Interactive Rhythmic Auditory Stimulation Reinstates Natural 1/f Timing in Gait of Parkinson's Patients

Abstract

Parkinson's disease (PD) and basal ganglia dysfunction impair movement timing, which leads to gait instability and falls. Parkinsonian gait consists of random, disconnected stride times—rather than the 1/f structure observed in healthy gait—and this randomness of stride times (low fractal scaling) predicts falling. Walking with fixed-tempo Rhythmic Auditory Stimulation (RAS) can improve many aspects of gait timing; however, it lowers fractal scaling (away from healthy 1/f structure) and requires attention. Here we show that interactive rhythmic auditory stimulation reestablishes healthy gait dynamics in PD patients. In the experiment, PD patients and healthy participants walked with a) no auditory stimulation, b) fixed-tempo RAS, and c) interactive rhythmic auditory stimulation. The interactive system used foot sensors and nonlinear oscillators to track and mutually entrain with the human's step timing. Patients consistently synchronized with the interactive system, their fractal scaling returned to levels of healthy participants, and their gait felt more stable to them. Patients and healthy participants rarely synchronized with fixed-tempo RAS, and when they did synchronize their fractal scaling declined from healthy 1/f levels. Five minutes after removing the interactive rhythmic stimulation, the PD patients' gait retained high fractal scaling, suggesting that the interaction stabilized the internal rhythm generating system and reintegrated timing networks. The experiment demonstrates that complex interaction is important in the (re)emergence of 1/f structure in human behavior and that interactive rhythmic auditory stimulation is a promising therapeutic tool for improving gait of PD patients.

Introduction

Human timing systems involve a distributed and interactive network that relies heavily on the basal ganglia [1]. Impairments of the basal ganglia, such as in Parkinson's disease (PD) and Huntington's disease, lead to problems of movement timing and rhythm [2], [3], [4]. Among the most debilitating symptoms of PD are gait timing disturbances, for they can lead to falls, reduced independence, and the associated problems of isolation, cognitive decline, and increased mortality [5]. These gait disturbances are manifest in numerous ways including a slow shuffling gait, accelerated walking, or highly variable stride timing [6].

Deficient internal rhythms can be compensated for with external Rhythmic Auditory Stimulation (RAS), as auditory rhythms are thought to entrain motor rhythms via the relatively close neural connections between auditory and motor areas [7], [8]. Extensive clinical studies have shown that fixed-tempo Rhythmic Auditory Stimulation improves many aspects of gait timing (for reviews see [8], [9], [10]). Fixed-tempo RAS can increase gait tempo and stride length [11] and decrease the magnitude of stride-time variability [12], [13]. Improvements in timing continue in the short term after the auditory cues are removed, suggesting that the external rhythms can stabilize internal rhythm generating networks [11], [13]. A 3-week home rhythmic-cueing program improved gait speed and balance, but effects reduced substantially at a 6-week follow-up [14].

Another important method for assessing gait impairment examines the fractal scaling of stride times, and how walking dynamics unfold over time [5]. In healthy adults the small timing fluctuations from stride-to-stride are not random (white noise); instead, a stride time is related to adjacent stride times and to stride times hundreds of strides later. The distribution of stride times in a healthy walk has a 1/f-like structure [5], [15], [16] similar to the fractal-like long-range correlations observed in many complex systems in nature (e.g. [17], [18]). In 1/f relations, the fluctuations are self-similar across multiple time scales (scale invariance), and in a spectral power analysis, log power is roughly proportional to log frequency. While many sources of 1/f have been proposed, prominent theories suggest that 1/f structure emerges from the complex interactions or integration between components in a self-organized system (e.g. [19], [20], [21], [22], [23]).

In Parkinson's disease, the fractal scaling of stride times is considerably weaker; each stride time is relatively random and unrelated to other strides [5], [24], [25]. Decreased fractal scaling is associated with pathology in gait and in cardiovascular activity [26]. The increased randomness and lack of ‘memory’ suggests defective activity among interacting subcomponents (e.g., basal ganglia). Elderly adults with low fractal scaling (i.e., high stride-to-stride randomness and low predictability) are more likely to fall than those with a high fractal scaling, and this index is a better predictor of falling than other indices [27].

