Retention and Transfer of Fractal Gait Training

Abstract

Background/Purpose: Fractal gait patterns have been shown to be modifiable, but the extent to which they are retained and transferred to new contexts is relatively unknown. This study aimed to close those gaps by enrolling participants (N = 23) in a seven-day fractal gait training program. Methods: Building on related work, the fractal gait training occurred on a treadmill over a 10-min period. Before and after the treadmill training, each participant walked for 10 min overground without the fractal stimulus used during training. The daily post-test was used to examine immediate retention and transfer of the fractal gait patterns from the treadmill to overground. The pre-tests in days 2–7 were used to examine the extent to which the fractal gait patterns from the preceding day were retained 24 h later. Inertial measurement units were used to measure stride time so a consistent measurement method could be employed in the treadmill and overground phases of the study. Results: Our results showed that multiple days of treadmill training led to elevated fractal patterns, indicating a positive training effect. However, the positive training effect observed on the treadmill did not transfer to overground walking. Conclusions: Collectively, the data show that fractal patterns in gait are modifiable across multiple days of training, but the transferability of these patterns to new contexts needs to be further explored.

1. Introduction

It was observed nearly three decades ago that the natural variation from stride-to-stride during steady-state gait is not random, but rather, exhibits a fractal pattern [1]. Follow-up work showed that task constraints [2,3,4,5,6,7], injury [8], aging across the lifespan [9,10], and disease [9,11,12] can alter the fractal patterns. Beyond a quantitative observation, it has been suggested that the nature of fractal patterns relate to gait adaptability [13] and fall risk [14], an assertation that links back to the original implementation of fractal pattern analysis in physiological systems [15,16]. The connection to adaptability has been strengthened with the recent observation that fractal patterns—in particular, pink noise—promote earlier coordination transitions in movement [17], reinforcing the postulate that fractal patterns afford flexible movement options that can be adopted based on the needs of the task.

With the acknowledgement that fractal gait patterns change after injury, aging, or disease, and the postulate that they reflect a person’s ability to exhibit adaptive movement, it stands to reason that enhancing fractal gait patterns in clinical populations could lead to positive outcomes, such as a decline in fall risk [18]. One potential way to alter fractal patterns in movement is to provide a fractal stimulus to which participants can synchronize their movement. The theoretical framework for such an intervention was first articulated by Dubois using a mathematical model of strong and weak anticipations [19] and further expanded upon by West and colleagues with the complexity matching framework [20]. This phenomenon was first demonstrated empirically in human movement data utilizing a finger tapping paradigm [21]. In that study, Stephen and colleagues asked participants to tap a key on the keyboard in synchrony with each flash on the screen in front of them. The visual stimulus on the screen acted as a visual metronome, similar to the rhythmic auditory stimulation (RAS) paradigm commonly used in rehabilitation where an auditory metronome provides a cue to which a patient attempts to synchronize their movements [22,23]. However, there is one very important distinction differentiating the metronome used by Stephen and colleagues. Typical RAS paradigms utilize a consistent time interval between the “beeps”, whereas the metronome used by Stephen and colleagues utilized a variable time interval between the stimulus presentation, such that the variation in time intervals exhibited a fractal structure. With this implementation, Stephen and colleagues created a fractal metronome and postulated that participants would be able to synchronize to the metronome, using the strong anticipation framework from Dubois as their rationale. Their hypothesis was supported, and they showed that the fractal structure of movement patterns could be influenced by a fractal metronome.

A logical extension of this work was to determine if similar synchronization behavior occurred in gait. Some early studies employed a fractal auditory metronome to modify fractal gait patterns [24,25]. Rhea et al. used a visual metronome to more closely replicate and extend Stephen et al.’s work to gait [26]. Their study showed that fractal gait patterns in young healthy adults could be either strengthened or weakened, depending on the structure of the fractal visual stimulus. The observation that fractal gait patterns can be modified using a fractal stimulus has since been replicated in various forms [27,28,29,30,31,32,33]. Moreover, it has been shown that the newly developed fractal gait patterns are retained—at least in the short-term—after training [24,27,34].

