Effect of sampling frequency on fractal fluctuations during treadmill walking.

The temporal dynamics of stride-to-stride fluctuations in steady-state walking reveal important information about locomotor control and can be quantified using so-called fractal analyses, notably the detrended fluctuation analysis (DFA). Gait dynamics are often collected during treadmill walking using 3-D motion capture to identify gait events from kinematic data. The sampling frequency of motion capture systems may impact the precision of event detection and consequently impact the quantification of stride-to-stride variability. This study aimed i) to determine if collecting multiple walking trials with different sampling frequency affects DFA values of spatiotemporal parameters during treadmill walking, and ii) to determine the reliability of DFA values across downsampled conditions. Seventeen healthy young adults walked on a treadmill while their gait dynamics was captured using different sampling frequency (60, 120 and 240 Hz) in each condition. We also compared data from the highest sampling frequency to downsampled versions of itself. We applied DFA to the following time series: step length, time and speed, and stride length, time and speed. Reliability between experimental conditions and between downsampled conditions were measured with 1) intraclass correlation estimates and their 95% confident intervals, calculated based on a single-measurement, absolute-agreement, two-way mixed-effects model (ICC 3,1), and 2) Bland-Altman bias and limits of agreement. Both analyses revealed a poor reliability of DFA results between conditions using different sampling frequencies, but a relatively good reliability between original and downsampled spatiotemporal variables. Collectively, our results suggest that using sampling frequencies of 120 Hz or 240 Hz provide similar results, but that using 60 Hz may alter DFA values. We recommend that gait kinematics should be collected at around 120 Hz, which provides a compromise between event detection accuracy and processing time.

Introduction

The temporal organization of stride-to-stride fluctuations during steady-state walking can reveal important information about locomotor control [1-6]. With aging and neurodegenerative diseases, gait variability become more random [7-8], compared to the persistent, fractal-like pattern of fluctuations observed in healthy young adults, where large fluctuations are likely to be followed by larger fluctuations, and vice-versa [4,9]. In healthy adults, the temporal organization of fluctuations may also change under different conditions: during metronomic walking (i.e., stepping in time with an auditory metronome), stride time fluctuations become anti-persistent, i.e., large fluctuations are likely to be followed by smaller fluctuations, and vice-versa [1,9]. Similarly, stride length and stride speed become anti-persistent when healthy young adults step on visual targets or walk on a treadmill, respectively [3,10]. More recent studies also evidenced that stride time fluctuations can become more persistent when gait is paced by visual or auditory cues [9-14].

A dominating method to analyze stride-to-stride fluctuations is the detrended fluctuation analysis (DFA) [14], because it provides more accurate results for ‘short’ time series (<1000 data points) compared to other techniques such as power spectral analysis or rescaled range analysis [15-17]. DFA partitions a time series (e.g., stride time intervals) of length N into nonoverlapping windows and calculates the average root mean square (RMS) at each window size. The average RMS at every window size is then plotted against the corresponding window size on a log-log plot. The slope resulting from the line of best fit produces the scaling exponent α-DFA. In an effort to standardize DFA processing, researchers determined some gait-specific parameters required to produce accurate DFA results. Based on both experimental and artificial time series, it is recommended to consider time series of at least 500 data points [16,18-20]. The recommended range of window sizes is 16 to N/9 stride (or step) intervals [21], although for shorter time series a range of 10 to N/4 may be preferred [18,22]. Recent investigations also recommended to use a modified version of the original DFA algorithm, namely the evenly spaced average DFA, to increase the precision of the estimation of the scaling exponent [22-23].

In the context of locomotion, it is also important to consider the parameters underlying data acquisition and pre-processing before applying DFA. In particular, motion capture systems are typically used to record gait kinematics during treadmill walking, but there is no consensus on the most appropriate sampling frequency to reliability apply DFA [24]. While sampling frequency may not have a significant effect on linear measures of gait (e.g., mean and coefficient of variation), it is more likely to influence DFA, because this technique directly depends on the accuracy and precision of gait event detections. In the context of postural control, Rhea et al. [25] found that downsampling linearly decreased the α-DFA scaling exponent of center of pressure (CoP) displacement and CoP velocity. On the other hand, higher sampling frequencies are more likely to introduce artificial white noise (i.e., to decrease α-DFA toward more randomness) [26], and may increase the processing time for little or no benefits.

The goal of this study was to provide guidelines regarding the best sampling frequency to capture fractal dynamics of gait during treadmill walking. We calculated α-DFA values from spatiotemporal variables in different conditions where motion was captured at different sampling frequencies. We compared the average values between conditions, but also the reliability of α-DFA between conditions, using intraclass correlation (ICC) coefficients. Low ICC between different conditions may be due to low between-trial consistency, independently from the sampling frequency. Therefore, we also compared data from a high sampling frequency condition to downsampled data from the same condition.

In summary, this study addressed the following research questions: does motion capture sampling frequency affect α-DFA of spatiotemporal parameters during treadmill walking? What is the reliability of α-DFA values across downsampled conditions? Our central hypothesis was that lower sampling frequency and downsampling will shift α-DFA values toward 0.5, i.e., more randomness due to lower precision in the estimation of gait events.

Materials and methods

Participants

Seventeen young adults (Age 23.9 ± 2.7 years, 7 females) were recruited through convenience sampling to participate in the study. All participants self-reported no cognitive, neurological, muscular, or orthopedic impairments. All participants provided written informed consent according to the procedures approved by the local Institutional Review Board at the University of Nebraska Medical Center.

Equipment

All participants wore their preferred walking shoes and wore a tight-fitting suit. Participants were affixed with 11 retroreflective markers on the following anatomical landmarks to track their motion while walking on a motorized treadmill (Bertec, Columbus, OH): left and right anterior iliac spines, left and right posterior iliac spines, sacrum, dorsal region of the left and right foot between the great toe and long toe, left and right heels, and left and right lateral malleoli. Marker motion was captured through 8 infrared cameras (Vicon, Centennial, CO) at different sampling frequencies in each condition (cf. below).

Protocol

Participants completed three 15-minute walking trials at their preferred speed. Prior to the trials, individual preferred speed was determined by gradually increasing and decreasing the treadmill speed. The speed at which participants reported being comfortable walking for 15 minutes was selected as their preferred walking speed. Participants were given two minutes to walk at their preferred speed for familiarization before the experimental trials begins. Each trial was collected at a different sampling frequency—60 Hz, 120 Hz, and 240 Hz—in a randomized order. Experimental conditions are described later in this paper by the sampling frequency number (i.e., conditions 60, 120, 240).

