Spatio-temporal gait parameters obtained from foot-worn inertial sensors are reliable in healthy adults in single- and dual-task conditions

Inertial measurement units (IMUs) are increasingly popular and may be usable in clinical routine to assess gait. However, assessing their intra-session reliability is crucial and has not been tested with foot-worn sensors in healthy participants. The aim of this study was to assess the intra-session reliability of foot-worn IMUs for measuring gait parameters in healthy adults. Twenty healthy participants were enrolled in the study and performed the 10-m walk test in single- and dual-task ('carrying a full cup of water') conditions, three trials per condition. IMUs were used to assess spatiotemporal gait parameters, gait symmetry parameters (symmetry index (SI) and symmetry ratio (SR)), and dual task effects parameters. The relative and the absolute reliability were calculated for each gait parameter. Results showed that spatiotemporal gait parameters measured with foot-worn inertial sensors were reliable; symmetry gait parameters relative reliability was low, and SR showed better absolute reliability than SI; dual task effects were poorly reliable, and taking the mean of the second and the third trials was the most reliable. Foot-worn IMUs are reliable to assess spatiotemporal and symmetry ratio gait parameters but symmetry index and DTE gait parameters reliabilities were low and need to be interpreted with cautious by clinicians and researchers.


Methods
Participants. All participants signed informed consent and approved to participate in Folomi study as healthy control participants 31 . The study was approved by local ethic committee (CPP Ile De France 1, RCB: 2017-A03468-45, date of agreement: July 17th, 2018, Last version: V6.0, June 17th, 2020), is registered in Clinical trials (NCT03761212) and was performed in accordance with relevant guidelines and regulations.
In line with previous studies on reliability on healthy 10,17,19 and pathological gait 20,22,32,33 , twenty healthy participants (10 first men and 10 first women of healthy participants of the Folomi study 34 ) were included in the present study.
Participants should be aged between 18 to 65 years, able to walk 180 m without technical help, with a public health insurance (French social security). The non-inclusion criteria were: (1) Musculo-skeletal, cardiorespiratory or neurologic disease that could affect gait, (2) Hip or knee arthroplasty done, (3) Not able to speak French, (4) Desire of pregnancy in the following 18 months and (5) Adults protected by laws (Article L1121-5) 31 . Demographic and anthropometric characteristics of study participants (age, height, leg height, body mass, body mass index) were obtained from the participants. Leg length (in meters) was measured from the anterior superior iliac spine to the medial malleolus 35 . Experimental protocol. A 10-m Walk test (10MWT) was performed on a 14 m walkway for a rolling start (2 m) and finish (2 m) of the 10 m walk 29 , at comfortable walking speed 36 . This walking task was performed in single-and dual-task conditions (3 trials per condition) 31 .
In the dual-task condition, participants had to carry a full cup of water in their dominant hand with the following instruction: "perform both tasks as well as possible" 26,37 . The examiner noted whether there was any spillage of water 26 . This manual task has been shown to significantly alter spatiotemporal gait parameters during walking in healthy adults with significant reduction of gait speed, stride length and cadence 38 . Gait assessment. Two wireless inertial sensor systems (Physilog5, 200 Hz, BioAGM, Gait Up, CH), fixed on the dorsal part of the participant's feet using Velcro straps (behind the base of the fifth metatarsal 22 ), were used to collect gait data ( Supplementary Fig. S1). Gait assessments were performed by the same examiner.
Spatiotemporal gait parameters (Table 1) were calculated with the Gait Analysis Software provided by Gait Up (CH) 39 . The two first and last steps were removed from the analysis 40 Table 1. Means and standard deviations of gait parameters for each trial and for the three trials, in the single-and dual-task conditions, and DTE and DTE% parameters, with p values obtained from RM-ANOVA to compare trials 1,2 and 3. Abbreviations: DS = double support, N = normalized, slength = stride length, LDr = Load Ratio, FFr = Foot flat ratio, Pur = Push ratio, SI = symmetry index, SR = symmetry ratio.  www.nature.com/scientificreports/ -Push (%): Portion of the stance between the foot being flat on the ground and the toe leaving the ground at take off Speed, cadence and stride length were normalized to have non dimensional values using the formula described by Hof 42 and Pinzone et al. 35 : with g the acceleration of gravity (= 9.81 m/s 2 ) and l 0 leg length; Normalizedcadence(cadenceN) = Cadence * l 0 g with g the acceleration of gravity and l 0 leg length; Normalizedstridelength stridelengthN = stridelength l 0 with l 0 leg length.

