Reliability of the walking speed and gait dynamics variables while walking on a feedback-controlled treadmill

Multifractality in stride-to-stride variations reveals that walking involves more movement tuning and adjusting than running

Introduction: The seemingly periodic human gait exhibits stride-to-stride variations as it adapts to the changing task constraints. The optimal movement variability hypothesis (OMVH) states that healthy stride-to-stride variations exhibit "fractality"-a specific temporal structure in consecutive strides that are ordered, stable but also variable, and adaptable. Previous research has primarily focused on a single fractality measure, "monofractality." However, this measure can vary across time; strideto-stride variations can show "multifractality." Greater multifractality in stride-tostride variations would highlight the ability to tune and adjust movements more. Methods: We investigated monofractality and multifractality in a cohort of eight healthy adults during self-paced walking and running trials, both on a treadmill and overground. Footfall data were collected through force-sensitive sensors positioned on their heels and feet. We examined the effects of self-paced walking vs. running and treadmill vs. overground locomotion on the measure of monofractality, α-DFA, in addition to the multifractal spectrum width, W, and the asymmetry in the multifractal spectrum, WAsym, of stride interval time series. Results: While the α-DFA was larger than 0.50 for almost all conditions, α-DFA was higher in running and locomoting overground than walking and locomoting on a treadmill. Similarly, W was greater while locomoting overground than on a treadmill, but an opposite trend indicated that W was greater in walking than running. Larger WAsym values in the negative direction suggest that walking exhibits more variation in the persistence of shorter stride intervals than running. However, the ability to tune and adjust movements does not differ between treadmill and overground, although both exhibit more variation in the persistence of shorter stride intervals. Discussion: Hence, greater heterogeneity in shorter than longer stride intervals contributed to greater multifractality in walking compared to running, indicated by larger negative WAsym values. Our results highlight the need to incorporate multifractal methods to test the predictions of the OMVH.

A Comparison of Force-Plate Based Center of Mass Estimation Algorithms

Estimating horizontal center of mass (CoM) is an important process that is used in the control of self-paced treadmills, as well as in clinical and scientific biomechanical analysis. Many laboratories use motion-capture to estimate CoM, while others use force-plate based estimates, either because they cannot access motion-capture or they do not want to be taxed with post-processing optoelectronic data. Three force-plate derived center of mass estimation algorithms were compared against a benchmark motion-capture technique. Two of them have recently been reported in the literature, and both rely on numerical integration of 2nd-order differential equations. We propose a third technique that uses an algebraic equation to directly relate center of pressure to center of mass without numerical drift. Twenty-four healthy adults participated in a five-minute steady-state walking test to compare these algorithms. The sample-by-sample standard deviation of the three force-plate based algorithms from the motion-capture benchmark algorithm was evaluated. The algebraic technique provided less error than either of the two more common integration techniques (p<0.05). The results of this study support the viability of using only ground reaction forces for self-paced treadmills and also show that a simple algebraic model is preferred to integration approaches. The use of an algebraic estimation simplifies control implementation for self-paced treadmill applications and eliminates the need for event-based drift recalibration.

6MWT on a new self-paced treadmill system compared with overground

The 6-min walk test (6MWT) is a useful tool for clinicians and researchers to estimate gait performance and fatigue affecting functional mobility. A modified 6MWT administered on a treadmill (TM) can be an efficient, space-saving alternative to perform the 6MWT. The aim of this study was to investigate if a 6MWT on a self-paced (SP) TM produced similar results compared to an overground (OG) 6MWT among healthy participants with the hypothesis that users would demonstrate similar gait parameters. The second aim was to assess the reliability of SP TM sessions with the hypothesis that gait parameters would be reliable. Twelve healthy young adults performed one OG 6MWT and two SP TM 6MWTs, with the TM tests performed on two different testing days. The OG 6MWTs were conducted along a 20 m corridor with a portable optometric system. The SP TM 6MWTs were performed using a dual-belt instrumented TM with speed controlled by feedback from a LIDAR sensor. In the OG condition, participants walked 664.8 m ± 48.9 m when the standard method was used to calculate distance and 721.3 m ± 56.2 m with an average-speed-based estimation of distance, which corrects for U-turns. For the SP TM 6MWT, they covered 729.4 m ± 45.8 m in the first session and 727.4 m ± 56.0 m in the second session. Gait parameters showed good to excellent within- and between-day reliability on the adaptive TM. Gait parameters were similar between modalities. A significant difference in the 6MWT distance was found between modalities. This is attributable to the U-turns, because a comparison between TM 6MWT distance and the average-speed-based estimation of the distance for the OG modality showed no significant difference. However, this system produced similar spatiotemporal gait parameters among participants compared to OG.