Data processing

Gait events were automatically identified with a custom Matlab function based on the heel, toe, and the average antero-posterior position of hip markers to find the heel strikes and toe offs [27]. We also downsampled the kinematic data from the 240 condition to 120 Hz and 60 Hz (i.e., further referred as DS120 and DS60 conditions, respectively), using Matlab downsample function. In this study, we focused on the following spatiotemporal variables from each of the five conditions (three experimental conditions: 60, 120 and 240; two downsampled conditions: DS60 and DS120): step length, stride length, step time, stride time, step speed and stride speed.

Each time series were reduced to the length of the shortest time series (i.e., 740 intervals) for reliable comparisons across participants and conditions. The first 60 step or stride intervals in each time series were removed to reduce the potential confounding effect of gait initiation. Therefore, further analyses considered only 679 step or stride intervals (Fig 1). We calculated the mean, coefficient of variation (CV) and scaling exponent (α-DFA) from each spatiotemporal variable. The scaling exponent was calculated using the evenly spaced average DFA, which was briefly described in the Introduction. We used a range of window from 10 to N/8, where N is the time series length. We selected 18 points in the diffusion plot for the evenly spaced average DFA [24]. An α-DFA value between 0.5 and 1 indicates persistent fluctuations, whereas 0.5 indicates random fluctuations.

Fig 1

Time series.

Representative time series from a participant in the three experimental conditions (top three) and the two downsampled conditions (bottom two).

Statistical analysis

One-way repeated measure ANOVAs were performed 1) between conditions 240, 120, and 60, and 2) between conditions 240, DS120, and DS60 (mean, CV and α-DFA) for each of the six spatiotemporal variables. Post-hoc analysis entailed Tukey’s multiple comparison’s tests, and the level of statistical significance was set at a p-value < 0.05.

For each spatiotemporal variable, intraclass correlation (ICC) estimates and their 95% confident intervals were calculated using SPSS statistical package version 23 (SPSS Inc, Chicago, IL) based on a single-measurement, absolute-agreement, two-way mixed-effects model (ICC 3,1) to determine the reliability of mean, CV and α-DFA [28-29]. We compared 1) conditions 240, 120 and 60, and 2) conditions 240, DS120 and DS60. The reliability was graded based on the lower 95% CI values [29], with values less than 0.50 indicating poor reliability, values between 0.50 and 0.75 indicating moderate reliability, values between 0.75 and 0.90 indicating good reliability and values above 0.90 indicating excellent reliability [28].

We also computed Bland-Altman bias and limits of agreement (LoA) on α-DFA for all possible pairs of conditions, for all spatiotemporal variables. Bland-Altman bias and 95% LoA basically assess agreement between two methods [30-31], by studying the mean difference between paired measured (bias), and the agreement interval, within which 95% of the differences of the second method, compared to the first one, fall. The 95% LoA is typically defined as the bias plus or minus 1.96 the standard deviation of the paired differences for two methods. In this study, we will report LoA, defined as 1.96 the standard deviation of the paired differences for two methods (i.e., to find 95% LoA, simply add or subtract LoA from bias). It is recommended that acceptable limits of agreement should be defined a priori [31]. In the present study, values of LoA equal or below 0.05 for α-DFA were defined as acceptable, based on previous studies using artificial time series to evaluate the proportion of variance due to the computational technique in estimating α-DFA values [16].

Results

Data from three participants were excluded due to technical difficulties. Data from the remaining 14 participants (Age 23.9 ± 2.8 years, 5 females) were further processed. There was no statistically significant difference between sides for any analyses, so we only report results from the right side in further analyses for the sake of clarity. The spatiotemporal time series from both sides are available in S1 Dataset.

Effect of sampling frequency

There was no statistically significant difference between any conditions for any measures of any spatiotemporal variables (p>0.05). The ICCs revealed good to excellent reliability for mean of step length and step speed, and excellent reliability for all other spatiotemporal variables (Table 1). Based on the 95% confidence interval, the reliability of CV was poor to good for stride length, step time, stride time and stride speed, and moderate to excellent for step length and step speed. In contrast, for α-DFA the ICC coefficients were poor to good, and the 95% confidence interval revealed poor to moderate reliability for step length, step time, step speed and stride speed, and poor to good reliability for stride length and stride time (Fig 2). Bland-Altman bias and LoA showed similar results (Table 2): for all spatiotemporal variables, there was no consistent bias between conditions 240 and 120, but there was a negative bias between conditions 240 and 60 for step length and stride length α-DFA, indicating lower values in condition 60. Similarly, a small negative bias was observed for most spatiotemporal variables between conditions 120 and 60. In addition, for every pair of conditions, the LoAs ranged from 0.120 to 0.289, well above the acceptable limits of agreement defined at 0.05.

Table 1

Mean and standard deviation (SD) of time series mean, coefficient of variation (CV) and α-DFA from condition 240, condition 120 and condition 60, and corresponding intraclass correlations and 95% confidence intervals.

