Toward Convenient and Accurate IMU-based Gait Analysis

1. Introduction

The gait of a person is the manner in which this person walks or, more generally, moves on its feet. Gait analysis refers to the analysis of this gait, and the methods for performing this analysis can be broadly classified into visual methods and instrumental methods, with the latter ones providing numerical parameters (often spatiotemporal in nature), and thus providing a better description of the gait [1]. These numerical (and thus quantitative) parameters may guide healthcare professionals in making detailed diagnoses and optimal treatment decisions for conditions that impact the ability of a patient to walk (e.g., [2,3,4,5,6]). The instrumental methods rely on advanced systems consisting, in a broad way, of hardware, control software, and signal-processing algorithms. Very often, these systems are cumbersome and expensive, and thus available only in well-equipped environments, thereby necessarily preventing their widespread use in the typical clinical contexts [7]. Advancements in microelectronics have led to the development of small devices containing inertial sensors (namely accelerometers and gyroscopes) providing (raw) inertial measurement signals, with each such device being commonly called an “inertial measurement unit (IMU)”. These small and lightweight IMUs can easily be placed in wearables, which can be used as the basis of gait analysis systems usable in healthcare settings (e.g., [8]), furthermore saving space, labor, and time. These IMU-based wearable systems can also record gait data over extended and continuous time periods, overcoming the limitations of measurement volume typically encountered in some systems like instrumented mats and motion capture setups.

While previous research using IMU-based systems for gait analysis has shown promising results in quantifying key gait features/parameters (e.g., [9,10,11]), significant work remains to be done to support the use of these systems in clinical settings [12]. In particular, there is a lack of studies that thoroughly evaluate the reliability of gait parameter values provided by these systems across different walking speeds, while accounting for gender, leg length, and body height characteristics, in a large sample of healthy adults [10,13]. The accuracy and reliability of these parameters has, however, to be examined before they can be used in clinical gait studies. Reliability refers to the consistency or reproducibility of accurate measurements when repeated for the same participant. Intra-session reliability refers to the degree of consistency in measurement outcomes across repeated trials performed within the same time session.

Additionally, fewer studies provide reference values for gait parameters quantified using IMU-based systems. It is, however, crucial to establish such reference values and to verify their consistency with existing normative gait data; this would then support the use of IMU-based systems in clinical studies. When applying these systems to assess abnormal gait, the extracted parameters can help quantify deviations from normal gait patterns. Moreover, establishing reference parameters that account for participant characteristics could improve the accuracy of medical diagnoses and enhance the evaluation of responses to gait rehabilitation.

The aim of the present paper is, therefore, twofold: (1) to evaluate thoroughly the level of intra-session reliability of various gait parameters and compare the results with those from previous studies, and (2) to establish reference values for these parameters, specific to gender, leg length, and body height, during over-ground walking at three different speed conditions: preferred, dual-task, and fast walking. These parameters include 15 spatiotemporal gait parameters; 4 symmetry indices of 10 spatiotemporal gait parameters; dual-task cost, and fast-walking performance indices of 15 spatiotemporal gait parameters. The three speed conditions are considered to provide a comprehensive assessment of an individual’s walking performance: (1) preferred walking establishes a baseline of the normal walking pattern, (2) dual-task walking evaluates the cognitive-motor integration under divided attention, and (3) fast walking determines the maximal functional capacity. Furthermore, the work described here considers individuals aged 40 to 65 years to cover a representative sample of middle-aged adults and to quantify IMU-based reference gait parameters while minimizing the confounding effects of age-related changes. For instance, gait speed has been shown to begin declining at age 65 [14]. The chosen age range aligns with established reference gait parameters for this group and enables meaningful comparisons with other similar studies in the existing literature [15,16,17,18,19,20]. As outlined in the following sections, the major contributions of this work include quantifying and establishing the reliability level of some key reference gait parameters not readily available in the literature. To our knowledge, this is the first study to obtain these parameters by analysing gait signals measured from IMUs attached to the heels of regular shoes, using dedicated and validated signal-processing algorithms.

2. Materials and Methods

2.1. Participants

We used G*Power software G*Power (version 3.1.9.7; universities of Kiel, Düsseldorf, and Mannheim, Germany) to calculate the sample size required for healthy women and men groups aged 40-50 years. We conducted a pilot study that provided the following mean and SD values for walking speed [m/s]: 1.469±0.170 and 1.559±0.118 at PW, 1.409±0.184 and 1.629±0.278 at DTW, and 1.927±0.252 and 2.100±0.261 at FW, in 10 healthy men and 10 healthy women aged 40-65 years, respectively. Using a 2-tailed test with an alpha of 0.05, the calculated sample sizes per group needed to achieve a power of at least 0.8 were 43 for PW, 20 for DTW, and 36 for FW. We therefore aimed to recruit at least 43 participants per group. This effort resulted in a total of 46 healthy women and 55 healthy men who agreed to participate in the study (Table 1). They were able to walk without any musculoskeletal pain and had no history of hip or knee prostheses or neurologic disorders. The local ethic committee of the University Hospital of Liège, Belgium, approved the study protocol.