Between-day repeatability of sensor-based in-home gait assessment among older adults: assessing the effect of frailty

BACKGROUND

While sensor-based daily physical activity (DPA) gait assessment has been demonstrated to be an effective measure of physical frailty and fall-risk, the repeatability of DPA gait parameters between different days of measurement is not clear.

AIMS

To evaluate test-retest reliability (repeatability) of DPA gait performance parameters, representing the quality of walking, and quantitative gait measures (e.g. number of steps) between two separate days of assessment among older adults.

METHODS

DPA was acquired for 48-h from older adults (age ≥ 65 years) using a tri-axial accelerometer. Continuous walking bouts (≥ 60 s) were identified from acceleration data and used to extract gait performance parameters, including time- and frequency-domain gait parameters, representing walking speed, variability, and irregularity. To assess repeatability, intraclass correlation coefficient (ICC) was calculated using two-way mixed effects F-test models for day-1 vs. day-2 as the independent random effect. Repeatability tests were performed for all participants and also within frailty groups (non-frail and pre-frail/frail identified using Fried phenotype).

RESULTS

Data was analyzed from 63 older adults (29 non-frail and 34 pre-frail/frail). Most of the time- and frequency-domain gait performance parameters showed good to excellent repeatability (ICC ≥ 0.70), while quantitative parameters, including number of steps and walking duration showed poor repeatability (ICC < 0.30). Among majority of the gait performance parameters, we observed higher repeatability among the pre-frail/frail group (ICC > 0.78) compared to non-frail individuals (0.39 < ICC < 0.55).

CONCLUSION

Gait performance parameters, showed higher repeatability compared to quantitative measures. Higher repeatability among pre-frail/frail individuals may be attributed to a reduced functional capacity for performing more intense and variable physical tasks.

TRIAL REGISTRATION

The clinical trial was retrospectively registered on June 18th, 2013 with ClinicalTrials.gov, identifier NCT01880229.

Speed-related but not detrended gait variability increases with more sensitive self-paced treadmill controllers at multiple slopes

Self-paced treadmills are being used more frequently to study humans walking with their self-selected gaits on a range of slopes. There are multiple options to purchase a treadmill with a built-in controller, or implement a custom written self-paced controller, which raises questions about how self-paced controller affect treadmill speed and gait biomechanics on multiple slopes. This study investigated how different self-paced treadmill controller sensitivities affected gait parameters and variability on decline, level, and incline slopes. We hypothesized that increasing self-paced controller sensitivity would increase gait variability on each slope. We also hypothesized that detrended variability could help mitigate differences in variability that arise from differences in speed fluctuations created by the self-paced controllers. Ten young adults walked on a self-paced treadmill using three controller sensitivities (low, medium, and high) and fixed speeds at three slopes (decline, -10°; level, 0°; incline, +10°). Within each slope, average walking speeds and spatiotemporal gait parameters were similar regardless of self-paced controller sensitivity. With higher controller sensitivities on each slope, speed fluctuations, speed variance, and step length variance increased whereas step frequency variance and step width variance were unaffected. Detrended variance was not affected by controller sensitivity suggesting that detrending variability helps mitigate differences associated with treadmill speed fluctuations. Speed-trend step length variances, however, increased with more sensitive controllers. Further, detrended step length variances were similar for self-paced and fixed speed walking, whereas self-paced walking included substantial speed-trend step length variance not present in fixed speed walking. In addition, regardless of the self-paced controller, subjects walked fastest on the level slope with the longest steps, narrowest steps, and least variance. Overall, our findings suggest that separating gait variability into speed-trend and detrended variability could be beneficial for interpreting gait variability among multiple self-paced treadmill studies and when comparing self-paced walking with fixed speed walking.