		Mean (SD) for conditions
		240	120	60	ICC [95% CI]
Step length	Mean (m)	0.63 (0.06)	0.62 (0.06)	0.62 (0.07)	0.915 [0.811–0.969]
	CV (%)	1.75 (0.64)	1.81 (0.57)	2.00 (0.58)	0.804 [0.585–0.929]
	α-DFA	0.72 (0.13)	0.68 (0.09)	0.67 (0.08)	0.309 [-0.004–0.652]
Stride length	Mean (m)	1.26 (0.11)	1.26 (0.11)	1.26 (0.11)	0.991 [0.979–0.997]
	CV (%)	1.30 (0.43)	1.41 (0.51)	1.45 (0.32)	0.620 [0.326–0.840]
	α-DFA	0.77 (0.13)	0.75 (0.12)	0.73 (0.11)	0.536 [0.214–0.797]
Step time	Mean (s)	0.54 (0.04)	0.53 (0.04)	0.54 (0.04)	0.992 [0.981–0.997]
	CV (%)	1.55 (0.47)	1.67 (0.46)	1.93 (0.33)	0.509 [0.175–0.783]
	α-DFA	0.73 (0.11)	0.68 (0.09)	0.65 (0.09)	0.382 [0.079–0.697]
Stride time	Mean (s)	1.07 (0.07)	1.07 (0.07)	1.07 (0.07)	0.993 [0.984–0.998]
	CV (%)	1.25 (0.54)	1.28 (0.48)	1.32 (0.30)	0.542 [0.222–0.801]
	α-DFA	0.79 (0.14)	0.77 (0.10)	0.77 (0.11)	0.546 [0.227–0.803]
Step speed	Mean (m/s)	1.17 (0.12)	1.17 (0.12)	1.15 (0.14)	0.911 [0.801–0.968]
	CV (%)	1.74 (0.57)	1.71 (0.42)	1.88 (0.39)	0.861 [0.680–0.950]
	α-DFA	0.55 (0.06)	0.56 (0.06)	0.54 (0.05)	-0.072 [-0.290–0.301]
Stride speed	Mean (m/s)	1.18 (0.12)	1.18 (0.12)	1.18 (0.12)	0.998 [0.995–0.999]
	CV (%)	1.34 (0.84)	1.17 (0.25)	1.39 (0.32)	0.370 [0.040–0.698]
	α-DFA	0.43 (0.07)	0.50 (0.20)	0.53 (0.26)	0.382 [0.052–0.706]

Fig 2

DFA results.

Individual α-DFA values for stride length (left), stride time (middle) and stride speed (right) in the three experimental conditions and the two downsampled conditions.

Table 2

Bland-Altman bias and limits of agreement [LoA], defined as 1.96 standard deviation of the differences, of α-DFA values for each pair of conditions, for all spatiotemporal variables (right side only).

A negative bias indicates that the condition in the top row produced higher α-DFA estimates on average than the condition in the corresponding row.

Conditions		240		120		60		DS120
Spatiotemporal variable		Step	Stride	Step	Stride	Step	Stride	Step	Stride
120	Length	-0.035 [0.268]	-0.016 [0.289]
	Time	0.013 [0.165]	-0.016 [0.276]
	Speed	0.008 [0.182]	0.013 [0.165]
60	Length	-0.052 [0.241]	-0.062 [0.175]	-0.017 [0.173]	-0.046 [0.205]
	Time	0.017 [0.161]	-0.020 [0.158]	-0.030 [0.157]	-0.004 [0.208]
	Speed	-0.011 [0.167]	0.017 [0.161]	-0.020 [0.132]	0.004 [0.120]
DS120	Length	-0.007 [0.035]	-0.019 [0.048]	0.028 [0.257]	-0.002 [0.273]	0.045 [0.232]	0.044 [0.162]
	Time	-0.004 [0.054]	-0.010 [0.015]	0.034 [0.256]	0.006 [0.276]	0.064 [0.197]	0.011 [0.156]
	Speed	-0.005 [0.044]	-0.004 [0.054]	-0.014 [0.173]	-0.017 [0.138]	0.006 [0.155]	-0.021 [0.133]
DS60	Length	-0.040 [0.109]	-0.042 [0.090]	-0.005 [0.253]	-0.025 [0.271]	0.012 [0.221]	0.021 [0.162]	-0.033 [0.088]	-0.023 [0.080]
	Time	0.014 [0.084]	-0.052 [0.068]	-0.026 [0.262]	-0.036 [0.280]	0.004 [0.180]	-0.032 [0.159]	-0.059 [0.088]	-0.042 [0.058]
	Speed	-0.011 [0.086]	0.014 [0.084]	-0.020 [0.151]	0.001 [0.142]	0.000 [0.149]	-0.003 [0.143]	-0.006 [0.078]	0.018 [0.091]

Effect of downsampling

There was no statistically significant difference between any conditions for any measures of any spatiotemporal variables (p>0.05), except for CV of step time (F(2,39) = 3.917, p = 0.028). The ICCs revealed excellent absolute agreement of means for all spatiotemporal variables (Table 3). For CV, while ICC coefficients were above 0.9 for all spatiotemporal variables, based on the 95% confidence interval the reliability was poor to excellent for step length, moderate to excellent stride length, stride time and step speed, good to excellent for stride speed and excellent for step time. For α-DFA, the 95% confidence interval revealed moderate to excellent reliability for step length, step time, stride time, step speed and stride speed, and good to excellent for stride length (Fig 2). Bland-Altman bias and LoA showed different results for conditions DS120 and DS60 when compared to condition 240. Condition DS120 showed very little bias for every spatiotemporal variable, and the LoAs were all within the acceptable limits of 0.05 (step time and stride speed showed LoA of 0.054, which was still deemed acceptable). In contrast, condition DS60 showed a negative bias, in particular for step length, stride length and stride time. In addition, all the LoA values were above 0.05. Similar results were also found when comparing conditions DS120 to DS60: a negative bias for step length, stride length, step time and stride time, and LoA values above 0.05 for all spatiotemporal variables.

Table 3

Mean and standard deviation (SD) of time series mean, coefficient of variation (CV) and α-DFA from condition 240, condition DS120 and condition DS60, and corresponding intraclass correlations and 95% confidence intervals.

		Mean (SD) for conditions
		240	DS120	DS60	ICC [95% CI]
Step length	Mean (m)	0.63 (0.06)	0.63 (0.06)	0.63 (0.06)	0.999 [0.998–1]
	CV (%)	1.75 (0.64)	1.80 (0.61)	1.98 (0.59)	0.958 [0.475–0.991]
	α-DFA	0.72 (0.13)	0.71 (0.11)	0.68 (0.11)	0.906 [0.747–0.968]
Stride length	Mean (m)	1.26 (0.11)	1.26 (0.11)	1.26 (0.11)	1 [1–1]
	CV (%)	1.30 (0.43)	1.34 (0.41)	1.45 (0.39)	0.959 [0.501–0.991]
	α-DFA	0.77 (0.13)	0.75 (012)	0.73 (0.11)	0.952 [0.888–0.983]
Step time	Mean (s)	0.54 (0.04)	0.54 (0.04)	0.54 (0.04)	1 [1–1]
	CV (%)	1.55 (0.47)	1.65 (0.77)	1.98 (0.37)	0.978 [0.946–0.992]
	α-DFA	0.73 (0.11)	0.72 (0.10)	0.66 (0.10)	0.88 [0.736–0.956]
Stride time	Mean (s)	1.07 (0.07)	1.07 (0.07)	1.07 (0.07)	1 [1–1]
	CV (%)	1.25 (0.54)	1.28 (0.53)	1.41 (0.50)	0.97 [0.594–0.993]
	α-DFA	0.79 (.14)	0.78 (0.14)	0.74 (0.14)	0.945 [0.662–0.986]
Step speed	Mean (m/s)	1.17 (0.12)	1.17 (0.12)	1.17 (0.12)	1 [1–1]
	CV (%)	1.74 (0.57)	1.79 (0.56)	1.95 (0.49)	0.952 [0.532–0.989]
	α-DFA	0.55 (0.06)	0.54 (0.06)	0.54 (0.04)	0.767 [0.537–0.909]
Stride speed	Mean (m/s)	1.18 (0.12)	1.18 (0.12)	1.18 (0.12)	1 [1–1]
	CV (%)	1.34 (0.84)	1.38 (0.83)	1.58 (0.83)	0.964 [0.768–0.991]
	α-DFA	0.43 (0.07)	0.43 (0.06)	0.45 (0.06)	0.820 [0.624–0.932]