While fractal gait training appears promising, it should be noted that the retention characteristics of this type of training are relatively unknown. For example, 15 min of training led to strengthened fractal gait patterns in the post-test immediately after the training, but the strength of the patterns began to drop back down at the end of the retention period (albeit still elevated relative to the pre-training fractal levels) [34]. In patients with Parkinson’s disease, it was shown that fractal patterns could be altered during training and 5 min afterwards, but more extended retention was not assessed [24]. In another study, four days of fractal gait training were shown to increase the strength of the fractal gait patterns, but retention was not assessed [35]. Thus, the effect of multiple days of fractal gait training on immediate and longer-term retention is unclear. Furthermore, it is unknown whether fractal gait training on a treadmill transfers to overground walking, which is important to know not only from a neuromotor control perspective, but from a practical perspective in order to help identify the efficacy of this type of training for use in rehabilitation settings. The incorporation of inertial measurement units (IMUs) in this line of research is important, as they afford the possibility of a consistent data collection method across treadmill and overground settings. Video-based motion capture is not a good candidate for this line of research since typically hundreds of strides are necessary to reliably calculate fractal gait patterns [36]. Such a volume is difficult to capture with video-based motion capture, especially in overground gait in large areas, making IMUs a stronger data collection candidate.

In summary, there is a long history of examining fractal gait patterns in the context of injury [8], aging across the lifespan [9,10], and disease [9,11,12]. What has been consistently shown is that fractal gait patterns change in these contexts. The extent to which these changes have any functional meaning is still an empirical question. Some have postulated that fractal patterns are related to fall risk and/or adaptability based on empirical evidence [13,14,18,37,38]. However, these observations lack large sample sizes with a variety of populations, which would provide stronger evidence for the connection between fractal gait patterns and adaptability. Nevertheless, the empirical observations showing that fractal gait patterns may be related to adaptability provide credence for the exploration of pathways to positively alter the fractal gait pattern. It is important to show this proof-of-concept first in healthy populations to avoid burdening clinical populations unnecessarily. Our study tackles this issue by exploring the extent to which fractal gait patterns in healthy young adults are modifiable over a 7-day training period.

The purpose of this study was to determine the extent to which training to synchronize stride timing to a fractal visual metronome while walking on a treadmill would affect the adopted stride time variability pattern during overground locomotion. Two hypotheses were tested: (1) participants would exhibit stronger coupling to the fractal visual metronome with practice and (2) immediate retention (i.e., directly after training) and longer-term retention (i.e., 24 h after training) would increase as a function of increased practice.

2. Materials and Methods

2.1. Participants

A convenience sample of healthy young adults (N = 23; 22.0 ± 2.5 yrs; 172.7 ± 11.1 cm) primarily consisting of students from the University of North Carolina at Greensboro (UNCG) were enrolled in the study. Potential volunteers who were notified of the opportunity to participate via flyers in public locations, presentations in their courses by a member of the study team, and via word of mouth. Participants self-reported to be free of neuromuscular injuries or pathologies that might cause abnormal biomechanics and had normal or corrected-to-normal vision. Study procedures were approved by the Institutional Review Board (IRB) at the University of North Carolina at Greensboro (IRB study number 15-0370).

2.2. Materials

Three IMUs from the APDM Mobility Lab Opal system (APDM, Inc., Portland, OR, USA) were attached to the participants with elastic straps: two on top of each foot (center on the front of the ankle) and one on the lumbar spine (centered at the base of the spine), identical to the ADPM sensor placement in [39]. Stride time was extracted from the acceleration and orientation time series recorded by the APDM sensors using APDM Mobility Lab software version 2, which has been shown to provide valid measurement of gait stride time [40,41,42]. Sensor data were collected at 128 Hz.

