Validity of linear and nonlinear measures of gait variability to characterize aging gait with a single low back accelerometer

doi:10.21203/rs.3.rs-4485214/v1

Purpose

This study investigates the validity of the attractor complexity index (ACI), a recently developed gait analysis tool based on nonlinear dynamics. The analysis assesses ACI's sensitivity to motor-cognitive interference and its potential for characterizing age-related changes in gait patterns. Furthermore, the study compares ACI with classical gait metrics to determine its efficacy relative to established methods.

Methods

A 4x200m indoor walking test with a triaxial accelerometer attached to the lower back was used to compare gait patterns of younger (N = 42) and older adults (N = 60) during normal and metronome walking. The other linear and non-linear gait metrics were movement intensity, gait regularity, local dynamic stability (maximal Lyapunov exponents), and scaling exponent (detrended fluctuation analysis).

Results

In contrast to other gait metrics, ACI demonstrated a specific sensitivity to metronome walking, with both young and old participants exhibiting altered stride interval correlations. Furthermore, there was a significant difference between the young and old groups (standardized effect size: -0.77). Additionally, older participants exhibited slower walking speeds, a reduced movement intensity, and a lower gait regularity. Inferential statistics using linear mixed-effects models confirmed the responsiveness of ACI to metronome walking and its efficacy in differentiating between the gait patterns of older and younger adults.

Conclusion

The ACI is likely a sensitive marker for cognitive load during walking and can effectively discriminate age-related changes in gait patterns. Its ease of measurement makes it a promising tool gait analysis in unsupervised (free-living) conditions. Future research will focus on the ACI’s clinical utility for fall risk assessment.

gait analysis

accelerometers

gait variability

nonlinear dynamics

aging

fall prevention

metronome walking

As individuals age, their ability to walk is significantly impacted by a convergence of biomechanical and physiological changes. These changes are a result of age-related physiological and neurological alterations, including decreased muscle strength, lower cardiorespiratory fitness, degeneration of the sensory system, impaired neuromuscular coordination, or diminished joint mobility [1]. Compared to young adults, older people exhibit distinct gait characteristics: notably slower preferred walking speeds, shorter stride lengths, longer double-support stance times, reduced push-off forces, and a more flat-footed landing [2, 3].

These adaptations appear to also reflect a shift toward a safer gait pattern, potentially compensating for reduced balance control efficiency. This cautious walking pattern increases the amount of attention required for motor control, as has been shown in dual-task experiments. Dual-tasking tests, involving walking and another concurrent task, evaluate how divided attention impacts motor and gait performance [4]. Known as motor cognitive interference, these gait alterations are more pronounced in older adults, particularly in those with a history of falls or cognitive impairments, compared to their younger or cognitively healthy counterparts [5].

Another key characteristic of gait in older individuals is the increased variability [3, 6]. Gait variability refers to the natural variation in the spatial and temporal characteristics of walking [7]. Classically, linear statistical measures of gait variability, such as standard deviation or range, focus on quantifying the amount of variation in a set of gait parameters. In contrast, nonlinear approaches—as delineated in nonlinear dynamical system theory [8]—can reveal the structured temporal patterns underlying this variability, emphasizing its deterministic rather than random nature. Nonlinear tools, such as entropic measures, fractal analysis, or those developed for the study of deterministic chaos, are used to evaluate this temporal structure of variability [9, 10]. Both linear and nonlinear strategies have been used effectively to describe gait variability in the older population and predict the likelihood of falls [6, 11–15].

Because age-related decline in walking ability increases the risk of stumbling and subsequent falls [16], it is critical to identify changes in gait with age. The analysis of age-related gait modifications not only allow for early identification of older adults at risk for falls but also facilitates the development and evaluation of intervention strategies to maintain a safe mobility [17]. In addition, gait analysis also offers a means to monitor individual progress during rehabilitation, providing insight into the patient's recovery trajectory [18–20]. Gait analysis, which has traditionally relied on motion capture systems in laboratory settings, has evolved with the advent of inertial sensors, such as accelerometers, facilitating real-world gait quality measurements [21]. These developments underscore the potential of portable, accessible tools in public health, especially for older adults, to provide continuous, objective data that may indicate subtle changes in gait or balance that are predictive of fall risk [22].

The assessment of gait parameters in ecological contexts presents unique challenges. The process requires the use of simple, non-intrusive devices designed for prolonged use over several days. As a result, a single point measurement cannot provide a comprehensive understanding of gait kinematics and kinetics. A recent systematic review highlights that traditional linear variability metrics, including step time and step length variability, are inadequately captured using a single accelerometer positioned at the lower back [23]. The problem may arise because these methods need to accurately record each gait event to evaluate variance without noise, something that is difficult with a single accelerometer [23]. In addition, this systematic review emphasizes that while nonlinear measures can serve as valuable complements to linear measures of variability, there remains a need for more high-quality studies to confirm their validity.

Over the last decade, three high-quality studies have suggested that accelerometric measures are effective in predicting fall risk in older adults within their everyday home environment. The article by Weiss et al. (2013 [24]) describes a study that utilize acceleration-derived measures, collected over three days, to evaluate the quality and quantity of walking in a home setting. The findings highlight that these measures are sensitive to fall risk, effectively distinguishing between individuals with high and low fall risks. The derived measures from acceleration signals included amplitude, width, and slope of the power spectral density (PSD) peak. Additional measures included average step and stride duration, regularity measures (autocorrelation function (ACF) method), the harmonic ratio (an index of gait smoothness), and acceleration ranges.

The study by van Schooten et al. (2015 [25]) compares associations between both retrospective and prospective falls with gait quality measured by daily-life accelerometry. The research involved collecting one week of trunk accelerometry data from 169 older adults. Similar algorithms were used as in the Weiss et al. study. In addition, nonlinear variability measures, namely the local dynamic stability (LDS) were also utilized. They highlight that a higher rate of divergence, indicating lower local stability, was associated with prospective falls.

In their 2016 study, the same team of researchers conducted an in-depth analysis of gait quality in 294 older adults [26]. This study was conducted under real-world conditions, with participants wearing a single 3-D accelerometer. The research took a one-year prospective approach using survival analysis to focus on time to first and second falls as primary outcomes. A comprehensive set of gait parameters were used to assess the gait quality, including both kinematic variables and variability indices, both linear and nonlinear. The results found significant predictor of time to fall, including walking speed, stride length, stride frequency, intensity, regularity, smoothness, symmetry, and complexity. Notably, however, linear measures of variability, such as step time and step length variability, did not show a direct correlation with time to fall.

These recent studies provide compelling evidence that assessing gait quality with a single accelerometer is effective in identifying older adults at higher risk for falls. However, there remains a need to develop advanced methods for analyzing acceleration signals that capture the full spectrum of gait characteristics in older adults. In particular, a proxy measure for motor-cognitive interference—the attentional and cognitive demands of the task of locomotion—could significantly improve our understanding of balance deterioration.