Discussion

The goal of this study was to determine how motion capture sampling frequency and downsampling procedures affect DFA during treadmill walking. Our four main findings are that i) in general, mean, CV and α-DFA values of all spatiotemporal variables were similar between conditions, as revealed by ANOVAs, whether the data was collected at different sampling frequencies or downsampled, ii) α-DFA values were not reliable between conditions using different sampling frequencies, as revealed by ICCs, iii) α-DFA values were reliable between original and downsampled spatiotemporal variables, in particular between 240 Hz and 120 Hz, as revealed by ICCs and Bland-Altman analyses, and iv) α-DFA from stride intervals were more reliable than α-DFA from step intervals.

Our original hypothesis that lower sampling frequency shift α-DFA values toward more randomness was not supported. We observed a small, non-significant trend toward a reduction in the scaling exponent α-DFA for step length, stride length, step time and stride time, for data originally sampled at 60 Hz or downsampled at 60 Hz. Previous studies have used a range of sampling frequencies to study gait dynamics during treadmill or overground walking [2,5,21,32-34]. Our results suggest that when the research question focuses on within-group or between-group comparisons, a sampling frequency as low as 60 Hz may be able to capture differences. While the reductions in α-DFA were not significant, 120 Hz may allow for more precise event detection. In addition, walking speed may also play a role: as lower limbs move faster, a greater sampling frequency is needed to capture gait events with the same precision. While this question was beyond the scope of this study and will need to be addressed later, it is an important factor to consider when selecting motion capture sampling frequency. It is also important to note that the number of potential individual values present in a time series depends not only from the sampling frequency, but also from the coefficient of variation (or the range) in that time series. As an illustration, for a stride time series centered around 1-sec with a CV of 5% (i.e., a range of [0.95–1.05]), sampling at 100 Hz would lead to 11 potential values (i.e. 0.95, 0.96, 0.97, etc.). In contrast, a CV of 2% (i.e., a range of [0.98–1.02]) would lead to only 5 potential values and a much more ‘squared’ signal.

While α-DFA values were not significantly different between conditions, they were not very reliable. Based on the lower 95% confidence intervals, the reliability was graded as poor for all spatiotemporal variables (Table 1). Bland-Altman analyses indicated a similar trend, with limited biases but high limits of agreement, above the a priori defined threshold of 0.05 (Table 2). This is an important finding, as it suggests that collecting data from the same participant using different sampling frequencies would lead to very different scaling exponents in each condition. However, as stressed in the Introduction, a low reliability between conditions may also arise independently from sampling frequencies. While previous studies have shown that α-DFA presented relatively high within-day reliability [33,35-36], it is possible to observe within-subject differences in gait dynamics between conditions. This may arise from different factors such as fluctuations in attention levels, fatigue or habituation to treadmill walking. We anticipated such potential confounding effects, and therefore studied the effect of downsampling (from the highest sampling frequency).

We found that the reliability of α-DFA values graded as moderate and good between original and downsampled spatiotemporal variables (Table 3). Bland-Altman analyses further showed that the data downsampled at 120 Hz provided very similar results as the original data sampled at 240 Hz, with no consistent bias and limits of agreement below the threshold of 0.05. This suggests that using a sampling frequency of 240 Hz does not provide more benefit than 120 Hz to capture the ‘true’ α-DFA values. In contrast, the Bland-Altman bias was higher between conditions 240 and DS60, and the limits of agreement were above 0.05 for all spatiotemporal variables. This suggests that sampling motion capture at 60 Hz (i.e., as in condition DS60) may lead to less accurate α-DFA values, assuming condition 240 as the gold-standard. These results contrast with our previous finding (comparing different conditions), and suggests that the low reliability observed between conditions sampled at different frequencies originated from within-subject differences more than reflecting a true effect of sampling frequency.

It should also be stressed that α-DFA from stride intervals were more reliable than step intervals. This may be because a single stride interval ‘encompasses’ two step intervals (i.e., one from each side). Therefore, small corrections occurring at the step level may not be reflected in a more global stride interval.

Our study presents several limitations. First, our final sample size (N = 14) may be relatively small, considering that each participant underwent three conditions [37]. While the results from intraclass correlations and Bland-Altman analyses lead to similar conclusions, the small sample size remains a major limitation of the present study. We also collected only healthy young adults, as in previous methodological studies, because healthy gait patterns are often used as a reference [21,32-33,35-36]. We cannot exclude the possibility that the results would be different with other populations such as older adults or people with gait disorders. Another limitation of our study is that we only considered three different sampling frequencies. While technically motion can be captured at any sampling frequency (i.e., on a continuous scale), we chose to focus on the most representative values reported in previous literature. In addition, collecting human gait below 50 Hz would certainly alter not only DFA results but also mean and CV, and collecting above 240 Hz would increase processing time. Finally, there is little reason to think that DFA results from data sampled at 120 Hz would significantly differ from data sampled at a slightly lower frequency (e.g., 100 Hz), because our results at 240 Hz or 120 Hz were very similar. As mentioned earlier, walking speed and the coefficient of variation of time series may also play a role. Future studies should investigate the reliability of DFA results at different walking velocity. Another limitation is that we only considered treadmill walking, but our conclusions may not hold true for overground walking. Note that the study of fractal dynamics during overground walking is often performed on data captured with small accelerometers or footswitches [1,4,7,10,18-20]. Footswitches in particular–while limited in capturing only temporal variables such as stride time intervals–are often capable of higher sampling frequency (e.g., data is often collected at 1000 Hz or more). A final limitation of this study was that we focused solely on the scaling exponent α-DFA, and did not test other techniques. While this may be considered a limitation, our goal in this paper was to provide guidelines specifically related to the application of DFA to spatiotemporal variables. Previous studies have already compared the effect of sampling frequency on other measures of gait [38], and future studies may use our data (S1 Dataset) to ask other questions related to the reliability of gait parameters during treadmill walking.