Fixed-tempo RAS has proven very promising in gait rehabilitation, but has a few limitations. First, when synchronized with fixed-tempo RAS, the fractal scaling of stride times decreases away from healthy 1/f structure [15], as stride-time variability becomes organized around a single frequency rather than retaining fluctuations [28]. Fixing on a single tempo can decrease adaptability by overtraining one tempo during rehabilitation. Additionally, fixed-tempo RAS requires that the human synchronizes to the external rhythms, but the ability to synchronize with auditory stimuli is impaired in Parkinson's [29] and basal ganglia patients [4]. One possible method to increase gait stability and flexibility and concurrently circumvent Parkinson's patients' impaired synchronization capabilities is to offload some of the synchronization task to an interactive external timing system.

Here, we compare the effects of walking with fixed-tempo RAS and interactive rhythmic auditory stimulation generated by a computer system that can track and interact with a person's gait. The interactive “WalkMate” system developed by Miyake and colleagues generates rhythmic pacing sequences using nonlinear limit-cycle oscillators [30], [31], [32], [33]. The system's intrinsic oscillators transmit auditory pacing signals and receive information about human step times from pressure sensors in the human's shoes (Fig. 1). The system calculates the relative phase difference between its auditory output signal and the human's step timing, and in real time adjusts its phase and frequency (period) to correct a portion of the relative phase difference. This in turn affects the human's gait, thus creating reciprocal interaction and mutual entrainment [33].

Figure 1. WalkMate overview.

A) Schematic depiction of the WalkMate system. B) The computer's timing system used nonlinear oscillators and was organized hierarchically in two modules. Module 1 mutually entrained the gait frequencies of the computer and the participant. Module 2 adjusted the relative phase difference between the computer's auditory onset and the participant's step contact to a target phase difference [more details in the Materials and Methods section].

In the experiment, Parkinson's patients and healthy participants walked around a long corridor with three rhythmic cueing conditions: interactive rhythmic cueing set to mutually entrain with the human (“WalkMate”); non-interactive fixed-tempo Rhythmic Auditory Stimulation set to the individual's spontaneous walking tempo (“RAS”); and a silent control condition (“Silent Control”). For the PD patients, each of these experimental conditions was followed by a lap without auditory stimulation to look for carry-over or memory effects. The dynamics of how walking unfolded over time were analyzed using Detrended Fluctuation Analysis (DFA) [26], [34]. The primary dependent measure of interest was the DFA fractal-scaling exponent as this is an indicative measure of healthy gait [5] and a predictor of falling [27].

Materials and Methods

Participants

Twenty patients (12 women, 8 men) with idiopathic Parkinson's Disease participated in the experiment (mean age = 69.2 years; SD = 7.7). Patients' disease severity was Hoehn and Yahr Stage 2–3, and they did not exhibit freezing or festinating gait. Mean duration of disease was 3.6 years. All were tested while ‘on’ dopaminergic medication. Eighteen healthy controls (16 men) also participated (mean age = 24.7 years; SD = 2.7). Written informed consent was provided and participants were paid for participating. Experimental procedures were approved by the Kanto Central Hospital Ethics Committee.