Gait symmetry measures.
To assess the contribution of each limb to propulsion and control during walking 8,9 , symmetry gait parameters can be used 9 . Among these parameters, the symmetry index (SI) 9 and the symmetry ratio (SR) 43 are the more commonly used. The SI, which is the most commonly used and cited in published studies on gait symmetry 9,43,44 , was calculated. SI was calculated with the following formula for each spatiotemporal gait parameter (except double support) 9 : with X L the value of each parameter of left foot and X R the value of each parameter of right foot. A value of SI of 0 indicates full symmetry, while SI ≥ 100% indicates its asymmetry. The symmetry ratio (SR), described as easier to interpret, is recommended on the basis of potential clinical utility in patients after stroke which often display asymmetry between left and right leg 43 . SR was calculated with the following formula for each spatiotemporal gait parameter (except double support) 43 : with X L the value of each parameter of left foot and X R the value of each parameter of right foot.
A SR of 1 indicates full symmetry, while a SR of 2.0 on gait speed indicates that the right foot is twice faster than left foot.
Dual task effects parameters. Dual task effects (DTE) were calculated to assess the influence of the addition of a secondary attention demanding task 23,26 . DTE can be calculated as a relative measure of change (DTE) or in percentage (DTE%) 26 . DTE, as the relative measure of change in performance 45 , was calculated from mean parameters as 26 : DTE = single task performance − dual task performance. DTE has the same unit as the gait parameter that is used in the calculation. A negative value of DTE for gait speed, cadence, stride length, swing and foot flat is associated to better performance in dual task; while a negative value for stance, double support, load and push is associated to worse performance in dual task 26 . DTE can also be calculated as a percentage (DTE%), being unit-less, and permitting comparison between parameters 26 : DTE% = single task performance−dual task performance single task performance X100. Same interpretation as DTE can be done regarding positive and negative values. Statistical analysis. Spatiotemporal gait parameters, gait symmetry measures, and dual task effects, were normally distributed (Shapiro-Wilk normality test). A repeated measures analysis of variance (RM-ANOVA) with the number of trials used as within subject factor was performed on gait parameters, ICC and SEM values 46 . When significant effect of the number of trials was found, a Tukey post-hoc test was used to compare differences between trials 46 .
Intraclass correlation coefficients (ICC) were used to compute the relative reliability, and standard error of measurement (SEM) and minimal detectable change (MDC) were used to compute the absolute reliability across the trials 1-2-3 in each condition (single-and dual-task).
The relative reliability was evaluated by the calculation of a 2-way fixed ICC 2,1 (for absolute agreement) 47 . ICC values inferior to 0 were considered as poor reliability, between 0.01 to 0.2 as slight, between 0.21-0.4 as fair, between 0.41-0.6 as moderate, 0.61-0.8 as substantial and 0.8-1.00 as almost perfect 48 . SEM, expressed in the same unit as gait parameters, corresponds to the absolute measure of the variability of the errors of measurements. SEM informs on the precision of gait parameters of individual examinees 49 . SEM was calculated with the following formula 50 : with SD the standard deviation of the parameters from all patients and ICC the relative reliability.
MDC is the minimum value for which a difference can be considered as "real", and was generated with the formula 15 : with SEM the Standard Error of Measurement.
SEM% and MDC% were also calculated as a percentage of mean for each parameter. SEM% values were classified as 'low' (SEM% ≤ 10%) or 'high' (SEM% > 10%) 51 . MDC% values were classified as 'low' (MDC% ≤ 20%), www.nature.com/scientificreports/ 'acceptable' (20% < MDC% < 40%) and 'high' (MDC% ≥ 40%) 51 with a MDC% < 10% considered as excellent and a MDC% < 40% as acceptable 52 . These two classifications were based on previous publications 32,51,53 as no clear criteria for interpretation of SEM% and MDC% are available. Limits of agreements (LOA) and Bland and Altman plots of the differences between trials against their mean, were used to assess the magnitude of disagreement between trials. A difference between trials outside the LOA can be considered as real change ( Fig. 2 and Supplementary Fig. S2) 53 .