In conclusion, sampling frequency seems to have little effect on α-DFA applied to spatiotemporal variables during treadmill walking. Overall, stride intervals seem to provide more reliable results than step intervals. While no significant differences were observed between conditions, a small trend toward lower α-DFA values with lower sampling frequencies lead us to recommend that data should be collected at around 120 Hz. This seems to be the best compromise between precise event detection and reduced processing time.

Raw data.

Spatiotemporal time series from 14 healthy young adults walking on a treadmill at their self-selected speed, in different conditions characterized by different sampling frequency of the 3D motion capture system. Conditions '240ds120' and '240ds60' correspond to the downsampled data from 240 Hz to 120 Hz and 60 Hz, respectively.

(MAT)

Click here for additional data file.

7 Aug 2019

PONE-D-19-16440

Effect of sampling frequency on fractal fluctuations during treadmill walking

PLOS ONE

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Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Partly

Reviewer #2: Yes

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2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: No

Reviewer #2: Yes

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Reviewer #1: Yes

Reviewer #2: Yes

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5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: The authors examine whether capturing spatiotemoral gait data on a treadmill at different sampling frequencies affects either the (1) magnitude or (2) reliability of fractal indices (DFA alpha) from various time series (step & stride length, step & stride time, step & stride speed). They report data from 14 participants who walked on a treadmill at their preferred speed during each of three 15-minute bouts. Each bout was captured at a different sampling frequency (60 Hz, 120 Hz, 240 Hz) in a randomized order. The study’s purpose was well-justified and the paper was well-written. The protocol and data processing methods were sufficiently described. Nevertheless, I have two primary concerns with the study’s methods: (1) sample size and (2) data analysis approach. The following specific comments are not intended to be critical, but rather are intended to help the authors improve the study and/or paper.

(Methods section, line 86 & line 144) The authors did not provide justification for their sample size and I believe the study was underpowered to accurately estimate measurement reliability. Per line 86, 17 individuals participated but per line 144, data from 3 participants were excluded, which further diminishes the sample size. The effective sample size was n = 14. Given the authors’ use of the following guidelines for interpreting ICCs (ICC < .50 = poor reliability, ICC of .50 to .75 = moderate reliability, ICC of .75 to .90 = good reliability, ICC > .90 = excellent reliability), I might have expected the authors to power the study in a way that the sample size would have been sufficient to detect reliability coefficients of .75 or higher against a minimally acceptable reliability coefficient of .50. Using those parameters across 3 measurement conditions, approximately 27 or more participants would have been required to adequately power the study (Walter SD, Eliasziw M, Donner A. Sample size and optimal designs for reliability studies. Statistics in Medicine. 1998;17:101-110.).

(Methods section, lines 133-135) In my opinion, the study design is more representative of an alternate forms reliability study, i.e., evaluating agreement between methods of measurement. Bland-Altman plots and limits of agreement analyses are perhaps better designed to address questions of agreement than are ICCs (Bland JM, Altman DG. A note on the use of the intraclass correlation coefficient in the evaluation of agreement between two methods of measurement. Computers in Biology and Medicine. 1990;20(5):337-340). Would the authors consider re-analyzing their data with Bland-Altman plots either instead of or as a supplemental analysis to the ICCs?

(Results section, lines 153-155) Per my previous comment regarding sample size, I would suggest the study was underpowered to detect accurate reliability coefficients and is a major reason the 95% confidence intervals reported in Table 1 are so wide. Informing the reader that measuring DFA alpha has “poor to moderate” or “poor to good” reliability may therefore be misleading. Those interpretations would be much more valid if the study was appropriately powered. Additionally, analyzing limits of agreement and/or systematic bias across measurement methods with Bland-Altman analyses may provide an alternative interpretation.

(Results section, Table 1) The step speed and stride speed DFA alpha values are approximately .50 (i.e., white noise) with very small standard deviations, suggesting little between-subject variability. ICC values are artificially deflated when between-subject variability is low, which would partially explain why those ICCs are so poor. I suspect that if the authors create Bland-Altman plots and analyze limits of agreement between the 60 Hz, 120 Hz and 240 Hz methods of measurement, the results will show strong agreement between methods with little to no evidence of systematic bias.

(Discussion section, line 184) Per my preceding comment, it is potentially misleading to conclude that DFA alpha “values were not reliable between conditions using different sampling frequencies.” If results are similar with an adequately powered sample size and/or systematic biases in the measures are apparent with Bland-Altman analyses, then the conclusion would be more valid.

(Discussion section, lines 205-209) The discussion content represented in lines 205-209 is potentially misleading for reasons listed above. The discussion content will be acceptable—in my opinion—only if the ICCs remain low with an adequately powered sample and if Bland-Altman analyses provide evidence of poor agreement (systematic bias) between methods.

(Discussion section, lines 225-249) The authors neglected the major limitation in their study: sample size. If the authors choose not to collect data from more participants and revise the manuscript accordingly, then the sample size limitation must be addressed as a major limitation to the study’s findings.

Reviewer #2: General: This paper provides an important technical contribution to the field of gait measurement. The authors examined the role of sample frequency and downsampling on prominently used gait metrics. Their results highlight the strengths and challenges of different sampling/processing techniques that people working in this area should be aware of. My comments below are minor and are aimed to help provide clarification in a few places in the text.

Comments and suggestions to the authors:

ABSTRACT

Lines 29-30: “Our results suggest that sampling frequency (between 60 and 240 Hz) does not significantly alter DFA”. Does the data support this? Lines 27-28 said “Intraclass correlation analysis revealed a poor reliability of DFA results between conditions using different sampling frequencies.” This seems to be a disconnect and could use some clarification in the text. (See my second comment in the Discussion section below for more context on this)

Line 32: The word “optimal” implies a data driven approach that provides support for such a claim. Since it appears that the relationship between detection accuracy and processing time was not quantified in this study, I recommend removing the word “optimal” from this sentence.

