Modality-specific communication enabling gait synchronization during over-ground side-by-side walking

Human Movement Science 31 (2012) 1268–1285

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Modality-specific communication enabling gait synchronization during over-ground side-by-side walking Ari Z. Zivotofsky a,⇑,1, Leor Gruendlinger b,1, Jeffrey M. Hausdorff b,c,d a

Gonda Brain Research Center, Bar-Ilan University, Ramat-Gan 52900, Israel Laboratory for Gait & Neurodynamics, Movement Disorders Unit, Department of Neurology, Tel-Aviv Sourasky Medical Center, Tel-Aviv, Israel c Department of Physical Therapy, Sackler Faculty of Medicine, Tel-Aviv University, Tel-Aviv, Israel d Harvard Medical School, Boston, MA, USA b

a r t i c l e

i n f o

Article history: Available online 22 June 2012 PsycINFO classification: 2540 Keywords: Stride length Cadence Synchronization Human Gait Rhythm Dual tasking Entrainment

a b s t r a c t An attentive observer will notice that unintentional synchronization of gait between two walkers on the street seems to occur frequently. Nonetheless, the rate of occurrence and motor-sensory mechanisms underlying this phase-locking of gait have only recently begun to be investigated. Previous studies have either been qualitative or carried out under non-natural conditions, e.g., treadmill walking. The present study quantitatively examined the potential sensory mechanisms that contribute to the gait synchronization that occurs when two people walk side by side along a straight, over-ground, pathway. Fourteen pairs of subjects walked 70 m under five conditions that manipulated the available sensory feedback. The modalities studied were visual, auditory, and tactile. Movement was quantified using a trunk-mounted tri-axial accelerometer. A gait synchronization index (GSI) was calculated to quantify the phase synchronization of the gait rhythms. Overall, 36% of the walks exhibited synchrony. Tactile and auditory feedback showed the greatest ability to synchronize, while visual feedback was the least effective. The results show that gait synchronization during natural walking is common, quantifiable, and has modalityspecific properties. Ó 2012 Elsevier B.V. All rights reserved.

⇑ Corresponding author. Tel.: +972 3 531 7796; fax: +972 3 535 2184. 1

E-mail address: [email protected] (A.Z. Zivotofsky). The first two authors contributed equally to this paper.

0167-9457/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.humov.2012.01.003

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1. Introduction Two people who walk from one point to another and wish to travel together need to match their momentary gait speeds. To achieve this, each can select from an array of cadence and stride length combinations. Surprisingly, casual observation suggests that people who ambulate together side-by-side often appear to be walking in perfect synchrony, with an identical stride length, cadence, and even heel strike timing. This phenomenon has recently been studied in a qualitative manner under natural, overground walking conditions (Zivotofsky & Hausdorff, 2007) and more quantitatively during treadmill walking (Nessler, De Leone, & Gilliland, 2009; Nessler & Gilliland, 2009, 2010; van Ulzen, Lamoth, Daffertshofer, Semin, & Beek, 2008). The fact that bipedal locomotion is so central to the human movement repertoire, together with the observed existence of interpersonal synchronization in both movement amplitude (stride length) and movement frequency (cadence), makes its study especially interesting within the field of interpersonal synchronization. However, the emotional, cognitive, motor, and sensory mechanisms whereby two people synchronize their gait, either with or without any conscious awareness or effort, are not well understood and have only recently begun to be studied. A previous paper investigated synchronized walking (Zivotofsky & Hausdorff, 2007) in a qualitative manner by having experts review and score videos of the walkers’ leg movements to determine the degree of synchronization under varying visual, auditory, and tactile conditions during natural walking. Nessler and Gilliland (2009) documented interpersonal synchronization patterns for the same sensory modalities during treadmill walking. It is important to note, however, that treadmill walking differs from natural over-ground walking in that it involves a quasi-periodic visual, auditory, and tactile sensory environment and is known to alter gait kinematics. For example, it reduces the natural variability of speed, stride length, and stride time (Frenkel-Toledo et al., 2005) observed in overground walking, likely affecting the temporal structure, mechanisms, and even likelihood of occurrence of interpersonal gait synchronization. Thus, quantitatively studying this phenomenon in natural over-ground walking is likely to yield different synchronization structures from treadmill walking and may more closely reflect the natural phenomenon. The aim of the current study is to evaluate interpersonal, unintentional gait synchronization of two people during natural over-ground walking and to evaluate the ability of each sensory modality to induce it. Previous studies have demonstrated that healthy adults and different patient groups can match their gait rhythm to external cues, essentially synchronizing with the external source (Hausdorff et al., 2007; Roerdink, Lamoth, Kwakkel, van Wieringen, & Beek, 2007; Rubenstein, Giladi, & Hausdorff, 2002; Thaut et al., 1996; van Ulzen, Lamoth, Daffertshofer, Semin, & Beek, 2010). Visual cues (e.g., stripes on the floor), auditory cues (e.g., a metronome, rhythmic music), tactile cues (e.g., vibration inside the shoe), and combined tactile/mechanical/proprioceptive cues (e.g., a treadmill) have successfully entrained the speed, stride length, or stride time of patients with Parkinson’s disease (Hausdorff et al., 2007; Herman, Giladi, & Hausdorff, 2009; Herman, Mirelman, Giladi, Schweiger, & Hausdorff, 2010; Holt, Hamill, & Andres, 1990; Nieuwboer et al., 2007; Rochester et al., 2005; Rubenstein et al., 2002; van Wegen et al., 2006). In other words, visual, auditory and tactile cues can be used therapeutically to provide a pacemaker for walking, at least when one person is involved. Given that two people walking together can synchronize, the question is which, if any, of the cues known to be effective at entraining a single walker may be at work during the mutual synchronization of a pair of walkers. The present study was designed, therefore, to address the following questions under natural, overground walking conditions: (1) Which sensory modalities may be utilized to achieve rhythm entrainment during side-by-side, over-ground walking? (2) Does the sensory modality affect the properties of the synchronized state? (3) Does the gait of synchronized walkers differ from that of unsynchronized walkers? 2. Methods 2.1. Subjects Fourteen pairs of healthy young adults (mean age: 26 ± 2 yrs; M ± SD) were studied. Subjects within each pair were matched for height (less than 3% difference; mean height: 175 ± 6 cm) and gender (2