Procedure and Equipment

Participants were instructed to walk at a natural and comfortable pace around a long corridor. Rhythmic auditory stimuli (100 ms sine tones at 523 and 700 Hz) were played over circumaural headphones. Three types of auditory stimulation were presented in separate, counter-balanced blocks: interactive rhythmic cueing with period and phase adjustment (“WalkMate”); fixed-tempo rhythmic auditory stimulation (“RAS”); and unassisted silent control condition (“Silent Control”). For the PD patients, each block consisted of three separate trials: first, a pretest trial without auditory stimulation to establish baseline performance; second, a test trial with one of the three auditory stimulation conditions to establish the immediate efficacy of stimulation; and third, a post-test trial without auditory stimulation to examine potential carry-over effects. Trials within a block were separated by 5-minute breaks, and blocks were separated by 30-minute breaks. No baseline differences, nor order effects, were observed among the pretest trials during the experiment, indicating no significant fatigue or end-of-dose effects at the end of the experimental session. After each trial, patients reported their perceived movement stability on a 7-point Likert scale (1 = my walking felt very stable; 7 = my walking felt very unstable). The healthy control experiment omitted the baseline and carry-over trials, and thus consisted of the three rhythmic cueing conditions counter-balanced in order. The corridor was 200 m long. The exact distance walked varied slightly between participants, and distance was not recorded so we could not calculate gait speed. Trials typically contained three wide 90 degree turns; a wide angle turn should not substantially affect stride times, compared to a sharp turn, a stop-and-restart, or a 180 degree turn-around. On average, each trial lasted 3 minutes and contained 320 footsteps.

Gait timing information was collected via pressure sensors attached to participants' shoes, was relayed to a laptop via radio frequency every 10 ms, and was processed in real time for the requisite auditory stimulation. In trials with auditory stimulation, the rhythmic auditory presentation started after 25 seconds of walking. The participant's walking tempo from this initial stage determined the stimulus start tempo (based on the mean of 5 step periods after excluding extreme values). In the fixed-tempo RAS condition, the stimulus tempo remained constant throughout the trial; setting the stimulus tempo to the participant's natural tempo, rather than 10% faster as sometimes used, should encourage synchronization. In the interactive WalkMate condition, the stimulus tempo changed in response to the participant's gait timing. The computer algorithms controlling the stimulus tempo were run in Matlab on a Panasonic CF-W5 laptop.

The computer's timing system used nonlinear oscillators and was organized hierarchically in two modules. Module 1 mutually entrained the frequencies of the computer's auditory outputs and the participant's strides. Module 2 adjusted the relative phase difference between the computer and the participant to a target phase difference.

Module 1 utilized phase oscillators in its control law, as shown in equation (1). Here, θ_m represents the computer system's phase of its cycle, and ω_m designates its natural frequency. When θ_m in equation (1) attained an integer multiple of 2π, the system transmitted a tone to the participant. The input variable of this equation, θ_h, presents the phase of the participant's gait cycle, estimated from the discontinuous timing of the participant's heel strike. K_m (>0) designates the coupling constant.

(1)

Module 2 was responsible for adjusting the relative phase difference to a target value. The relative phase between the human's step time and the computer system's auditory output from Module 1 is Δθ_m = θ_h−θ_m. The control law for Module 2 could then be presented as in equation (2), in which Δθ_m, Δθ_d, and μ denote the Module 1 phase difference, the target phase difference, and the control gain, respectively.

(2)

The above equations can be applied for both the right and left legs, with a phase shift of π. In this study values of 0.5, 0.32, and 0.2 rad were used for K_m, μ, Δθ_d respectively.

Data Analysis

Temporal processes often show long-range correlations and fractal scaling. Long-range dependence, “long memory,” power laws, and 1/f-like noise have been observed in time series from many domains (for reviews see [17] [35]).

One can inspect the degree of scale invariance by plotting the fluctuations at different temporal resolutions. We quantified the long-range correlations using detrended fluctuation analysis (DFA) [5], [26], [34]. This technique offers certain advantages over other methods (e.g., spectral or Hurst analyses) when dealing with non-stationary time series, for it “avoids spurious detection of apparent long-range correlations that are an artifact of non-stationarity” [34]. We briefly describe the DFA algorithm following Peng et al. [34] and Goldberger et al. [26]. First the human's gait-period time series is integrated, and then this integrated time series is split into equal boxes of size n. In each box, a least-squares line is fit to the data, which represents the trend in that box. The fluctuation F(n) for each box is then calculated as the root-mean-square deviation between the integrated time-series and its local trend. This calculation is repeated for all possible time scales (box sizes); here the box sizes ranged from a minimum of 7 data points to a maximum of N/2, where N is the length of the time series. Typically, the fluctuation, F(n), will increase with larger box sizes. A linear relationship on a log-log plot indicates self-similar scaling, in that fluctuations in the smaller boxes are related to the fluctuations in the larger boxes in a power-law relation. The slope of the line log F(n) over log n is the scaling exponent α, and gives a measure of the “roughness” of the original gait time-series (see Fig. 2). Using DFA, a scaling exponent α≈0.5 corresponds to rough and unpredictable white noise; α≈1.0 corresponds to 1/f-like noise and long-range correlations; α≈1.5 corresponds to a random walk process or Brownian noise [26]. Analyses were performed on the stride times of one leg (typically the right side, but due to occasional sensor error (<3% of trials), the left side was analyzed). The first 30 seconds and last 5 strides of each trial were not analyzed.