The ACIER (attractor complexity index empirical rationalization) study, endeavors to fill this gap by validating an approach based on nonlinear analysis of acceleration signals measured at the lower-back level. We sought to validate a novel method, derived from nonlinear dynamic analysis of chaotic systems (Lyapunov exponents), that assesses the correlation patterns that are present among consecutive strides in long duration walking [27]. This particular structure of variability, characterized by a scale-free organization of temporal variance, is also known as 1/f noise, power-law correlation, or fractal pattern [28]. Recognizable in various physiological signals, fractal dynamics has been proposed as a signature of the elaborate complexity found in living organisms [29]. A recent study has shown that the variability of lower limb muscle activity, as recorded by surface electromyography, has a similar correlation pattern to the time series of gait intervals. This finding sheds light on the neurological basis of nonlinear gait variability [30]. It has been hypothesized that changes in the correlation pattern may be related to the motor-cognitive interference observed in older adults. For example, empirical evidence shows that older adults exhibit a significantly altered correlation structure when exposed to visual field perturbations, a phenomenon not paralleled in younger controls [31].

In the ACIER study, metronome walking was proposed as a strategy to mimic conditions that require increased cognitive effort in gait control. This approach, in which individuals match their steps to the steady rhythm of a metronome, is known to alter the correlation dynamics in stride intervals, resulting in an anticorrelated pattern [32, 33]. In treadmill experiments, a relationship has been observed between the amount of attention paid to gait control and the degree of stride anticorrelation [34, 35]. It appears that executive function is involved in the regulation of anti-persistence in the variable relevant to treadmill walking goal attainment [35].

In the initial phase of the ACIER study [36], our goal was to evaluate, in older people, the responsiveness of the proposed method (attractor complexity index, ACI) to metronome walking relative to an established reference technique (DFA). This involved optimizing the parameterization of the ACI algorithm and examining its intrasession reliability. The present article describes the second phase of the study, in which our focus shifted to determining the efficacy of this new method in characterizing the gait patterns of older individuals through comparative analyses with a younger cohort. In addition, we investigated the effectiveness of ACI relative to other established gait variability metrics. A central hypothesis tested was the unique sensitivity of ACI to metronome walking, which we hypothesized would induce distinct changes not observable with traditional variability parameters. The secondary hypothesis was that ACI could discriminate age-related changes in gait patterns as efficiently as other gait metrics.

Study rationale and design

In the context of identifying older individuals at increased risk of falling in their daily environment, the rationale behind the ACIER study centered on the use of a single triaxial accelerometer attached to the lower back, a methodology that represents the norm among researchers in this field [22,24,26]. To specifically validate our novel approach, (ACI [27,36,37]), metronome walking was used to alter the correlation structure of gait and thus confirm the specific sensitivity of the ACI to cognitive load.

Our validation study implemented a standardized indoor walking circuit, thereby mitigating biases due to environmental variables. In addition, the indoor setting facilitated accurate measurement of average walking speed, allowing for a more nuanced interpretation of the collected gait metrics and their interrelationships. In particular, we sought to classify gait metrics according to their relationships with preferred walking speed, taking into account the potential influence of age group on these associations.

The second phase of the ACIER study used a cross-sectional design and aimed to compare 40 younger adults with the 60 older adults enrolled in the Phase 1 [36]. Like the older participants, the younger participants were required to walk four 200-meter segments that included both normal and metronome walking. As in Phase 1, in addition to the lumbar device, the younger participants wore a 3D accelerometer attached to the foot, which served as a reference standard for calculating the correlation structure between strides. In addition to calculating both short- and long-term logarithmic divergence exponents (using the Lyapunov exponent method), several other gait metrics were derived from the lumbar acceleration signals for comparative analysis. These metrics included movement intensity (measured by root mean square, RMS) and gait regularity (assessed by the ACF method). Linear mixed-effects models were used as the method of inference to examine the effects of age group (older versus younger), walking condition (metronome versus normal), and walking speed, as well as potential interactions between these factors.

For additional insights into the ACIER study, particularly the study rationale, settings, recruitment and characteristics of older participants, detailed experimental procedures, and an in-depth explanation of the ACI algorithm, readers are encouraged to refer to the companion article [36].

Participants

In addition to older adults already enrolled in Phase 1, our goal was to recruit 40 healthy adult participants between the ages of 18 and 40 without gait disorders of orthopedic or neurologic origin. The minimum age limit was set in response to legal restrictions, thus excluding minors. The maximum age limit was determined based on epidemiologic [38,39] and experimental [40,41] studies that have shown that changes in both static and dynamic balance can occur in individuals in their forties or fifties, similar to those observed in older adults. Young participants were recruited through a combination of personal networks and electronic advertisements. The research team used connections within our institution (HE-Arc), including students, colleagues, friends, and family, supplemented by targeted email campaigns to partner institutions and internal mailings within HE-Arc. This approach aimed to ensure a diverse pool of participants.

The protocol for this study was approved by the local ethics committee ("commission cantonale d'éthique de la recherche sur l'être humain du canton de Vaud", ID 2021-01937). All participants were thoroughly informed of study procedures and provided signed informed consent. They also agreed that their data would be anonymized and made publicly available.

Experimental procedures

Participants were equipped with two triaxial accelerometers (Physilog 6S, Gaitup, Switzerland): one attached to the lower back at the L4-L5 level and the other attached to the instep of the right foot. They walked a 205-meter corridor four times at their natural pace, completing two round trips. Each lap was timed to measure their preferred walking speed. After the first round trip, there was a five-minute break during which walking cadence (step frequency, SF) was calculated from the lower back acceleration signal. On the next round trip, participants adjusted their gait to an electronic metronome, the rhythm of which was matched to the cadence determined during the break. A 30-second walk with the metronome was performed before the start of the second round-trip to familiarize participants with gait synchronization. Like the older participants, the young participants wore their own low-rise, comfortable shoes during the walking test; high heels were not allowed.

Data analysis

Acceleration data—sampled at a rate of 256Hz—were transferred from the devices to the institutional server. Calculations and analyses were performed in MATLAB R2021a (The MathWorks Inc., Natick, MA). By visual inspection of the acceleration signals, segments indicative of steady walking were selected for subsequent analysis. Raw acceleration data are available online [42].

Table 1 presents a summary of the gait metrics derived from the acceleration signals (with the exception of the preferred walking speed, which was assessed by timing the walks). The goal was to justify the selection of these metrics for characterizing gait quality in free-living conditions. The first column briefly outlines the methodology, explains its basic rationale, and cites key papers that provide comprehensive descriptions of the algorithms used. The subsequent column references studies that have applied these metrics in unsupervised settings.