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pairs of females and 12 pairs of males). They were recruited from the local student population at Tel Aviv University and provided written informed consent prior to participation. The study was approved by the human studies committee of the Tel Aviv Sourasky Medical Center. All subjects were healthy and had no known musculo-skeletal, orthopedic, or neurological conditions. 2.2. Protocol Each pair of subjects walked along a straight, 70 m obstacle-free and sunlit flat path made of hard concrete under five conditions that modified the available sensory feedback. Footwear was the subject’s own shoes. There was no pre-experiment practice. Subjects walked using their comfortable gait such that each walk lasted approximately 40 s. The sensory feedback manipulations were: (1) obstructing peripheral visual feedback by means of dust-impermeable glasses whose sides were covered with black opaque tape; (2) blocking auditory communication with ‘‘walkman’’ headphones that supplied white noise to block out sounds; (3) providing tactile/mechanical feedback by means of handholding. The conditions were coded as follows: 3F (all three feedback modalities were available, i.e., visual, tactile (handholding), and auditory); TF (only tactile feedback, i.e., handholding); AF (only auditory feedback); VF (only visual feedback, i.e., being able to see the other walker with peripheral vision); and 0F (no feedback available, i.e., no visual, tactile, or auditory feedback). The various feedback conditions were presented in a fixed sequence. Subjects were told that the purpose of the experiment was to test the influence of sensory feedbacks on gait by evaluating the effects of different types of sensory feedback on walking. The instructions to the subjects were to ‘‘walk side-by-side’’ along the path, without further elaboration. Subjects were simultaneously instructed to start walking using a gentle tap on their backs, delivered by the two hands of the experimenter. Subjects were told not to speak to each other or to communicate in any other form during the walks. There were no explicit instructions about gaze direction in any of the conditions. 2.3. Measurements and data analysis Data were recorded using identical trunk-mounted tri-axial accelerometers (JAS Technologies, MA, USA) that were time-locked and then secured on the back of each subject at the height of L5. The data were sampled at 256 Hz and were downloaded offline. All subsequent mathematical analyses were performed using Matlab (MathWorks, USA). The vertical acceleration component was extracted and used to calculate mean stride time, asymmetry of the cadences of the two walkers and a gait synchronization index (GSI). Specifically, accelerometer signals were verified to be stationary, low-pass filtered at 3 Hz using an FIR filter, shifted to have a mean value of zero, Hilbert-transformed, and the phases were extracted from the analytic signal, as described previously (Tass et al., 1998; van Ulzen et al., 2008). We note that since the momentary phase of a signal that is not a pure sine wave is not uniquely defined mathematically (see, e.g., Fuchs, Jirsa, Haken, & Kelso, 1996, Section 4), there are several working definitions of phase in the literature. We chose a method that is widely applicable in physics (see, e.g., Pikovsky, Rosenblum, & Kurths, 2001, Chapter 6) and captures the intuitive notion of a phase. In the vertical acceleration data of young adults, each full cycle of the phase corresponded to one step, rather than one stride, because of the clear dominance of the second spectral peak over the first one in trunk vertical acceleration during gait, even in the case of somewhat asymmetric gait. As a consequence, our synchronization measures do not distinguish between in-phase and anti-phase gait synchronization, i.e., whether heel strikes are synchronized between ipsilateral or contralateral legs of the walkers, and both states would result in a 0° phase difference between the walkers. After calculation of the phases of the two walkers, they were subtracted from each other to yield a time-varying phase difference. To quantify the constancy of the phase difference, we estimated its entropy. A histogram of the phase differences during the walk (modulus 2p) was constructed and its Shannon entropy was calculated as described previously (Pikovsky et al., 2001; Tass et al., 1998). The entropy value was then linearly normalized to yield a GSI score on a scale of 0 to 1, where 0 indicates a uniform distribution of the phase difference (i.e., a high entropy, corresponding to no synchronization) and 1 corresponds to a constant phase difference (low entropy, maximum synchronization). The resulting GSI is thus a dimensionless number, measuring the ratio between the observed degree of

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synchronization and the maximum possible level of synchronization. In other words, it is a ‘‘soft’’ quantification method, which does not declare a walk (or a certain sub-period of it) to be either ‘‘synchronized’’ or ‘‘unsynchronized’’, but rather quantifies the degree of synchronization on a scale of 0 to 1. In addition to the GSI value obtained for each walk, a GSI reference value (‘‘random’’ level of synchronization) for each pair of subjects was also calculated by computing the GSI for the same two walkers, taken as the average over all artificially paired signals from different walks. This is a virtual, surrogate condition where the GSI is calculated, for example, from the phases of walker 1 in the VF condition subtracted from those of walker 2 in the AF condition. Theoretically, the GSI values should be 0 for two randomly chosen walks. This method was used in order to control for any non-specific interpersonal tendency for synchronization between the two walkers, for example due to a natural similarity between their cadences. Since the GSI is based on the entropy of the phase difference between the walkers, it gives no information on the average phase difference. The latter was, therefore, separately calculated as the circular mean of the phase difference along the walk (Zar, 2007). The resulting mean phase difference, u, ranges between 180° and 180°, where 0° indicates no phase lag between the walkers. For walks with zero degree of synchronization, we expect the value of u to be some random number between 180° and 180°. In this case, the average absolute value of u across all unsynchronized walks would be close to 90°. In contrast, when there is a high degree of synchronization, u quantifies the average phaseshift between the walkers and its value would be close to zero for either in-phase or anti-phase synchronization, as previously mentioned. As described above, u is expressed in step-based units. To convert stride-based phases in the range 0°–360°, reported in several other studies, into the same form as (the absolute value of) average step-based phases, we used the formula:

j ustep j¼j ðð2ustride þ 180Þmod 360Þ  180 j To obtain an indicator for the similarity between the average stride times of the two walkers, the asymmetry of their cadences was calculated as:

Cadence asymmetry ¼ jcadence1  cadence2 j=ðcadence1 þ cadence2 Þ where cadence is defined as 120/(average stride time). In addition, the coefficient of variation (CV) for the series of stride times of each walker was calculated as:

CVð%Þ ¼ 100  ðstandard deviation of stride timeÞ=ðmean of stride timeÞ Note that, for an uninterrupted walk, average stride time is easily calculated as twice the average step time. Since average stride time generally depends on height (see, e.g., Pierrynowski & Galea, 2001), some studies report a normalized value by dividing by the square root of the average height of the walkers. This normalization was previously shown to reduce inter-subject variability of average stride times, and is derived from the natural period of a leg-length pendulum (Hof, 1996; Pierrynowski & Galea, 2001 for details). When used, statistical comparisons between normalized stride times are often reported alongside the non-normalized results. As an initial investigation of the effect of feedback condition, repeated measures analysis of variance was applied to the outcome measures (i.e., GSI, stride time, CV). Subsequently, pairs of walkers were divided into two groups, as described below. Statistical analysis for comparing feedback conditions and groups of walkers was performed using repeated measures ANOVA to test for the effect of condition, with planned post-hoc comparisons (2-tailed paired t-tests; due to the small group size, p-values were not corrected for multiple comparisons). Independent t-tests were used to compare the gait and subject characteristics of two groups of walkers (i.e., those that displayed synchrony and those that did not) in order to try and determine why some pairs displayed synchronization and others did not. Summary measures are reported as means ± SEM (Standard Error of the Mean). Hartigan’s dip test for unimodality was used to quantify how likely it was for an observed distribution of GSI values to be unimodal (Hartigan & Hartigan, 1985). SPSS was used for the statistical analyses. A p-value 6.05