INTRODUCTION

Lines 39-44: You accurately identify that stride-to-stride fluctuations can become anti-persistent in various conditions. However, it would provide a more holistic view of work in this area if you were to also include text and references indicating that stride-to-stride fluctuations can also become more persistent in some conditions. This inclusion is important because it demonstrates gait fluctuations are modifiable in either direction (toward anti-persistence or persistence), which could be valuable for readers of this paper. In addition to some of the references you already cited, below are some additional references to consider including that show a shift toward persistence.

Rhea, C. K., Kiefer, A. W., Wittstein, M. W., Leonard, K. B., MacPherson, R. P., Wright, W. G., & Haran, F. J. (2014). Fractal gait patterns are retained after entrainment to a fractal stimulus. PLOS ONE, 9(9), e106755.

Rhea, C. K., Kiefer, A. W., D’Andrea, S. E., Warren, W. H., & Aaron, R. K. (2014). Entrainment to a real time fractal visual stimulus modulates fractal gait dynamics. Human Movement Science, 36, 20-34.

Wittstein, M. W., Starobin, J. M., Schmitz, R. J., Shulz, S. J., Haran, F. J., & Rhea, C. K. (2019). Cardiac and gait rhythms in healthy younger and older adults during treadmill walking tasks. Aging Clinical and Experimental Research, 31(3), 367-375.

Line 67-69: Please add a reference to support this statement.

METHODS

Lines 87-88: I assume this was verified via self-report, not medical record examination, correct? If so, please change this sentence to read “All participants self-reported no cognitive, neurological, muscular, or orthopedic impairments.”

RESULTS

Line 144: Please report the age (mean+/-SD) and gender of the 14 participants who were included in the analysis since these data reported in the Methods section pertains to the original 17 included in the study.

Line 166: Please add the degrees of freedom prior to your F-statistic.

DISCUSSION

Lines 182-184: It’s not clear how the following can co-exist for α-DFA:

“i) in general, mean, CV and α-DFA values of all spatiotemporal variables were similar between conditions, whether the data was collected at different sampling frequencies or downsampled, ii) α-DFA values were not reliable between conditions using different sampling frequencies”

How can α-DFA be similar between conditions collected at different sampling frequencies AND not reliable between conditions using different sampling frequencies? Some clarification needs to be made for these two points. You bring up this point again in lines 205-206. Your position on this appears to be accurate, but it would be helpful to readers if you can describe how data can be similar between conditions, yet unreliable. Many people many not understand how those two things can independently fluctuate.

Lines 192-193: Please describe how your data supports these two statements:

“Our results suggest that when the research question focuses on within-group or between-group comparisons, a sampling frequency as low as 60 Hz may be able to capture differences. While the reductions in α-DFA were not significant, 120 Hz may allow for more precise event detection.”

Line 233: The use of “dramatically” is relative and likely not a problem for most computers given current processing speeds. It will, however, increase processing speeds. Thus, I recommend removing “dramatically” from this sentence.

**********

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Reviewer #1: No

Reviewer #2: Yes: Christopher K. Rhea

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While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email us at figures@plos.org. Please note that Supporting Information files do not need this step.

7 Oct 2019

Response to reviewers

We thank the editor and reviewers for their comments. We have addressed each comment and made revisions that we hope will be satisfactory.

Editor’s comment

When submitting your revision, we need you to address these additional requirements.

1. Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found at

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We have revised the manuscript format according to PLOS ONE’s style requirements, including files names.

2. Please include captions for your Supporting Information files at the end of your manuscript, and update any in-text citations to match accordingly. Please see our Supporting Information guidelines for more information: http://journals.plos.org/plosone/s/supporting-information.

We apologize for missing this in the first place. We have revised accordingly the file title, added the title of the subsection ‘Supporting information’ and revised in-text citations.

Reviewer’s comment

Reviewer #1: The authors examine whether capturing spatiotemporal gait data on a treadmill at different sampling frequencies affects either the (1) magnitude or (2) reliability of fractal indices (DFA alpha) from various time series (step & stride length, step & stride time, step & stride speed). They report data from 14 participants who walked on a treadmill at their preferred speed during each of three 15-minute bouts. Each bout was captured at a different sampling frequency (60 Hz, 120 Hz, 240 Hz) in a randomized order. The study’s purpose was well-justified and the paper was well-written. The protocol and data processing methods were sufficiently described. Nevertheless, I have two primary concerns with the study’s methods: (1) sample size and (2) data analysis approach. The following specific comments are not intended to be critical, but rather are intended to help the authors improve the study and/or paper.

Thank you for your insightful comments. We have made our best to address each of them.

(Methods section, line 86 & line 144) The authors did not provide justification for their sample size and I believe the study was underpowered to accurately estimate measurement reliability. Per line 86, 17 individuals participated but per line 144, data from 3 participants were excluded, which further diminishes the sample size. The effective sample size was n = 14. Given the authors’ use of the following guidelines for interpreting ICCs (ICC < .50 = poor reliability, ICC of .50 to .75 = moderate reliability, ICC of .75 to .90 = good reliability, ICC > .90 = excellent reliability), I might have expected the authors to power the study in a way that the sample size would have been sufficient to detect reliability coefficients of .75 or higher against a minimally acceptable reliability coefficient of .50. Using those parameters across 3 measurement conditions, approximately 27 or more participants would have been required to adequately power the study (Walter SD, Eliasziw M, Donner A. Sample size and optimal designs for reliability studies. Statistics in Medicine. 1998;17:101-110.).

We agree that this study may be underpowered, and we have now explicitly stated this as a limitation in the Discussion.

According to Table II in Walter et al. (1998), for n=3, ρ0 = 0.5 (i.e., testing the null hypothesis ρ = ρ0, where ρ0 is the minimally acceptable level of reliability), and ρ1 = 0.8 (where ρ1 is a specific underlying value of ρ under H1, i.e., ρ > ρ0), only 15 subjects would be enough. We agree that, based on our guidelines for interpreting ICC values (i.e., ρ1 = 0.75), a sample size of 25 subjects should be more adequate. We also want to stress that our guidelines are very conservatives in estimating reliability, because we considered the lowest 95% confidence interval for our comparisons and conclusions. This approach may be more pragmatic, in that we reduce the risk of estimating a measure as ‘reliable’ while it may have very large CIs.