Ethics approval and consent to participate. The study was approved by local ethic committee (CPP Ile
De France 1, RCB: 2017-A03468-45, date of agreement: July 17th, 2018, Last version: V6.0, June 17th, 2020). The study is registered on ClinicalTrials.gov, with the following ID: NCT03761212 and follow the SPIRIT checklist. Written informed consent were obtained from all participants by a physiotherapist or a doctor. Any modification to the initial protocol will be presented to the local ethic committee and has to be accepted before application and registered in ClinicalTrials.gov.

Results
Healthy adults included in the present study were 44.9 (11.7) years old. They were 174.7 (8.1) meters height and 69.3 (11.6) kg weight. Table 1 reports means and standard deviations of gait parameters obtained for each trial and for the three trials, in the single-task and the Table 2. Intraclass correlation coefficients (ICC) and limits of agreement (LOA) values for spatiotemporal gait parameters obtained in single task condition between the mean of the first and second trials (T1-T2), the first and the third trials (T1-T3), the second and the third trials (T2-T3) and the means of the three consecutive trials (T1-T2-T3). Abbreviations: ICC = intraclass correlation coefficient, LOA = limits of agreement, SI = symmetry index, SR = symmetry ratio, lb = lower bound, ub = upper bound, DS = double support, LDr = Load Ratio, FFr = Foot flat ratio, Pur = Push ratio, N = normalized.  www.nature.com/scientificreports/ dual-task condition, and for dual task effects (DTE) and DTE% parameters. p values obtained from RM-ANOVA for differences between trials are also reported. Results showed that no significant difference was found between trials in all gait parameters in single-and dual-task conditions and for DTE and DTE% parameters (Table 1). Tables 2 and 3 report relative reliability with intraclass correlation coefficients (ICC) and limits of agreement (LOA) values for spatiotemporal gait parameters obtained in the single-task and the dual-task condition, respectively.

Intra-session relative and absolute reliability of gait parameters.
On the one hand, results showed that almost all ICC of spatiotemporal gait parameters were above 0.81 and considered as almost perfect relative reliability in single-and dual-task conditions 49 , except for cadence, normalized cadence, swing, and stance with ICC above 0.61 and considered as substantial reliability. On the other hand, symmetry index (SI) and symmetry ratio (SR) gait parameters showed lower ICC values with ICC ranging from 0 to 0.25 for speed and cadence, and from 0.15 to 0.88 for slength, swing, stance, LDr, FFr and PUr. Figure 1 present relative reliability with ICC values for spatiotemporal and symmetry gait parameters in the single-task and the dual-task conditions. Table 4 (single task condition) and Table 5 (dual task condition) report absolute reliability with standard error of measurement (SEM) and minimal detectable change (MDC) in the same unit as the parameter and in percentage, calculated between each trial (T1-T2, T1-T3, T2-T3 and T1-T2-T3). The results showed that SEM percentages were comprised between 1.05 and 6.58% in the single-task condition for spatiotemporal and normalized spatiotemporal gait parameters. For symmetry ratio, SEM percentage ranged from 1.66 to 27.22%, while symmetry index ranged from 42.76 to 193.73%. In the dual-task condition, comparable values for SEM and MDC were found. Table 3. Intraclass correlation coefficients (ICC) and limits of agreement (LOA) values for spatiotemporal gait parameters obtained in dual task condition between the mean of the first and second trials (T1-T2), the first and the third trials (T1-T3), the second and the third trials (T2-T3) and the means of the three consecutive trials (T1-T2-T3). Abbreviations: ICC = intraclass correlation coefficient, LOA = limits of agreement, SI = symmetry index, SR = symmetry ratio, lb = lower bound, ub = upper bound, DS = double support, LDr = Load Ratio, FFr = Foot flat ratio, Pur = Push ratio, N = normalized.  www.nature.com/scientificreports/ The comparisons of means of ICC between trials showed that slightly higher ICC and lower SEM and MDC were obtained when pooling gait parameters from the second and the third trials, compared to the first and second trials, to the first and third trials, or to the three trials in the single-task and the dual-task conditions.
