Adaptive Treadmill Walking Encourages Persistent Propulsion

Abstract

Background:

Adaptive treadmills allow real-time changes in walking speed by responding to changes in step length, propulsion, or position on the treadmill. The stride-to-stride variability, or persistence, of stride time during overground, fixed-speed, and adaptive treadmill walking has been studied, but persistence of propulsion during adaptive treadmill walking remains unknown. Because increased propulsion is often a goal of post-stroke rehabilitation, knowledge of the stride-to-stride variability may aid rehabilitation protocol design.

Research question:

How do spatiotemporal and propulsive gait variables vary from stride to stride during adaptive treadmill walking, and how do they compare to fixed-speed treadmill walking?

Methods:

Eighteen young healthy subjects walked on an instrumented split-belt treadmill in the adaptive and fixed-speed modes for 10 minutes at their comfortable speed. Kinetic data was collected from the treadmill. Detrended fluctuation analysis was applied to the time series data. Shapiro-Wilk tests assessed normality and one-way repeated measures ANOVAs compared between adaptive, fixed-speed, and randomly shuffled conditions at a Bonferroni-corrected significance level of 0.0055.

Results:

Stride time, stride length, step length, and braking impulse were persistent (α > 0.5) in the adaptive and fixed-speed conditions. Adaptive and fixed-speed were different from each other. Stride speed was persistent in the adaptive condition and anti-persistent (α < 0.5) in the fixed-speed condition. Peak propulsive force, peak braking force, and propulsive impulse were persistent in the adaptive condition but not the fixed-speed condition (α ≈ 0.5). Net impulse was non-persistent in the adaptive and fixed-speed conditions. All variables were non-persistent in the shuffled condition.

Significance:

During adaptive treadmill walking, increases in propulsive force and impulse persist for multiple strides. Persistence was stronger on the adaptive treadmill, where increased propulsion translates into increased walking speed. For post-stroke gait rehabilitation where increasing propulsion and speed are goals, the stronger persistence of adaptive treadmill walking may be beneficial.

INTRODUCTION

Adaptive treadmills (ATMs), also known as self-paced treadmills, change the speed of an instrumented treadmill in real time in response to the user’s gait mechanics [1–3]. By changing propulsive impulse, step length, or anterior-posterior position on the ATM, the user can adjust their speed as if they were walking overground [2]. For healthy adults, self-selected walking speed on the ATM is faster than on the fixed-speed treadmill (FSTM) but similar to overground [2]. Kinematic variability inherent to overground walking is reduced during FSTM walking but restored during ATM walking [4]. Because of the similarity between ATM and overground walking [2,4], ATM walking may be beneficial for gait rehabilitation and improve translation of learned biomechanics to community ambulation. However, it is unknown how gait varies from stride to stride during ATM walking, which would provide insight into how people modulate their gait on the ATM to achieve and maintain their speed.

Detrended fluctuation analysis (DFA) assesses stride-to-stride variability and quantifies persistence in gait data with the coefficient α. Persistent data have fluctuations from the mean at one stride that are more likely to be followed by subsequent strides that fluctuate from the mean in the same direction. Anti-persistent data have fluctuations from the mean that are more likely to be followed by subsequent fluctuations in the opposite direction. Non-persistent data fluctuate randomly, as white noise, where fluctuations from the mean are equally likely to be followed by subsequent fluctuations in the same or the opposite direction [5–8]. Studies have assessed the persistence of stride time, stride length, and stride speed [5–7,9], but only overground or on a FSTM. Some analyses exist on the persistence of spatiotemporal parameters during self-paced treadmill walking, suggesting that stride time, length, and speed are persistent during self-paced treadmill walking [10–12] but more likely to be non-persistent during FSTM walking [11]. Persistence may be beneficial for rehabilitation by providing a similar environment to overground walking, as stride time is persistent overground [6]. Only Jordan et al. (2007) [13] have studied the persistence of kinetics, specifically vertical impulse, but the variability of propulsion, either on a FSTM or an ATM, remains unknown. Since propulsion is correlated to walking speed [14] and increasing propulsion is one way to increase walking speed in poststroke individuals, determining the variability of propulsive measures may provide insight into the development of post-stroke gait rehabilitation protocols. By understanding propulsive variability in young healthy subjects, rehabilitation protocols can be designed to target differences between unimpaired and impaired variability to restore healthy gait biomechanics.