2.2. IMU-Based Hardware System

To record the raw gait signals, we use a stand-alone hardware system that is based on commercially-available IMU modules and that we have developed, designed, and implemented at the University of Liège (ULiège), Belgium [21], including the hardware, control software, and signal-processing algorithms. The hardware consists of (1) a central unit with memory, a microcontroller, and a battery, (2) four small IMU modules (2 cm × 0.7 cm × 0.5 cm), and (3) four wires connecting the IMUs to the central unit. The central unit is positioned at the waist. For each test, we attach in a rigorous and systematic way two IMU modules to each shoe of each participant, one at the toe and one at the heel (Figure 1), thus for a total of four modules for each participant. We strap the wires on the legs in such a way as to prevent interference with movement. The system measures 3-axis accelerations (up to ±16 g) and 3-axis angular velocities (up to ±2000°/second). This paper focuses solely on the raw signals from the two heel IMUs to extract reference values for gait parameters. Specifically, the analysis of the signals from the toe IMUs is beyond the scope of this study and will be considered in future work (see Section 4.4).

2.3. Experimental Procedure

Participants wore their own regular shoes (excluding sandals and high heels). Before data recording, they performed one warm-up trial at their self-selected speed. Each participant completed two consecutive gait trials, denoted here by trial1 and trial2, along a 30 m distance in a wide, clear, straight hallway at (1) preferred walking (PW), (2) dual-task walking (DTW), and (3) fast-walking (FW) speeds. We added 3 m to the nominal 30 m to allow for the exclusion of the first and last two strides during the processing of the gait signals, which minimizes the effects of the periods of gait initiation/termination, acceleration, and deceleration [12]. We focus here on the analysis of the intra-session reliability of parameter reference values extracted during steady-state walking periods in trial1 and trial2. For FW, we asked the participants to walk as fast and safely as possible without running. To assess the effect of a concurrent task on gait, DTW included a cognitive task, namely “serial sevens subtractions” [22], where the subject must announce in an audible voice the results of subtracting 7 from a starting number while walking. Participants were not instructed to prioritize either the gait or the cognitive task. We conducted all the gait tests at the Laboratory of Movement Analysis of ULiège.

2.4. Quantification of Gait Parameters

From the two raw, time-synchronized signals from the two heel IMUs, we extract the spatiotemporal gait parameters by using the method that we describe in [23], where we successively (1) parse heel acceleration data into flat and non-flat phases, and (2) apply appropriate signal-processing algorithm to the acceleration sub-signals delimited by the non-flat phases to identify heel strike (HS) and toe-off (TO) timings [23]. This algorithm uses distinctive and remarkable features in these sub-signals to extract HSs and TOs with a good accuracy and precision [24]. Accuracy and precision correspond to the averages of the mean and standard deviation (SD), respectively, of the (signed) differences between IMU-derived method and reference method timings (e.g., timings from methods based on kinematic and force plates). For instance, the accuracy±precision values for HS and TO are respectively 1ms±12ms and 0ms±7ms for older adults during the comfortable walking condition [25]. The individual values of the gait parameters are computed using the HSs and TOs in consecutive and overlapping left gait cycles i and right gait cycles j as summarized in Table 2 and illustrated in Figure 1.

In [25], we show that the accuracy±precision values are for Sr: 0ms±15ms, Sa: 0ms±14ms, Sw: 0ms±14ms, and DS: 0ms±14ms. Additionally, we use the method in [21] to quantify the individual stride lengths and gait speeds. This method robustly detects zero-velocity update regions in the gait signals and applies adequate initial conditions to minimize integration drifts during successive strapdown integrations at the level of individual strides. This method yields an accuracy and precision of −0.7±4.4 cm for SL, and −6.7±6.7 cm/s for GS, during preferred walking.

We assess the differences between gait parameters from trial1 and trial2, for each of the three walking conditions, by using, first the Shapiro−Wilk parametric test to check whether a corresponding distribution is normal (i.e., Gaussian) or not, and then either the Student t-test for normal distributions and the nonparametric Wilcoxon rank sum test otherwise. Mean and SD values of the gait parameters from left and right sides are calculated intra- and inter-participants. Supplementary Table S1 shows there is no significant differences between left and right values. We then provide all the gait parameter values as the mean and SD of combined left and right gait parameters. SL and GS are divided by the leg length and body height, yielding, respectively, normalized parameters SL_n1 [dimensionless], GS_n1 [s^-1], SL_n2 [dimensionless], and GS_n2 [s^-1] [26]. The leg length is calculated as the average of left/right leg lengths as no significant difference is found when comparing left leg lengths to right ones. We also examine the intra-session reliability of dimensionless symmetry indices, symmetry index (SI1), symmetry ratio (SI2), symmetry angle (SI3), and an alternative version of the symmetry ratio (SI4). Since we have access to gait parameters extracted on a stride-by-stride basis, we calculate these quantities as the mean of individual symmetry indices $I_k$ using four commonly reported formula (e.g., [27]) as follows,

$$\mathrm{S}\mathrm{I}1={\displaystyle \frac{1}{n}}{\sum }_{k=1}^n{I}_k,\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}{I}_k={\displaystyle \frac{1}{m}}{\sum }_{i=1}^{m}100·{\displaystyle \frac{\left|{\mathrm{X}}_{\mathrm{D}}\left(i\right)-{\mathrm{X}}_{\mathrm{n}\mathrm{D}}\left(i\right)\right|}{0.5·\left({\mathrm{X}}_{\mathrm{D}}\left(i\right)+{\mathrm{X}}_{\mathrm{n}\mathrm{D}}\left(i\right)\right)}}$$