Figure 2. Examples of two trials.

On the left, the stride times of one leg are plotted against trial time. On the right, the DFA technique plots the average fluctuation per box size. Using DFA, a scaling exponent α≈0.5 corresponds to rough and unpredictable white noise; α≈1.0 corresponds to 1/f-like noise and long-range correlations [26]. The mean and SD of stride times are similar in both trials, but the fractal scaling differs considerably. During the Silent condition (A), the PD patient's strides are unpredictable and akin to white noise, whereas during interactive rhythmic stimulation (B), the stride fluctuations have a 1/f-like structure.

Descriptive statistics report mean values ± standard deviation. Step-to-tone synchronization was analyzed using circular statistical methods including circular variance and a Rayleigh test of uniformity (see [36] for an in-depth treatment of circular methods). Planned comparisons between groups used independent samples t-tests. Comparisons between the three experimental conditions (fixed-tempo RAS, interactive WalkMate, Silent Control) were analyzed with repeated-measures ANOVAs separately for each group; and subsequent pairwise tests used Fisher's Least Significance Difference test. The step-to-tone synchronization with fixed-tempo RAS and interactive WalkMate were compared with paired-samples t-tests. Reported p-values are for two-sided tests, and the level of significance was p = 0.05.

Results

During unassisted walking (Silent Control), the stride time DFA fractal-scaling exponent for Parkinson's patients (M = 0.92±0.14) was significantly lower than for healthy participants (M = 1.03±0.11), t(36) = 2.50, p = .017 (Fig. 3). This reduced fractal scaling in PD away from healthy 1/f structure is indicative of impaired gait (e.g., [25]).

Figure 3. DFA fractal-scaling exponent results by condition.

A) Parkinson's patients during rhythmic treatment, B) healthy participants during rhythmic treatment, and C) Parkinson's patients carry-over effect during a silent trial five minutes after the rhythmic treatment. The cueing conditions are unassisted Silent Control; interactive WalkMate rhythmic auditory stimulation; and Fixed-tempo rhythmic auditory stimulation (RAS). Error bars represent ± SEM. *p<.05; n.s. = non-significant.

Rhythmic stimulation affected PD patients' fractal scaling, F(2,38) = 3.46, p = .042 (Fig. 3A). The interactive WalkMate auditory stimulation lead to significantly higher fractal scaling compared to unassisted Silent Control and fixed-tempo RAS conditions (pairwise ps<.05); no difference was observed between Silent and fixed-tempo RAS (p>.4). The mean and standard deviation of stride times did not differ among the three conditions (see Table 1), nor did they correlate with fractal scaling; thus dynamic analyses can capture important signals in gait not revealed with more conventional analyses [5]. Importantly, fractal scaling for PD patients with WalkMate (M = 1.01±0.19) did not differ from healthy participants' normal walking (M = 1.03±0.11), t(36) = 0.4, p>.6. This suggests that for Parkinson's patients, interacting with the WalkMate system can reinstate healthy gait dynamics.

Table 1. Stride Times (Mean and Standard Deviation) of one leg in seconds for Parkinson's patients (PD) and healthy participants with rhythmic cueing treatment, and for the PD patients' post-treatment carry-over.