To strengthen the validity of gait metrics for unsupervised settings where direct speed measurement is not possible, we chose to measure average preferred walking speed by timing of participant displacement. An analytical framework was then developed to categorize gait metrics based on their association with speed and responsiveness to age. Some gait metrics may characterize aspects of gait decline that are unrelated to the expected decline in preferred walking speed. No correlation with walking speed is expected. These have been termed "speed-independent" metrics. Conversely, "speed-surrogate" metrics show a strong correlation with walking speed, with this association expected in both younger and older adults. Finally, "mixed metrics" represent an intermediate category. They show a correlation with speed, but this correlation is likely to be stronger in older adults than in younger individuals.

We define 'basic gait parameters' as a commonly used gait metrics that describe the step pattern during ambulation. These parameters include step length, SF (inverse of step duration), and walking speed. Given that step length can be derived from speed and step frequency, we opted to exclude it from the analysis to avoid redundancy. We calculated average SF during the corridor ambulation using spectral analysis of the vertical acceleration from the lumbar accelerometer, specifically by identifying the dominant frequency within the signal (fast Fourier transform (FFT) analysis). We determined the average preferred walking speed by timing participants with a stopwatch as they walked the length of the corridor (205 m).

After the calculation of average SF, we calibrated the raw 3D acceleration signals by using the method proposed by Moe-Nilssen [43]. This algorithm corrects accelerometer data for tilt for obtaining meaningful acceleration information in a horizontal-vertical coordinate system. In addition, we used an alternative methodology to generate gait metrics that are robust to orientation or shift issues with the motion sensor. The vector norm (or magnitude) of the 3D acceleration signals was calculated as the square root of the sum of the squares of the individual acceleration components. It should be noted that, to be consistent with the Moe-Nilssen procedure, the effect of the earth's acceleration was cancelled by subtracting one of the raw vector norms.

To ensure uniformity of gait metrics across participants, we standardized acceleration signal lengths by truncating them to a duration of 250 steps (125 gait cycles or strides). This standardization was achieved by using the individual SF and accelerometer sampling rate (256 Hz): the retained number of data points simply equaled the product of SF and sampling rate multiplied by the desired number of steps (250). The resulting signals, measured in the anteroposterior (AP), vertical (V), and mediolateral (ML) directions, as well for the vector norm, differed in length (i.e., duration) but were equally representative of the walking activity in terms of number of steps. Note that these procedures (calibration and length standardization) were not apply to the foot accelerometer data (see below).

To assess the intensity of the walking movements, The RMS of the vector norm was determined over the 250 steps. It is well known that gait RMS has a significant correlation with walking speed [37], and thus can serve as an effective proxy measure for this parameter in unsupervised conditions (speed-surrogate metric) [44]. It has been suggested that standardization of the root mean square (RMS) may provide a linear variability index that is less sensitive to gait speed but more indicative of gait abnormalities [45]. Consequently, the RMS ratio is defined as the quotient of the RMS of the acceleration signal measured in the mediolateral direction and the RMS of the vector norm.

In order to quantify the degree of regularity of gait pattern, an unbiased autocorrelation analysis was performed using the vector norm as input (ACF method [46]). The autocorrelation of a signal analyzes the degree of similarity between a given signal and a delayed version of itself over varying intervals of time, or lags. The Matlab built-in function xcorr was used with the option “unbiased”. The normalization of the autocorrelation sequence was achieved by dividing each element by the value at zero lag, thereby scaling the sequence to yield values in the range of -1 to 1, analogous to a correlation coefficient. The first dominant period corresponds to a phase shift equivalent to a single step, while the second dominant period corresponds to a phase shift equivalent to the duration of an entire gait cycle (i.e., stride). The maximal values corresponding to the peaks of the first and second dominant periods were defined as step regularity and stride regularity, respectively. To increase the robustness of statistical inference, following the recommendation of Auvinet et al. (1999 [47]), we normalized these values by applying Fisher’s transform (or inverse hyperbolic tangent).

As nonlinear variability measures indicative of gait stability and automaticity, we calculated logarithmic divergence exponents using the maximal Lyapunov exponent method and the Rosenstein’s algorithm [48–50]. A detailed description of how to compute both short-term (LDS) and long-term (ACI) divergence exponents can be found in the companion article [36]. In short, the acceleration signals were further standardized to a length of 18,750 samples (75 samples per step). Following Taken's theorem, we constructed a multidimensional attractor representative of the gait dynamics. We used a uniform embedding dimension of five and adjusted the time delay based on the average mutual information. Next, we calculated the logarithmic divergence between adjacent trajectories and normalized it by the number of strides. Finally, divergence rates (corresponding to divergence exponents) were determined over two distinct ranges: 0-0.5 strides (LDS) and 5-12 strides (ACI). Following the recommendations of previous research [36,51], we focused our analysis on LDS measured along the mediolateral axis (LDS-ML), and ACI along both the anteroposterior (ACI-AP) and vertical (ACI-V) axes. In addition, we applied the ACI algorithm to the vector norm (ACI-N).

The primary goal of attaching an accelerometer to the foot was to improve the accuracy of gait event identification, thereby generating a refined time series of stride intervals. This improvement is critical because the reference method for assessing the correlation structure of gait, the detrended fluctuation analysis (DFA), requires a discrete time series of gait events. A comprehensive rationale for this methodology and an in-depth explanation of the procedure can be found in the companion article [36]. Briefly, a peak detection algorithm was applied to the foot acceleration signal to delineate and separate individual strides, allowing the duration of each stride to be calculated. The time series of stride intervals was then analyzed by DFA, using a box size ranging from 16 to N/2, where N is the total number of strides.

Statistics

Our approach to characterizing gait metrics used a combination of visualization, descriptive statistics, and further exploration techniques. For better interpretation, the outcomes of the two laps (back and forth) were aggregated (mean). Visualization used boxplots and univariate scatterplots (Fig. 1–6) to initially explore the distribution of the data. Descriptive statistics summarized central tendencies and variability for both normal and metronome walking conditions across age groups, presented as means and standard deviations in Table 2 and 3. These tables also included standardized differences between young and older participants (Hedges’g [52]), along with 99% confidence intervals (CI) calculated using bootstrapping. Further exploration, detailed in the Supplementary Material, included histograms and bivariate scatterplots with linear fits and corresponding Pearson’s correlation coefficients, allowing for more in-depth examination of data relationships.

We used linear mixed-effects models to assess the influence of age and walking conditions on gait metrics [53]. This approach accounts for the potential correlations between values measured repeatedly in each participant and for the nested structure of the data, with two laps performed for each condition. After visual inspection of the histograms to confirm normality and removal of outliers greater than 3 standard deviations above the mean, gait metrics were used as dependent variables. Group (older vs. young) and walking condition (metronome vs. normal) were transformed into dummy variables for inclusion as fixed effects. The random part of the model included a slope effect to account for individual variability in response to walking condition (participant by condition interaction). To assess whether young and older participants responded differently to the metronome, we first included a group-by-condition interaction term in the model as a fixed effect. Maximum likelihood estimation was used as the fitting method, with F-tests used to assess the significance of all fixed-effect terms (ANOVA method). If the interaction term did not reach statistical significance (p > 0.01), it was removed from the final model, which was then re-fitted using restricted maximum likelihood estimation. A detailed report of these analyses can be found in the Supplementary Material. Table 4 presents the fixed-effects coefficients with 99% confidence intervals.