(1)

$$\mathrm{S}\mathrm{I}2={\displaystyle \frac{1}{n}}{\sum }_{k=1}^n{I}_k,\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}{I}_k={\displaystyle \frac{1}{m}}{\sum }_{i=1}^m{\displaystyle \frac{\min \left({\mathrm{X}}_{\mathrm{D}}\left(i\right),{\mathrm{X}}_{\mathrm{n}\mathrm{D}}\left(i\right)\right)}{\max \left({\mathrm{X}}_{\mathrm{D}}\left(i\right),{\mathrm{X}}_{\mathrm{n}\mathrm{D}}\left(i\right)\right)}}$$

(2)

$$\mathrm{S}\mathrm{I}3={\displaystyle \frac{1}{n}}{\sum }_{k=1}^n{I}_k,\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}{I}_k={\displaystyle \frac{1}{m}}{\sum }_{i=1}^{m}100·{\displaystyle \frac{45°-\mathrm{atan}\left(\frac{{\mathrm{X}}_{\mathrm{n}\mathrm{D}}\left(i\right)}{{\mathrm{X}}_{\mathrm{D}}\left(i\right)}\right)}{90°}}$$

(3)

$$\mathrm{S}\mathrm{I}4={\displaystyle \frac{1}{n}}{\sum }_{k=1}^n{I}_k,\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}{I}_k={\displaystyle \frac{1}{m}}{\sum }_{i=1}^m{\displaystyle \frac{{\mathrm{X}}_{\mathrm{n}\mathrm{D}}\left(i\right)}{{\mathrm{X}}_{\mathrm{D}}\left(i\right)}}$$

(4)

where ${\mathrm{X}}_{\mathrm{n}\mathrm{D}}\left(i\right)$ and ${\mathrm{X}}_{\mathrm{D}}($i) are individual values of a gait parameter from the non-dominant (nD) and dominant (D) sides, respectively, n is the total number of participants, and m is the smallest value of the total numbers of left parameters and right parameters, for a given participant. The ability of a participant to handle a second task while walking is characterized using the dual-task cost (DTC) with

$$\mathrm{D}\mathrm{T}\mathrm{C}={\mathrm{X}}_{\mathrm{D}\mathrm{T}\mathrm{W}}-{\mathrm{X}}_{\mathrm{P}\mathrm{W}}$$

(5)

$$\mathrm{D}\mathrm{T}\mathrm{C}\mathrm{\%}=100·{\displaystyle \frac{{\mathrm{X}}_{\mathrm{D}\mathrm{T}\mathrm{W}}-{\mathrm{X}}_{\mathrm{P}\mathrm{W}}}{{\mathrm{X}}_{\mathrm{P}\mathrm{W}}}},$$

(6)

where ${\mathrm{X}}_{\mathrm{D}\mathrm{T}\mathrm{W}}$ and ${\mathrm{X}}_{\mathrm{D}\mathrm{T}\mathrm{W}}$ are the average values of a gait parameter from DTW and PW tests, respectively. Analogously, we define the fast-walking performance index (FWP) as

$$\mathrm{F}\mathrm{W}\mathrm{P}={\mathrm{X}}_{\mathrm{F}\mathrm{W}}-{\mathrm{X}}_{\mathrm{P}\mathrm{W}}$$

(7)

$$\mathrm{F}\mathrm{W}\mathrm{P}\mathrm{\%}=100·{\displaystyle \frac{{\mathrm{X}}_{\mathrm{F}\mathrm{W}}-{\mathrm{X}}_{\mathrm{P}\mathrm{W}}}{{\mathrm{X}}_{\mathrm{P}\mathrm{W}}}},$$

(8)

where ${\mathrm{X}}_{\mathrm{F}\mathrm{W}}$ is the average value of a gait parameter from the FW tests.

2.5. Reproducibility Analysis of Gait Parameters

This paper examines the relative and absolute intra-session reliability of gait parameters from trial1 and trial2 across the three walking conditions.

We use the intraclass correlation coefficient ICC(2,1) and its 95% confident interval (95% CI) to estimate the relative intra-session reliability [28]. Moreover, we adopt the following interpretation of ICCs to evaluate the level of the relative intra-session reliability [29]: $\mathrm{I}\mathrm{C}\mathrm{C}<0.50$: poor, $0.50\le \mathrm{I}\mathrm{C}\mathrm{C}<0.75$: moderate, $0.75\le \mathrm{I}\mathrm{C}\mathrm{C}<0.90$: good, and $\mathrm{I}\mathrm{C}\mathrm{C}\ge 0.90$: excellent relative reliability.

