Ten methods for marker-based GE identification were evaluated in this study (Table 1). Among these, six methods, using either marker-trajectory positions (M1 and M2), velocities (M3 and M4), or accelerations (M8 and M9), were implemented as described in the literature (Hreljac and Marshall, 2000; Ghoussayni et al., 2004; Hsue et al., 2007; O’Connor et al., 2007; Zeni et al., 2008; Desailly et al., 2009). The main features of these methods, all using heel and toe markers (Figure 1), are summarized in Table 1. All methods except for M3 (O’Connor et al., 2007) used the anterior–posterior (AP) components of displacements, velocities, or accelerations. To this purpose, a reference system was identified in each frame (Cappozzo et al., 2005) using markers from a rigid cluster attached to the pelvis (Figure 1) and foot marker displacements, velocities, or accelerations were calculated along the three identified directions (anterior–posterior, AP; medio–lateral, ML; and vertical, V; Figure 1). Marker trajectories were filtered using a zero-lag fourth order Butterworth filter (cut-off frequency 7 Hz).

A modified version of M4, M6, was also implemented using an adaptive velocity threshold (Bruening and Ridge, 2014). The use of 3D rather than the marker velocity in the sagittal plane (AP-V plane) was also explored. In particular, candidate IC instances of time ( t I C , H ) were identified as those for which the magnitude of the 3D heel velocity vector was lower than 0.5 m/s (M5, fixed threshold) or 0.5*walking speed (M7, adaptive threshold). Since an IC might also occur with the forefoot (Bruening and Ridge, 2014), a further set of potential IC ( t I C , T ) was identified imposing a threshold on the 3D toe velocity vector magnitude [either fixed = 0.5 m/s (M5) or adaptive = 0.8*walking speed (M7)]. For each t I C , H , two checks were then performed:

1) If t I C , H ≤ t I C , T (rearfoot contact), then mIC = t I C , H

For the FC detection (Figure 1), a threshold [fixed = 1.0 m/s (M5) or adaptive = 0.8*walking speed (M7)] was initially set on the 3D toe velocity. The instant ( t F C , T ) in which this threshold passed was used as the center of a 100 ms window within which a local peak of the magnitude of the 3D heel velocity vector was then sought. If this peak was found, indicating the initiation of the lifting of the foot (rotation around the ankle joint), then the mFC was set at the following instant (corresponding to a zero acceleration). If the peak was not found, then mFC = t F C , T (Figure 1).

A further new method, M10, was defined: estimations of both IC and FC were initially provided by M1, to reduce potential false positives exploiting the existence of markers on the pelvis, and then refined using the relevant events detected using M7. If the pelvic markers were occluded, the events were directly detected using M7.

Curvilinear walking ( C W ) was identified from the pelvis markers using simultaneous thresholds on the rotations around the V axis (≥45°) and the vertical angular velocity (peak ≥15°/s), with a constraint on duration ranging between 0.5 and 10 s (El-Gohary et al., 2014). Step negotiations ( S N ) were identified from the heel marker vertical displacement when the difference between consecutive ICs of the same foot was higher than 0.15 m. Each GE belonging to neither C W nor S N was labeled as included in straight-line walking ( S W ).

A cohort of 20 YAs (Table 2) was recruited across two centers (University of Sheffield and University of Sassari) for the concurrent evaluation of the ten GE identification methods. All participants signed a consent form before taking part in the investigation (University of Sheffield Research Ethics Committee, Application number 029143).

The generalizability of the results was then evaluated using a subset of the data from a multicentric study (Mobilise-D Technical Validation Study, Mazzà et al. [2021]), including 10 OAs, and 10 participants from the following four cohorts: COPD, MS, PD, and PFF. Participants (demographic and clinical characteristics shown in Table 2) were recruited from five centers and included in the study after providing written informed consent (Ethics approvals: Tel Aviv Sourasky Medical Center: the Helsinki Committee, 0551-19TLV; Robert Bosch Foundation for Medical Research: Medical Faculty of the University of Tübingen, 647/2019BO2; University of Kiel: Medical Faculty of Kiel University, D540/19; The Newcastle upon Tyne Hospitals NHS Foundation Trust and Sheffield Teaching Hospitals NHS Foundation Trust: London–Bloomsbury Research Ethics committee, 19/LO/1507). The adopted inclusion and exclusion criteria are detailed in Mazzà et al. (2021).