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Fig. 1. The average level of the GSI changes based on feedback modality. (a) Pooling of data from all 14 walks. Bars show means ± standard errors of the mean (S.E.M.) of the GSI. Gray bars are used to indicate conditions that were determined to be unsynchronized. All conditions except 0F had higher GSI’s than both the VF and the random (p < .05). In addition, the 3F condition had a significantly higher average GSI than the 0F condition (p < .05). It is noteworthy that the VF and random conditions, marked in gray, had similar GSI averages, indicating the poor ability of VF to induce synchronization; (b) A histogram of all GSI values shows a strongly bimodal distribution, where most values are either close to zero, or above 0.2. See text for a mathematical test (Hartigan’s dip test for unimodality) that suggests that the data is indeed unlikely to come from a unimodal distribution. Thus, walks can be said to be either ‘‘synchronized’’ or ‘‘unsynchronized’’. Walks on the right side of the histogram were labeled as ‘‘synchronized’’ (see text); (c) Effect of sensory feedback on the level of synchrony: Of the 7 pairs that synchronized on some of the walks, all of them did so on the 3F condition, 6 did so on TF, 5 on AF, 2 on VF and, surprisingly, 5 synchronized on the 0F condition; (d) Histogram showing how many pairs had synchronized walks. While 7 pairs had 0 synchronized walks (the ‘‘unsynchronized pairs’’), the other 7 pairs had at least 2 synchronized walks each; (e) Effect of sensory feedback on the average GSI for the seven ‘‘synchronizable’’ pairs. Error bars show the S.E.M. In these 7 pairs, all conditions, including 0F, had higher GSI’s than both the VF and the random conditions, marked in gray (p < .05). In addition the 3F condition had a significantly higher average GSI than the AF condition (p < .05).

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was considered to indicate significance. Finally, we note, that the words ‘‘faster’’ and ‘‘slower’’ always refer to the stride frequencies of the walkers, and not to their velocities, because during side-by-side walking the velocities are, by definition, equal. 3. Results Accelerometer data was collected from 14 pairs that performed 5 walks each, yielding a total of 70 walks with an average of 69.3 ± 14.6 steps per subject per walk. 3.1. Synchronization among subjects The effects of different sensory feedback conditions on the degree of synchrony, as measured by the GSI, are summarized in Fig. 1a. The GSI score tended to be largest in the 3F condition (all 3 modalities present), followed by the TF and AF. The VF and the random, surrogate condition (‘‘crossing’’ acceleration signals that were recorded during different walks of the same two subjects) were indistinguishable from each other. Note that the 0F condition (no feedback) showed a trend toward synchronization. Specifically, repeated-measures ANOVA indicated a significant difference between the six conditions (F = 5.7, p < .01, using GSI scores from five walks and the one random, ‘‘crossed’’ condition), with the GSI score for 3F significantly higher than that for 0F, and with scores for each of 3F, AF and TF being significantly higher than those for VF and the random condition.

3.2. Evidence for two subgroups (‘‘synchronizers’’ and ‘‘non-synchronizers’’) The histogram of the seventy GSI scores from all of the walks (Fig. 1b) indicates that their distribution was not unimodal (Hartigan’s dip statistic for unimodality = .066; p-value = .015). Rather, almost all GSI values were either below .15 or above .25, suggesting a bimodal distribution. Bimodality was also present in the distribution of the cadence asymmetries (data not shown). The bimodality indicates that the walks were usually either synchronized or unsynchronized, with few in-between cases. Furthermore, it suggests that, when present, synchronization usually lasted throughout the majority of the walk, perhaps due to the relatively short duration of the walks (about 40 s for a walk of 70 m). Indeed, an intermediate GSI score of around .2 was observed in only three walks out of the seventy, in which synchronization either started, ended, or was momentarily perturbed in the middle of the walk (data not shown). As a result of this bimodality, walks were classified as either ‘‘synchronized’’ or ‘‘unsynchronized’’, based on a cutoff value of GSI = .21, which corresponds to 3 standard deviations above the average ‘‘random’’ level for all of the pairs. The results reported below were robust to changes in the location of the cutoff point by up to ± .05. Using this cut-off, 25 out of 70 walks (36%) were classified as synchronized, and the rest were deemed unsynchronized. Among the different conditions, 50% (7/14) of the walks were synchronized for the 3F condition, 36% (5/14) for AF, 43% (6/ 14) for TF, 14% (2/14) for VF, and 36% (5/14) for 0F (see Fig. 1c). Interestingly, synchronization was not only associated with specific sensory modalities, but also with specific pairs. Seven of 14 couples (50%) never walked synchronized, regardless of the sensory feedback. Of the remaining seven pairs, two synchronized in all five walks, two synchronized on four occasions, and the three remaining pairs synchronized in at least two feedback states (see Fig. 1d). There was no pair who synchronized in only one walk. We, therefore, divided the pairs into two groups: ‘‘synchronizers’’ and ‘‘non-synchronizers’’, and tested the effect of sensory modality on the GSI within each group.

3.3. Synchronization within the two subgroups Not surprisingly, there was a significant Group  Sensory Modality effect on the GSI after the separation into groups (F = 8.3, p = .001). Among the ‘‘synchronizers’’, the sensory feedback condition had a significant influence on the quality of the synchronization (F = 9.4, p < .01, repeated measures

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Fig. 2. Correlations between the GSI and other properties of the walk. (a) Relationship between sensory feedback modality and average stride times for the synchronized and unsynchronized pairs. (b) Relationship between sensory feedback modality and stride time variability. F values were 3.3⁄, 0.02, and 1.6 for the effects of modality, group, and Modality  Group, respectively. The points marked ‘‘All’’ in (a) and (b) show the average stride time and CV for the two groups across all feedback conditions and pairs. Error bars show the S.E.M. (c) Cadence asymmetry and GSI are highly correlated with each other (rho = .92 for correlation of log (asymmetry) with GSI, p < .001, Spearman correlation). (d) Relation between phase difference and GSI. The phase difference is random for low GSI values, and close to zero for high GSIs. (e) Pooled data from (d) shows the average absolute value of the phase difference for the synchronized and unsynchronized groups. Note that the average would have been zero only if all phase differences were exactly zero.