The purpose of this study was to evaluate the stride-to-stride variability of spatiotemporal and propulsive variables during ATM walking in comparison to FSTM walking and randomly shuffled controls. Because increases in step length and propulsive impulse enable increased speed on the ATM, it was hypothesized that step length and propulsive impulse would be persistent on the ATM and non-persistent on the FSTM.

METHODS

Participants

Eighteen participants were recruited from the University of Delaware community (Table 1). Power analysis determined that for a power of 0.8, at least 17 subjects were needed to distinguish a mean difference in α of 0.2 ± 0.2 based on preliminary analysis of short ATM and FSTM trials. This study was approved by the University of Delaware’s Institutional Review Board and participants gave informed consent.

Table 1:

Participant demographics, presented as mean ± standard deviation.

Gender	8 M/10 F
Age (years)	24 ± 3
Height (m)	1.71 ± 0.12
Mass (kg)	75.32 ± 11.94

Data Collection

Participants walked on an instrumented split-belt treadmill (Bertec Corp., Worthington, OH, USA; 2000 Hz) in its tied-belt mode in both FSTM and ATM conditions, with the ATM first. Subjects were given 5 minutes of familiarization with both conditions. Participants could use the handrails for stability with a “light touch,” although no participants used the handrails.

Three repetitions of a 10-meter overground walking test were performed to determine average overground speed. For the FSTM trials, participants walked for 10 minutes at their self-selected speed. Walking speed was determined as in Ray et al. (2018) [2], where the FSTM was started at the subject’s overground walking speed and adjusted in increments of 0.05 m/s until the subject indicated their comfortable speed. For the ATM trials, participants took up to one minute to reach their self-selected speed, after which they walked for 10 minutes (~600 strides) [8]. Speed was visually monitored to ensure that it remained within ± 0.2 m/s [2,3].

Analysis

Force data was filtered with a fourth order 30 Hz low-pass Butterworth filter. Heel strike and toe-off times were detected when the force on each treadmill belt crossed a 20 N threshold [15]. Center-of-pressure data determined the position of each foot at heel strike. Stride time (s) was calculated as the time between ipsilateral heel strikes. Stride length (m) was calculated as the anterior-posterior distance between ipsilateral heel strikes plus the distance the belt traveled during that time. Stride speed (m/s) was stride length divided by stride time. Step length (m) was determined as the anterior-posterior distance between contralateral heel strikes plus the distance the belt traveled during that time. Peak anterior ground reaction force (AGRF; N) was the maximum anterior-posterior ground reaction force (APGRF) between heel strike and toe-off, while peak posterior ground reaction force (PGRF; N) was the minimum APGRF during the same time. AGRF impulse, PGRF impulse, and net APGRF impulse (Ns) were the positive, negative, and total areas under the APGRF curve, respectively, from heel strike to toe-off.

Detrended fluctuation analysis was applied to the time series data of each variable using a custom MATLAB algorithm (MathWorks, Natick, MA, USA) [6–8,10,16]. First, DFA integrates the data (Eq. 1),

$$y\left(k\right)={\sum }_{i=1}^k\left[I\left(i\right)-I_{avg}\right]$$ (1)

Where y(k) is the cumulative sum of the difference between the value at each point I(i) and the mean value over the series of data I_avg. Then, y(k) with N data points is divided into boxes of length n, a linear regression is fit to the subset of data within each box, and the fluctuation F(n) is calculated (Eq. 2).

$$F\left(n\right)=\sqrt{\frac{1}{N}{{\sum }_{k=1}^N\left[y\left(k\right)-y_n\left(k\right)\right]}^2}$$ (2)