Besides, we use the standard error of measurement (SEM) and minimal detectable change (MDC) to estimate the absolute intra-session reliability. The SEM measures the absolute reliability by estimating the variation in measurement errors [30]. It is calculated as $\mathrm{S}\mathrm{E}\mathrm{M}=\mathrm{S}\mathrm{D}\sqrt{1-\mathrm{r}}$, where SD is the standard deviation of the gait parameter across participants, and $\mathrm{r}$ is the reliability coefficient (i.e., ICC(2,1) here). Smaller SEM values indicate higher absolute reliability. The SEM estimates how repeated measurements of a participant’s gait parameter are distributed around the true value. The MDC is the smallest measurement change value above which a real change has occurred (e.g., [31]); it is calculated as $\mathrm{M}\mathrm{D}\mathrm{C}=1.96\sqrt{2}·\mathrm{S}\mathrm{E}\mathrm{M}$. The SEM is multiplied by 1.96 to determine the 95% CI, and by $\sqrt{2}$ for repeated measurement error adjustment [32]. Both SEM and MDC are also expressed as percentages, SEM% and MDC%, of the gait parameter mean.

The literature lacks clear criteria for evaluating absolute intra-session reliability. One remarks, however, that SEM% and MDC% are related to the coefficient of variation ($\mathrm{C}\mathrm{V}=100·\mathrm{S}\mathrm{D}/\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}$) using the following formula: $\mathrm{S}\mathrm{E}\mathrm{M}\mathrm{\%}=\mathrm{C}\mathrm{V}\sqrt{1-\mathrm{r}}$ and $\mathrm{M}\mathrm{D}\mathrm{C}\mathrm{\%}=1.96\sqrt{2}·\mathrm{C}\mathrm{V}\sqrt{1-\mathrm{r}}$. Since $0\le \sqrt{1-\mathrm{r}}\le 1$ (as $\left|r\right|\le 1$), we have $\left|\mathrm{S}\mathrm{E}\mathrm{M}\mathrm{\%}\right|\le \left|\mathrm{C}\mathrm{V}\right|$ and $\left|\mathrm{M}\mathrm{D}\mathrm{C}\mathrm{\%}\right|\le 1.96\sqrt{2}·\left|\mathrm{C}\mathrm{V}\right|$. Besides, $\left|\mathrm{C}\mathrm{V}\right|>20\mathrm{\%}$ can be considered as poor, $10\mathrm{\%}<\left|\mathrm{C}\mathrm{V}\right|\le 20\mathrm{\%}$: moderate, $5\mathrm{\%}<\left|\mathrm{C}\mathrm{V}\right|\le 10\mathrm{\%}$: good, and $\left|\mathrm{C}\mathrm{V}\right|\le 5\mathrm{\%}$: excellent. Assuming these CV’s cut-offs, we propose the following criteria to evaluate the level of absolute intra-session reliability: $\left|\mathrm{S}\mathrm{E}\mathrm{M}\mathrm{\%}\right|>20\mathrm{\%}$ or $\left|\mathrm{M}\mathrm{D}\mathrm{C}\mathrm{\%}\right|>60\mathrm{\%}$: poor, $10\mathrm{\%}<\left|\mathrm{S}\mathrm{E}\mathrm{M}\mathrm{\%}\right|\le 20\mathrm{\%}$ or $30\mathrm{\%}<\left|\mathrm{M}\mathrm{D}\mathrm{C}\mathrm{\%}\right|\le 60\mathrm{\%}$: moderate, $5\mathrm{\%}<\left|\mathrm{S}\mathrm{E}\mathrm{M}\mathrm{\%}\right|\le 10\mathrm{\%}$ or $15\mathrm{\%}<\left|\mathrm{M}\mathrm{D}\mathrm{C}\mathrm{\%}\right|\le 30\mathrm{\%}$: good, and $\left|\mathrm{S}\mathrm{E}\mathrm{M}\mathrm{\%}\right|\le 5\mathrm{\%}$ or $\left|\mathrm{M}\mathrm{D}\mathrm{C}\mathrm{\%}\right|\le 15\mathrm{\%}$: excellent absolute reliability.

The Bland-Altman plots provide the 95% limits of agreement (LOA) for intra-session gait parameters. Data are analysed using Matlab (R2018b, MathWorks, Natick, MA, USA) and the significance level is set at p-value of 0.05.

3. Results

We quantified the gait parameters from total numbers of 6405, 6804, and 5425 individual strides extracted at PW, DTW, and FW conditions, respectively, after having carefully and visually inspected all the results from each of the algorithm steps (e.g., the segmentation, the extracted HSs and TOs). Supplementary Figures S1−S3 provide the Bland-Altman plots and distributions of individual spatiotemporal gait parameters from each side in trial1 and trial2, for each walking condition. We obtained these distributions by pooling all the individual left/right parameters. The corresponding average values (i.e., 101 values) were obtained and their Bland-Altman plots and distributions are given in Supplementary Figures S4−S6, all showing values well distributed around zero.

This section places more weight on presenting the results of the relative and absolute reliability of the gait parameters and their reference values.

3.1. Reliability of Spatiotemporal Gait Parameters and Symmetry Indices

Table 3 and Table 4 and Supplementary Tables S2−S4 show the obtained values for spatiotemporal gait parameters and symmetry indices, and their intra-session reliability at PW, DTW, and FW. No significant differences are found between these values in trial1 and trial2.