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ANOVA). The GSI value for 3F was significantly larger than that for AF (p < .05). As expected, the 3F, AF, and TF conditions all had significantly higher GSI values than the VF and random states for the same seven pairs (p < .05) (see Fig. 1e). In contrast, among the non-synchronizers there was no significant difference in the level of GSI as a function of sensory modality (F = 1.1, p > .3). Fig. 2a demonstrates that the seven synchronizers had significantly larger average stride times (i.e., lower cadence), compared to the other seven couples. This was true in all of the walks except in the VF condition, in which synchronization was rare and occurred only in 2 out of all 14 couples (repeated measures ANOVA: F = 4.4, p < .02 for Group  Walk effect; p < .07 for group effect in each walk except VF). The p-values for all walks except VF became significant when stride times were normalized according to height. The difference in average stride time between the two groups was not associated with any significant group differences in gender composition, average height or in the average asymmetry between the heights of the two walkers (p = 1.0, .18 and .25, respectively). However, height asymmetry was significantly correlated with the GSI across the 14 pairs in each walk (Spearman rho of .68 to .55, with p < .05 for all walks except 3F, and rho = .45 with p = .11 for 3F). Within each group, the average stride times were not significantly different across the feedback conditions, except for a tendency of the VF condition to have the longest average stride time among non-synchronizers (ANOVA: F = 3.4, p < .05; With p < .01 for VF vs. TF and 0F, p < .1 for VF vs. 3F and AF). On the other hand, stride time variability was affected by the presence of sensory feedback, but not by synchronization (see Fig. 2b), with the lowest stride time CV occurring in the 0F condition (p < .01 vs. 3F and AF; p < .05 vs. VF; p < .1 vs. TF) and no differences between the other four feedback conditions, a finding that is further discussed below. 3.4. Is synchronization related to cadence or cadence asymmetry? To further understand the relationship between stride time and synchrony, we tested whether having approximately equal average cadences is a reliable marker of synchrony. In principle, this need not be the case because, over a long enough walk, momentary cadence fluctuations can be uncorrelated among the walkers, leading to gradual loss of synchrony even when the average stride time is identical. As illustrated in Fig. 2c, cadence asymmetry, which is a dimensionless measure of the deviation between the stride times of the walkers, apparently went hand in hand with the GSI in this study, and contained essentially the same information, with a Spearman correlation of .92 between cadence asymmetry and GSI (p < .001). The high correlation of GSI with cadence asymmetry is – not surprisingly – accompanied by a bimodal distribution of cadence asymmetries (data not shown). Note that the cutoff value for cadence asymmetry (separating between synchronized and unsynchronized walks) is 1%, which, for our walkers that have average stride times of 1 s, is equivalent to a difference of 0.02 Hz between their stride frequencies. Van Ulzen et al. (2008) and Nessler and Gilliland (2009) defined frequency locking according to the momentary difference of the stride frequencies of the walkers, using a cutoff value of 0.02 Hz to define locking. This is equivalent to defining synchronization to occur when the absolute value of the slope (i.e., the derivative) of the phase difference is below 0.02 Hz. In our data, there was a bimodal distribution of the slope of the phase difference, with a minimum of the histogram (a putative cutoff point) at a frequency of 0.025 Hz (data not shown). When plotting GSI vs. the percentage of the walk during which stride frequencies differed by less than 0.025 Hz, the synchronization condition of a GSI above .21 was exactly equivalent to requiring a below-threshold frequency difference during at least 70% of the walk (data not shown). Thus, in the present study, synchronization could be equivalently defined using GSI, cadence asymmetry, or the percentage of the walk exhibiting below-threshold frequency difference. During synchronized walks, the frequency difference fluctuated continuously. Using the threshold of 0.025 Hz, it became evident that large fluctuations were significantly more common in the synchronized AF walk, compared to the other walks, since the frequency difference crossed the threshold quite often among synchronizers in this feedback condition. The number of threshold crossings was minimized in 3F (p < .05 for all comparisons of 3F with the other conditions; p < .05 for the comparison of AF with 3F and 0F; p < .08 for the comparison with TF and VF). Despite the large number of threshold crossings, synchronized AF walks included just one synchronization episode, during which the

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phase difference fluctuated considerably, e.g., between 70° and +70°, but its average remained around the same baseline value, usually not far from zero, without phase slips. Since cadence asymmetry was never exactly zero, there was always one walker whose cadence was faster than the other. It is perhaps interesting that the identity of the faster walker remained constant during the five walks for all pairs of non-synchronizers, but only in two pairs of synchronizers. Moreover, in eight out of the nine pairs for which one walker consistently had a faster gait frequency than the other, the walker with the larger height was always the one with the smaller gait frequency, which, in the case of matched velocities, implies a longer average stride length. In the remaining pair, the heights were measured to be equal. To test for possible differences in the reaction of the two walkers to the sensory feedback conditions, we consequently defined the ‘‘fast’’ walker within each pair to be the one whose cadence was faster in the majority of the walks. In the VF walk, fast walkers in both groups had similar average stride times, and the same was true for slow walkers. Surprisingly, fast and slow walkers had different behaviors in the other feedback conditions. The fast walkers in the group of non-synchronizers were much faster than their synchronized counterparts, but the slow walkers from both groups had only slightly different cadences (F = 8.4, 0.8 and 5.3 for group, walk and Walk  Group effect for fast walkers, with p < .02 for group and Group  Walk effects; F = 1.4, 2.6 and 2.7 for group, walk and Walk  Group effects for slow walkers, with p < .08 for walk and Group  Walk effects). When the (largely non-synchronized) VF walk was treated as a baseline, the cadences of fast and slow walkers changed in different ways in the two groups. Among non-synchronizers, both fast and slow walkers had higher cadences in non-VF walks (3F, TF, AF and 0F), compared to VF. In contrast, among the synchronizers, only the fast walkers had lower cadences in non-VF walks, compared to VF. The slow synchronizers had similar cadences in all of the walks. This can be taken to suggest that in the synchronized walks the faster walkers adapted to the cadence of their slower partners. Conversely, among non-synchronizers, both walkers increased their cadences in non-VF, compared to VF (see also Fig. 2a). In repeated measures ANOVA: F = 15.2 and 10.5 with p < .01 for the existence of a group (but not walk or Group  Walk) effect in the magnitude of cadence changes from baseline (VF), for both fast and slow walkers, respectively. Among non-synchronizers: for fast walkers, cadence significantly increased from baseline only in the 0F walk, with insignificant trends for the other non-VF walks; for slow walkers, the cadence increase was significant for all non-VF walks. Among synchronizers: for fast walkers, p < .05 for cadence decrease from baseline in TF, AF and 0F; p < .1 in 3F; for slow walkers, p > .2 for all non-VF walks.

3.5. Is synchronization related to the phase difference? Another aspect of the synchronized state is (the absolute value of) the average phase difference between the walkers. As seen in Fig. 2d, the phase difference decreased as GSI increased, reflecting phase differences closer to 0° in the more synchronized walks (Spearman rho between (.75) and (.55) with p < .05 for non-VF walks; rho = .66 with p < .02 for the VF walk). As expected, the average phase difference in each of the 3F, TF, AF and 0F walks was significantly lower for synchronizers, compared with non-synchronizers, but – surprisingly – it was significantly higher in the group of synchronizers in the VF walk, where average phase difference was supposedly meaningless because these walks were mostly unsynchronized in both groups. The average phase difference over all the walks tended to be lower in the 3F walk, compared to all other conditions (repeated measures ANOVA: F = 9.2, 2.8 and 7.2 for group, walk and Group  Walk effect; p = .01, p < .05 and p < .001, respectively. In post-hoc tests: p < .05 for 3F walk vs. each of the other walks, except p = .06 vs. the 0F walk; also, p < .05 for different phases in the two groups in each walk, with p < .01 for the 3F and VF walks). The absolute value of the phase differences was, on average, significantly larger than 0° in all walks except the synchronized 3F and AF; it was significantly smaller than 180° in all walks, and it was significantly smaller than 90° in the unsynchronized 3F and VF walks, as well as in synchronized 3F, TF and 0F walks, with a trend for synchronized AF walk (p < .1, in one-sample t-test). In general, for the unsynchronized walks, the average absolute phase difference was 92.6°, which is close to the expected value of 90° when the absolute value of the phase difference is