Spatial-Temporal Parameters of Gait Associated With Alzheimer Disease: A Longitudinal Analysis

Alzheimer's disease (AD) is one of the biggest social and medical concerns in the aging world. A dual task of walking and talking is a particularly practical means to assess AD considering the cognitive and behavioral changes that characterize the disease. The purpose of the study was to assess the effect of the dual task of walking and talking on people with early stage AD under differing cognitive load levels of talking. Participants (9 women and 5 men, mean age (years) = 78.03, standard deviation [SD] = 12.06) with mild or moderate AD (mean Dementia Rating Scale 2 score = 88.14, SD = 7.07) completed 12 monthly walking sessions under no, low, or high cognitive load. They also completed the low and high cognitive load tasks while seated. Linear mixed-effects modeling revealed that values in the Functional Ambulation Profile, stride length, and velocity decreased as tasks became more complex and double support time increased at the same rate. The walking and seated conditions comparison indicated that participants' performance on both low and high cognitive tasks was poor when they were walking rather than seated. The results show that people with early stage AD exhibited gait impairments that increased over time and when completing tasks with greater cognitive load.

Test-Retest Reliability and the Effects of Walking Speed on Stride Time Variability During Continuous, Overground Walking in Healthy Young Adults

Studies have investigated the reliability and effect of walking speed on stride time variability during walking trials performed on a treadmill. The objective of this study was to investigate the reliability of stride time variability and the effect of walking speed on stride time variability, during continuous, overground walking in healthy young adults. Participants completed: (1) 2 walking trials at their preferred walking speed on 1 day and another trial 2 to 4 days later and (2) 1 trial at their preferred walking speed, 1 trial approximately 20% to 25% faster than their preferred walking speed, and 1 trial approximately 20% to 25% slower than their preferred walking speed on a separate day. Data from a waist-mounted accelerometer were used to determine the consecutive stride times for each trial. The reliability of stride time variability outcomes was generally poor (intraclass correlations: .167-.487). Although some significant differences in stride time variability were found between the preferred walking speed, fast, and slow trials, individual between-trial differences were generally below the estimated minimum difference considered to be a real difference. The development of a protocol to improve the reliability of stride time variability outcomes during continuous, overground walking would be beneficial to improve their application in research and clinical settings.

A comparison of variability and gait dynamics in spatiotemporal variables between different self-paced treadmill control modes

This study investigates the effects of treadmill control algorithms on spatiotemporal variables when walking on a self-paced (SP) treadmill. Ten healthy subjects walked at their preferred walking speed for 15 min under three different treadmill control modes. Stride time, stride length, and stride speed were measured using an inertial measurement unit. The mean, coefficient of variance, Poincaré descriptors, and gait dynamics were calculated for each parameter. The mean values of stride length and stride speed were significantly increased when the treadmill had a quick response speed to the user's walking behavior. The long-term variability of stride length and stride speed was significantly affected by the treadmill control algorithms. A reduced strength of long-range correlations of stride time and stride speed was found when walking on the SP treadmill with suppressed treadmill accelerations and small velocity variations. We suggest that the suppression of treadmill acceleration provides more adaptability and less constraint to the user during SP treadmill walking. Although further research is required, the present work provides a basis for interpreting the influence of treadmill control algorithms on human gait.

Assessing the Temporal Organization of Walking Variability: A Systematic Review and Consensus Guidelines on Detrended Fluctuation Analysis

Human physiological signals are inherently rhythmic and have a hallmark feature in that even distant intrasignal measurements are related to each other. This relationship is termed long-range correlation and has been recognized as an indicator of the optimal state of the observed physiological systems, among which the locomotor system. Loss of long-range correlations has been found as a result of aging as well as disease, which can be evaluated with detrended fluctuation analysis (DFA). Recently, DFA and the scaling exponent α have been employed for understanding the degeneration of temporal regulation of human walking biorhythms in, for example, Parkinson disease (PD). However, heterogeneous evidence on scaling exponent α values reported in the literature across different population groups has put into question what constitutes a healthy physiological pattern. Therefore, the purpose of this systematic review was to investigate the functional thresholds of scaling exponent α in young vs. older adults, as well as between patients with PD and age-matched asymptomatic controls. Aging and PD exhibited a negative effect size (i.e., led to decreased long-range correlations) of -0.20 and -0.53, respectively. Our meta-analysis based on 14 studies provides evidence that a mean scaling exponent α threshold of 0.86 [2 standard error (0.76, 0.96)] is able to optimally discriminate temporal organization of stride interval between young and old, whereas 0.82 (0.72, 0.92) differentiates patients with PD and age-matched asymptomatic controls. The optimal thresholds presented in this review together with the consensus guidelines for using DFA might allow a more sensitive and reliable application of this metric for understanding human walking physiology than has been achieved to date.