2.3. Procedures

Participants synchronized with a fractal visual metronome over seven consecutive sessions separated by 24 h (±30 min). Within each session they completed a pre-test, training, and post-test phases, each phase lasting 10 min. The pre-test phase consisted of overground walking at preferred speed around a 62 m gymnasium track. The training phase consisted of walking on a treadmill at individually determined preferred walking speed while synchronizing left and right leg steps with the appearance of the corresponding foot on display positioned on the treadmill panel directly in front of them (Figure 1; Apple iPad, Cupertino, CA, USA). The timing of appearance of the right footprint was determined by a strongly persistent fractal time series, as characterized by detrended fluctuation analysis alpha (DFA α) of 0.98 (Figure 2), consistent with our previous research on fractal gait training [26,34]. Fractal time series contained 500 data points bounded within 1.00–1.35 s (1.17 ± 0.07 s). Left footprints appeared halfway through each right foot phase. The post-test phase was identical to the pre-test. Participants were asked to maintain consistent walking speed throughout the sessions.

Preferred treadmill walking speed was determined for each participant in the first session using the following procedure: speed of the treadmill was increased from 0.5 m/s in increments of 0.05 m/s until participant verbally indicated that a given speed was their normal walking speed. The second estimate was started from the speed that was too fast (2.0 m/s) and incrementally slowed until they verbally indicated that the speed was their normal pace. If the two speeds were within 10% of each other, the average of the two speeds was set as the preferred walking speed. If there was more than 10% difference in the speeds, participant completed the procedure again. All subjects self-selected a walking speed within less than two attempts. This speed was used for all consequent treadmill training sessions.

2.4. Data Analysis

Adaptive Fractal Analysis (AFA) [43,44,45] was used to characterize serial correlations in the stride interval time series produced by right foot heel strikes. This method is more accurate than the DFA for short signals [46] and when signals have nonlinear trends [43,45]. A full tutorial on AFA has been previously published [47]. Briefly, AFA uses the following steps: (1) integrate the time series; (2) generate a globally smooth trend signal to the integrated time series by patching together local polynomial fits to the data at a time scale determined by the selected window size (w); (3) calculate variance of the data around the polynomial trend (termed fluctuation function, F(w)); (4) examine the relationship between the F(w) as function of w on a log-log plot. The slope of the linear relationship between log₂ (F(w)) and log₂ (w) provides a characterization of the serial correlations in the time series: α = 0.5 indicates random noise, 0 < α < 0.5—anti-persistent dynamics, 0.5 < α < 1—persistent dynamics. When α values are greater than 1, this indicates a different class of signals: Brownian noise processes (1 < α < 1.5—under-diffusive random walk, α = 1.5—random walk, 1.5 < α < 2—hyper-diffusive random walk.

We estimated the scaling exponent α within two regions similarly to Marmelat et al. [31]: a short-term region (αST) spanning window sizes from 5 to 9 strides and long-term region (αLT) spanning from 13 to 183 strides. The rationale for choosing these regions was that participants have been reported to synchronize to unpredictable fractal signals only on long-term scales (termed “complexity matching”), even without being able to synchronize on the short stride-by-stride scale. The increase in global coupling over practice is illustrated for a single subject in Figure 3. All analyses were performed in Matlab 2017a (Mathworks, Natick, MA, USA).

2.5. Statistical Analysis

Linear mixed models (LMM) were used to evaluate the effects of metronome training on gait performance. An LLM approach was better suited for our study design relative to a typical repeated measures analysis of variance (ANOVA) approach for several reasons. First, an ANOVA assumes data normality, homogeneity, and sphericity, all of which can be particularly challenging with longitudinal datasets. The LLM approach allows for different variances across levels or groups, affording greater flexibility to model the data. Regarding sphericity, an ANOVA assumes that variance is equal between the combinations of levels or groups, whereas LLM does not have this assumption and can model the covariance in the data. Lastly, LLM can model individual difference trajectories over time, which is important for longitudinal study designs. The LLM analysis for our study design led to the modeling of an estimated marginal mean at each session (day) and condition (pre-test, training, post-test), which afford the comparison of across the longitudinal analysis. Collectively, the flexibility and robustness afforded by an LLM approach was optimal for our longitudinal study design.