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randomly distributed between 0° and 180°. For the synchronized walks, the average phase difference was 31.7°, significantly closer to 0° (Fig. 2e). 3.6. Another look at cadence and synchronization In view of (a) the strong link between frequency difference (as measured by cadence asymmetry) and synchronization; (b) the apparent lack of a significant effect of sensory feedback condition on average stride frequency, and (c) the observation that synchronization occurred only within specific pairs, we asked whether synchronization may have resulted from an ‘‘accidental’’ match between the independent ‘‘intrinsic’’ frequencies of the walkers, rather than by the presence of actual sensory coupling between them. Note, however, that any such frequency match would have to be accompanied by an equally ‘‘accidental’’ match of stride lengths (and hence, velocities), in order for the partners to be able to walk side by side. To rule out the possibility that walkers had fixed, matching intrinsic cadences, while the coupling strength was zero, we quantified the natural walk-to-walk variability of a walker’s cadence, by comparing, for the same walker, the average magnitude of the change in cadence from the first to the second half of each walk, with the average magnitude of the cadence change between the first half of one walk and the second half of another walk. If cadence asymmetry – as a measure of how the cadence diverges over time – was higher between walks, as compared to within walks (for the same walker), this would suggest that the ‘‘natural’’ cadence has indeed significantly changed from one walk to another. As expected, cadence asymmetries were higher in the ‘‘crossed walk’’ mode for all walkers, compared to the ‘‘same walk’’ halves. Average asymmetry between the two halves was 0.6% ± 0.3% (M ± SD) for the two halves of the same walk in the synchronized pairs, vs. 1.4% ± 0.4% for two halves from different walks (p < .0001). For the unsynchronized pairs, the corresponding values were 0.9% ± 0.4% and 1.6% ± 0.6%, with p < .001. This finding suggests that the walkers had no fixed ‘‘intrinsic’’ cadence.2 4. Discussion To our knowledge, the present study is the first to apply quantitative methods to measure gait synchronization during natural, over-ground, side-by-side walking. Previous studies demonstrated the possibility of interpersonal synchronization of rhythmic movements in man (Oullier, de Guzman, Jantzen, Lagarde, & Kelso, 2008; Richardson, Marsh, Isenhower, Goodman, & Schmidt, 2007; Richardson, Marsh, & Schmidt, 2005). A principal objective of the present study was to ascertain by what sensory interaction two walkers may communicate with each other in order to synchronize their gait, a phenomenon that was observed in half of the pairs. In general, the present findings are consistent with those reported in a qualitative pilot study of natural over-ground walking (Zivotofsky & Hausdorff, 2007) and quantitative studies of treadmill walking (Nessler & Gilliland, 2009, 2010; Nessler et al., 2009; van Ulzen et al., 2008). Effective synchronizing modalities apparently include auditory and tactile feedback while visual information seems to be an ineffective modality for generating interpersonal gait synchronization while walking side-by-side. The present results extend previous studies by demonstrating that the gait of synchronized walkers apparently differs from that of unsynchronized walkers during over-ground walking. In what follows, we discuss the main results of the study and compare it with the results of several other studies of interpersonal synchronization (e.g., Nessler & Gilliland, 2009, 2010; Nessler et al., 2009; van Ulzen et al., 2008; Richardson et al., 2005, 2007; Oullier et al., 2008; van Ulzen et al., 2010). 2 As noted above, somewhat counter-intuitively, synchronization was observed in the 0F condition. To better understand this result, we confirmed that GSI values reflect synchronization (or lack thereof) by asking an additional group (n = 8) of height and gender matched subjects to: a) walk, one at a time, over a pathway while the other participant was quietly standing and facing away from the walker (putatively an unsynchronized condition); b) intentionally walk together in synch over the same pathway. In the first condition, average GSI values were near zero (0.07 ± 0.08), consistent with a lack of synchronization, and in the second condition, high GSI values (0.40 ± 0.07; all above the cutoff value of 0.21) were obtained, consistent with synchronization (p < 0.001 in a paired t-test). The results in this additional group support the idea that the GSI method successfully detects synchronization and its absence.

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4.1. The binary (yes/no) nature of synchronization Synchronized walking in this study, as measured by both the GSI and cadence asymmetry, was largely a binary finding, with a bimodal distribution (see Fig. 2c and d) that reflected the lack of in-between cases, except for a small number of walks where the phase difference stabilized and/or destabilized in the middle of the walk. This result agrees with previous studies of interpersonal synchronization, in which spontaneous synchronization was a binary (yes/no) phenomenon that occurred in well-defined episodes that typically lasted tens of seconds (van Ulzen et al., 2008). A closer look at the small number of walks with cadence asymmetry close to 1% suggested that these walks included exactly one phase slip, i.e., a temporary loss of synchrony (Kelso, 1995), which led to a 1% asymmetry in average cadences as the walkers attempted to ‘‘catch up’’ with each other, temporarily increasing their gait frequency differences. Interestingly, the average phase difference for these ‘‘borderline’’ walks was about 60°. The finding that all synchronized walks contained either zero or one phase slip, but not more, might have stemmed from the fact that the typical duration of the walks in the present study was smaller than the duration of a typical gait synchronization episode (the average inter-slip-interval). Future studies of longer walks will allow for further investigation of this issue and characterization of the time varying nature of synchronization. In treadmill studies of gait synchronization, synchronization tended to wax and wane, with considerable time spent in the unsynchronized state (Van Ulzen et al., 2008). It is possible that the near-constant velocity required in treadmill walking modifies the natural phase adjustment process that takes place during over-ground walking and we therefore hypothesize that phase slips will be more quickly corrected during over-ground walking than during treadmill walking. Nessler and Gilliland (2009) defined synchronization according to the momentary difference of the stride frequencies of the walkers, using a cutoff value of 0.02 Hz to define synchronization. In the present study, the putative cutoff point was located at a similar stride frequency difference of 0.025 Hz. The appropriate location of a cutoff point is somewhat arbitrary, and depends on the specific proportions of synchronizers and non-synchronizers among the pairs. In the present study, synchronization could be equivalently defined as having a GSI < 0.21, cadence asymmetry < 1%, or at least 70% of the walk exhibiting a frequency difference below 0.025 Hz. Finally, note that in theory a small frequency difference may either occur accidentally, as the walkers happen to have similar cadences, or may be a result of a true phase coupling between them. In the latter case, one expects the walkers to be sensitive to each other’s phase. One method to test for an interaction is to count how many times each pair of phases (u1(t), u2(t)) appears in the data, where u1(t) and u2(t) are the phases of walker 1 and walker 2, respectively, at time t. If all phase pairs within the square [2p, 2p]  [2p, 2p] occur equally likely, there is no evidence for phase coupling. The GSI measures the entropy of the phase difference (u2(t)  u1(t)) as an approximation for the entropy of this two-dimensional histogram. The phase difference of two walkers who accidentally happen to have similar stride frequencies, without being coupled, will slowly diverge across time, and hence all possible pairs of phases will be equally likely to occur, resulting in a GSI of 0 (recall also Fig. 2d). Thus, the GSI method can, at least in theory, separate between the case of accidentally similar stride frequencies and true coupling, given a sufficiently long walk. 4.2. Synchronized over-ground walking Over-ground side-by-side gait synchronization differs from other interpersonal synchronization paradigms in three important aspects: (i) the walkers are not coupled to any external device, such as a metronome or a treadmill; (ii) there is an inherent aspect of intentional synchronization in the paradigm because the two walkers attempt to remain within a small distance from each other (‘‘position-synchronization’’); and (iii) the sensory information from the environmental background is not constant, and changes non-rhythmically as the walkers progress along the pathway. The presence of an ever-changing sensory environment, together with the lack of rhythmic external stimuli, endow the walkers with more flexibility, e.g., for spontaneous speed changes. On the other hand, the positionsynchronization constraint is likely to have a strong influence on any phase-synchronization process, as shown e.g., in the model of (Mukovskiy, Slotine, & Giese, 2011) and also discussed below.

