in the Supplemental Materials checks the effect of walking speed instruction (command to walk normal, slow, or fast) on measured walking speed, Table A-2 available in the Supplemental Materials tests the effect of walking speed instruction on DMAMA, and Table A-3 available in the Supplemental Materials tests the effect of ground incline category on DMAMA.

Results

General Results.

The overall mean and standard deviation of DMAMA for each activity can be found in Table 1. Statistical results for the LMMs can be seen in Table 2. DMAMA for all participants in all activities is represented in Fig. 1.

Table 2.

Results from the linear mixed-effects model for all activities

Mode	Formula [43]	Sensitivity	Units	Intercept	R2c	p
Walking speed	DMAMA∼ SPEED + (1|ID)	−0.023	Foot lengths per (m/s)	0.259	0.557	0.016
Ramp	DMAMA ∼ INCLINE + (1|ID)	0.002	Foot lengths per degree ground incline	0.238	0.521	0.013
Stairs	DMAMA∼ CATEGORY + (1|ID)	−0.046	Foot lengths per category	0.306	0.559	0.006

Fig. 1.

DMAMA for all participants in the seven activities. Mean values are provided in Table 1. Each color represents a different participant; each symbol is the DMAMA value for a single stride; all values are normalized to foot length. In the Tukey boxplot, the top of the box (upper hinge) represents the 75th percentile, the bottom of the box (lower hinge) represents the 25th percentile and the line in the middle represents the 50th percentile. The whiskers represent the largest and smallest values within 1.5 times the interquartile range from the upper and lower hinges, respectively. The half violin represents the continuous distribution of all DMAMA values in each activity.

Walking Speed.

Average walking speeds for the “slow” (S-LG), “normal” (N-LG), and “fast” (F-LG) categories were 0.98 ± 0.16 m/s, 1.43 ± 0.18 m/s, and 1.75 ± 0.17 m/s (mean ± SD), respectively (p < 0.001; see Table A-1 available in the Supplemental Materials). The LMM found a borderline-significant negative sensitivity of DMAMA to increased walking speed (sensitivity: −0.023 foot lengths per m/s, p = 0.016, R²c = 0.557), see Fig. 2. In this category, sensitivity is defined as foot lengths per meter per second. Four participants had their highest mean DMAMA at the “slow” speed, five others at the “normal” speed, and one at the “fast” speed. Using coefficients from Table 2, the equation relating DMAMA to walking speed was

$$\text{DMAMA}\hspace{0.17em}=\hspace{0.17em}-0.023\times \text{Speed}\hspace{0.17em}+\hspace{0.17em}0.259$$ (2)

Fig. 2.

(a) DMAMA for all participants and trials versus walking speed and (b) mean DMAMA for each participant versus walking speed category. The thick gray line represents the linear mixed- effect model. The dashed line represents a second mixed-effects model with a quadratic speed term (see Discussion). Each color symbol represents the mean value of a different participant, the semitransparent colored line connects data points for clarity, and all values are normalized to foot length.

The mixed-effects ANOVA, Table A-2 available in the Supplemental Materials, found that there was not a statistically significant difference in DMAMA across walking speed instruction categories (p = 0.067), despite the linear trend in the LMM.

Ramps.

The average walking speeds for “down ramp,” “level ground” (normal speed, N-LG), and “up ramp” were 1.35 ± 0.13 m/s, 1.43 ± 0.18 m/s, and 1.33 ± 0.13 m/s, respectively. The LMM model across these three conditions revealed a significant (p < 0.05) positive sensitivity of DMAMA to increasing ground incline (sensitivity: 0.002 foot lengths per degree of ground incline, p = 0.013, R²c = 0.521), see Fig. 3. Eight of the ten participants had their highest mean DMAMA when ascending the ramp. The equation that relates DMAMA to incline (in degrees) is as follows, using the coefficients from Table 2:

$$\text{DMAMA}\hspace{0.17em}=\hspace{0.17em}0.002\times \text{Incline}\hspace{0.17em}+\hspace{0.17em}0.24$$ (3)

Fig. 3.

(a) DMAMA for all participants in each ramp category and (b) mean DMAMA for each participant in each ground incline category. The thick, light gray line represents the linear mixed-effects model. Each color represents the mean value of a different participant, the semitransparent colored line connects data points for clarity, and all values are normalized to foot length.