To facilitate comparison of effect sizes across gait measures, we conducted additional inferential analyses using mixed-effects models with standardized coefficients. We standardized the dependent variables by first subtracting the mean and then dividing by the standard deviation, which ensured that the fixed-effects coefficients were expressed in units of standard deviation, making them directly comparable. As in the first analyses, the models included dummy variables for group and conditions, as well as random slopes (condition-by-participant interaction). To further account for walking speed effects and refine our interpretation of the results, we included preferred walking speed as a continuous covariate. This allowed us to better distinguish between the three gait metric categories (speed-independent, speed-surrogate, and mixed) defined earlier. The results are shown graphically in Fig. 7.

In our analysis, 10 gait metrics derived from lumbar and foot accelerometers were analyzed using linear mixed-effects models. These gait metrics are expected to exhibit some degree of interdependence. To account for the potential inflation of Type I error due to the increased number of parallel statistical tests, we chose a significance threshold of 0.01. We believe that a more stringent correction method such as Bonferroni, which assumes independence between tests, may be overly conservative in this context. A 0.01 threshold balances the need to control for false discovery while maintaining sufficient statistical power (reducing Type II error).

The second phase of the ACIER study targeted a sample size of 100 participants (60 older adults, 40 young adults). As described in the companion article focusing on the first phase [36], a substantial metronome effect on the ACI was expected based on previous treadmill experiments (absolute effect size > 2 [50]). This effect size requires a relatively small minimum number of participants to detect (N < 10). The secondary objective was to assess age-related differences in ACI, which guided the sample size calculation. In the absence of existing data on the variance and responsiveness of ACI with age, we referred to studies using the scaling exponent (derived from DFA, the established method for assessing the correlation structure of gait [36]). However, a 2020 meta-analysis of eight DFA studies revealed significant heterogeneity in scaling exponents and age effects (standardized ES ranging from -1.26 to +1.14, mean ES=-0.20). This is likely due to differences in measurement methods and algorithm parameterizations. In addition, most studies included older adults who were younger than our target population. The study with the highest mean age (76 years [49]) reported an effect size of -1.26. Notably, a recent study (not included in the meta-analysis) with a rigorous methodology compared 23 older adults (mean age 72 years) with 22 young controls and reported an effect size of -0.91 [50]. Therefore, we conservatively selected an effect size of ‑0.7 to account for both recent advances in the field and the results of the meta-analysis. To achieve 80% power with a type I error rate of 1% and a minimum estimated effect size of -0.7, our calculations indicated a need for 90 participants (36 young, 54 older). We adjusted this to 100 participants (60 older adults, 40 young adults) to account for potential data loss and dropouts.

Participants

Between the second semester of 2022 and June 2023, 42 young adults, including 16 males (38%) and 26 females (62%), participated in the indoor walking test. Their mean age was 27 years (SD = 5.9), with a body mass of 68.9 kg (SD = 17.7) and height of 1.71 m (SD = 0.08). For the older adult group of Phase 1 (N = 60), the mean age was 76 years (SD = 6), body mass was 74 kg (SD = 16), and height was 1.68 m (SD = 0.08), with 60% females (n = 36) and 40% males (n = 24).

Data visualization and cleaning

There were no missing data for gait parameters within the young adult group. Detailed breakdowns of sample size for each variable are presented in Tables 2 and 3.

Visual inspection of boxplots (Fig. 1–6), univariate and bivariate scatter plots (Fig. 1–6 and Supplementary Figures, respectively), and histograms (Supplementary Material) revealed no substantial deviations from normality in the distribution of the dependent variables. Consequently, using parametric linear models instead of generalized or non-parametric models was justified, especially considering their robustness to violations of normality assumptions [54]. No data points were identified as outliers.

Descriptive statistics

Examination of difference between the older and the young group (Table 2 and 3) revealed that older people walked under non cued (normal) condition with a lower speed (ES=‑0.80) and a lower movement intensity (RMS ES=‑0.58), a lower step (ES=‑0.97) and stride (ES=‑0.91) regularity, a lower ACI along both axes (ES= ‑0.77 and ‑0.69) and considering the vector norm (ES= -0.53). Standardized differences between age groups measured from the metronome walking conditions were mostly slightly higher: speed ES= ‑0.77; step regularity ES= ‑1.02; stride regularity ES=‑1.01; ACI-AP ES= ‑0.95; ACI-V ES=‑0.92; ACI-N ES= -0.87. In contrast, movement intensity, as measured by RMS, showed a lower contrast between age group in metronome walking (RMS ES= -0.46). The other gait metrics showed lower differences between age group, with absolute value of ES not exceeding 0.38.

Examination of the differences between the normal and metronome walking conditions showed that the ACIs and scaling exponents (DFA) were substantially altered. In the older group, ACI-AP showed a relative change of ‑27 % (ES= ‑0.74), ACI-V of ‑26 % (ES= ‑0.78), and ACI-N of -30% (ES= -0.82). The relative difference for the scaling exponent was ‑47 % (ES= ‑1.75). In the younger group, ACI-AP showed a relative change of ‑14 % (ES= ‑0.57), ACI-V of ‑15 % (ES=‑0.63), and ACI-N of -13% (ES= -0.52). The relative difference between walking condition for the scaling exponent was ‑40 % (ES=‑1.79).

Analysis of correlations between gait metrics across groups and conditions revealed some recurrent patterns of associations (Supplementary Figures). Consistent with previous findings in older adults [36], we found moderate correlations between ACI and scaling exponent for young participants when both conditions were aggregated (N=84; ACI-N r= 0.45; ACI-AP r= 0.45, ACI-V r=0.45) and in the metronome walking condition (N=42; ACI-N r= 0.51; ACI-AP r= 0.49, ACI-V r=0.46). In the normal walking condition, the correlations were weaker and not significant (p>0.05) (N= 42; ACI-N r= 0.21; ACI-AP r= 0.18, ACI-V r=0.19). Finally, analyzing the entire dataset (both groups and conditions combined), the correlations between ACI and scaling exponent were significant, even with a stricter threshold (p<0.01) (N= 204; ACI-N r= 0.52; ACI-AP r= 0.45, ACI-V r= 0.50).

Unlike older participants [36], young participants did not exhibit significant correlations between ACI and walking speed for either axis (r= -0.19 to 0.11) and for the norm (r= 0.00 to 0.10) across conditions. Similarly, for older participants, a robust positive association between ACI and stride and step regularity was observed (r = 0.58 to 0.68). But, in contrast, this association was weaker in younger participants (r = 0.16 to 0.31).