Relative reliability is excellent for all spatiotemporal gait parameters ($0.92\le \mathrm{I}\mathrm{C}\mathrm{C}<0.99$) across all walking conditions (Table 3). Relative reliability for symmetry indices SI1 and SI2 is moderate across the walking conditions, except for (1) SI1 and SI2 of SL and GS at PW and DTW: good reliability, and (2) SI2 of Sa at PW and of St and St% at FW: poor reliability (Supplementary Tables S2 and S3). Relative reliability for SI3 and SI4 is good to excellent at PW, DTW, and FW, except for (1) SI3 and SI4 of Sa and St at DTW, and of St, DS%, and St% at FW: moderate reliability, and (2) SI4 of DS at FW: moderate reliability (Table 4 and Supplementary Table S4).

Absolute reliability is excellent for all spatiotemporal gait parameters across the three walking conditions (Table 3), with SEM and MDC small values, and SEM% and MDC% not exceeding 4.4% and 12.1%, respectively. Absolute reliability is poor for symmetry indices SI1 ($21.5\mathrm{\%}\le \mathrm{S}\mathrm{E}\mathrm{M}\mathrm{\%}\le 35.1\mathrm{\%}$ and $59.5\mathrm{\%}\le \mathrm{M}\mathrm{D}\mathrm{C}\mathrm{\%}\le 97.2\mathrm{\%}$) and SI3 ($94.5\mathrm{\%}\le \left|\mathrm{S}\mathrm{E}\mathrm{M}\mathrm{\%}\right|\le 1145.1\mathrm{\%}$ and $262.0\mathrm{\%}\le \left|\mathrm{M}\mathrm{D}\mathrm{C}\mathrm{\%}\right|\le 3174.1\mathrm{\%}$) (Supplementary Tables S2 and S4). Excellent absolute reliability is, however, found for symmetry indices SI2 ($0.3\mathrm{\%}\le \mathrm{S}\mathrm{E}\mathrm{M}\mathrm{\%}\le 3.1\mathrm{\%}$ and $0.9\mathrm{\%}\le \mathrm{M}\mathrm{D}\mathrm{C}\mathrm{\%}\le 8.6\mathrm{\%}$) and SI4 ($0.5\mathrm{\%}\le \mathrm{S}\mathrm{E}\mathrm{M}\mathrm{\%}\le 4.5\mathrm{\%}$ and $1.4\mathrm{\%}\le \mathrm{M}\mathrm{D}\mathrm{C}\mathrm{\%}\le 12.4\mathrm{\%}$) (Supplementary Tables S5 and S6).

3.2. Reliability of Dual-Task Cost and Fast-Walking Performance

Table 5 and Supplementary Table S5 provide the results of the intra-session reliability of the dual-task cost and fast-walking performance values. There are no significant differences between these values in trial1 and trial2.

Relative intra-session reliability is excellent for (1) all DTC features ($0.90\le \mathrm{I}\mathrm{C}\mathrm{C}\le 0.96$) except for those of Sa% and Sw% where ICC is good (ICC = 0.89) (Supplementary Table S5), and (2) all DTC% features ($0.91\le \mathrm{I}\mathrm{C}\mathrm{C}\le 0.96$) except for those of Sa%, Sw%, and DS% where ICC is good (ICC = 0.89) (Supplementary Table S5). Relative reliability is also excellent for all FWP and FWP% features ($0.91\le \mathrm{I}\mathrm{C}\mathrm{C}\le 0.96$) (Table 5).

Absolute reliability is poor for DTC and DTC% ($45.1\mathrm{\%}\le \left|\mathrm{S}\mathrm{E}\mathrm{M}\mathrm{\%}\right|\le 107.7\mathrm{\%}$ and $125.1\mathrm{\%}\le \left|\mathrm{M}\mathrm{D}\mathrm{C}\mathrm{\%}\right|\le 298.6\mathrm{\%}$) (Supplementary Table S5). The FWP absolute reliability is good for Sr, Sa, DS, St, GS, GS_n1, and GS_n2 ($8.7\mathrm{\%}\le \left|\mathrm{S}\mathrm{E}\mathrm{M}\mathrm{\%}\right|\le 10.0\mathrm{\%}$ and $24.2\mathrm{\%}\le \left|\mathrm{M}\mathrm{D}\mathrm{C}\mathrm{\%}\right|\le 27.6\mathrm{\%}$), and moderate for Sw, SL, Cad, Sa%, Sw%, DS%, SL_n1, and SL_n2 ($11.2\mathrm{\%}\le \left|\mathrm{S}\mathrm{E}\mathrm{M}\mathrm{\%}\right|\le 13.6\mathrm{\%}$ and $31.1\mathrm{\%}\le \left|\mathrm{M}\mathrm{D}\mathrm{C}\mathrm{\%}\right|\le 37.7\mathrm{\%}$) (Table 5). The FWP% absolute reliability is good for Sr, Sa, DS, and St, ($8.4\mathrm{\%}\le \left|\mathrm{S}\mathrm{E}\mathrm{M}\mathrm{\%}\right|\le 9.2\mathrm{\%}$ and $23.4\mathrm{\%}\le \left|\mathrm{M}\mathrm{D}\mathrm{C}\mathrm{\%}\right|\le 25.5\mathrm{\%}$), almost good for GS (SEM% = 10.3% and MDC% = 28.4%), and moderate for Sw, SL, Cad, Sa%, Sw%, and DS% ($11.2\mathrm{\%}\le \left|\mathrm{S}\mathrm{E}\mathrm{M}\mathrm{\%}\right|\le 13.6\mathrm{\%}$ and $31.1\mathrm{\%}\le \left|\mathrm{M}\mathrm{D}\mathrm{C}\mathrm{\%}\right|\le 37.7\mathrm{\%}$) (Table 5).