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When attempting to walk side-by-side with a partner, two parallel mechanisms may affect gait frequency and phase (Mukovskiy et al., 2011): distance-related coupling (‘‘distance-coupling’’), and phase-related coupling (‘‘phase-coupling’’). The first one adapts gait frequency (and also stride length) in order to maintain the distance from the partner within some tolerable limit, the other reflects the tendency to synchronize one’s steps (or strides) with those of the partner. 4.3. What are the mechanisms of synchronization? The effects of sensory feedback In the present study, gait synchrony was most common in the presence of auditory and tactile feedback. Auditory feedback may work by sensing and acting on discrete rhythmic events, e.g., heel strikes, perhaps similar to the principle of a phased-locked-loop (PLL), e.g., through first-order linear phase correction (Schulze & Vorberg, 2002). In addition, acoustic information may aid in localizing the partner in space to aid side-by-side walking. Handholding may synchronize gait via upper limb coupling, which combines a mechanical effect with tactile and proprioceptive sensory information. Pendular arm swings are known to affect the gait pattern (Barthelemy & Nielsen, 2010; Eke-Okoro, Gregoric, & Larsson, 1997) and to relay information about the gait phase, potentially enabling the synchronization between the two walkers. Synchrony was relatively rare in the VF condition. This does not stem from a general inability to use visual information in order to synchronize, as many studies have demonstrated that visual information may enhance the synchrony of repetitive human movements (see, e.g., Oullier et al., 2008; Richardson et al., 2005, 2007). The synchrony of two people seated side-by-side in rocking chairs was enhanced by visual information and the ability to detect information about each other’s movements (Richardson et al., 2007). Similarly, the unintentional coordination of two subjects swinging pendulums was better coordinated when the pair was visually coupled (Richardson et al., 2005). Oullier et al. (2008) reported that visual information promoted synchronization when two subjects who had different intrinsic frequencies performed rhythmic finger movements. Importantly, both Nessler and Gilliland (2009) and Harrison and Richardson (2009) found that visual information was effective for unintentional gait synchronization, during side-by-side treadmill walking or in an over-ground walker-behind-walker setting, respectively. As described above, treadmill walking differs from over-ground walking because of several factors. The existence of an external pacer reduces the natural variability of stride time (Frenkel-Toledo et al., 2005), facilitating the prediction of heel strike timing by the partner and potentially making synchronization easier. Another factor is the variability of background sensory information, which is higher during over-ground walking, when the walker moves with relation to the surrounding environment. As more attention – especially visual – is paid to the changing sensory environment, the movements of the partner may attract less spontaneous attention, leading to lower coupling and less synchronization. This effect was countered in Harrison and Richardson (2009) by instructing the partners to stay within a fixed distance of 0.75 m, one behind the other. During treadmill walking, visual attention is either free to wander, or may putatively include the section of the belt just in front of the walker’s feet, in order to judge the distance from the end of the walking surface. If the (upper or lower) limbs of the partner are within the walker’s field of view, as occurred in both studies, synchronization may be more likely to occur (van Ulzen et al., 2008). Finally, Nessler and Gilliland (2009) reported that the treadmill itself was a source of some auditory and mechanical information about the partner’s stepping. During parallel over-ground walking the available visual information is much more suited for distance coupling than for phase coupling. Head movement is known to be less variable than limb movements during the gait cycle, and if the two parallel walkers were mainly focusing on each other’s head to estimate mutual distance, the amount of available gait phase information was probably much smaller than the amount of distance information. Another aspect that separates VF from both TF and AF is the asymmetric nature of vision. The organs that sense both AF and TF are located at the sides of the body, and hence may provide equal amounts of sensory information for the leading and trailing walker (whose distance from each other is very small, but not zero). In contrast, the eyes are located at the front of the head, providing disproportionately more information to the trailing walker. Such an asymmetry may weaken the total coupling strength, making synchronization less likely. As expected for a mostly unsynchronized condition, the two groups had similar gait characteristics in the VF walk in

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terms of GSI, cadence asymmetry, average stride time, and stride time variability (recall Fig. 2a and b). We thus hypothesize that VF involved mainly distance-coupling, AF – mostly phase-coupling, and handholding (in TF and 3F) provided both types of coupling. None of the conditions was assumed to cause changes in the ‘‘intrinsic’’ frequencies of the walkers, beyond those implied by the constraint of walking side-by-side. Somewhat surprisingly, five pairs managed to match both their speed and cadence in the 0F condition. i.e., without visual, tactile or auditory feedback. All couples that walked in synchrony in the 0F condition also walked in synchrony during the 3F and AF conditions. It is possible that these walkers adjusted their cadences according to some memorized gait parameters in the absence of external sensory feedback. This explanation is perhaps related to the ‘‘social memory’’ described by Oullier et al. (2008). If so, this would imply that the memory is not only of gait frequency, but also of its amplitude, because both stride time and stride length need to be matched. Exact replication of the cadence from the previous walk did not occur, because average stride times in synchronized 0F walks were not equal to those in the walk that immediately preceded them, though the differences tended to be small. Note that while Oullier et al. (2008) reported that social memory did not decay even 60 s after the removal of the coupling, it existed only as long as subjects continued the rhythmic movement. At the beginning of each new trial, subjects seemed to revert to their preferred movement frequency. On the other hand, studies on rhythmic auditory stimulation have shown carry-over effects on gait even 15 min after the end of a metronome-paced walk. Another possibility is that in the 0F condition, some communication between the subjects took place because visual and/or auditory feedback was not completely blocked. Indeed, Nessler and Gilliland (2009) reported that under their ‘‘No Vision No Sound’’ condition on a treadmill, some synchronization was observed and subjects reported that feedback (both auditory and mechanical) was still detectable. We believe that feedback during the 0F walk must have been weak because, for several couples and exclusively in the 0F walk, the walkers did not manage to stay side-by-side. If a leak of sensory information did take place, the most likely modality might have been the auditory one, since exactly the same pairs synchronized in AF and 0F. Lastly, the possibility remains that communication may have taken place using another, unblocked modality. Further study is needed to understand precisely what takes place in this feedback condition. Sensory feedback also had an effect that did not depend on its ability to synchronize, namely an increase in stride time variability in 3F, AF and VF (and, marginally, TF), when compared to 0F (see Fig. 2b). It has been suggested that increased synchrony is likely to be accompanied by larger fluctuations in each oscillator’s period, because of the excess variability caused by the phase correction process (Schulze & Vorberg, 2002). One exception to the lack of Group  Walk effect in stride time fluctuations was the finding of multiple threshold crossings of the frequency difference in the AF walk. The phase difference in this walk seemed to fluctuate more widely than in 3F, TF or 0F, despite having an average value close to zero. The fluctuations suggest an ongoing process of cadence adjustment, where frequency differences between the walkers develop and are corrected as soon as the phases deviate by more than, e.g, 70°. Accordingly, stride time CV tended to be higher in AF, compared to 3F, among synchronizers (p < .01 for AF vs. 0F; p < .06 for AF vs. 3F; paired t-tests among synchronizers). Our results about elevation of CV with increasing sensory feedback (e.g., from 0F to AF) seem to differ from those of Nessler and Gilliland (2010). They found no difference between the stride time CVs of solo treadmill walking, compared to walking side by side on two treadmills. The CVs during the treadmill walks were about 1%, i.e., about half the typical values measured during over-ground walking. We hypothesize that pairing did not significantly elevate the CV because of the strong pacing effect of the treadmill, known to reduce stride time variability (Frenkel-Toledo et al., 2005). In a similar setting, Nessler et al. (2009) reported a significant increase in step length standard deviation from the solo to the paired condition, but did not report any change in the standard deviation of step time. 4.4. Which factors affect the propensity of two over-ground walkers to synchronize? The major factor predicting gait synchronization in this study was the presence of synchronization in the maximally-coupled 3F walk, which was used to separate the walkers into synchronizers and