In examining other relevant associations between gait metrics and preferred walking speed, consistent with expectations, stride frequency (SF) showed a moderate to strong correlation with speed (r = 0.43 to 0.69 across groups and conditions). Similarly, as predicted, movement intensity (RMS) showed a robust correlation with speed (r = 0.73 to 0.79). In contrast, gait parameters such as scaling exponents (r = -0.10 to 0.19), LDS (r = -0.28 to 0.04), and ACI-AP (r = -0.19–0.34) were observed to have negligible associations with walking speed. Furthermore, when considering age groups, differences were observed between young and older participants: older group showing a moderate correlation between speed and step regularity (r = 0.42 to 0.58), whereas the younger group showed minimal to no correlation (r = 0.00 to 0.21).

Inferential statistics

The primary hypothesis of this study was that ACI would be specifically sensitive to metronome walking, in contrast to other gait parameters measured by the lumbar accelerometer. Linear mixed-effects regression analyses supported this hypothesis. When controlling for age group, models including the anteroposterior (ACI-AP) and the vertical (ACI-V) components showed significant regression coefficients (t-test, p < 0.0001 for both; Table 4 and Supplementary Material). ACI of the vector norm (ACI-N) also showed a significant association (p<0.0001). This conclusion held true when walking speed was added as a covariate (Fig. 7). Scaling exponents obtained from the foot accelerometer, used as a reference metric, showed a comparable responsiveness to metronome walking (Table 4 and Fig. 7). Conversely, the remaining gait metrics remained largely unaffected when gait was synchronized to the metronome. Note, however, that movement intensity (RMS) showed a significant sensitivity to the metronome (p = 0.002), but the strength of the association was very weak (Fig. 7). The regression model predicts a relative difference of 3.8%.

The secondary objective of this study was to assess the ability of the ACI to characterize aging gait patterns. In support of this, regression models (Table 4 and Supplementary Material) revealed a significant effect of age groups on ACI-N (p<0.001), ACI-AP (p<0.0001), and ACI-V (p<0.0001). Fig. 7 illustrates the effectiveness of the ACI in discriminating between older and younger adults compared to other gait metrics. The figure presents standardized coefficients indicating the strength of association adjusted for speed and condition, ranked from highest (top) to lowest (bottom) group effect, adjusted for the walking condition and speed. Step and stride regularity, ACI-AP, and stride variability showed similar magnitudes. ACI-V and ACI-N had a slightly lower beta coefficient. The remaining gait metrics showed no significant response to age groups. However, it is important to recognize that the wide confidence intervals (Table 4 and Fig. 7) may imply insufficient statistical power, potentially masking truly relevant effects.

Finally, to further explore the responsiveness of gait metrics to age, we investigated their potential co-associations with preferred walking speed. The right subplot of Fig. 7 shows the covariances between walking speed and each gait metric, after accounting for age and condition effects. Movement intensity (RMS), stride variability, and SF were the parameters with the strongest correlations with speed. Weaker, yet significant, associations were observed for stride and step regularity, as well as ACI-V and ACI-N. Conversely, ACI-AP, LDS, scaling exponent, and RMS ratio did not exhibit significant associations with preferred walking speed.

The second phase of the ACIER study was designed to evaluate the effectiveness of the recently proposed ACI method in discriminating gait patterns between younger and older adults and to investigate its responsiveness to cognitive load during walking tasks compared to other linear and nonlinear gait metrics. Our findings support the primary hypothesis, demonstrating a specific sensitivity of the ACI compared to other gait metrics derived from the lumbar accelerometer, when participants walked in synchrony with a metronome compared to normal walking. In addition, the study aimed to assess the ability of ACI to characterize age-related differences in gait patterns. Consistent with the secondary hypothesis, ACI, along with step and stride regularity, demonstrated a significant ability to discriminate between older and younger adults. These findings indicate that ACI may serve as a sensitive marker for detecting changes in gait control and cognitive demands during walking, which can be useful in predicting fall risk in older individuals.

Building on the responsiveness of the ACI to metronome walking observed in older adults (Phase I [36]), this study confirms this effect in young adults (Table 2–4 and Fig. 7). In addition, we demonstrate a significant correlation between the ACI and the reference standard (scaling exponent of the stride interval time series) in young adults (see Supplementary Material). These findings are consistent with previous research showing similar responsiveness to voluntary synchronization and correlations with the reference standard (DFA) in both treadmill [27, 37, 50, 55] and overground [56] walking studies. Descriptive statistics (Table 2–3) revealed a trend for younger individuals to have smaller differences in ACI-AP (-14%) and ACI-V (-15%) between normal and metronome walking compared to older adults (-27% and − 26%, respectively). This age-related discrepancy is consistent with the observed differences in scaling exponents (Table 2–3, young: -40%, older: -47%). This finding may parallel observations in treadmill walking, where lower scaling exponents are associated with tasks requiring tighter gait synchronization and potentially higher cognitive demands [34]. Similarly, in our study, synchronizing gait with a metronome might require a greater cognitive load for older adults compared to younger participants. However, the regression analyses considering within-subject correlations (multiple regressions, mixed effect models) did not yield a significant condition-by-group interaction for either ACI-AP (p = 0.27), ACI-V (p = 0.16), or ACI-N (p = 0.06) (Supplementary Material, ANOVA F-tests). A possible explanation for this lack of interaction effect could be insufficient statistical power, as interaction terms may require four times the sample size for detection compared to main effects [57]. Future adequately powered studies specifically designed to investigate this potential age effect are warranted.

Our novel contribution lies in the specific sensitivity of the ACI to metronome walking compared to other gait variability metrics used in unsupervised settings. Specifically, walking in synchrony with an isochronous metronome tuned as the preferred SF did not affect gait regularity as assessed by ACF with the lumbar accelerometer. Similarly, other gait metrics, including RMS ratio and LDS, remained unaffected by metronome walking. However, we observed a small (+ 4%) but significant increase in movement intensity (RMS) during this condition, even after accounting for potential within-participant correlations and adjusting for age group and speed using mixed effects models (Fig. 7). Although a type I error cannot be entirely ruled out, we can consider the following explanation: it is possible that participants may have unconsciously adjusted their gait pattern by striking their heels more forcefully to synchronize with the metronome, resulting in higher peak accelerations and, as a result, a slightly higher RMS value.

Our validation study used an indoor circuit, which offered the advantage of directly measuring preferred walking speed through timed travel. Walking speed is a valuable health biomarker [58]. Age-related conditions can limit gait speed in older adults. These conditions include sarcopenia (muscle loss [59]), reduced cardiorespiratory fitness [60], increased energetic cost [61], mitochondrial dysfunction [62], joint stiffness [63] or impaired sensory feedbacks [64]. As a result, older adults typically have a slower preferred walking speed than younger adults, which was confirmed in our study. Indeed, we found that older participants had an average speed of 1.27 m/s (Table 2–3), which is consistent with the reference value of 1.30 m/s reported for highly functional older individuals (mean age 79 years) in a recent large-scale study with a comparable socio-cultural context (Germany, [65]). In contrast, the walking speed of the younger participants was 1.43 m/s, which is slightly higher than the reference value of 1.37 m/s for adults between 20 and 40 years of age calculated from the data of a meta-analysis including 23,000 individuals measured worldwide [66]. Overall, there was an 11% relative difference between young and older participants. This difference was highly significant in both descriptive statistics (standardized ES: -0.77) and in the multiple regression analysis adjusted for walking condition (regression coefficient b = -0.167 m/s, t-test p < 0.0001, Table 4 and Supplementary Material).