Differences in reproducibility of gait variability and fractal dynamics according to walking duration

BACKGROUND

Gait variability and fractal dynamics may be affected by the walking duration.

OBJECTIVE

The purpose of this study is to examine the reproducibility of stride time while walking on a self-paced treadmill.

METHODS

Fifteen young and healthy subjects walked on the treadmill for 10 minutes. Three to eight minutes duration of the data were used to compare the trial-to-trial and day-to-day reproducibility of the average, variability, and fractal dynamics of stride time.

RESULTS

The results show that all variables had high trial-to-trial reproducibility. In the day-to-day results, the average walking speed and mean stride time showed reproducibility without regard for duration, but the variability and gait fractal dynamics showed differences in reproducibility according to duration. The variability and fractal dynamics showed better reproducibility in less than 5 minutes and over time, respectively. However, both variables generally showed improved reproducibility when average data from two to three rounds were used.

CONCLUSION

Based on the results of this study, it is proposed that variability should be examined using data of 5 min or less, and fractal dynamics should be examined using 5 min or more of repeated data when performing walking tests from a gait dynamics perspective.

MEASUREMENT SYSTEM FOR DELAY-TIME OF GAIT EVENT DUE TO A DUAL-TASK DURING WALKING

During walking, attuning the heel contact to the external cueing is attentional and physical demanding. Based on this point of view, this is a preliminary study conducted for identifying the temporal accuracy of subjects for rhythmic auditory cueing, and to identify the balancing ability of the elderly based on this information. A measurement system was constructed to measure the motion delay time for the given rhythm and a pilot gait experiment was conducted for young adults while performing a cognitive dual task. The system consisted of a metronome and an accelerometer sensor measurement unit and is implemented as a program using LabVIEW. This pilot gait experiment measured individual delay times in 15 healthy adults in their 20s under two conditions: metronome walking (MET) and metronome walking with backward counting (MET+BC). Consequently, the delay time of MET and MET+BC conditions was [Formula: see text][Formula: see text]msec and [Formula: see text][Formula: see text]msec, respectively ([Formula: see text]). Further experiments with the elderly will be needed to confirm whether such delay time can be used as an indicator for balancing ability.

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.

Quantitative analysis of the bilateral coordination and gait asymmetry using inertial measurement unit-based gait analysis

Inertial measurement unit (IMU)-based gait analysis can be used to quantitatively analyze the bilateral coordination and gait asymmetry (GA). The purpose of this study was to investigate changes in bilateral coordination and GA due to gait speed using an IMU based gait analysis and identify spatiotemporal factors affecting bilateral coordination and GA. Eighty healthy adults (40 men and 40 women) participated in the study. The mean age was 26.2 years, and the mean body mass index was 22.8 kg/m2. Three different walking speeds (80%, 100%, and 120% of preferred walking speed) on a treadmill were applied for 1 min of continuous level walking using a shoe-type IMU-based gait analysis system. The phase coordination index (PCI) and GA were calculated on three different walking speeds. Several variables (gait speed, height, body mass index, cadence, and step length) were analyzed as possible factors affecting the PCI and GA. Bilateral coordination and GA improved during fast walking (p = 0.005 and p = 0.019, respectively) and deteriorated during slow walking (p<0.001 and p = 0.008, respectively), compared with the participants' preferred walking speeds. The correlation analysis revealed that PCI was negatively correlated with step length at each walking condition and lower gait speed was negatively correlated with PCI and GA during slow walking. Both bilateral coordination and GA had a negative linear relationship with gait speed, showing an improvement in the fast walking condition and deterioration in the slow walking condition. Step length was the factor associated with the change in the bilateral coordination.