(Methods section, lines 133-135) In my opinion, the study design is more representative of an alternate forms reliability study, i.e., evaluating agreement between methods of measurement. Bland-Altman plots and limits of agreement analyses are perhaps better designed to address questions of agreement than are ICCs (Bland JM, Altman DG. A note on the use of the intraclass correlation coefficient in the evaluation of agreement between two methods of measurement. Computers in Biology and Medicine. 1990;20(5):337-340). Would the authors consider re-analyzing their data with Bland-Altman plots either instead of or as a supplemental analysis to the ICCs?

We thank the reviewer for this comment. We agree that Bland-Altman plots and limits of agreement are relevant complementary analyses to our work. We have conducted this analysis on DFA values, for all possible pairs of conditions, for all spatiotemporal variables (left and right side). As for the other analyses, there was no differences between left and right side, so we reported results for right side only for the sake of clarity. While Bland-Altman plots are a clear visual representation of agreement between methods, due to the number of comparisons in this study we decided to report the bias within a table (Table 2 in the revised manuscript), defined as the mean difference between paired measures, and the 95% limits of agreement, defined as the bias � 1.96 standard deviation of the differences.

As recommended by Giavarina (2015), we defined a priori the limits of agreement (LoA) expected (limits of maximum acceptable differences) to 0.05, i.e., for a bias of 0 the α-DFA values measured in one condition are deemed similar to those measured in another condition if they fall within a range of 0.1.

(Results section, lines 153-155) Per my previous comment regarding sample size, I would suggest the study was underpowered to detect accurate reliability coefficients and is a major reason the 95% confidence intervals reported in Table 1 are so wide. Informing the reader that measuring DFA alpha has “poor to moderate” or “poor to good” reliability may therefore be misleading. Those interpretations would be much more valid if the study was appropriately powered. Additionally, analyzing limits of agreement and/or systematic bias across measurement methods with Bland-Altman analyses may provide an alternative interpretation.

Bland-Altman analyses did not show any systematic bias, although the bias was higher when comparing condition 240 vs. ds60 (compared to condition 240 vs. ds120), for all spatiotemporal variables.

In addition, the limits of agreement were all above the (a priori determined) threshold of 0.05, expect when comparing condition 240 to ds120. This result may actually strengthen our conclusion that using a sampling frequency of 240 Hz does not provide more benefits than 120 Hz, but that 60 Hz alters DFA results.

(Results section, Table 1) The step speed and stride speed DFA alpha values are approximately .50 (i.e., white noise) with very small standard deviations, suggesting little between-subject variability. ICC values are artificially deflated when between-subject variability is low, which would partially explain why those ICCs are so poor. I suspect that if the authors create Bland-Altman plots and analyze limits of agreement between the 60 Hz, 120 Hz and 240 Hz methods of measurement, the results will show strong agreement between methods with little to no evidence of systematic bias.

Results from the Bland-Altman analysis supported the results from ICCs and our original conclusions: while the bias was very low for both step speed and stride speed when comparing condition 240 to both conditions 120 and 60, the 95% LoA were still very high (between 0.16 and 0.18), well above the threshold of 0.05. In our opinion, the low ICC results from the fact that despite relatively low between-subject variability (at least lower than for stride and step time and length), there was no consistent trend in DFA changes (cf. figure 2).

(Discussion section, line 184) Per my preceding comment, it is potentially misleading to conclude that DFA alpha “values were not reliable between conditions using different sampling frequencies.” If results are similar with an adequately powered sample size and/or systematic biases in the measures are apparent with Bland-Altman analyses, then the conclusion would be more valid.

While the limitations about sample sizes remains, we think the results from the Bland-Altman analysis support our original conclusion. In particular, the Bland-Altman analysis allowed us to study pairwise comparisons of conditions. Interestingly, the data from condition ds60 compared to ds120 showed 95% LoA above the (a priori) threshold of 0.05, with a negative bias, suggesting that ds60 produced lower DFA values and reinforcing our impression that sampling at 60 Hz is not recommended.

(Discussion section, lines 205-209) The discussion content represented in lines 205-209 is potentially misleading for reasons listed above. The discussion content will be acceptable—in my opinion—only if the ICCs remain low with an adequately powered sample and if Bland-Altman analyses provide evidence of poor agreement (systematic bias) between methods.

While we were not able to increase the sample size, the results from the Bland-Altman analysis seems to support the conclusion that there are few differences between data sampled at 240 Hz and downsampled at 120 Hz, but that 60 Hz is less ‘similar’ than both 240 and 120. In particular, there was a systematic bias for DFA values from ds60, which were always lower than ds120 (expect for Stride speed).

(Discussion section, lines 225-249) The authors neglected the major limitation in their study: sample size. If the authors choose not to collect data from more participants and revise the manuscript accordingly, then the sample size limitation must be addressed as a major limitation to the study’s findings.

We agree that this study may be underpowered. We have now explicitly stated this as a limitation in the Discussion.

Reviewer #2: General: This paper provides an important technical contribution to the field of gait measurement. The authors examined the role of sample frequency and downsampling on prominently used gait metrics. Their results highlight the strengths and challenges of different sampling/processing techniques that people working in this area should be aware of. My comments below are minor and are aimed to help provide clarification in a few places in the text.

Comments and suggestions to the authors:

ABSTRACT

Lines 29-30: “Our results suggest that sampling frequency (between 60 and 240 Hz) does not significantly alter DFA”. Does the data support this? Lines 27-28 said “Intraclass correlation analysis revealed a poor reliability of DFA results between conditions using different sampling frequencies.” This seems to be a disconnect and could use some clarification in the text. (See my second comment in the Discussion section below for more context on this)

The first sentence referred to ANOVA results while the second referred to ICC results. In other words, while there was no statistical significant differences between conditions from the ANOVAs, the individual values were not ‘similar’ between conditions.

Line 32: The word “optimal” implies a data driven approach that provides support for such a claim. Since it appears that the relationship between detection accuracy and processing time was not quantified in this study, I recommend removing the word “optimal” from this sentence.

We agree with this comment and the sentence has been revised.