In our effort to establish an analytical framework for categorizing gait metrics based on their correlation with observed walking speed, we anticipated that both movement intensity (RMS of lumbar acceleration) and SF would fall into the speed-surrogate category. Unsupervised gait analysis employing a single lumbar accelerometer relies on simplified gait models (e.g., inverted pendulum) or speed-surrogate metrics, such as SF or RMS, to estimate walking speed (Table 1). Inverted pendulum models are typically derived through a double integration procedure of the trunk acceleration to estimate step lengths [67], in conjunction with anthropometric measurements. It is noteworthy that RMS captures the average amplitude of the signal, which is somewhat analogous to integrating the signal. In experimental studies involving subjects walking across a wide spectrum of speeds, a curvilinear relationship has been therefore observed between acceleration RMS and walking speed [68–70]. Our findings corroborate this relationship, demonstrating that the RMS of acceleration and preferred walking speed are positively correlated (correlation coefficients: 0.73 to 0.79, Supplementary Figures). This correlation holds true for both older and younger participants. Consequently, individuals who spontaneously walk at slower speeds also tend to exhibit lower RMS values. Our results confirm therefore that older participants exhibit lower RMS values compared to their younger counterparts. Specifically, during normal walking, the RMS values were 0.38 for older participants versus 0.46 for younger participants (absolute difference: -0.08, relative difference: -17%). Similarly, during metronome walking, the corresponding values were 0.40 and 0.47, respectively (-0.07, -15%). The regression model shows a coefficient of -0.084 for age group adjusted for walking conditions (Table 4). When the regression model is further adjusted for walking speed, the age group effect vanishes (Fig. 7), as logically expected given the strong RMS-speed relationship. However, while the RMS of trunk acceleration holds promise as a surrogate of a direct measure of walking speed, it is essential to consider its sensitivity to factors beyond velocity. Notably, RMS can be influenced by external conditions, including the nature of the walking surface [71] and the slope [72, 73]. This sensitivity to environmental variables may complicate the use of RMS as a robust proxy for walking speed in unsupervised conditions.

As a second speed-surrogate metric, SF, which is biomechanically related to walking speed as the product of cadence and step length, also showed a systematic correlation with walking speed (supplementary figures). However, the strength of this association across groups and conditions (r = 0.43 to 0.69) was weaker than that observed for RMS (r = 0.73 to 0.79). In contrast to RMS, SF did not differ significantly between young and older participants (1.89 vs. 1.90), as confirmed by the multiple regression analyses (Table 4 and Fig. 7). This finding is consistent with the expected pattern in which older adults typically have shorter step lengths compared to younger adults [2], resulting in a similar cadence despite their reduced preferred walking speed (Table 2). Although SF may serve as a surrogate for walking speed, its utility in characterizing age-related gait changes in unsupervised settings seems therefore limited. However, more research is needed to further evaluate the usefulness of SF in assessing fall risk.

To attenuate the speed sensitivity of RMS, the RMS ratio has been proposed as a metric for gait quality assessment [45]. This approach aimed to normalize the mediolateral acceleration RMS by the global RMS of the vector magnitude, potentially revealing gait instability in the frontal plane. While several studies have investigated this hypothesis, the results have been mostly inconclusive [74–76]. In our large study including 100 subjects of various ages, we found no significant change of RMS ratio across the lifespan [40]. Here, too, we observed that RMS ratio was not different between young and older participants (Table 2–4 and Fig. 7). Although the concept of RMS normalization initially appeared promising, the use of the RMS ratio to characterize age-related gait changes seems to have limited utility.

Our results show a significant difference in step and stride regularity between age groups, as measured by the ACF analysis. The ES for normal walking was large (-0.97 and − 0.91, Table 2), which was further supported by the results of the multiple regression analyses (Table 4 and Fig. 7). This is consistent with previous research highlighting similar age-related reductions in regularity [77, 78]. In particular, the previous work by Auvinet et al. [79], which characterized gait patterns across different age groups, reported a substantial difference in stride regularity (standardized ES = -1.22) between the youngest (20–29 years) and oldest (> 70 years) cohorts, although no significant change was found across the lifespan. This observed change in acceleration signal regularity with age suggests that a convergence of musculoskeletal and neurological deficits may limit the ability to maintain consistent gait patterns across strides. Note also that a correlation was observed between ACI and ACF measures in the older group specifically (supplementary material, r = 0.58 to 0.68). This supports the hypothesis that both gait regularity and ACI are concomitant signs of gait quality degradation in older adults. Regarding the categorization of step and stride regularity according to their associations with walking speed, they can be considered as mixed-metrics. Indeed, while only weak correlations were observed in the young group (r = 0.0 to 0.36, Supplementary Figures), stronger associations were observed in the older group (r = 0.42 to 0.58). Finally, ACF analysis shares an advantage with the LDS and ACI methods in that it does not rely on gait event detection to assess gait variability. This is particularly beneficial when analyzing gait in variable environments, where frequent transient events can lead to irregular steps and prevent clear gait cycle delineation.

LDS is a popular nonlinear gait variability metric that reflects gait robustness to perturbations and is considered a predictor of fall risk [15, 49]. Unlike the ACI, where higher values indicate better gait quality, higher LDS results correspond to greater instability and a degraded gait pattern [12, 27]. Therefore, it is expected that older adults, who have a higher risk of falling, will exhibit higher short-term divergent exponents compared to younger individuals. This assumption is partially supported by observational studies. However, definitive conclusions are hindered by methodological inconsistencies in measurement methods, algorithm implementations, and experimental designs [14]. Our 2015 study investigated changes in gait stability between the ages of 20 and 70 in 100 participants using the same LDS calculation as this work. Our model predicted a 13% higher LDS-ML at age 75 than at age 25. Previous studies have also reported varying relative differences between younger and older cohorts: +40% (graphical estimation, Kang & Dingwell 2009 [80]), + 10% (Bruijn et al., 2014 [81]), + 7% (Hamacher et al. 2015 [82]), + 6% (non-significant, Bizovska et al., 2018 [83]), + 5% (non-significant, Lin et al., 2015 [84]), or + 2% (non-significant, Franz et al. 2015 [31]). The observed relative difference in the present study was + 14% during normal walking and + 8% during metronome walking (Table 2–3), which is consistent with previous research. However, the null hypothesis of no difference between age groups could not be rejected due to large confidence intervals (Table 4 and Fig. 7). Further research is necessary to specifically determine the discriminatory power of the LDS in identifying individuals at risk of falls compared to those who are not.