The mixed-effects ANOVA, Table A-3 available in the Supplemental Materials on the ASME Digital Collection, revealed that there was a statistically significant difference in DMAMA in across ramp categories (p = 0.015). Tukey adjusted posthoc p-values found that mean DMAMA was significantly different in the DR $-$UR (p = 0.027) and N-LG $-$UR (p = 0.029) comparisons. There was no statistical significance between the N-LG $-$DR conditions (p = 0.999).

Stairs.

When descending stairs, the average speed was 0.83 ± 0.10 m/s; when ascending, the average speed was 0.76 ± 0.08 m/s. The LMM revealed a significant (p < 0.05) negative sensitivity of DMAMA to stairs category (sensitivity −0.046, p=0.006, R² = 0.559), see Fig. 4. We define sensitivity in this category as normalized DMAMA per change in category (downstairs = −1, upstairs = +1). Eight of nine participants showed a decreased DMAMA when ascending stairs versus descending stairs (though two participants showed almost no difference). Equation (4) relates DMAMA to stair direction, using the coefficients from Table 2

$$\text{DMAMA}\hspace{0.17em}=\hspace{0.17em}-0.046\times \text{stairDirection}\hspace{0.17em}+\hspace{0.17em}0.306$$ (4)

Fig. 4.

(a) DMAMA for all participants when ascending and descending stairs and (b) mean DMAMA for each participant when ascending and descending stairs. The thick gray line represents the linear mixed-effects model. Each color represents the mean value of a different participant, the semitransparent colored line connects data points for clarity, and all values are normalized to foot length. Participant 10's data for stairs were excluded.

Discussion

Motivated to inform the control of future semi-active prostheses, our study observed changes in DMAMA in nonprosthesis-using individuals when walking over stairs, ramps, and level ground at different speeds. The results showed that DMAMA has borderline-significant negative sensitivity to walking speed, significant positive sensitivity to ground incline, and a significant decrease when ascending stairs versus descending. While the sensitivities in Table 2 may appear small, it is important to note that possible DMAMA values fall within a narrow numerical range: −0.15 (near the middle of the heel pad) to 0.55–0.60 (slightly past the metatarsal head) [31]. Thus, the sensitivities can be translated into about 0.24% of possible range per degree incline (about $\pm$1.2% total for five-degree ramps, relative to level), −3.29% of possible range per m/s walking speed, and −6.57% of possible range when switching from down stairs to up stairs. Practically observed ranges are much narrower, roughly 0.1–0.45, so the observed changes are yet more substantial in comparison to this range.

The overall LMM regression (which accounts for participant-specific differences) found that when increasing walking speed, DMAMA decreased, moving toward the heel, supporting our initial hypothesis. This may be due to ankle plantarflexor moment decreasing during early to midstance [46,47], causing a lower, more rearfoot, DMAMA as the ankle attempts to reduce the slowing of the body. More forefoot (higher value) DMAMA at slower speeds may be due to an increased plantarflexor moment during midstance [46] and may be indicative of the ankle's effort to slow the body. We have previously interpreted this as related to the mechanics of accelerating and decelerating steps, in which the ankle moment decreases or increases in early-to-midstance to facilitate or slow tibial progression and thus overall speed [31,48,49]. This decreasing trend is very close to the trend found in the original DMAMA publication [31]; Adamczyk found a slope of −0.022 foot lengths per meter per second, compared to our −0.023 foot lengths per meter per second. This slight difference may be caused by changes in ankle and foot length definition or subtle deviations in marker placement. Alternatively, the similar values could merely be serendipitous, as the individuals' trends were clearly variable (Fig. 2) and changes of measurement equipment can influence the detailed results. For example, the original DMAMA paper found differences in the trend of DMAMA with speed when comparing measurements from force plates versus pressure insoles (−0.022 and −0.017 foot lengths per meter per second, respectively). Thus, while the trends across conditions are reliably captured across both studies and multiple forms of instrumentation, comparison of quantitative DMAMA measures across studies would require more precise standardization.