Reflective markers were attached bilaterally to participants’ shoes, in correspondence of the posterior side of calcaneus (HEEL) and of the second metatarsal head (TOE). Four markers were attached on the pelvis using a rigid cluster (Figure 1). The marker trajectories were acquired using different SP systems (8-camera Vicon T10, 10-camera Vicon T160, 12-camera Qualisys Miqus, 12-camera Vicon Vero, and 14-camera Vicon Bonita). Before data collection, a spot-check was performed to quantify the accuracy of the different SP systems, following the works of Scott et al. (2021). Pre-processing procedures were standardized with an ad-hoc pipeline, where foot trajectories were gap-filled only for gaps lower than 0.5 s (10.15131/shef.data.19115450). Participants were also equipped with a multi-sensing wearable system including two PIs, synchronized with the SP using a hardware-based solution (sampling frequency 100 Hz, Salis et al. [2021]).

Participants were asked to perform five structured mobility tasks (Mazzà et al., 2021):

• Straight-line walking: walk for 5 m at three self-selected speeds (slow, comfortable, and fast, twice each)

The PI signals were used to isolate the different walking bouts [defined as comprising of at least two right and two left strides (Kluge et al., 2021)] and all reference GEs (rGEs) were identified according to the methodology proposed and validated by Salis et al. (2021).

The ten GE methods were compared using the YA data and the following performance criteria:

• Sensitivity (S), positive predictive values (PPV), and F1 values: for each rGE, a marker-based GE was classified as a true positive (TP), false negative (FN), or false positive (FP) using a tolerance window (TW) of 0.5 s centered on rGE.

Reference stride, stance, and swing phase durations were quantified using the rGEs, and foot marker trajectories were used to calculate the reference length and speed during these time intervals. The impact of the GE detection inaccuracies on all other parameters was then assessed for each method and condition. The errors were computed only for the strides identified by TP ICs, with the remaining strides counted as missing. TP strides were further labeled as curvilinear or step negotiation strides if they had at least one IC belonging to either C W or S N , respectively. Accuracy, bias, and precision, both absolute and relative, were calculated for all parameters as previously described for the GEs.

The aforementioned analyses allowed the method that best satisfied the GE performance criteria to be chosen. Its generalizability was then established by applying it to the data from the five different cohorts and repeating all the aforementioned analyses, both at the event level and stride level.

Kolmogorov–Smirnov tests were used to assess the normality of the error distributions for the Δ t M , W in the YA group. A Friedman test assessed differences in performance among the methods for identification of both ICs and FCs under all walking conditions and a Wilcoxon signed–rank post hoc test evaluated pairs of methods, using a Bonferroni Holm’s correction for multiple comparisons. For the statistical analysis, FN events were assigned the highest error observed for each adopted method when more than 5% of the expected errors were missing or the mean error values otherwise (Scheffer, 2002). FP events were not included in the analysis.

For all cohorts, Bland–Altman (BA) plots (Martin Bland and Altman, 1986) were used to visually compare the marker-based parameters and check for nonlinear or heteroscedastic distributions of the differences between them. Absolute agreements were tested using intraclass correlation coefficients ( I C C 2,1 ) and their 95% confidence intervals [absolute-agreement, two-way mixed-effects model, Koo and Li (2016)] and relative agreement using Spearman correlation coefficients. Limits of agreement (LoA) and root mean square errors (RMSE) were calculated for the TP strides parameters of each cohort. All analyses were conducted using SPSS (version 26-IBM SPSS Inc., Chicago, United States ) and statistical significance for all tests was set to p < 0.05.

Overall, 4,476 GEs (2,427 ICs) were detected with the PIs for the YA cohort, of which 2,876 were in S W , 1,468 in C W , and 132 in S N . For each method M and walking condition W , Table 3 shows sensitivity, PPV, F1 scores, and performance metrics for the different methods for both GEs, while Figure 2 shows the distribution of the temporal inaccuracies ( Δ t M , W ).