Our findings (Table 2–3, Fig. 7) strongly support the hypothesis that the ACI can distinguish age related changes in the gait patterns. This new discovery has not direct precedent in the literature, given that ACI has only been recently proposed as a gait metrics for replacing DFA in gait analysis under free-living conditions [27, 36, 37]. Based on the mixed-effects models outcomes (Table 4), we can predict a relative change of -24% between the young and older populations. To put this in perspective, we found a contrast of -18% between healthy adults and adults suffering from chronic pain of lower limbs using ACI (still referred to as LDS-L in this 2017 study [44]) in unsupervised gait analysis. This comparison is instructive because chronic pain patients may use greater voluntary control of limb movements to adopt a less painful gait (antalgic gait [85]), possibly similar to the increased cognitive interference observed in older adults.

In the initial phase of the ACIER study, which focused exclusively on older adults, our analysis showed that the ACI measured in the frontal plane (ACI-ML) was inadequate for assessing gait correlation structure [36], while both ACI-AP and ACI-V could be used interchangeably. Additionally, we hypothesized that ACI-N, as an orientation-free metric, may be advantageous in unsupervised gait analysis scenarios where maintaining a consistent sensor position is difficult. However, adding the results from the young adult cohort leads to a more nuanced interpretation. ACI-AP showed increased sensitivity to age-related changes in gait patterns compared to ACI-V and ACI-N, as shown in Fig. 7. Furthermore, ACI-AP appears to be a speed-independent metric, whereas ACI-V and ACI-N are categorized as mixed metrics that exhibit a correlation with walking speed that is stronger in older adults (Supplementary Figures). While the pronounced sensitivity of the ACI-AP requires further investigation, it is plausible to suggest that accelerations within the sagittal plane—aligned with the displacement of the body—may contain information for the regulation, and thus for correlation structure, of stride length and duration. These insights are likely to be less pronounced for accelerations that occur perpendicular to the direction of displacement.

In contrast to the observed age-related differences in ACI, scaling exponents derived from foot acceleration data using DFA did not show significant age group differences in the mixed model analysis (p = 0.06, Supplementary Material, t-test). This lack of significance may be due to limitations of the DFA method, as highlighted in our companion article regarding its potential inaccuracy at short measurement times [36]. Although the observed standardized difference between age groups in normal walking (effect size = -0.19, Table 2) lacks statistical significance, it aligns with the findings of the above-mentioned meta-analysis (ES= -0.20, combining eight studies [13]). This suggests that ACI (ES=-0.77, Table 2) may be more effective than DFA in detecting age-related changes in gait patterns, particularly in shorter walking bouts or in unsupervised settings. However, further independent studies are needed to consolidate this observation.

Overall, our findings reinforce the notion that reliance on a single metric may not adequately capture the complexity of age-related decline in walking abilities. A comprehensive suite of both linear and non-linear gait metrics derived from acceleration signals appears to be essential to identify the various age-related adaptations in gait patterns. We propose that the ACI-AP, considered as a speed-independent metric, could reveal subtle changes in the automated control of gait—a modification not necessarily associated with reduced walking speed. At the same time, metrics of step and stride regularity, which we categorize as mixed-metric, could reveal difficulties in maintaining a consistent gait pattern from one stride to the next. This inconsistency could be caused by a reduced lower limb strength, potentially leading in parallel to a reduced preferred walking speed.

In conclusion, ACI shows a unique sensitivity to metronome walking in both young and older adults. This suggests that ACI specifically captures changes in gait control associated with increased cognitive demands during synchronized walking. Second, the ACI appears to be a valuable tool for discriminating age-related differences in gait patterns. This finding is consistent with the observed differences in step and stride regularity, further highlighting the potential of ACI as a complementary marker of gait quality decline in older populations, and thus as a tool for identifying older adults at risk for falls. In addition, due to the relative ease of measuring ACI, it could be used to evaluate practical interventions, such as in the recent clinical trial aimed at restoring gait automaticity in older adults that began in parallel with the ACIER study [86]. The broader implications of these findings go beyond fall risk assessment. The sensitivity of ACI to cognitive load during gait opens new avenues for investigating the intricate interplay between cognitive function and motor control of human locomotion, which may help to gain deeper insights into the mechanisms underlying gait disorders.

Building on these promising findings, the next phase of the ACIER study will focus on the clinical utility of the ACI for fall risk assessment. We will use a retrospective approach to differentiate between participants who have recently fallen and those who have not. This will involve the analysis of gait data collected in the first phase of the ACIER study and the comparison of ACI scores between these two groups of older individuals. Subsequently, the final phase will use a prospective approach with a longitudinal design and survival analysis. This involves following older participants over a two-year period to assess the association of ACI and other gait measures with time to first and second falls.

By addressing these future directions, the ACIER study can significantly contribute to the development of novel and reliable gait assessment tools using readily available wearable sensors, ultimately aiding in fall prevention strategies, and improving mobility monitoring in older adults.

ACI Attractor complexity index

ACIER Attractor complexity index empirical rationalization

ACF Autocorrelation function

AP Anteroposterior

CI Confidence interval

DFA Detrended fluctuation analysis

ES Effect size

FFT Fast Fourier transform

HE-Arc Haute École Arc (University of Applied Sciences and Arts of Western Switzerland)

LDS Local dynamic stability

ML Mediolateral

N Norm

RMS Root mean square

SD Standard deviation

SF Step frequency

V Vertical

Competing interests

The authors have no competing interests to declare that are relevant to the content of this article.

Funding

The ACIER study was supported by the “fonds recherche et impulsion” (research and impulse fund) granted by the “commission scientifique du domaine santé” (scientific commission of the health faculty) at HES-SO, University of Applied Sciences and Arts Western Switzerland.

Author contributions

Conceptualization: PT; Methodology: PT; Formal analysis: PT; Investigation: SP; Data curation: SP, PT; Writing – original draft: PT, SP; Writing – review & editing: PT, SP; Visualization: PT; Supervision: PT; Project administration: SP; Funding acquisition: PT.

Supplementary information

Supplementary information can be found online.

Supplementary Figures: contains the details of the correlations between gait metrics.

Supplementary statistics: contains the details of the inferential statistics (mixed-effect models).

Acknowledgements

The authors would like to thank Pr. Marco Pedrotti and Martine Segessemann for their assistance.