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non-synchronizers. The number of synchronized pairs dropped slightly in the non-3F feedback conditions, but 5 out of 7 pairs still synchronized even in the minimally-coupled 0F walk. We take this finding to suggest that the identity of the walkers, rather than the specific non-VF sensory feedback condition (whether TF, AF or 0F), was the major factor that influenced synchronization. Above we also discuss (and reject) an alternative hypothesis: that walkers who happened to be gait-synchronized in the first, 3F walk, had a memory for rhythm (and stride length) that enabled them to synchronize in the next three walks without any ongoing coupling. What might have been the predisposing factors for gait-synchronization? Except for a slight and insignificant trend for larger average height and smaller height asymmetry among synchronizers, we did not detect any intrinsic differences between synchronizers and non-synchronizers, and both groups had similar average cadences in the mostly-unsynchronized VF walk which was generally characterized by distance-coupling without phase-coupling. The two groups also had similar stride time CVs, suggesting that increased intrinsic gait variability was not a contributing factor for the difference in synchronization. Height asymmetry, a proxy of leg-length asymmetry, was correlated with the GSI, suggesting that it is indeed a relevant factor for gait synchronization, as reported by Nessler and Gilliland (2009) for treadmill walking. 4.5. What are the properties of the synchronized state? Part 1: frequencies In the present study, the presence of gait synchronization between a pair of walkers was associated with lower cadence (i.e., higher stride times, see Fig. 2a). When examining each sensory feedback condition independently, the average stride times of synchronized and unsynchronized walks still tended to be different for that specific condition, when synchronization was defined according to the GSI cutoff point of 0.21. (p < .01 within AF and 0F, 5/14 synchronized; p < .05 for VF, 2/14 synchronized; p < .06 for 3F, 7/14 synchronized; p < .12 for TF, 6/14 synchronized). We defined within each pair the ‘‘faster’’ partner to be the walker having a larger stride frequency in the majority of the walks. These walkers turned out to always be the faster ones in the AF and VF walks, and in at least one additional walk. Among synchronizers, when comparing 3F, AF, TF and 0F (non-VF walks) to the mostly-unsynchronized VF walk, only the faster walkers significantly changed (usually reduced) their cadence. Actually, in the 5 pairs of synchronizers whose VF walk was unsynchronized, the faster walker always had a larger cadence change (in absolute value, compared to VF) than the slower one, in all the 15 synchronized walks of these pairs. In 11 of these cases the cadence change (from VF) of the faster walker was negative. It was also negative and larger (in absolute value) than the cadence change of the slower walker in the 5 unsynchronized walks of these pairs in the non-VF walks (15+5 = 20 is the total number of the non-VF walks for these pairs). In contrast, among non-synchronizers, the average cadence in non-VF walks was significantly faster than in the VF walk, and the change occurred for both the faster and slower partner: out of 28 non-VF walks of non-synchronizers, in 24, 24 and 22 walks the cadence was increased (compared to VF) by the faster walker, the slower one, and both, respectively. Slower walkers made a larger cadence change than their partners in 19/28 non-synchronized walks. These results can be compared with those of the finger movement experiment of Oullier et al. (2008), where, in response to visual coupling of rhythmic finger movements, the ‘‘intrinsically’’ faster paced subjects usually decreased their movement frequency, on average, and the slower subjects increased it. 4.6. What are the properties of the synchronized state? Part 2: phases The synchronized walks tended to have an average phase difference closer to 0° than to 180° (see Fig. 2d and e). Since each cycle of the vertical acceleration signal reflected one step, rather than one stride, a phase difference of zero can reflect either in-phase synchronization between the matching legs of both walkers, or anti-phase synchronization, where the left leg of walker A moves in sync with the right leg of walker B, and vice versa. The average phase difference was significantly and negatively correlated with the GSI in non-VF walks (3F, AF, TF and 0F). For unsynchronized walks, the average phase difference was close to 90° and seemed to be uniformly distributed between 0° and 180°. The finding of low average phase differences for unsynchronized VF walks was not expected. The positive correlation was even more significant when only unsynchronized VF walks (GSI between 0.01