To address Hypothesis 1, we examined change of αST and αLT during the synchronization phase over 7 sessions. The null model was compared to the model with the main effect of session to evaluate statistical significance (alpha = 0.05). To address Hypothesis 2, we used LMM with Condition (pre- and post-test) and Session (1 through 7) on αST and αLT. The main effects and the interaction were evaluated by comparing LMM with and without these effects. All statistical analyses were performed in R version 3.3.3 using the lme4 toolbox.

3. Results

3.1. Hypothesis 1: Participants Exhibit Stronger Coupling to the Fractal Visual Metronome with Practice

Participants successfully modified their gait dynamics to synchronize with the fractal metronome, as both αST and αLT were greater during the synchronization phase compared to pre- and post-test (Figure 4). However, upon visual inspection of individual data, we identified four participants (S1, S5, S8, and S11) who were not able to synchronize to the metronome—they did not match the period of the metronome and thus did not follow task instruction. Their data were excluded from further analyses.

Local coupling between right leg stride time and fractal visual metronome during synchronization phase did not change with practice as indicated by constant αST over the seven practice sessions (p > 0.05; Figure 4A). Values of αST were greater than 1, indicating strongly persistent under-diffusive Brownian motion dynamics of stride time on short-term time scales. Global coupling of stride time to the metronome, however, became stronger with practice as indicated by an increase in the αLT toward to the exponent prescribed by the metronome (p < 0.001; Figure 4B).

3.2. Hypothesis 2: Immediate Retention (i.e., Directly After Training) and Longer-Term Retention (i.e., 24 h After Training) Would Increase as a Function of Increased Practice

There was an immediate effect of metronome synchronization treadmill training on short-term dynamics of stride time during overground walking, such that αST became smaller in the post-test phase compared to the pre-test phase (p < 0.001; Figure 4A). This suggests that the short-term dynamics of stride time became more random immediately after metronome training. However, metronome training on the treadmill did not alter the long-term scaling exponent during overground locomotion, as there was no statistical difference between the pre- and post-test long-term scaling exponent in all testing sessions (Figure 4B).

4. Discussion

The purpose of this study was to determine the extent to which training to synchronize stride timing to a fractal visual metronome while walking on a treadmill would affect the adopted stride time fractal pattern during overground gait. To our knowledge, this is the first study to explore fractal gait training across multiple days that also included a transfer test to overground. Our most impactful finding was that multiple days of treadmill training led to elevated fractal patterns in the long-term region, indicating a positive training effect. However, the effect of positive training that was observed on the treadmill did not transfer to overground walking.

Our first hypothesis was partially supported with the observation that both the local coupling (αST) and global coupling (αLT) were elevated during the treadmill training. However, the local coupling did not increase across days, whereas the global coupling exhibited a relatively linear increase across days. These data provide support for the complexity matching framework, such that the one system attempts to synchronize with the global dynamics exhibited by a connected system [20]. Our data replicate and extend the findings from Uchitomi et al. where they showed a positive training effect from synchronizing to a fractal metronome over four training sessions on consecutive days [35]. Our seven consecutive day study design shows that the linear increase in fractal patterns can continue beyond the initial four-day period tested by Uchitomi and colleagues. Furthermore, our results align with a study showing that higher dosage of training positively effects the enhancement of movement patterns [48].