One curiosity is that five out of the ten participants had the highest average DMAMA at their “normal” speed, straying from the continuous downward trend demonstrated in the linear LMM fit. Because this observation suggests a nonlinear relationship between DMAMA and speed, we performed a second LMM with an added quadratic transformation of speed (Model: DMAMA ∼ speed + speed² + (1|ID)). This LMM regression, represented by the dashed line on Fig. 2, resulted in an increase of R² from 0.55 (linear model) to 0.76 (quadratic model); the regression equation was DMAMA $=0.190\times \mathrm{speed}-0.079\times {\mathrm{speed}}^2+0.124$ (95% CI of coefficients: speed [0.083, 0.296], speed² [−0.117, −0.039], intercept: [0.055, 0.195], p-values: speed = 0.002, speed² < 0.001). In the original study of DMAMA [31], six out of ten participants also showed a similar tendency where the slowest (1 m/s) and fastest (2 m/s) walking speeds showed more rearfoot DMAMA values than some of the intermediate speeds. The linear downward trend selected in that paper's analysis may have been appropriate due to the range of speeds studied (1.0–2.0 m/s), which were primarily above the speed of peak DMAMA observed here (1.21 m/s according to the quadratic fit). It is possible that intermediate, customary speeds represent specialized behavior—and that other speeds deviate, perhaps due to consciously regulating speed to other less comfortable, less natural speeds. This phenomenon may be worth further study.

When accounting for participant-specific differences, DMAMA increased with changes in ground incline from downhill to uphill—implying a more forefooted walk. This result is consistent with prior findings that when descending a ramp, ankle plantarflexor moment decreases during the majority of stance phase, and when ascending it increases [35–37,50,51]. While more subtle, this is also consistent with prior work by Leestma et al. [32] who showed an increase in DMAMA with increasing ground incline, albeit in participants with amputation using an experimental foot-ankle prosthesis.

When ascending stairs, participants showed a markedly lower value of DMAMA versus when they were descending. This trend contrasts with any concept that stairs are just a steep ramp, because the DMAMA change with ground incline is opposite in sign: a shallow up-ramp resulted in more forefoot DMAMA, but up-stairs resulted in more rear-foot DMAMA. The reason for this difference is unclear. Past research has focused on differences in ankle moment specific to early or late portions of stance phase [52–54]. In early stance, stair descent demonstrates high ankle moment as a person lands on their forefoot, and stair ascent has low ankle moment as the person lands on the heel/midfoot. Conversely, in late stance, descent shows reduced ankle moment as the body is lowered to the next stair, whereas ascent demonstrates a high ankle moment which is part of an overall leg thrust to drive the body upwards [54]. But, none of these findings quantifies the cumulative effect of ankle moment across the stride (i.e., DMAMA or ankle impulse); thus, they have not explained the finding observed here.

Past studies of DMAMA have suggested that more rearfoot DMAMA indicates a reduced tendency to slow the body during a stance phase, alternatively interpreted as an increased tendency to speed it up [31]. This effect was interpreted in relation to accelerating and decelerating steps during speed changes on level ground [48]. The same concept may be useful to interpret the present findings on stairs. In stair descent, the body continually speeds up through the action of gravity and needs to be slowed down to avoid falling; thus, the more forefoot DMAMA would act as part of this slowing process. Conversely, in stair ascent, the body needs to be pulled and pushed forward up the stairs; the more rearfoot DMAMA could represent a stance-phase effort to help the body “fall uphill” with less resistance. Stated differently: the trailing leg pushes the body upward, and the new stance leg may lower its DMAMA, moving it more rearfoot, to reduce its resistance to forward progression.

Alternatively, the observations could be interpreted as a safety measure: stairs are a risk, and it is better to fall up the stairs than down. Hence, a larger (forefoot) DMAMA when descending, and a smaller (midfoot) DMAMA when ascending, both act to bias the body's movement in an ascending direction, which is less risky. A more comprehensive study of DMAMA in stair climbing, across shallower to steeper stairs [54], larger and smaller stairs, multiple speeds [55,56], different levels of traction [57], and different stepping strategies [58], could reveal the trends that drive changes in DMAMA and other aspects of ankle control on stairs.

Consistent with the original DMAMA paper and the findings by Leestma et al., there were some participants whose DMAMA data showed trends opposite to the overall regression. This reinforces the suggestion that the control of devices may need to be verified/tuned to individual preference. In addition, all three studies report different overall ranges of DMAMA values—original DMAMA paper [31]: ∼0.25–0.40; DMAMA in a variable stiffness prosthesis [32]: ∼0–0.30; our findings: ∼0.15–0.30. As mentioned above, this may be attributed to differences such as methodology (force treadmill versus pylon-embedded load cell versus force plates), or the estimation of ankle center or foot length.

In both speed and ramps, the individual participants' data show that a simple linear fit may not represent the participants' behavior perfectly. Mean values for Slow-Level Ground, Normal-Level Ground, and Down Ramp conditions are all nearly identical, whereas Fast-Level Ground and Up Ramp conditions departed from these (both stair conditions are different). Thus, an alternative interpretation could be that DMAMA is conserved at a constant value in a certain range of gait conditions and changes outside that range. If further research corroborates that idea, it could lead to an even more nuanced understanding of ankle control.