			Condition			F-test
Group	Category	Variable	Silent Control	WalkMate	Fixed-tempo RAS	p-value
PD patients	Rhythmic Cueing	M	1.022 (.081)	1.027 (.082)	1.031 (.088)	0.68
		SD	0.028 (.008)	0.026 (.007)	0.028 (.010)	0.19
Healthy Ps	Rhythmic Cueing	M	1.131 (.074)	1.120 (.071)	1.135 (.073)	0.37
		SD	0.023 (.007)	0.020 (.004)	0.024 (.008)	0.11
PD patients	Carry-Over	M	1.015 (.085)	1.017 (.076)	1.008 (.079)	0.24
		SD	0.027 (.009)	0.026 (.007)	0.026 (.010)	0.77

Standard deviations of each measure are in parentheses.

For the healthy participants, rhythmic stimulation also affected fractal scaling, but differently than for PD patients, F(2,34) = 3.19, p = .05 (Fig. 3B). Unlike the PD patients, fractal scaling did not differ between WalkMate and silent baseline (p>.2), but fixed-tempo RAS drove fractal scaling lower than baseline (p = .011). A reduction in fractal scaling with fixed-tempo RAS has been previously observed, as the variance becomes organized around the stimulus tempo [15], [28]. WalkMate boosted fractal scaling only for PD patients.

Closer inspection of the step-to-tone phase differences showed that stable synchronization was uncommon for fixed-tempo RAS (despite setting the tempo to the participant's spontaneous walking tempo). Five of 18 healthy participants and only 2 of 20 PD patients stably synchronized with the fixed-tempo RAS, as indicated by a unimodal distribution of step-to-tone phase differences (Rayleigh test of uniformity p-values <.01). Other studies show that PD patients can synchronize their steps to fixed-tempo RAS when instructed to synchronize [8], [9]; but our data indicate that if they are not explicitly instructed to synchronize, they often will not. Regardless, across groups the fractal scaling tended to be lower when synchronized with fixed-tempo RAS (M = .84; n = 7) than when un-synchronized (M = .91, n = 31).

With WalkMate, all PD patients and healthy participants exhibited stable synchronization between their footsteps and the auditory stimuli (Rayleigh test p-values <.01 for all trials). Even without explicit instruction, the PD patients and healthy participants coupled with the WalkMate system.

The stability of step-to-tone synchronization was also assessed in terms of circular variance, which indexes the variance of step-to-tone relative phases on a scale from 1 (no synchronization between steps and tones, with relative phases distributed uniformly around the unit circle) to 0 (perfectly stable synchronization with a unimodal distribution of relative phases). This index of step-to-tone synchronization was far lower with WalkMate than with fixed-tempo RAS for both groups. For the PD patients, mean circular variance with WalkMate (M 0.038±0.036) was lower than with fixed-tempo RAS (M = 0.937±0.082), t(19) = 50.2, p<.001; and for the healthy participants, mean circular variance with WalkMate (M = 0.012±0.007) was lower than with fixed-tempo RAS (M = 0.753±0.372), t(17) = 8.5, p<.001.

In addition to higher fractal scaling and more stable step-to-tone coupling with WalkMate compared to fixed-tempo RAS, the patients also preferred WalkMate. After each trial, patients rated their perceived movement stability on a 7-point Likert scale (1 = highly stable; 7 = highly unstable). Subjective stability ratings differed between conditions, F(2,38) = 3.24, p = .050. Patients reported that their body movements with WalkMate (M = 3.8±0.8) felt significantly more stable than with fixed-tempo RAS (M = 4.2±0.7), p = .015; and WalkMate tended to feel more stable than the silent control condition (4.2±0.6), p = .070. Perceived stability did not differ between fixed-tempo RAS and silent control (p>.5).

Finally, potential carry-over effects from the rhythmic stimulation were examined. After each trial, the PD patients rested for 5 minutes then walked another trial without sound. The carry-over fractal scaling differed between conditions, F(2,38) = 4.31, p = .021 (Fig. 3C). Trials without sound post-WalkMate retained higher fractal scaling (M = .97±0.14), compared to post-fixed-tempo RAS (M = .92±0.10) or post-Silent (M = .90±0.12) (ps<.05). This ‘memory’ effect indicates that the rhythmic stabilization induced by the interactive system carries over into the short term.