INTRODUCTION

Lines 39-44: You accurately identify that stride-to-stride fluctuations can become anti-persistent in various conditions. However, it would provide a more holistic view of work in this area if you were to also include text and references indicating that stride-to-stride fluctuations can also become more persistent in some conditions. This inclusion is important because it demonstrates gait fluctuations are modifiable in either direction (toward anti-persistence or persistence), which could be valuable for readers of this paper. In addition to some of the references you already cited, below are some additional references to consider including that show a shift toward persistence.

Rhea, C. K., Kiefer, A. W., Wittstein, M. W., Leonard, K. B., MacPherson, R. P., Wright, W. G., & Haran, F. J. (2014). Fractal gait patterns are retained after entrainment to a fractal stimulus. PLOS ONE, 9(9), e106755.

Rhea, C. K., Kiefer, A. W., D’Andrea, S. E., Warren, W. H., & Aaron, R. K. (2014). Entrainment to a real time fractal visual stimulus modulates fractal gait dynamics. Human Movement Science, 36, 20-34.

Wittstein, M. W., Starobin, J. M., Schmitz, R. J., Shulz, S. J., Haran, F. J., & Rhea, C. K. (2019). Cardiac and gait rhythms in healthy younger and older adults during treadmill walking tasks. Aging Clinical and Experimental Research, 31(3), 367-375.

That is a good point, we have revised the introduction to reflect that change and included additional references, including those suggest by the reviewer.

Line 67-69: Please add a reference to support this statement.

The following reference has been added:

Wijnants ML, Cox RFA, Hasselman F, Bosman AMT, Van Orden G. Does sample rate introduce an artifact in spectral analysis of continuous processes? Front Physio. 2013; 3:495.doi: 10.3389/fphys.2012.00495.

METHODS

Lines 87-88: I assume this was verified via self-report, not medical record examination, correct? If so, please change this sentence to read “All participants self-reported no cognitive, neurological, muscular, or orthopedic impairments.”

This sentence has been revised accordingly.

RESULTS

Line 144: Please report the age (mean+/-SD) and gender of the 14 participants who were included in the analysis since these data reported in the Methods section pertains to the original 17 included in the study.

We have included the following sentence:

Data from the remaining 14 participants (Age 23.9 ± 2.8 years, 5 females) were further processed.

Line 166: Please add the degrees of freedom prior to your F-statistic.

Thank you for noticing this typo, it has been revised accordingly.

DISCUSSION

Lines 182-184: It’s not clear how the following can co-exist for α-DFA:

“i) in general, mean, CV and α-DFA values of all spatiotemporal variables were similar between conditions, whether the data was collected at different sampling frequencies or downsampled, ii) α-DFA values were not reliable between conditions using different sampling frequencies”

How can α-DFA be similar between conditions collected at different sampling frequencies AND not reliable between conditions using different sampling frequencies? Some clarification needs to be made for these two points. You bring up this point again in lines 205-206. Your position on this appears to be accurate, but it would be helpful to readers if you can describe how data can be similar between conditions, yet unreliable. Many people many not understand how those two things can independently fluctuate.

Indeed, we may have failed to give a simple description of our main conclusion, which is that DFA values may not be reliable from one condition to the other, despite the absence of significant differences between conditions. We have revised this section of our discussion by including to which statistical analyses each conclusion is based on, to hopefully better explain how we interpret our results.

Lines 192-193: Please describe how your data supports these two statements:

“Our results suggest that when the research question focuses on within-group or between-group comparisons, a sampling frequency as low as 60 Hz may be able to capture differences. While the reductions in α-DFA were not significant, 120 Hz may allow for more precise event detection.”

The first sentence is supported by results from the ANOVA: there were no statistically significant differences between conditions 240 and 60. We attempted to explain why 120 Hz would allow more precise estimation of event detection in the following sentences describing how walking speed and CV also influence the choice of sampling frequency.

Line 233: The use of “dramatically” is relative and likely not a problem for most computers given current processing speeds. It will, however, increase processing speeds. Thus, I recommend removing “dramatically” from this sentence.

We agree and have revised accordingly.

Submitted filename: Response to reviewers.docx

Click here for additional data file.

23 Oct 2019

PONE-D-19-16440R1

Effect of sampling frequency on fractal fluctuations during treadmill walking

PLOS ONE

Dear Dr. Marmelat,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

==============================

The revised version of this manuscript has been reviewed and both reviewers felt that the authors satisfactorily addressed their concerns.  There remain 3 minor details that should be addressed.

1) It seems from context that the statement on line 264-265 is specific to DS60, but this is not clear in the statement.  Please clarify.

2) Table 1: Leading zero missing for ICC 95% CI for Step Length  [0.811-969] should probably be [0.811-0.969]

3) Table 2: Leading zero missing for a-DFA Stride Time in Table 2 (.14) should be (0.14)

==============================

We would appreciate receiving your revised manuscript by Dec 07 2019 11:59PM. When you are ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: All comments have been addressed

Reviewer #2: All comments have been addressed

**********

2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: I appreciate the thoroughness of the authors' response to reviewers and appreciate their revisions to the manuscript. The paper will provide a valuable technical contribution to gait researchers.

Reviewer #2: The authors did an excellent job revising this manuscript. They are commended on their effort and the manuscript is recommended for publication in its current form.

**********

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Reviewer #1: No

Reviewer #2: No

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23 Oct 2019

Response to reviewers

We thank the editor and reviewers for their comments. We have addressed each comment and revised the small typos.

1) It seems from context that the statement on line 264-265 is specific to DS60, but this is not clear in the statement. Please clarify.

We have clarified the statement as follow:

This suggests that sampling motion capture at 60 Hz (i.e., as in condition DS60) may lead to less accurate α-DFA values, assuming condition 240 as the gold-standard.

2) Table 1: Leading zero missing for ICC 95% CI for Step Length [0.811-969] should probably be [0.811-0.969]

Revised.

3) Table 2: Leading zero missing for a-DFA Stride Time in Table 2 (.14) should be (0.14)

Revised.

Submitted filename: Response to reviewers.docx

Click here for additional data file.

28 Oct 2019

Effect of sampling frequency on fractal fluctuations during treadmill walking

PONE-D-19-16440R2

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30 Oct 2019

PONE-D-19-16440R2

Effect of sampling frequency on fractal fluctuations during treadmill walking

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