Validation of an algorithm to assess regular and irregular gait using inertial sensors in healthy and stroke individuals

Participants

Healthy participants aged between 40 and 90 years old, who were able to walk for at least two minutes without assistance were recruited from the community between April 2021 and February 2022. We included five participants per age category, 40–49, 50–59, 60–69 and 70+ years, resulting in a total of N = 20 healthy participants (Table 1). Exclusion criteria were any diseases affecting gait or balance, such as osteoarthritis, neurological or neuromuscular disease or deformities of the lower extremities, and BMI >30 kg/m².

Stroke participants were able to walk for at least two minutes without assistance, participated in a walking therapy group due to their stroke, were above 18 years, and had to understand verbal instructions. Exclusion criteria were any other diseases affecting gait or balance, hemispatial neglect, and a BMI >30 kg/m². A total of N = 10 stroke patients from the gait rehabilitation program of the Sint Maartenskliniek were included in this study. Clinical data of the stroke participants were derived from the electronic patient record. Participant characteristics can be found in Table 1, the Chi-square and Mann–Whitney U tests revealed no significant differences (p ≥ 0.05) between the groups based on gender, age, height or weight.

The study protocol was in line with the Declaration of Helsinki and was granted an exemption of the Dutch medical scientific research act (WMO) by ‘METC Oost-Nederland’ (identification number: 2021-8191). Prior to study participation, written informed consent was provided by all participants.

Materials

Participants were equipped with 4 IMUs (MTw Awinda, Xsens, Enschede): at the dorsal side of both feet, sternum, and lower back (L4/5) and 26 reflective markers for the OMCS according to the VICON plug-and-gait lower body model (Vicon, 2021). Xsens MT Manager software suite version 2019.2 was used for data capture of the IMUs. All treadmill walking conditions were performed on the GRAIL (Gait Real-time Interactive Analysis Lab, (Motek Forcelink, Amsterdam, the Netherlands)); an instrumented treadmill with an ten-camera OMCS (VICON, Oxford, United Kingdom). All overground walking conditions were performed in the overground gait lab, with a ten-camera OMCS (VICON, Oxford, United Kingdom). The IMU system and OMCS recorded at 100 Hz and were synchronized by a high-low pulse with OMCS as master.

Measurement protocol

During treadmill walking, healthy and stroke participants wore a harness attached to the ceiling for safety precautions. All participants walked on the treadmill at a self-selected speed before data collection for approximately four minutes for familiarization purposes. Subsequently, they walked on the instrumented treadmill in two conditions: regular and irregular treadmill walking.

In the regular treadmill walking condition, participants walked for 2 min at a self-paced, comfortable walking speed. Self-paced walking allowed participants to adjust the speed of the treadmill by walking more at the front of the belt (increase in speed) or at the back of the belt (decrease in speed). The participants with stroke performed the regular walking task in self-paced mode if possible, but in fixed speed mode if their walking capacity was insufficient to regulate the treadmill’s speed. After the regular walking condition, all participants performed the irregular walking condition, consisting of a precision stepping task at the average walking speed during the regular walking condition. Rectangular stepping stones (30x15 cm) were projected on the treadmill, functioning as step targets. The stepping stones were projected at stride lengths randomly varying between 80–120% (80, 90, 100, 110, 120) of the preferred stride length of the individual participant. Participants were instructed to walk without holding the handrail bars if possible but were allowed to do so if needed. Participants were allowed to rest between walking conditions. For each of the measurements, data collection was started once participants indicated they had reached a comfortable walking speed. Data were recorded for a duration of two minutes and stopped before participants were decelerating, ensuring no accelerating and decelerating phases were included in the dataset for further analysis.

The healthy participants performed an additional overground walking task. They were asked to walk ten times back and forth through the measurement volume of the overground gait lab (approximately 5 m) at a comfortable walking speed.

Data processing

All data processing and analysis described in this paragraph and in ‘Data analysis’ are included in the algorithm code available at: https://github.com/SintMaartenskliniek/IMU_GaitAnalysis (Release ‘Validation study’, tag ‘v1.1.0’).

IMU data captured by MT Manager software (2019.2) included angular velocity and acceleration in the sensor frame, acceleration in the earth frame, and orientation in quaternion and Euler angle format. OMCS data was captured by VICON Nexus software (version 2.4). All further data processing and analyses were performed in Python 3.10.