Bland and Altman plots for speed, cadence, and stride length in single task and dual task conditions can be found in Fig. 2. Table 6 presents relative reliability with ICC and LOA values on gait parameters for DTE and DTE%. Table 7 shows absolute reliability of DTE with SEM and minimal detectable change (MDC) calculated between each trial (T1-T2, T1-T3, T2-T3 and T1-T2-T3) for DTE and DTE% respectively. The results showed that DTE (0.00 < ICC < 0.82, 61.05 < SEM% < 3666.49) and DTE% (0.00 < ICC < 0.82, 68.03 < SEM% < 14,994.32) reliabilities were low. Relative reliability of DTE % expressed with ICC was comprised between 0.61 and 1.00 for speed, stride length and double support, between 0.21 to 0.41 for cadence, load ratio and foot flat ratio (0.21 < ICC < 0.41), and between 0.00 and 0.21 for swing, stance and push ratio.

Intra-session relative and absolute reliability of dual-task effects on gait parameters.
Bland and Altman plots for speed, cadence, and stride length DTE and DTE% can be found in Supplementary  Fig. S2. www.nature.com/scientificreports/

Discussion
The aim of the present study was to assess the reliability of Physilog5 foot-worn IMUs to assess gait in healthy adults during the 10-m walk test in single and dual task conditions. The objectives were 1) to evaluate the reliability, standard error of measurement (SEM) and minimal detectable change (MDC) values of spatiotemporal gait parameters and symmetry gait parameters obtained, (2) to evaluate the reliability, SEM and MDC values of dual task effects obtained from gait parameters, and (3) to determine the number of trials required to ensure reliable gait assessment. Relative reliability (ICC) was considered as substantial to perfect for spatiotemporal gait parameters in both single-and dual-task conditions. Speed and stride length were the most reliable parameters in line with previous studies on healthy participants 3 . In a study using also Physilog IMUs with patients after stroke, comparable results on relative reliability (0.639 < ICC0.999) were found 22 . Absolute reliability (SEM and MDC) is not always reported in reliability studies 3 and SEM was reported by only one study using Physilog sensors in healthy participants for local dynamic stability parameter 54 . Absolute reliability on stroke patients was lower (i.e. higher SEM% = 3.4 < SEM% < 14.8) but could be explained by the typical pathologic gait associated with stroke and hemiparesis that could lead to more variability (illustrated with higher SEM on paretic leg) 22 . In a study on healthy adults (n = 39, mean age: 23.8 ± 6.2) assessing gait with foot-worn IMUs 15 , MDC in single task was comparable to the results of the present study with 0.12 m.s −1 for gait speed (between 0.13 and 0.16 m.s −1 in the present study), 0.11 for stride length (between 0.07 and 0.09 m in the present study). However, lower MDC were found for cadence (2.72 15 vs between 7.58 and 9.52 steps/minute in the present study), and for stance and swing percentage (1.49 15 vs between 1.75 and 3.29% in the present study). These differences could be explained by the algorithm used to assess gait parameters as one used Mobility Lab (APDM, Inc., Portland, OR) while the present Table 4. Standard error of measurement (SEM) and minimal detectable change (MDC) for trial 1 and 2, 1 and 3, 2 and 3 and 1, 2 and 3 in single task condition. Abbreviations: SEM = standard error of measurement, MDC = Minimum detectable change, DS = double support, LDr = Load Ratio, FFr = Foot flat ratio, Pur = Push ratio, SI = symmetry index, SR = symmetry ratio, N = normalized. www.nature.com/scientificreports/ study used Gait Analysis Software (V5.3.0) from Gait Up (CH). MDC is used to evaluate the difference to be considered "real" than measurement error. It is important to note that MDC values reported in the present study can be used for an individual subject to assess change in performance before and after intervention 15 . However, MDC used to determine meaningful improvement in a group of participants has to take into account the size of the group (n) and is