For each walking condition W , the Friedman tests highlighted significant differences in Δ t M , W values for both GEs (p < 0.001) and pairwise comparisons showed that the newly proposed methods M5, M7, and M10 outperformed most of the others (Supplementary Table S1 and Supplementary Table S2). Since M10 also had the highest F1 scores under all walking conditions for both GEs, it was selected as the best performing method. Using M10, the gait events were identified with a 40 ms (4 frames) accuracy ranged from 89% ( S W ) to 91% ( C W ) for ICs and from 86% ( S W ) to 89% ( S W ) for FCs.

Overall, 1,000, 981, and 89 strides were detected for the YA cohort in S W , C W , and S N , respectively. Bias, precision, and accuracy for the stride parameter errors for the ten methods are reported in Supplementary Table S3. For the best performing method (M10), the median absolute percentage error (i.e., accuracy) was ≤1% for the stride duration, length, and speed under all walking conditions, except for the S N stride duration (1.9%). For stance and swing duration, absolute accuracy errors were similar to those of the stride duration, but caused larger relative accuracy errors (between 2.4% for stance duration in both S W and C W , and 7.1% in S N ). Around 20% of the TP strides had errors in length lower or equal to the accuracy of the two SP systems (linear RMSE = 1.2 mm). Overall, stride length errors had virtually no bias and an MAE ≤ 0.5% for both S W and C W ; a M A E ≤ 1% was observed in S N , resulting from the observed temporal inaccuracies. About a quarter of the detected strides had duration errors equal to or lower than the system temporal resolution ( Δ t m i n = 10 ms for a sampling frequency of 100 Hz). The same applied to 15.2% of the stance and 20.9% of the swing phase errors. Almost 70% (69.2%) of TP strides had speed errors equal to or lower than 0.01 m/s.

Overall, 2,514 (1,337 ICs) gait events were detected for the OA cohort, 3,172 (1,681 ICs) for the COPD, 3,548 (1,879 ICs) for the MS, 2,766 (1,468 ICs) for the PD, and 3,042 (1,609 ICs) for the PFF cohorts. Figure 3 shows the sensitivity, PPV, F1 scores, and performance metrics for M10 in the three walking conditions. The IC events identified within four frames (40 ms) ranged between 65% ( S N , PFF) and 93% ( S W , PD) and the FCs between 75% ( C W , PFF) and 100% ( S N , COPD).

The overall detected strides were 1,174 in the OA (39% in S W , 55% in C W , and 6% in S N ), 1,483 in the COPD (36% in S W , 59% in C W , and 5% in S N ), 1,582 in the MS (49% in S W , 49% in C W , and 2% in S N ), 1,294 in the PD (37% in S W , 58% in C W , and 5% in S N ), and 1,315 in the PFF cohorts (59% in S W , 39% in C W , and 2% in S N ). Bias, precision, and accuracy of the errors for the stride-level parameters are reported in Table 4. A 10 ms bias (1 frame delay) was observed in the IC identification for most cohorts and walking conditions (Figure 3). In most cases, this error propagated with a virtually null bias in the stride duration (Table 4).

In light of the spatial resolutions assessed for each cohort, virtually null errors in the stride length were observed in 14.7%, 10.5%, 25.4%, 23.5%, and 12.8% of the cases for the OA (<1.5 mm), COPD (<0.6 mm), MS (<2.0 mm), PD (<1.3 mm), and PFF (<0.8 mm) cohorts, respectively. Similarly, the percentage of strides in which the errors in the stride duration were equal to or lower than the temporal resolution ( Δ t m i n ) ranged between 18.5% (PFF) and 24.1% (MS), those for the stance duration between 8.3% (PFF) and 16.4% (OA), and those for the swing duration between 9.5% (PFF) and 17.8% (PD). Finally, more than 70% of the errors in the stride speed were equal to or lower than 0.01 m/s in all cohorts (OA: 71.3%, COPD: 76.6%, MS: 77.3%, PD: 77.9%, and PFF:71.3%).

For the TP strides, the relevant errors for each cohort are shown using Bland–Altman plots; errors for the YA group are also provided in (Figure 4). Excellent absolute ( I C C 2,1 >0.9) and relative agreement ( ρ > 0.9 ) were observed in all cohorts and for most of the stride-related parameters, except for swing duration (Table 5; Figure 4). For the latter parameter, a heteroscedastic distribution of the error can be observed, especially in the PFF cohort (Figure 4).