Fractal analysis of gait in people with Parkinson's disease: three minutes is not enough

BACKGROUND

The fractal dynamics of gait variability in people with Parkinson's disease has been studied by applying the detrended fluctuation analysis (DFA) to short time series (<200 strides). However, DFA is sensitive to time series length, and it is unclear if DFA results from short time series are reliable and if they reflect the fractal dynamics of longer time series.

RESEARCH QUESTION

Is DFA reliable when applied to short time series?

METHODS

We applied DFA to stride time series from five 3-min trials and one 15-min trial in 12 people with Parkinson's disease, 14 healthy older adults and 14 healthy young adults walking overground. Within each group, intraclass correlations (ICC 3,1) were performed to assess the reliability of i) the five 3-min trials together, ii) each 3-min trials to the 15-min trial, and iii) the first 150 strides from the 15-min trial to the full 15-min trial.

RESULTS

Our three main findings are that 1) stride time α-DFA values are not consistent from trial-to-trial for short stride time series, 2) stride time α-DFA values from each 3-min trials are not consistent when compared to stride time α-DFA values from a 15-min trial, and 3) stride time α-DFA values from the first 150 strides of the 15-min trial are not consistent when compared to α-DFA values from the full 15-min trial.

SIGNIFICANCE

Our results confirm that α-DFA values from 3-min walking trials are not reliable, and that they do not reflect the scale invariant properties of longer time series. This suggests that previous studies assessing the fractal dynamics of gait variability from about 3-min walking must be interpreted with caution. A major clinical implication is that DFA cannot be used to study gait in people unable to perform 500 strides continuously.

Walking speed and spatiotemporal step mean measures are reliable during feedback-controlled treadmill walking; however, spatiotemporal step variability is not reliable

The purpose of the study was to compare the effects of a feedback-controlled treadmill (FeedbackTM) to a traditional fixed-speed treadmill (FixedTM) on spatiotemporal gait means, variability, and dynamics. The study also examined inter-session reliability when using the FeedbackTM. Ten young adults walked on the FeedbackTM for a 5-minute familiarization followed by a 16-minute experimental trial. They returned within one week and completed a 5-minute familiarization followed by a 16-minute experimental trial each for FeedbackTM and FixedTM conditions. Mean walking speed and step time, length, width, and speed means and coefficient of variation were calculated from all experimental conditions. Step time, length, width, and speed gait dynamics were analyzed using detrended fluctuation analysis. Mean differences between experimental trials were determined using ANOVAs and reliability between FeedbackTM sessions was determined by intraclass correlation coefficient. No difference was found in mean walking speed nor spatiotemporal variables, with the exception of step width, between the experimental trials. All mean spatiotemporal variables demonstrated good to excellent reliability between sessions, while coefficient of variation was not reliable. Gait dynamics of step time, length, width, and speed were significantly more persistent during the FeedbackTM condition compared to FixedTM, especially step speed. However, gait dynamics demonstrated fair to poor reliability between FeedbackTM sessions. When walking on the FeedbackTM, users maintain a consistent set point, yet the gait dynamics around the mean are different when compared to walking on a FixedTM. In addition, spatiotemporal gait dynamics and variability may not be consistent across separate days when using the FeedbackTM.

Gait Dynamics in Parkinson's Disease: Short Gait Trials "Stitched" Together Provide Different Fractal Fluctuations Compared to Longer Trials

The fractal analysis of stride-to-stride fluctuations in walking has become an integral part of human gait research. Fractal analysis of stride time intervals can provide insights into locomotor function and dysfunction, but its application requires a large number of strides, which can be difficult to collect from people with movement disorders such as Parkinson's disease. It has recently been suggested that "stitching" together short gait trials to create a longer time series could be a solution. The objective of this study was to determine if scaling exponents from "stitched" stride time series were similar to those from continuous, longer stride time series. Fifteen young adults, fourteen older adults, and thirteen people with Parkinson's disease walked around an indoor track in three blocks: one time 15 min, five times 3 min, and thirty times 30 s. Stride time intervals were determined from gait events recorded with instrumented insoles, and the detrended fluctuation analysis was applied to each stride time series of 512 strides. There was no statistically significant difference between scaling exponents in the three blocks, but intra-class correlation revealed very low between-blocks reliability of scaling exponents. This result challenges the premise that the stitching procedure could provide reliable information about gait dynamics, as it suggests that fractal analysis of stitched time series does not capture the same dynamics as gait recorded continuously. The stitching procedure cannot be considered as a valid alternative to the collection of continuous, long trials. Further studies are recommended to determine if the application of fractal analysis is limited by its own methodological considerations (i.e., long time series), or if other solutions exists to obtain reliable scaling exponents in populations with movement disorders.