Supplementary results

Overall, the healthy participants had lower standard deviations of stride time (F(1,36) = 5.8, p = .021) and longer stride times (F(1,36) = 18.0, p<.001) than the Parkinson's patients (see Table 1), but these measures did not correlate with fractal scaling.

Previous work has shown that when synchronized with a fixed-tempo metronome, fractal structure can shift from the series of stride times (periods) to the series of asynchronies [28]; cf. [20]. However, we did not observe fractal structure in the asynchronies, because of either the unreliable or the impaired synchronization. Future work should examine fractal structure of asynchronies for patient populations instructed to synchronize.

In order to ensure that the 1/f fractal-scaling results arose from the sequential ordering or structure rather than the stride interval distribution, we ran surrogate tests with randomly shuffled data [15]. Each time series was randomly shuffled 20 times, and the scaling exponents for these shuffled time-series were calculated using DFA. The fractal scaling exponents of the shuffled data were far lower than original time series and indistinguishable from white noise (mean scaling exponent = .51±.03), so the results are not simply artifacts of the stride interval distribution.

Discussion

In the silent baseline condition, the PD patients' stride times had lower fractal scaling (higher randomness) than those of healthy participants. This low fractal scaling of stride times has been associated with impaired gait and basal ganglia dysfunction [24].

In the fixed-tempo RAS condition, the fractal scaling decreased when steps and tones were synchronized, as previously observed [15], since the stride times become organized around the metronome rather than flexibly fluctuating. We did not explicitly instruct synchrony; somewhat surprisingly, the patients rarely synchronized with the fixed-tempo RAS, and hence their fractal scaling remained at the impaired level. Synchronization is not automatic and the external cues were not strong enough to drive the system in unidirectional audio-motor entrainment. Fixed-tempo RAS effectively improves many gait impairments, but the attentional and/or volitional requirements diminish its applicability in a permanent cueing device (as was recommended by [14]). Previous research shows that attention to movement (involving fronto-cortical networks) can improve Parkinsonian gait by bypassing the defective basal ganglia mechanisms that normally subserve automatic movement [37]; however, attending to an external metronome, in addition to the already elevated attention to movement in PD [38], could create considerable cognitive load. Such “dual tasking” could burden a patient and deter use. Additionally, a walking support device with a fixed tempo (or requiring manual adjustment) is impractical in a dynamic real-world environment.

In the interactive WalkMate condition, the gait of patients and healthy participants always coupled with the tones, and patients' fractal scaling increased back to healthy 1/f levels. The computer system took over some of the synchronization task by correcting a portion of the relative phase difference and adjusting its period (frequency) to complement the human's timing. Previous work showed that healthy participants' finger-tapping was more synchronized with a slightly adaptive metronome than a fixed-tempo metronome [39], cf. [40]; such adaptivity might importantly compensate for PD patients' impaired synchronization abilities. In PD, disruption of the basal ganglia's direct pathway weakens the phasic cues from the basal ganglia that should boost cortical excitability for timing automatic movements [37], [41]. When these internal phasic cues are disrupted, external cues could boost excitability for movement (e.g. [37]). External auditory cues are integrated into rhythmic motor output timing when presented in temporal proximity to movement, but not when temporally distant [42]–[43] cf. [44]. Here, the interactive system kept tones consistently close to the motor output time, thus promoting integration of the tones into motor output timing. The tones constrained the nervous system's output and altered gait timing as indicated by the change in gait dynamics. In turn, gait timing altered the computer system's tone timing, thereby creating interactive, mutual entrainment.