3.3. Reference Values for Gait Parameters Quantified Using the IMU-Based Method

Supplementary Table S6 provides the reference values for the spatiotemporal gait parameters and SI4, along with the results of the following parameter comparisons: (1) PW vs DTW, (2) PW vs FW, and (3) DTW vs FW. The analysis of these results demonstrates the ability of the proposed method in distinguishing gait parameters across different walking speed conditions. For instance, the comparison between PW and FW parameters shows that participants significantly increase their stride length from 1.527 m to 1.777 m and significantly reduce their stride duration from 1.041s to 0.886s, leading to a substantial increase in gait speed from 1.471 m/s to 2.016 m/s. Moreover, these changes in parameters include a decrease in DS% from 12.5% to 9.9% and Sa% from 62.5% to 60.0%, along with an increase in Sw% from 37.5% to 40.0%. Furthermore, SI4 values for each parameter remain consistent across the three walking speed conditions. Table 6, Table 7 and Table 8 summarize the results of the gender effect on these reference values and those for the FWP, and FWP%. These results indicate that the following parameters are gender-independent (p>0.05) across the three walking conditions: (1) Sa, DS, GSn1, and GSn2, and (2) SI4 for Sa, Sw, SL, GS, Sa%, and Sw%. Furthermore, there is no gender effect on FWP and FWP% for Sr, Sa, Sw, DS, St, Cad, Sa%, and Sw%.

4. Discussion

The above sections present a validated IMU-based method that (1) assesses the intra-session reliability of various gait parameters in healthy men and women aged 40-65 at three walking conditions, and (2) establishes a new reference gait database. To our knowledge, this is the first study to obtain these results by analysing gait signals measured from IMUs attached to the heels of regular shoes, using dedicated and validated signal-processing algorithms.

4.1. Reliability of Gait Parameters

The obtained results strongly support previous studies on intra-session reliability of spatiotemporal gait parameters, which reported similar ICC, SEM (SEM%), and MDC (MDC%) values in healthy participants, mainly at PW condition. Fewer studies have reported these values at serial sevens DTW and FW conditions.

Table 9 compares some of these values to our results. Similar to [11], SL and SL_n1 show excellent relative reliability (ICC>0.90). Sa% and Sw% show, however, (1) excellent reliability (ICC = 0.99) here, and (2) moderate reliability (ICC = 0.69) in [11]. Our SEM (SEM%) and MDC (MDC%) values are smaller than those from [11,33] at PW condition. For instance, these values, obtained here, are at least five times less than those found for Sa% and Sw% in [11]. It's important to note that previous studies use different modalities — associated with manufacturer’s proprietary software — such as Gaitrite [33], OptoGait portable photoelectric cell system [34], and IMUs on the dorsal feet [11], while we use here two IMUs attached to the heels, resulting in different measured gait signals and extraction signal-processing algorithms.

Symmetry indices SI1 and SI3 for the spatiotemporal gait parameters show poor to good relative intra-session reliability, but consistently poor absolute intra-session reliability across all the three walking conditions. This may be due to natural gait variability, where slight fluctuations in gait parameters propagate into SI1 and SI3 calculation, reducing their absolute reliability.

One may use another measure of the dominant/non-dominant symmetry: $\mathrm{S}\mathrm{I}5=100·\left|\mathrm{l}\mathrm{n}\right(\mathrm{n}\mathrm{D}/\mathrm{D}\left)\right|$ [35]. The results of SI1 can, however, be extended to SI5: the series expansion of SI5 around 1 (i.e., when nD/D varies around 1) is $200·|\mathrm{n}\mathrm{D}-\mathrm{D}|/(\mathrm{n}\mathrm{D}+\mathrm{D})$, which corresponds to SI1. Besides, the results of SI2 and SI4 for all the gait parameters show an excellent absolute intra-session reliability across the three walking conditions. Compared to SI2, SI4 has a better relative intra-session reliability at the three walking conditions. These findings support previous results for SI1 and SI4 at PW such in [11] and provide new insights for SI1, SI2, SI3, SI4, and SI5 at serial sevens DTW and FW, which could aid in the selection of an appropriate symmetry formula to be applied to the adequately chosen gait parameter.

Our work suggests that any future gait-study procedure similar to the one presented in Section 2.3 could benefit from using SI4 for (1) Sa, Sw, DS, St, SL, GS, Sa%, Sw%, DS%, and St% at PW, (2) Sw, DS, SL, GS, Sa%, Sw%, DS%, and St% at the serial sevens DTW, and (3) Sa, Sw, SL, GS, Sa%, and Sw% at FW. SI4 has the advantage of being calculated as the average of individual symmetry indices accounting for the dominant/non-dominate sides (formula (4)), which may reflect the asymmetry nature of walking, particularly in pathological conditions.