Fractal fluctuations in spatiotemporal variables when walking on a self-paced treadmill

This study investigated the fractal dynamic properties of stride time (ST), stride length (SL) and stride speed (SS) during walking on a self-paced treadmill (STM) in which the belt speed is automatically controlled by the walking speed. Twelve healthy young subjects participated in the study. The subjects walked at their preferred walking speed under four conditions: STM, STM with a metronome (STM+met), fixed-speed (conventional) treadmill (FTM), and FTM with a metronome (FTM+met). To compare the fractal dynamics between conditions, the mean, variability, and fractal dynamics of ST, SL, and SS were compared. Moreover, the relationship among the variables was examined under each walking condition using three types of surrogates. The mean values of all variables did not differ between the two treadmills, and the variability of all variables was generally larger for STM than for FTM. The use of a metronome resulted in a decrease in variability in ST and SS for all conditions. The fractal dynamic characteristics of SS were maintained with STM, in contrast to FTM, and only the fractal dynamic characteristics of ST disappeared when using a metronome. In addition, the fractal dynamic patterns of the cross-correlated surrogate results were identical to those of all variables for the two treadmills. In terms of the fractal dynamic properties, STM walking was generally closer to overground walking than FTM walking. Although further research is needed, the present results will be useful in research on gait fractal dynamics and rehabilitation.

Reliability of a Feedback-Controlled Treadmill Algorithm Dependent on the User's Behavior

The reliability of the treadmill belt speed using a feedback-controlled treadmill algorithm was analyzed in this study. Using biomechanical factors of the participant's walking behavior, an estimated walking speed was calculated and used to adjust the speed of the treadmill. Our proposed algorithm expands on the current hypotheses of feedback-controlled treadmill algorithms and is presented below. Nine healthy, young adults walked on a treadmill controlled by the algorithm for three trials over two days. Each participant walked on the feedback-controlled treadmill for one 16-minute and one five-minute trial during day one and one 16-minute trial during day two. Mean, standard deviation, interclass correlation coefficient (ICC), and standard error of measurement (SEM) were analyzed on the treadmill belt speed mean, standard deviation, and coefficient of variation. There were significantly high ICC for mean treadmill speed within- and between-days. Treadmill speed standard deviation and coefficient of variation were significantly reliable within-day. These results suggest the algorithm will reliably produce the same treadmill belt speed mean, but may only produce a similar treadmill belt speed standard deviation and coefficient of variation if the trials are performed in the same day. A feedback-controlled treadmill algorithm that accounts for the user's behavior provides a greater level of control and minimizes any possible constraints of walking on a conventional treadmill.

Power considerations for the application of detrended fluctuation analysis in gait variability studies

The assessment of gait variability using stochastic signal processing techniques such as detrended fluctuation analysis (DFA) has been shown to be a sensitive tool for evaluation of gait alterations due to aging and neuromuscular disease. However, previous studies have suggested that the application of DFA requires relatively long recordings (600 strides), which is difficult when working with clinical populations or older adults. In this paper we propose a model for predicting DFA variance in experimental data and conduct a Monte Carlo simulation to estimate the sample size and number of trials required to detect a change in DFA scaling exponent. We illustrate the model in a simulation to detect a difference of 0.1 (medium effect) between two groups of subjects when using short gait time series (100 to 200 strides) in the context of between- and within-subject designs. We assumed that the variance of DFA scaling exponent arises due to individual differences, time series length, and experimental error. Results showed that sample sizes required to achieve acceptable power of 80% are practically feasible, especially when using within-subject designs. For example, to detect a group difference in the DFA scaling exponent of 0.1, it would require either 25 subjects and 2 trials per subject or 12 subjects and 4 trials per subject using a within-subject design. We then compared plausibility of such power predictions to the empirically observed power from a study that required subjects to synchronize with a persistent fractal metronome. The results showed that the model adequately predicted the empirical pattern of results. Our power simulations could be used in conjunction with previous design guidelines in the literature when planning new gait variability experiments.