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and 0.06, for 12 out of 14 VF walks) were taken into account, and suggests that some form of very light coupling might have occurred between two walkers with unequal cadences. It further supports the special nature of VF, compared with the other sensory feedback conditions. We do not have an explanation, and can only speculate that the walkers unintentionally changed their posture and/or walking style in a manner that suited their sensory needs, as well as those of their partners, e.g., with more pronounced heel strikes during AF; with smoother, less ‘‘jumpy’’ steps in VF in order to minimize the inter-stride variability of velocity, etc. Our results generally agree with the findings of van Ulzen et al. (2008) with respect to the observed phases. They reported varying phase differences between two walkers on a treadmill, but most of the reported stride-based phases fell within the intervals (0, 45), (135, 225) or (315–360), which correspond, in step-based phases, to an absolute phase difference between 0° and 90° (26 of 36 synchronization episodes; averages of reported phases from their Table 1 are: 38°, 57°, 77° and 64° for the four speeds, in step-based phases). Similarly, Harrison and Richardson (2009) found that stride-based average phase differences tended to cluster within 45° of either 0° or 180°, corresponding to absolute values of between 0° and 90° in step-based phases. We also found that phase differences in synchronized walks tended to be significantly lower than 90°, with phase differences decreasing towards zero with increasing GSI. This type of correlation between step-based phase difference and GSI is consistent with the so-called ‘‘seagull effect’’ (see, e.g., van Ulzen et al., 2010), that predicts lower phase variability (as measured e.g., by the GSI or circular standard deviation) near stride phases of 0° and 180°. Finally, since the momentary phase of a signal that is not a pure sine wave is not uniquely defined mathematically (see, e.g., Fuchs et al., 1996, Section 4), it is possible that phase differences estimated from the acceleration signal were inaccurate, possibly with a systematic deviation towards or away from 0°. A potentially less ambiguous definition of phase may either be based on the occurrence of a quasi-discrete event in the step cycle, e.g., heel strike, or based on some variable that has sinusoidal fluctuations during walking. It is also possible that the definition of phase would depend on the sensory modality used, as the heel strike may function as an acoustical signal, yet have less prominence in TF or VF, where movements of the hands or the head may function as carriers of phase information. While these different components of the locomotion rhythm are believed to have a roughly constant phase shift between them, the stride-to-stride fluctuations of the phase shift may not be entirely constant, potentially decomposing gait synchronization into (possibly separate) sub-phenomena, such as leg-synchronization, head-synchronization, etc. 5. Final Remarks Synchronized walking that occurs under natural walking conditions may arise through a variety of mechanisms. It may be the result of a one- or two-way interaction where each walker mutually influences the other using some form of feedback or communication. Another possibility is that one individual sets the pace and the partner senses it using auditory, visual, tactile, or another form of feedback and modifies her gait to match the pacesetter. Our results do not yield a clear result as to which mechanism is involved in either a uni- or bi-directional communication. Another less intuitive possibility is that this synchronization may be the by-product of two uncoupled internal ‘‘oscillators’’ with ‘‘similar’’ natural frequencies. However, the fact that synchronization was observed even though cadence significantly changed across conditions for each pair suggests that this mechanism is not consistent with the observed results. Irrespective of how it occurs, for synchronized side-by-side walking to occur, three conditions need to be fulfilled on an ongoing, step-by-step basis: matching of gait speed, cadence, and phase. A priori, one could suggest that the matching of each of these conditions could occur by chance or via coupling. Indeed, the couples in the present study were matched for height, essentially matching, to a large degree, their preferred average gait speed and cadence. Still, it seems unlikely that all three conditions are met merely by chance. Gait speed and cadence generally fluctuate over time (Frenkel-Toledo et al., 2005; Hausdorff, 2007; Hausdorff et al., 1996) such that even if the mean values happen to be similar at the start of a walk, chance is not sufficient to ensure continued matching over time, given that each subject would normally walk with a varying cadence within a given walk. The fact that the average cadence changed from condition to condition, even among the synchronized pairs (where it changed

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to a very similar value in both subjects), also suggests that some form of coupling took place. For example, for a typical 35-stride walk with a stride-to-stride standard deviation of about 20 msec, the average stride time has a standard error of the mean of about 3.3 ms, as it decreases roughly with the square root of the number of strides. However, the typical change in the stride time of subjects between the walks was 23 ± 11 ms among the synchronized pairs (even after excluding the marginally faster, unsynchronized VF condition), which is almost an order of magnitude larger than the chance fluctuations of the average stride time. As described in the results section, the general observation of higher intra-subject cadence variability between, as compared to within walks, was strongly supported on a subject-by-subject basis. These data suggest that the natural cadence of the walkers indeed varied considerably from walk to walk, being perhaps affected by the passage of time, as well as the varying sensory context. Maintaining an accidental synchronization between the two walkers during several sensory feedback conditions without an active sensory-mediated coupling process seems therefore highly unlikely. We wanted to test whether the finding that synchronizers had longer average stride times than non-synchronizers (in 3F, TF, AF and 0F, but not in VF) was associated with a general adaptation of the synchronizers to side-by-side walking (i.e., inter-pair differences in distance synchronization strategy), or with the presence of gait synchronization in each individual walk (i.e., inter-pair differences in phase synchronization strategy). The average stride times of the synchronizers during the VF walks – and especially the 5 unsynchronized VF walks within this group – were indistinguishable from those of the non-synchronizers, suggesting no general tendency for slower side-by-side walking in this group. We hence favor the hypothesis that (unintentionally) synchronized over-ground gait is associated with a longer average stride time, even for different walks of the same pair of walkers. This hypothesis could not be adequately tested within our small sample of seven synchronized pairs and awaits future study. It is perhaps worth mentioning that in the AF, 0F and VF walks of the synchronizers, for which at least 2 pairs of ‘‘synchronizers’’ were unsynchronized, there was an insignificant trend towards longer stride times in the synchronized, compared to the unsynchronized pairs (5, 5 and 2 vs. 2, 2, and 5 pairs, respectively; p < .12). Also, for the 4 pairs that had at least 2 synchronized and at least 2 unsynchronized walks each, the average stride times for the synchronized walks (within each pair) were significantly longer than those for the unsynchronized walks (1.14 ± 0.05 vs. 1.07 ± 0.05 s, p < .05). One of the possible drawbacks in our study was that the various conditions were not randomized, in order to make the inter-walk breaks as short as possible, as young healthy adults often tend to increase their cadence with time, perhaps as they get impatient. Future studies should examine the possible effect of walk order. Theoretically, the fixed order might have led to ‘‘memory’’ effects, in which the walkers learn to adapt their cadences to each other. The results, however, do not seem to support such a conclusion. First, each successive walk required adaptation to a new, usually unfamiliar, sensory feedback setting. For example, the VF condition, which was the last one, was significantly less synchronized than the other ones, while the TF condition, which preceded it, frequently showed synchronization. Another important factor to consider is the length of the walk (i.e., time series). For walkers with low stride time variability, it is possible that the GSI index still reflects, to some degree, the similarity between the cadences of the different walkers because phases do not have enough time to drift to create a statistically significant dispersion. In the future, walks of longer duration could test this possibility. It is, however, unlikely that two walkers will, by chance, have tightly matched cadences as those observed here. This point is further exemplified by the large cadence asymmetries exhibited in the VF condition for nearly all pairs (as can be discerned from the association between cadence asymmetry and GSI, Fig. 2c), regardless of their walks being synchronized or unsynchronized in the 3F condition. In conclusion, the present findings shed light on the mechanisms whereby two people unintentionally synchronize their gait pattern when walking side-by-side on level ground and raise questions about the sensory-motor coupling that enables interpersonal synchronization. This is a non-trivial task as the Bible (Amos 3:3) already observes: Do two people walk together unless they have agreed to do so? In the future, it may be informative to study the effects of a secondary, dual task on synchronization as this may provide insight into the degree to which the coupling between the walkers takes place in an automated fashion (Herman et al., 2010; Srygley, Mirelman, Herman, Giladi, & Hausdorff,

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2009; Yogev-Seligmann, Hausdorff, & Giladi, 2008). Apparently, the task should be more demanding than performing mental arithmetic, as Nessler and Gilliland (2009) reported no effect of this cognitive task on uninstructed synchronixation. It might also be interesting to investigate whether the challenge of concurrently matching stride length and cadence while walking side-by-side can be used to enhance the gait pattern in neurological patients, perhaps augmenting existing cueing strategies that are beginning to be clinically applied for the rehabilitation of walking (Nieuwboer et al., 2007; Roerdink et al., 2007; van Wegen et al., 2006) with recent evidence suggesting (Nessler et al., 2009) that in rehabilitation of gait a different functional outcome might be achieved by practicing side by side walking as opposed to more commonly used strategies involving independent walking.

Acknowledgments We thank the participants for their time and Y. Galil, I. Tamir, R. Bartsch, M. Plotnik, and E. Lax for invaluable contributions. Portions of this work were presented at the International Society of Posture and Gait Research, Burlington, Vermont, July 2007 and the International Congress on Gait & Mental Function, Amsterdam, The Netherlands, 2008.

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