4.2. Reliability of Dual-Task Cost and Fast-Walking Performance

The DTC and DTC% indices have been used in several dual-task studies to assess the effect of secondary tasks on gait performance, including research on dementia (e.g., [36]), Alzheimer's disease (e.g., [37]), and fall prediction (e.g., [38]). Fewer studies report, however, on their relative and absolute reliability. It is crucial to assess the reliability of these dual-task indices before incorporating them into gait-related medical research. This study demonstrates that DTC and DTC% exhibit (1) excellent or almost excellent relative reliability ($0.89\le \mathrm{I}\mathrm{C}\mathrm{C}\le 0.96$), and (2) poor absolute reliability across all gait parameters and walking conditions. The poor absolute reliability may stem from the DTW instruction, where participants did not prioritize walking or the cognitive task, which might yield high variability in their walking. Nonetheless, the SEM% and MDC% values for DTC and DTC% (i.e., $45.1\mathrm{\%}\le \left|\mathrm{S}\mathrm{E}\mathrm{M}\mathrm{\%}\right|\le 107.7\mathrm{\%}$, $124.9\mathrm{\%}\le \left|\mathrm{M}\mathrm{D}\mathrm{C}\mathrm{\%}\right|\le 298.7\mathrm{\%}$) are lower than those reported in [11] (e.g., $68.0\mathrm{\%}\le \left|\mathrm{S}\mathrm{E}\mathrm{M}\mathrm{\%}\right|\le 14994.3\mathrm{\%}$ and $188.6\mathrm{\%}\le \left|\mathrm{M}\mathrm{D}\mathrm{C}\mathrm{\%}\right|\le 41562.1\mathrm{\%}$). The present study provides therefore less inflated values of SEM% and MDC% for DTC and DTC%.

Previous fast-walking studies have used FWP% for various gait parameters, such as investigating the relationship between walking speed and lower limb joint moments using cadence and stride length FWP% [39]. The reliability of the FWP and FWP% has, however, not been assessed so far and should be evaluated before their use in clinical gait studies. To the best of our knowledge, this is the first study to examine this reliability using data from heel-mounted IMUs. In particular, we provided the FWP and FWP% for several spatiotemporal gait parameters showing (1) excellent relative reliability ($0.91\le \mathrm{I}\mathrm{C}\mathrm{C}\le 0.96$), and (2) almost good ($10.3\mathrm{\%}\le \left|\mathrm{S}\mathrm{E}\mathrm{M}\mathrm{\%}\right|\le 13.6\mathrm{\%}$) to good ($8.4\mathrm{\%}\le \left|\mathrm{S}\mathrm{E}\mathrm{M}\mathrm{\%}\right|\le 9.2\mathrm{\%}$) absolute reliability.

4.3. Gender-Based Reference Values for IMU-Derived Gait Parameters

This paper quantifies gender-based reference gait parameters exhibiting almost good to excellent relative and absolute reliability ($0.7\le \mathrm{I}\mathrm{C}\mathrm{C}$, $\left|\mathrm{S}\mathrm{E}\mathrm{M}\mathrm{\%}\right|\le 13.6\mathrm{\%}$). These features include: (1) 15 parameters at PW, DTW, and FW ($0.92\le \mathrm{I}\mathrm{C}\mathrm{C}\le 0.99$, $0.3\mathrm{\%}\le \mathrm{S}\mathrm{E}\mathrm{M}\mathrm{\%}\le 4.4\mathrm{\%}$) (Table 6), (2) SI4 of 10 parameters at PW and DTW, and SI4 of 8 parameters at FW ($0.71\le \mathrm{I}\mathrm{C}\mathrm{C}\le 0.94$, $0.5\mathrm{\%}\le \mathrm{S}\mathrm{E}\mathrm{M}\mathrm{\%}\le 4.5\mathrm{\%}$) (Table 7), and (3) FWP and FWP% of, respectively, 15 and 11 parameters ($0.91\le \mathrm{I}\mathrm{C}\mathrm{C}\le 0.96$, $8.4\mathrm{\%}\le \left|\mathrm{S}\mathrm{E}\mathrm{M}\mathrm{\%}\right|\le 13.6\mathrm{\%}$) (Table 8).

Examining the gender comparison results of the reference spatiotemporal gait parameters reveals that men maintain higher swing duration and stride length across the three walking conditions. At the PW condition, men have a 5% increase in GS, which is associated with an 8% increase in SL and a 3% decrease in Cad, compared to women. These observations are supported by several laboratory-based gait studies in healthy adults aged 40-65 years (e.g., [15,16]). However, it is noteworthy that these reference values are more consistent with those obtained in relatively long walkways (which is the case here, i.e., 30 m) (e.g., [9]: 40 m; [10]: 20 m) than those obtained in short walkways (e.g., [17]: 5.5 m). For example, our GS values for men are 6% to 15% higher than those reported in [17].