F(n) is the root mean square error between the linear regression within each box and each point y(k). F(n) is calculated over a range of box lengths [$16:\frac{N}{9}$] [8]. A linear regression is fit to a log-log plot of the fluctuation F(n)versus box length n. The slope of the linear regression is called α and describes the persistence in the data. α < 0.5 indicates anti-persistence, α ≈ 0.5 indicates no persistence, and 0.5 < α < 1 indicates persistence [5–8,17]. Increasing values of α greater than 0.5 indicate stronger persistence [18].

Assuming bilateral symmetry, the leg used in DFA was randomized. Randomly shuffled surrogate data was created for each variable by rearranging the data points from each subject’s ATM trial in a random order to provide a non-persistent control group for comparison [7,19].

Distributions of α were tested for normality using the Shapiro-Wilk test. Normally distributed data were compared between ATM, FSTM, and shuffled using a one-way ANOVA, blocking for subject, with Tukey post-hoc testing performed if the ANOVA indicated significant differences at the 0.05 significance level. Non-normally distributed data were compared using the Friedman Test with Steel-Dwass post-hoc testing. Bonferroni corrections compensated for multiple comparisons caused by the number of variables, creating a new significance level of 0.0055.

RESULTS

Means and standard deviations for walking speed and each variable of interest were calculated (Table 2).

Table 2:

Mean ± standard deviation of each of the spatiotemporal and propulsive variables of interest. The randomly shuffled control dataset is excluded because the distributions are identical to the ATM dataset. Values with different characters are significantly different from each other at the 0.05 significance level.

		Mean ± SD
	ATM	FSTM	Overground
Walking Speed (m/s)	1.47 ± 0.12a	1.22 ± 0.07b	1.36 ± 0.13c
Stride Speed (m/s)	1.47 ± 0.08a	1.22 ± 0.00b	-------------------
Stride Time (s)	1.04 ± 0.03a	1.11 ± 0.02b	-------------------
Stride Length (m)	1.53 ± 0.07a	1.35 ± 0.03b	-------------------
Step Length (m)	0.77 ± 0.05a	0.67 ± 0.02b	-------------------
Peak AGRF (N)	175.81 ± 12.62a	145.21 ± 9.15b	-------------------
Peak PGRF (N)	−181.27 ± 18.20a	−145.91 ± 12.77b	-------------------
AGRF Impulse (Ns)	24.979 ± 2.528a	22.085 ± 2.702b	-------------------
PGRF Impulse (Ns)	−27.527 ± 3.190	−24.486 ± 2.849	-------------------
Net APGRF Impulse (Ns)	−2.585 ± 2.884	−2.401 ± 2.630	-------------------

Persistence of spatiotemporal variables is shown in Figure 1 and Table 3. Stride speed was persistent for ATM walking (α=1.08) but was anti-persistent during FSTM walking (α=0.32) and was non-persistent in the shuffled condition (α=0.48). All conditions were significantly different than each other (all p < 0.005) Stride time persistence for ATM walking (α=1.07) and FSTM walking (α=0.75) were significantly greater than the shuffled data (α=0.50, both p < 0.0001). ATM α was also significantly larger than FSTM α (p < 0.0001). Both ATM and FSTM α values were greater than 0.5, indicating persistence. Stride length for ATM (α=0.94) and FSTM (α=0.75) walking were also persistent but significantly different from each other (p=0.0015). The shuffled data showed no persistence (α=0.51), and the ATM and FSTM conditions were significantly greater than the shuffled condition (both p < 0.0001). Step length for ATM (α=0.85) and FSTM (α=0.66) walking were also persistent, and the shuffled data (α=0.47) showed no persistence. All conditions were significantly different from each other (all p < 0.0001).