calculated as: MDC group = MDC individual ÷ √ n. Foot-worn IMUs (Physilog5, BioAGM, Gait Up, CH) were thus reliable to assess spatiotemporal gait parameters during walking at comfortable speed, regardless of the single or dual-task condition in healthy adults. This was not the case for symmetry gait parameters which showed less reliability than spatiotemporal gait parameters. We believe that this result is of importance considering the popularity and the relevance of symmetry gait parameters in clinical setting 55 . Indeed, while under healthy conditions and unconstrained walking conditions, gait pattern is generally symmetric (i.e. the left and the right lower limbs behave similarly) 56 , increased levels of gait asymmetry are typically observed in a variety of clinical populations such as elderly fallers 57 , individuals with lower-limb amputations 58 , knee osteoarthritis 59 , hip arthroplasties 60 , or after knee anterior cruciate ligament reconstruction 61 , people with multiple sclerosis 62 , persons with diabetes and peripheral neuropathy 63 , patients with Lewy body disease 64 , with Parkinson disease 65,66 , or after a stroke 44,67 . For instance, Fling et al. 2018 recently reported that people with Parkinson disease exhibited significant increased spatial (e.g., step length) and temporal (e.g., step time) asymmetries of the lower extremities during gait than age-matched healthy control participants 66 . Recent results of Wei et al. (2017) further revealed that gait asymmetry is an important factor for the prediction of falls in stroke patients 68 . Also of note is that chronic gait asymmetry could also lead to increased risk of lower-limb overuse injuries and articular joint degeneration due to the increased weight bearing and propulsion demands placed on one lower limb during walking, in both pathological [69][70][71][72] and healthy populations 73 . Along Table 5. Standard error of measurement (SEM) and minimal detectable change (MDC) for trial 1 and 2, 1 and 3, 2 and 3 and 1, 2 and 3 in dual task condition. Abbreviations: SEM = standard error of measurement, MDC = Minimum detectable change, DS = double support, LDr = Load Ratio, FFr = Foot flat ratio, Pur = Push ratio, SI = symmetry index, SR = symmetry ratio, N = normalized. www.nature.com/scientificreports/ these lines, gait asymmetry can be used as (i) a metric to assess pathology status, patients' functional recovery or disease progression, (ii) a target for interventions aiming to improve gait performance, and (iii) outcome to evaluate and compare different gait rehabilitation programs interventions 43,55,[74][75][76][77] . Interestingly, various rehabilitation programs have been shown to improve gait to a more symmetric gait pattern in individuals with lowerlimb amputations (see for review 78 ), stroke survivors (see for review 79 ) or patients with Parkinson disease 80,81 .
In the present study, two formulae widely employed in clinical practice, namely symmetry ratio and symmetry index, were used to quantify gait symmetry 9,43,82 . Relative and absolute reliabilities of symmetry index of spatiotemporal gait parameters were low, as indicated by low values of ICC, high values of SEM% and high values of MDC%. Accordingly, following existing recommendations 22,51,52 , we would not recommend using SI of spatiotemporal gait parameters for the experimental conditions used in the present study at least. Interestingly, the symmetry ratio (SR) of spatiotemporal gait parameters showed better relative reliability that SI, as indicated by higher values of ICC (except for speed and stride length) and better absolute reliability, as indicated by acceptable SEM% and MDC% (SEM% and MDC% < 20%). This result is of particular interest since SR is easier to interpret by clinicians than SI 43 . Indeed, a SR of 2 indicates that the right foot was twice faster than left foot 43 , while SI gives a percentage of asymmetry that is more difficult to interpret 9 . All in all, SR of spatiotemporal gait parameters should be preferred to SI by clinicians and researchers to assess gait symmetry.