At the DTW condition with serial sevens subtractions, men exhibit a 4% increase in Sr, 3% increase in Sw, 9% increase in SL, and 4% decrease in Cad, compared to women, while their GSs remain similar (p>0.05). These gender-based DTW findings are not readily available in previous studies. Additionally, our DTW results align with those reported in [18]. The reported value for Sr was 1.1 (0.1) s vs 1.090 (0.124) s obtained here; for Sa%: 62.3 (1.2)% vs 62.87 (1.6)%; for SL: 1.4 (0.2) m vs 1.487 (0.158) m; and for GS: 1.3 (0.2) m/s vs 1.383 (0.223) m/s.

At the FW condition, men show a 10% increase in their GS compared to women. This increase is associated with higher SL, Sw, and Sw% values. These observations are consistent with those reported in [19] for healthy adults aged 40-65 years. However, contrary to this previous study, we found here that (1) men had a lower Sa% and DS%, while having a higher SL_n1 and SL_n2, and (2) higher SL and GS values in both genders. In this previous study, barefoot walking is considered, which can lead to differences in gait parameter values compared to those obtained using personal shoes [20] as used in our study.

The gait of the healthy participants is expected to be symmetric, which is reflected in the SI4 reference values that are all close to one. Interestingly, these values show a clear gender effect on the SI4 of DS, St, DS%, and St% at PW, and of DS and DS% at DTW and FW. In [10], no gender effect is found on SI4 of St at PW. This difference with our results may be due to the use of a different symmetry index. The latter is calculated in [10] using a formula equivalent to the one used for SI1. However, we demonstrate here that SI1 shows a moderate relative (ICC [95% CI] = 0.53 [0.38,0.66]) and poor absolute (SEM% = 29.5%, and MDC% = 81.9%) reliability, which may limit the usefulness of this symmetry outcome, at least in experimental conditions similar to the ones of our study.

Among all the gait parameters, SL and DS% are the key parameters for which FWP% reference values present a gender difference. Men mainly increased their SL and decreased their DS% to increase their GS from PW to FW. To the best of our knowledge, these FWP and FWP% reference values and gender comparisons are not readily available in previous studies. Fewer studies report some of these values but mainly for older adults aged at least 65 years (e.g., [38]). Based on these findings, one may consider the FWP and FWP% as reliable clinical features in fast-walking studies. Further work should focus on investigating whether these features are associated to mechanisms of abnormal gait.

4.4. Advancements in IMU-Based Gait Analysis, Study Limitations, and Directions for Future Research

During the development of the hardware and signal-processing algorithms of our system, we ensured that they complied with the transparency requirement necessary for a wearable system intended to derive medical-grade features. Transparency, related to traceability and explainability [40], is achieved by (1) validating this system, and (2) engaging in regular discussions with medical practitioners and doctors to (a) better define relevant features needed for their specific needs, and (b) provide detailed information on all steps involved in feature extraction, including fundamental gait event identification and pre- and post-processing methods. To enhance explainability, we directly apply the signal-processing algorithms on raw data, enabling easy visualization and verification of the results, which mitigates the algorithm “black box” issue in the context of using an IMU-based method for medical applications.

The current hardware configuration ensures a perfect time-synchronization in inertial data recording, allowing the signal-processing algorithm to accurately quantify gait parameters that require synchronized data from both feet, such as double support and step durations and associated symmetry and fast-walking performance indices. The results also demonstrate the system’s ability to handle the recording and analysis of many consecutive strides, which could yield reliable extraction of variability parameters. Additionally, our approach relies on versatile signal-processing algorithms, which provides a real advantage in quantifying other reference gait parameters such as the stride width, toe clearance, and durations of the sub-phases that refine the stance and swing phases [25]. The algorithms could be adapted to consider abnormal gait patterns, such as foot-drop after stroke [41] or freezing of gait in the Parkinson’s disease [42]. Overall, the proposed method shows significant potential in rehabilitation, geriatrics, orthopedics, and sports.

A limitation of this paper is its almost-exclusive focus on assessing the intra-session reliability of the gait parameters. Another limitation is the lack of a formal evaluation of the DTW outcomes. Additionally, future studies should examine both intra- and inter-session reliability in patient groups. By leveraging both the (raw) signals from the toe IMUs and the versatility of the signal-processing algorithms, we will also extract the sub-phase durations—that refine the stance and swing phases [25]—to assess their reliability.

5. Conclusions

Using a validated system using one IMU module on each of the two heels of each subject, we quantified clinically meaningful gait parameters including spatiotemporal gait parameters, symmetry, dual-task cost, and fast-walking performance indices, in 101 healthy adults (55 men and 46 women), aged 40-65 years, at normal, dual-task, and fast-walking speeds. We analysed these gait parameters (1) to evaluate the level of their relative and absolute intra-session reliability, and (2) to establish a new database of reference values for the parameters that show good to excellent reliability. The results show that this database offers accurate and reliable reference values related to gender, leg length, and body height. The results are consistent with previous studies, while also offering new gait parameter information seldom explored in the literature, such as gender-based FWP comparisons and the symmetry ratios at serial sevens subtractions DTW and FW. The proposed IMU-based system offers significant advantages including its transparency and ability to be used in clinical environments. Overall, the results obtained support its use in a variety of medical applications, such as prosthetic evaluation, fall risk assessment, and neurological rehabilitation (e.g., Parkinson’s Disease, Stroke).