Figure 1:

Mean ± standard deviation α for spatiotemporal gait variables. The Bonferroni corrected significance level is α=0.0055. Both ATM and FSTM variables were persistent and significantly different from the randomly shuffled data. The larger α values in the ATM condition than the FSTM condition indicate stronger persistence during ATM walking.

Table 3:

Mean ± standard deviation of DFA α parameter for spatiotemporal and propulsive variables of interest. 95% confidence intervals (CI) are shown along with p-values for each pairwise comparison. Bolded p values indicate a significant difference. The Bonferroni corrected significance level is α=0.0055. For most variables, ATM, FSTM, and shuffled conditions were all different from each other.

	Mean α ± SD			ATM vs. FSTM		ATM vs. Shuffled		FSTM vs. Shuffled
	ATM	FSTM	Shuffled	95% CI	p-value	95% CI	p-value	95% CI	p-value
Stride Speed	1.08 ± 0.16	0.32 ± 0.14	0.48 ± 0.06	[0.65, 0.85]	< 0.0001	[0.50, 0.71]	< 0.0001	[0.05 0.25]	0.0032
Stride Time	1.07 ± 0.17	0.75 ± 0.14	0.50 ± 0.07	[0.21, 0.42]	< 0.0001	[0.47, 0.67]	< 0.0001	[0.15, 0.35]	< 0.0001
Stride Length	0.94 ± 0.20	0.75 ± 0.14	0.51 ± 0.07	[0.07, 0.31]	0.0015	[0.31, 0.55]	< 0.0001	[0.13, 0.36]	< 0.0001
Step Length	0.85 ± 0.18	0.66 ± 0.11	0.47 ± 0.05	[0.09, 0.28]	< 0.0001	[0.29, 0.48]	< 0.0001	[0.10, 0.29]	< 0.0001
Peak AGRF	0.96 ± 0.23	0.59 ± 0.11	0.48 ± 0.08	[0.24, 0.50]	< 0.0001	[0.35, 0.61]	< 0.0001	[−0.02, 0.24]	0.0928
Peak PGRF	0.82 ± 0.22	0.63 ± 0.11	0.49 ± 0.07	[0.06, 0.31]	0.0021	[0.21, 0.45]	< 0.0001	[0.02, 0.27]	0.0187
AGRF Impulse	0.76 ± 0.17	0.61 ± 0.12	0.50 ± 0.08	[0.04, 0.24]	0.0037	[0.16, 0.37]	< 0.0001	[0.01, 0.22]	0.0223
PGRF Impulse	0.64 ± 0.17	0.66 ± 0.11	0.47 ± 0.07	[−0.07, 0.15]	0.6592	[−0.25, – 0.06]	0.0006	[−0.27, – 0.12]	< 0.0001
Net APGRF Impulse	0.57 ± 0.10	0.58 ± 0.09	0.49 ± 0.07	[−0.06, 0.11]	0.9609	[−0.15, 0.01]	0.1346	[−0.17, – 0.01]	0.0187

Persistence of propulsive variables is shown in Figure 2 and Table 3. Peak AGRF α for ATM walking (α=0.96) was significantly larger than α for FSTM walking (α=0.59, p < 0.0001) and the shuffled data (α=0.48, p < 0.0001). The FSTM and shuffled conditions were not significantly different from each other (p=0.0928). Peak PGRF for ATM walking (α=0.82) was persistent and significantly different from FSTM walking (α=0.63, p=0.0021) and the shuffled data (α=0.49, p < 0.0001). FSTM and shuffled α were not significantly different from each other (p=0.0187). AGRF impulse was persistent during ATM walking (α=0.76) and was significantly different from FSTM walking (α=0.61, p=0.0037) and the shuffled data (α=0.50, p < 0.0001). FSTM and shuffled conditions were not different from each other (p=0.0223). α for PGRF impulse during ATM walking (α=0.64) was not significantly different from FSTM walking (α=0.66, p=0.6592), but was larger than the shuffled data (α=0.47, p=0.0006). PGRF impulse during FSTM and shuffled conditions were significantly different from each other (p < 0.0001). ATM (α=0.57), FSTM (α=0.58) and shuffled (α=0.49) were not significantly different from each other for net APGRFimpulse (all p > 0.01).