A comparison of kinematic-based gait event detection methods in a self-paced treadmill application

Kinematic-based algorithms for detecting gait events are efficient and useful in the absence of (reliable) kinetic data. However, the validity of these kinematic-based algorithms for self-paced treadmill walking is unknown, particularly given the influence of walking speed on such data. We quantified offsets in event detection of four foot kinematics-based algorithms (horizontal position, horizontal velocity, vertical velocity, and sagittal resultant velocity) relative to events determined by a threshold in vertical ground reaction force among seven uninjured individuals - and nine with unilateral transtibial amputation - walking on a self-paced treadmill. Across walking speeds from 0.48-1.64m/s (0.5-31.7% CV), offsets ranged from -7 to +3 frames (≈83.3ms) in heel strike, and -3 to +5 frames (≈66.6 ms) in toe off. Regardless of method, offsets in heel strike were not influenced (-0.01<r<0.01, all P>0.61) by variability in walking speed. However, offsets in toe-off were positively correlated with variability in walking speed for the horizontal position (r=0.539; P<0.001) and velocity (r=0.463; P<0.001) algorithms, and negatively correlated (r=-0.317; P<0.001) for the vertical velocity algorithm; offsets from the sagittal resultant velocity algorithm, with thresholds adjusted for walking speed, were not strongly associated (r=0.126; P=0.27). Although relatively minimal offsets support the applicability of these algorithms to self-paced walking, for individuals with asymptomatic and pathological gait patterns, sagittal resultant velocity of the foot produces the most consistent event detection over the widest range of (and variability in) walking speeds.

Time and frequency domain characteristics of detrending-operation-based scaling analysis: Exact DFA and DMA frequency responses

We develop a general framework to study the time and frequency domain characteristics of detrending-operation-based scaling analysis methods, such as detrended fluctuation analysis (DFA) and detrending moving average (DMA) analysis. In this framework, using either the time or frequency domain approach, the frequency responses of detrending operations are calculated analytically. Although the frequency domain approach based on conventional linear analysis techniques is only applicable to linear detrending operations, the time domain approach presented here is applicable to both linear and nonlinear detrending operations. Furthermore, using the relationship between the time and frequency domain representations of the frequency responses, the frequency domain characteristics of nonlinear detrending operations can be obtained. Based on the calculated frequency responses, it is possible to establish a direct connection between the root-mean-square deviation of the detrending-operation-based scaling analysis and the power spectrum for linear stochastic processes. Here, by applying our methods to DFA and DMA, including higher-order cases, exact frequency responses are calculated. In addition, we analytically investigate the cutoff frequencies of DFA and DMA detrending operations and show that these frequencies are not optimally adjusted to coincide with the corresponding time scale.

Establishing a direct connection between detrended fluctuation analysis and Fourier analysis

To understand methodological features of the detrended fluctuation analysis (DFA) using a higher-order polynomial fitting, we establish the direct connection between DFA and Fourier analysis. Based on an exact calculation of the single-frequency response of the DFA, the following facts are shown analytically: (1) in the analysis of stochastic processes exhibiting a power-law scaling of the power spectral density (PSD), S(f)∼f(-β), a higher-order detrending in the DFA has no adverse effect in the estimation of the DFA scaling exponent α, which satisfies the scaling relation α=(β+1)/2; (2) the upper limit of the scaling exponents detectable by the DFA depends on the order of polynomial fit used in the DFA, and is bounded by m+1, where m is the order of the polynomial fit; (3) the relation between the time scale in the DFA and the corresponding frequency in the PSD are distorted depending on both the order of the DFA and the frequency dependence of the PSD. We can improve the scale distortion by introducing the corrected time scale in the DFA corresponding to the inverse of the frequency scale in the PSD. In addition, our analytical approach makes it possible to characterize variants of the DFA using different types of detrending. As an application, properties of the detrending moving average algorithm are discussed.