The interaction or integration among multiple components is a key factor in the (re)establishment of 1/f structure, as is consistent with prominent theoretical accounts for the source of fractal scaling and 1/f structure (e.g., [19], [22], [23], [35]). In gait, components across multiple time-scales interact in feedforward and feedback loops, including the neural-muscular periphery, the intraspinal nervous system, and central networks for motor control and timing that include the basal ganglia [45]. When an important interactive component like the basal ganglia is disrupted (as in Parkinson's or Huntington's disease), gait is impaired and fractal scaling decreases [24]. Replacing or restoring this damaged component could reestablish these loops and contribute to the return of 1/f structure, as observed here with the interactive system. On one hand, the interactive system could replace some of the impaired basal ganglia functionality of generating rhythmic oscillations, integrating sensorimotor information, and relaying timing signals for the motor system. On the other hand, the carry-over effect of higher fractal scaling 5 minutes after the interactive rhythmic stimulation suggests that auditory stimulation is not simply replacing the damaged component or acting as an external pacemaker driving motor systems, but that it temporarily restores the basal ganglia functionality and neural time-keeping circuitry [11], [13].

Parkinson's patients' basal ganglia functionality can be temporarily restored and carry-over after synchronizing with auditory rhythms [46]. In Parkinson's disease, decreased activity in the basal ganglia's direct pathway (including the striatum) results in excessive thalamic inhibition and reduced cortical excitability. Aligned rhythmic stimulation would activate the striatum [47]. In turn, this striatal activity could potentially boost activity in the direct pathway, resulting in less thalamic inhibition, allowing increased phasic timing cues to cortex.

The 1/f structure of stride times could serve to increase flexibility and stability of gait (rather than simply an epiphenomenal by-product of reintegrated circuits). The fractal scaling in healthy gait (as well as in healthy heart-beat time series) might benefit the system by avoiding “mode locking” to a single tempo, thereby increasing flexibility and responsiveness to environmental demands [5], [26]. Additionally, fractal scaling is an important index of gait stability [5]. The association between low fractal scaling and falling [27] might relate to decreased predictability: Highly random stride times undermine the temporal predictability of an upcoming stride time, which in turn would hinder corrective movement, balance, and stability. In a 1/f time series, the upcoming stride time is more predictable than in a random series, because a) short-range correlations have a more circumscribed set of temporal probabilities, and b) due to scale invariance, the long-range correlations can be used to predict the short-range ones and vice-versa (similarly, fractal structure in music improves predictability of tempo changes [48]). This increased predictability might explain the patients' higher perceived movement stability with the interactive rhythmic stimulation.

Some limitations of the current study should be noted. The patient group and the healthy participants were not age- or gender-matched. Due to our PD patients' state (and many experimental conditions), we could not collect very long trials. Three minute trials are relatively short for DFA analyses, and longer trials would be preferable in future work [49]. Additionally, the primary focus here was on fractal scaling, and it is unclear how the interactive system could affect variables such as gait speed. The distance of trials varied slightly and was not recorded, hence we cannot calculate speed. Based on the null effects of mean stride time, differences in gait speed are unlikely. Future work could systematically manipulate the target phase difference between step time and auditory onset, and examine potential effects on walking speed of PD patients.

In sum, PD patients' stride times had low fractal scaling at baseline, indicating gait impairment [5], [26]. When PD patients entrained with the interactive rhythmic system, their fractal scaling increased back to healthy 1/f levels, and their perceived stability improved. Elevated fractal scaling persisted 5 minutes after removing the interactive stimulation, potentially due to a stabilization of timing networks and basal ganglia functionality. This human-machine interaction provides a good example of coupling internal and external systems through dynamic feedback [30], [32] and is a promising rehabilitation tool. Previous work showed that the interactive system can stabilize gait in hemiparetic stroke patients [50] and in Parkinson's patients with strongly festinating gait [33]. Future work should investigate effectiveness in patients ‘off’ or with reduced dopaminergic medication. Offloading the synchronization task to an external device ensures alignment of tones and steps without attention or ‘dual tasking’; and this innovation could increase the usability and feasibility of a walking support device. Interactive rhythmic auditory stimulation offers a flexible, portable, low-cost, non-invasive therapeutic intervention that may improve the mobility, stability, and quality of life of Parkinson's Disease patients.