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Gait metrics		Principles & methodology	Applications in free-living conditions
Basic gait parameters	Walking speed	Natural pace measured by timing over the 200 m corridor.	N/A
Basic gait parameters	Step frequency (SF)	Mean number of steps per second. Computed from the vertical acceleration spectrum via Fast Fourier Transform (FFT). [87]	[25,26,44]
Variability parameters (lumbar accelerometer)	Movement intensity (RMS)	RMS quantifies the magnitude of a varying signal, as the square root of the average of the squared values over a period. Representative of the average amplitude of the acceleration during walking. Calculated using the vector magnitude of the 3D acceleration signals. [88]	[25,26,44]
	Lateral stability (RMS Ratio)	RMS Ratio represents the ratio between RMS in mediolateral direction and the RMS vector magnitude [45]. It attenuates the dependence of RMS to speed and is thought to be sensitive to impaired dynamic balance [40,45].	[76]
	Step regularity (ACF)	Autocorrelation function (ACF) analyzes cyclic patterns in acceleration signals by comparing values with time-shifted versions, with peak values indicating dominant periods. Higher peaks indicate a pronounced similarity across successive cycles. Step regularity corresponds to the first dominant period. Stride regularity corresponds to the second dominant period. [46].	[18,24–26]
	Stride regularity (ACF)		[18,24–26]
	Local dynamic stability (LDS)	LDS assesses the resilience of gait to perturbations. It is determined by calculating the logarithmic divergence rate between adjacent trajectories within a reconstructed attractor that reflects the gait dynamics (Rosenstein’s algorithm). [48–50]	[25,26,44]
	Attractor complexity index (ACI)	ACI has been empirically validated as a surrogate measure for the correlation structure between successive strides. Its calculation follows the same principles as LDS. [27,36,37]	[44]
Foot accelerometer	Scaling exponent α (DFA)	Detrended fluctuation analysis (DFA) of stride interval time series provides the scaling exponent (alpha, α), a measure of the correlation structure of gait. [89]	N/A

Table 1. Summary of the gait metrics used in the study.

	Normal walking
		Older participants			Young participants			Effect size	Confidence intervals
		N	Mean	SD	N	Mean	SD	g	CI low	CI high
Basic gait parameters	Walking speed (m/s)	58	1.27	0.24	42	1.43	0.15	-0.80	-1.25	-0.36
Basic gait parameters	Step frequency (Hz)	59	1.89	0.15	42	1.90	0.09	-0.11	-0.60	0.38
Variability measures	Movement intensity (g)	59	0.29	0.10	42	0.35	0.09	-0.58	-1.12	-0.08
	RMS Ratio	59	0.66	0.14	42	0.65	0.13	0.08	-0.39	0.6
	Step regularity	59	1.11	0.29	42	1.37	0.22	-0.97	-1.49	-0.54
	Stride regularity	59	1.17	0.30	42	1.42	0.24	-0.91	-1.39	-0.47
Local dynamic stability	LDS-ML	59	1.29	0.32	42	1.15	0.42	0.38	-0.15	0.99
Attractor complexity index	ACI-N	59	0.028	0.010	42	0.033	0.006	-0.53	-1.06	-0.07
Attractor complexity index	ACI-AP	59	0.022	0.009	42	0.028	0.006	-0.77	-1.33	-0.31
	ACI-V	59	0.027	0.010	42	0.033	0.006	-0.69	-1.23	-0.24
Foot accelerometer	Scaling exponent (DFA)	60	0.74	0.17	42	0.77	0.17	-0.19	-0.73	0.31

Table 2. Descriptive statistics of the normal walking condition. Sample size (N), mean, standard deviation (SD), standardized effect size (Hedges’ g) of the difference between age groups, and 99% confidence interval (CI) of the effect size. Results in bold are statistically significant. RMS: root mean square; LDS: local dynamic stability; ACI: attractor complexity index; DFA: detrended fluctuation analysis.

	Metronome walking
		Older participants			Young participants			Effect size	Confidence intervals
		N	Mean	SD	N	Mean	SD	g	CI low	CI high
Basic gait parameters	Walking speed (m/s)	58	1.26	0.24	42	1.42	0.14	-0.77	-1.23	-0.34
Basic gait parameters	Step frequency (Hz)	59	1.90	0.15	42	1.90	0.09	-0.06	-0.55	0.46
Variability measures	Movement intensity (g)	58	0.31	0.11	42	0.35	0.09	-0.46	-1.03	0.03
	RMS Ratio (%)	58	0.65	0.15	42	0.64	0.12	0.11	-0.41	0.64
	Step regularity (N/A)	58	1.09	0.27	42	1.35	0.21	-1.02	-1.57	-0.57
	Stride regularity (N/A)	58	1.15	0.28	42	1.41	0.20	-1.01	-1.51	-0.57
Local dynamic stability	LDS-ML	58	1.25	0.34	42	1.16	0.38	0.25	-0.26	0.81
Attractor complexity index	ACI-N	58	0.020	0.010	42	0.029	0.010	-0.87	-1.37	-0.38
Attractor complexity index	ACI-AP	58	0.016	0.008	42	0.024	0.01	-0.95	-1.47	-0.46
	ACI-V	58	0.020	0.010	42	0.028	0.01	-0.92	-1.46	-0.42
Foot accelerometer	Scaling exponent (DFA)	60	0.39	0.22	42	0.46	0.18	-0.33	-0.91	0.18

Table 2. Descriptive statistics of the metronome walking condition. Sample size (N), mean, standard deviation (SD), standardized effect size (Hedges’ g) of the difference between age groups, and 99% confidence interval (CI) of the effect size. Results in bold are statistically significant. RMS: root mean square; LDS: local dynamic stability; ACI: attractor complexity index; DFA: detrended fluctuation analysis.

		Multiple mixed-effects regression models (fixed effects)
		Group (older vs. young)			Condition (normal vs. metronome)
		Coef.	CI low	CI high	Coef.	CI low	CI high
Basic gait parameters	Walking speed	-0.167	-0.28	-0.06	0.000	-0.015	0.016
Basic gait parameters	Step frequency	-0.012	-0.078	0.054	0.002	-0.006	0.010
Variability measures	Movement intensity	-0.056	-0.104	-0.007	0.013	0.003	0.023
	RMS Ratio	0.013	-0.057	0.083	-0.001	-0.021	0.008
	Step regularity	-0.253	-0.379	-0.118	-0.013	-0.043	0.025
	Stride regularity	-0.249	-0.295	-0.109	-0.009	-0.051	0.010
Local dynamic stability	LDS-ML	0.111	-0.068	0.290	-0.017	-0.076	0.043
Attractor complexity index	ACI-N	-0.0063	-0.0102	-0.0024	-0.0067	-0.0095	-0.0038
	ACI-AP	-0.0069	-0.0102	-0.0035	-0.0055	-0.0079	-0.0030
	ACI-V	-0.0071	-0.0110	-0.0033	-0.0067	-0.0094	-0.0039
Foot accelerometer	Scaling exponent (DFA)	-0.047	-0.113	0.018	-0.335	-0.406	-0.264

Table 4. Inferential statistics. Fixed-effects of fitted linear mixed-effects models. Gait metrics were introduced as dependent variables. Group membership (young or older) and condition (normal or metronome) were introduced as categorical independent variables. Regression coefficients (coef.) are presented with their 99% confidence intervals. Results in bold are statistically significant. RMS: root mean square; LDS: local dynamic stability; ACI: attractor complexity index; DFA: detrended fluctuation analysis.

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Validity of linear and nonlinear measures of gait variability to characterize aging gait with a single low back accelerometer

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