An important extension of our work is the separation of short- and long-term regions in the AFA analysis, consistent with the approach taken by Marmelat et al. [31], whereas Uchitomi et al. utilized a single region for their DFA analysis. By utilizing short- and long-term regions, we were able to identify differentiating effects of the training. That is, the short-term region was elevated—indicating a response to the fractal training—but the response was not strengthened (or weakened) across the training days. Conversely, the long-term region showed a consistent increase across days, highlighting a dose response training effect. It is important to note that Uchitomi et al. used DFA to characterize fractal gait patterns in their study. While DFA has a long history of being utilized in this context [1,2,49], its challenges with short signals [46] and nonlinear trends [43,45] have been identified. Our use of AFA, an analysis with a similar mathematical foundation as DFA, prohibits a direct comparison to Uchitomi et al., but does provide a deeper dive into effects from fractal gait training.

For the second hypothesis, the results show that there was no immediate retention or 24-h retention of the fractal gait behavior adopted during the training phase. This is inconsistent with previous work that showed immediate retention when the participant stayed on the treadmill during the post-testing phase [34]. The current study was designed to extend the previous study by examining retention during a transfer test. Thus, immediate retention was tested by having the participants walk overground directly after the treadmill training, whereas longer-term retention was assessed 24 h later via the overground walking pre-test that preceded that day’s fractal gait training on the treadmill. The lack of retention and transfer on the same day suggests context dependence with respect to the training. The gait behavior learned during the training phase on the treadmill was not extended to overground walking. This was not completely surprising, as previous work has shown that spatiotemporal gait parameters can differ between treadmill and overground walking, especially with respect to gait variability [50,51]. The reasons for these differences may be contextual. For example, a treadmill provides a smaller ground reaction force than overground gait [52]. A smaller ground reaction force may lead to less salient feedback about foot position during the gait cycle, so a task learned on the treadmill may not be transferred to overground gait due to different ground reaction force profiles. Furthermore, the continuous belt of the treadmill propagates a movement that is outside of the body. The treadmill will not stop even if the subject does. This continuous movement may cause a sensory difference between the two conditions. The self-selected gait speed may have been different enough during overground gait to contaminate any learning that occurred on the treadmill. Previous work has shown that DFA α of stride time intervals changes with different gait speeds [4], so not precisely controlling for different walking speeds on the treadmill and overground may have influenced our results.

A unique contribution made by our study design was to explore the transferability of fractal patterns learned during a training session, which had not yet been empirically explored. Building on the growing literature of fractal gait training [24,25,26,27,28,29,30,31,32,33] and retention of the newly developed fractal patterns [24,27,34], exploring the extent to which treadmill training (which is conducive to clinical/rehabilitation programs) is transferred to overground gait (which aligns with activities of daily living) was a logical next step. Our data shows that the training paradigm can lead to stronger fractal patterns, but those patterns may be contextual and/or environmentally dependent. From a practical perspective, our data suggest that fractal gait training on a treadmill may not a plausible mechanism for altering fractal gait characteristics overground. Future studies should extend the previous fractal gait training work in overground contexts by adding a multi-day training component to explore the retention of the newly developed gait patterns in short- and longer-term durations. Furthermore, future studies should empirically test the extent to which fractal gait patterns relate to adaptability, such as recovery from a trip to avoid a fall. Such information would more firmly ground fractal gait training as a plausible addition to clinical rehabilitation. The continued adoption of IMUs in this context will afford the testing of fractal gait training across a variety of overground environments.

5. Conclusions

This study showed a dose response effect for fractal gait training across a seven-day period with respect to the global coupling to the metronome, the first observation of its kind. Although a stronger fractal pattern was observed during training across the days, transfer of the new pattern to overground gait was not observed. The innovation of our study design was the deployment of a fractal gait training paradigm over a seven-day period, with the limitation that only young healthy adults were enrolled. Future studies should focus on deploying fractal gait training in an overground environment, enrolling a wider spectrum of participants to measure generalizability, and develop study designs to empirically test the relationship between fractal gait patterns and adaptability. Collectively, the data show that fractal patterns in gait are modifiable, but the transferability of these patterns to new contexts needs to be further explored.