Figure 2:

Mean ± standard deviation α for propulsive gait variables. The Bonferroni corrected significance level is α=0.0055. Most ATM and FSTM variables were persistent and significantly different from the randomly shuffled data. Most ATM and FSTM variables were also different from each other, with the ATM α values typically being larger than the FSTM α values.

DISCUSSION

Many spatiotemporal and propulsive variables were persistent during ATM and FSTM walking, with the ATM variables having significantly larger α values than the FSTM variables and thus stronger persistence. Most ATM and FSTM variables were significantly different from the shuffled data, suggesting that both ATM and FSTM walking are modulated in a non-random manner, where the value of the variable at one stride affects the value of the variable in subsequent strides. The strengths of this study lie in the use of the ATM and novel analysis on the stride-to-stride dynamics of propulsive and braking measures. Examining persistence on the ATM provides insight into how people manipulate their gait to achieve and maintain their desired speed. Understanding how propulsive mechanisms vary during gait will allow for better design of rehabilitation techniques to encourage increased propulsion.

ATM Stride-to-Stride Variability

During ATM walking, stride speed, stride time, stride length, and step length were persistent, meaning they are modulated in a non-random manner on the ATM. α for stride length (α=0.94) was consistent with persistence during self-paced walking in the literature [10,12]. Persistence in both step length and stride length is logical because a stride includes two consecutive steps, so changing step length would affect stride length. If a participant takes a longer than average step, the ATM will respond to that increased step length by increasing walking speed, requiring the following several steps to be longer and thus persistent. This increased walking speed was reflected in the persistence of stride speed (α=1.08), which was also consistent with other studies [10]. Similarly, stride time showed persistence with α > 0.5 [5–8,17]. However, the mean stride time and stride speed α were greater than 1, where α=1 is the cutoff between stationary and nonstationary data. In nonstationary data, the magnitude of the variable has random drifts in either direction away from the mean for several subsequent data points [6,20]. Stride time in the literature was persistent during self-paced walking with α=0.93 [10] and α=0.8 [12], which is similar to these results. As variation between subjects during ATM walking included values both less than and greater than 1, it remains unclear if stride time during ATM walking is stationary.

Peak AGRF and AGRF impulse were both persistent during ATM walking, with α > 0.5, and were significantly different from the shuffled α values. Persistent peak AGRF suggests that increased propulsive force at one stride would be maintained in the following strides. Similarly, increases in propulsive impulse would be maintained for several strides, enabling increased walking speeds on the ATM. This persistence could be useful for post-stroke gait rehabilitation where increasing propulsive force and walking speed are primary goals [21,22]. Peak PGRF during ATM walking was persistent (α=0.82), suggesting that peak braking force is modulated similarly to peak propulsive force. This is reasonable because as propulsive force would increase for several consecutive strides, braking force would also increase for those strides [23]. Similarly, PGRF impulse was persistent, although α was closer to 0.5 so the persistence was weaker [18]. The hypothesis that ATM walking would be persistent was supported and suggests that ATM walking may be like overground walking [5,6] and beneficial for post-stroke gait rehabilitation.