During this study, walking speed was not controlled when the participants were walking on the ramp or stairs. Posthoc analysis when walking up ramp and down ramp compared to level ground revealed a significant difference in walking speed (see Table A-4 available in the Supplemental Materials on the ASME Digital Collection). However, these speeds span a narrow range (1.35 m/s on the downward ramp, 1.43 m/s on level ground, and 1.33 m/s on the upward ramp) that is very near to the peak of the nonlinear fit (1.21 m/s; see Fig. 2(b), dashed line), where there is minimal sensitivity of DMAMA to speed. Taken together, these differences do not appear to confound the changes in DMAMA with ground incline.

On stairs, participants walked substantially slower than during level ground walking and there was a significant difference in walking speed when ascending versus descending, see Table A-5 available in the Supplemental Materials. Specifically, the relatively slow mean speeds of 0.76 m/s during ascent and 0.83 m/s during descent, correspond to the portion of the nonlinear fit where DMAMA is increasing with increased walking speed (Fig. 2(b), dashed line). This may contribute to the observed more forefoot DMAMA during descent compared to ascent. Future studies may benefit from controlling for walking speed or performing testing at various speeds to further understand changes in DMAMA.

Based on results from the repeated measures ANOVA tests, we consider that DMAMA is relatively insensitive to changes in walking speed and ground incline. However, there is a drastic change when ambulating on stairs. This large change appears even more substantial considering that DMAMA spans only a small numerical range and is highly variable. Nonetheless, DMAMA does undergo systematic shifts in the different activities. When designing controllers for lower-limb assistive devices, it may be prudent to first allow the user to “tune” to a preferred value and then program changes across different activities.

Limitations

This study only included 10 participants (9 in the case of stairs), which spanned a narrow range of ages (23–38 years). Due to this, the claims in this paper may not translate into younger or older populations. As aging affects ankle mechanics, it would be beneficial to include older individuals in future DMAMA studies for a more comprehensive analysis.

When walking over ramps and stairs, speed was not controlled, which may have contributed to inter- and intrasubject variation in DMAMA (see Tables A-4 and A-5 available in the Supplemental Materials). Additionally, walking speed was not quantitatively controlled in the level ground walking trials, resulting in each participant having a different range of speeds in the “slow,” “normal,” and “fast” conditions (see Table A-1 available in the Supplemental Materials).

The accuracy of the center of pressure (COP) location on the bare force plates was verified using the Caltester procedure (visual3d) showing a high accuracy with a max error of 1.3 mm across the fore-aft and med-lat directions. A pole test was used to visually assess accuracy of the COP location and direction of the GRF vector with the ramp and stair structures attached. However, COP was not reverified with the addition of the structures so additional small inaccuracies may be present in the data. Replicating the study with portable measurement techniques (e.g., pressure insoles [31]) and/or utilizing an instrumented pole to calibrate the added structures (e.g., [59]) are recommended methods to further verify our findings.

While the ground inclines of −5°, 0°, and +5° reflect gradients seen during urban community ambulation due to being ADA compliant, this may be a limitation in this study. Lay et al. [37] posit that in up-ramp walking, only ground inclines of +10% (+5.74°) or higher cause the nervous system to change strategies from level ground walking to ramp walking. A larger range of ground inclines could be studied for a clearer understanding of the effect of ground incline on DMAMA. In addition, due to the length of the instrumented ramp, these results include either the first or second step on the ramp, which may not allow enough distance for the participant to reach steady-state walking speed [60]. Future assessment of DMAMA on instrumented treadmills, or on long ramps using wearable sensors [50,61], could corroborate or refute these conclusions.

Conclusions

Our study supports previous findings that when accounting for participant-specific differences, DMAMA decreases with walking speed, increases with ground incline, and is lower when ascending stairs than when descending them. In the future design of biomimetic assistive lower-limb devices, DMAMA could reasonably be used as a target metric, with both generic population-mimicking control laws and individual-specific customized behaviors.

Supplementary Material

Supplementary Material

Supplementary PDF

Funding Data

• DOD (Grant Nos. W81XWH-17-1-0427 and W81XWH-19-2-0024; Funder ID: 10.13039/100000005).

• US National Science Foundation (Grant No. HRD-1612530; Funder ID: 10.13039/100000001).

• Institutional Clinical and Translational Science (Award ID: UL1 TR002373; Funder ID: 10.13039/100005902).

Data Availability Statement

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