Dual task effects are often used to assess the cost of performing another task while walking and permits comparisons between studies with various secondary task 26,45 . However, the reliability of DTE is not commonly www.nature.com/scientificreports/ assessed in gait reliability studies but has to be tested to allow the use of this indicator in gait studies 24 . In our study, DTE% showed slightly better reliability with higher ICC for almost all gait parameters. Relative reliability of DTE % was considered as substantial to almost perfect for speed, stride length and double support (0.61 < ICC < 1.00), fair to moderate for cadence, load ratio and foot flat ratio (0.21 < ICC < 0.41), and slight to fair for swing, stance and push ratio (0.00 < ICC < 0.21). SEM percentage were high for all DTE parameters (68.03 < SEM% < 14,994.32%). These results are in line with previous studies reporting DTE reliability (0.19 < ICC < 0.55 24 ; 0.002 < ICC < 0.882 83 ) in participants with (n = 23, mean age: 80.6 ± 6.4) and without (n = 27, mean age: 76.1 ± 5.6) cognitive impairment disorders using a counting secondary task. One explanation of lower reliability of DTE is that measurement errors of each single task and dual task conditions tends to inflation of the overall measurement error when combined to obtain the DTE 83 . Besides, we asked participants not to prioritize one task 26,37 and some may have chosen a posture-first strategy 84 , while others may have chosen a posture-second strategy 85 , leading to variability of gait performance that could have been amplified with DTE calculation 24 . Besides, the reliability of gait performance in dual task conditions can be dependent of the complexity of the dual-task used as a concurrent task to gait 86,87 , of the level of cognitive state of participants 88 or of the educational level for verbal fluency tasks 89 . Thus, researchers or clinicians should be aware of the poor reliability of DTE. Even if DTE% of spatiotemporal gait parameters showed slightly better reliability than DTE of spatiotemporal gait parameters, their relative and absolute reliabilities were low (low ICC, and high SEM% and MDC%). Following existing recommendations 22,51,52 , we would not recommend using DTE and DTE% of spatiotemporal gait parameters for the experimental conditions used in the present study at least. In the present study, even if the reliability of spatiotemporal gait parameters was substantial to perfect in both the single-task and the dual-task conditions, we observed slightly better ICC (i.e. higher), SEM and MDC (i.e. lower) when the reliability was calculate from the second and the third trials for most of gait parameters. While numerous studies calculated gait parameters using the average of three trials in older adults 37,90 or pathological populations 91 , the number of trials to ensure reliable measurements using intra-session reliability has been less investigated 92,93 . Our results showed that the first trial appears less reliable and are in line with those reported in previous studies on healthy 93 and pathological populations 92 . Thus, the mean of at least two trials should be used for better reliability of spatiotemporal gait parameters and the first trial could be used, like other studies, as a warming trial 94 .
A first limitation of the study is the lack of formal cognitive assessment of the participants considering the presumable impact of individual cognitive function on gait performance 8895-99 . Growing evidence suggests that the reliance on cognitive control processes during walking can be increased when performing a more complex locomotor task 96 , or when concurrently executing a dual-task (see for reviews 88,98,99 ). Furthermore, a recent systematic review concluded that individuals with cognitive impairment can demonstrate decrease of gait performance 98 . What is more, previous studies have reported that motor slowing preceded cognitive decline in healthy older adults, suggesting that a decrease of gait performance could be a predictor of cognitive decline (see for recent reviews 100,101 ). Another limitation of the present study is that reliability was assessed during a single experimental session, which by definition did not permit the calculation of the inter-session reliability. www.nature.com/scientificreports/ Inter-session reliability refers to the extent of agreement between measurements of a measure in sessions performed at different moments (usually at 1 h or 1 week interval) 102 . It is used to describe error magnitude between two sessions of time to further study disease evolution or the impact of treatments 102,103 . Furthermore, reliability was tested in healthy middle-aged adults. To allow the use of these sensors in clinical practice, the reliability has to be further tested in elderly and pathological populations.
To conclude, foot-worn IMUs are reliable to assess spatiotemporal and symmetry ratio gait parameters in healthy participants in both single-and dual-task conditions. Reliability of symmetry index and DTE gait parameters was low and we do not recommend the use of these parameters for the experimental conditions used in the present study. Future studies should examine the number of strides necessary to ensure better reliability of these index to allow their use in clinical practice and research 104 . Future studies should also focus on the assessment of reliability of 10-m walk test in pathological populations and should open up perspectives with other clinical tests (e.g. 6MWT or Timed Up and Go test) that could capture different features of gait and mobility in daily life.

Data availability
The data of the present manuscript can be available on demand to the corresponding author.  Table 7. Standard error of measurement (SEM) and minimal detectable change (MDC) for DTE and DTE percentage for trial 1-2-3. Abbreviations: DTE = dual task effects, SEM = standard error of measurement, MDC = minimum detectable change, DS = double support, LDr = Load Ratio, FFr = Foot flat ratio.