FSTM Stride-to-Stride Variability

Like ATM walking, stride time, stride length, and step length were persistent during FSTM walking. However, α was significantly smaller on the FSTM than the ATM, suggesting weaker persistence on the FSTM [18]. Persistence in these spatiotemporal parameters is consistent with previous results in the literature for stride length [7,24], and stride time [6,25,26] overground and on a FSTM. Stride speed was anti-persistent on the FSTM, consistent with previous studies [7,10]. Fluctuations in stride speed are corrected in the following stride, likely to prevent the user from walking off the treadmill. In contrast, peak AGRF, peak PGRF, AGRF impulse, and net APGRF impulse were non-persistent during FSTM walking because the FSTM does not adjust the belt speed in response to changes in propulsive force or impulse. Only PGRF impulse was persistent, possibly because participants may rely on the treadmill to generate forward momentum but still need to modulate braking. Because the FSTM does not require users to intentionally control their propulsion and braking to achieve their desired speed, the propulsive variables fluctuate with less persistence than on the ATM. These differences in stride-to-stride variability between ATM and FSTM walking reinforce previous conclusions that ATM and FSTM walking utilize different kinetics and kinematics [4,27]. These results do not support the hypothesis that variables would be non-persistent on the FSTM. There may be some allowable range of persistent increases and decreases before the user must alter their gait to avoid walking off the treadmill, which is supported by persistence in the literature [6,7,24,25,26]. Because there is still some persistence on the FSTM, albeit less than on the ATM, FSTM walking may provide some benefit for rehabilitation.

Limitations

One limitation of this study is that not all participants achieved the recommended 600 strides for each trial, although both ATM (567 ± 45 strides) and FSTM (531 ± 34 strides) were close. Regardless, shorter trials do not affect the mean value of α [17,28,29] and only increase the variation in α [9,17]. Increasing the variation of α would decrease the likelihood that comparisons between conditions would be significant, but nearly all comparisons were significant as-is. Therefore, slightly decreased trial duration is not believed to have impacted the results or conclusions.

Another limitation is in using kinetics to detect heel strike and toe-off, as crossover steps had to be removed which interrupted the consecutive time series. However, this was necessary for analyzing the propulsive variables because a crossover step would alter the propulsive and braking measures. Participants were visually monitored and instructed to move laterally on the treadmill to minimize crossover steps, and subjects had an average of 15 of 549 strides removed due to crossover. Therefore, steps were largely consecutive, and this method is not believed to have impacted the results.

Additionally, the trial order was not randomized. However, trials were conducted on separate days several months apart owing to equipment malfunction. Trial order did not affect α in prior work [30] so over a span of several months, the lack of randomization is not believed to have affected the results.

Finally, data collection during the ATM trial for nine subjects was unexpectedly terminated due to equipment malfunction before the participant had walked for 10 minutes. In these cases, the existing data was saved, and the participant was asked to complete the remainder of the 10-minute trial. The shorter trials (two for seven subjects, three for two subjects) were directly appended to achieve a trial approximately 10 minutes long. A similar method of concatenating shorter trials has been used in pathologic gait and was determined to be a valid method to create longer trials [31]. Additionally, the appended trials were completed in quick succession and at comparable speeds, so this is not expected to have influenced the results.

Conclusions

In general, both ATM and FSTM walking were persistent, with α values significantly greater than 0.5. However, ATM and FSTM walking have different stride-to-stride variability for spatiotemporal and propulsive variables. Most spatiotemporal and propulsive variables had larger α values on the ATM than on the FSTM, suggesting that persistence is stronger on the ATM than the FSTM [18]. Stronger persistence suggests that changes in gait variables at one stride will be maintained for several subsequent strides. For example, increased propulsion at one stride on the ATM would lead to instantaneous increases in walking speed and increased propulsion for multiple consecutive strides. In contrast, increased propulsion on the FSTM would lead to no change in walking speed and fewer subsequent strides with increased propulsion. These results strengthen previous conclusions [2,4] that ATM walking and FSTM walking are different, and that ATM walking might be more like overground walking. Similarities between ATM and overground walking may increase translation of learned gait mechanics from training to the community. Because ATM walking demonstrates stronger persistence in propulsive mechanics, it may be beneficial for targeting propulsion and increasing walking speed during rehabilitation.

Highlights.

• This study used novel adaptive treadmill control with young healthy participants.

• Detrended fluctuation analysis was applied to spatiotemporal and propulsive variables.

• Adaptive treadmill variables were more persistent than fixed-speed variables.

• Adaptive treadmill walking and fixed-speed treadmill walking are different.

• Persistent propulsion on the adaptive treadmill may enable increased walking speed.