Prior to any data analysis, a second-order low-pass Butterworth filter was applied to the angular velocity (15 Hz cut-off frequency) and acceleration data (17 Hz cut-off frequency) of the IMUs, according to Sabatini et al. (2005). OMCS data was filtered with a second-order low-pass Butterworth filter (15 Hz cut-off frequency).

Data analysis

Figure 1 shows a typical gait cycle and corresponding mediolateral gyroscope and vertical accelerometer signals of the IMUs on the feet, and the velocity of the heel and toe markers of the OMCS. A gait cycle consists of a stance phase, initiated by an initial contact event (IC), and a swing phase, starting at a terminal contact event (TC). Accurate identification of IC and TC events is crucial for correctly calculating spatiotemporal gait parameters. They also define the time period for further integration of the IMU signals to determine spatial parameters.

Another important gait event for the IMU-based gait algorithm is the instant of mid-swing, which is used to identify the IC and TC. Based on Sabatini et al. (2005), mid-swing events were identified as the maximum in the clockwise direction of the angular velocity around the mediolateral axis (i.e., the axis of rotation for flexion-extension movements). To this end, scipy.signal.find_peaks function with peak distance at 0.7 s, prominence at 1 rad/s was used. Based on Behboodi et al. (2019), IC events were identified at the first instance of zero-crossing, positive to negative, after mid-swing in the angular velocity around the mediolateral axis. Peaks between mid-swing events in the vertical acceleration based on Mercer et al. (2003) were used to identify TC events (scipy.signal.find_peaks function with no further specifications) (Mercer et al., 2003; Mo & Chow, 2018). In case multiple peaks were found, the peak at the instance with the largest angular velocity in the anti-clockwise direction was identified as the actual TC event; the others were deemed as an artefact. Finally, foot flat was identified based on Behboodi et al. (2019). The start of foot flat was defined as the instant of TC on the contralateral side. The end of foot flat (i.e., heel-off) was identified at the instant of mid-swing on the contralateral side (Behboodi et al., 2019). Based on the instants of the gait cycle, stance phase (initial contact to terminal contact), swing phase (terminal contact to initial contact) and foot flat phase (start of foot flat to end of foot flat) were identified.

After gait event detection, spatial parameters were calculated. The tri-axial velocity of the foot was estimated by numerical integration of the accelerometer (earth frame) signal according to Eq. (1) over the duration of the trial (120 s). However, this involves some signal drift. To reduce this signal drift, a sigmoid curve, based on a p-chip interpolation (scipy.interpolate.pchip_interpolate function) was subtracted from the signal (zero-velocity updates) (Mariani et al., 2010). The p-chip interpolation function was defined between each period of foot flat (Eq. (2)). Hereafter, zero-velocity updates were applied at each foot flat (Eq. (3)) (Sukumar, 2010; Mohamed Refai et al., 2020; Wu et al., 2021). (1)${\displaystyle {\mathrm{velocity}}_{\mathrm{raw}}\left(\mathrm{t}\right)=\mathrm{acceleration}\left(\mathrm{t}\right)\ast {\mathrm{T}}_{\mathrm{s}}+\mathrm{velocity}\left(\mathrm{t}-1\right)}$ for each instant t, with T_s = 1/sample frequency (2)${\displaystyle {\mathrm{velocity}}_{\mathrm{de-drifted}}\left(\mathrm{t}\right)={\mathrm{velocity}}_{\mathrm{raw}}\left(\mathrm{t}\right)-\text{sigmoid curve of drift estimation (t)}}$ (3)${\displaystyle \text{velocity}\left(\mathrm{t}\right)={\text{velocity}}_{\mathrm{de-drifted}}\left(\mathrm{t}\right)-{\mathrm{velocity}}_{\text{de-drifted at foot flat}}}$

Note that the initial velocity at the start of the measurement (t = 0) was set at zero. Since the measurements started while participants were walking and the leg could be in the swing phase, this could result in an inaccurate velocity estimation until the first foot flat phase was reached.

Numerical integration of the velocity over the duration of the trial (120 s) results in tri-axial position estimation over the duration of the trial: (4)${\displaystyle \mathrm{position}\left(\mathrm{t}\right)=\mathrm{velocity}\left(\mathrm{t}\right)\ast {\mathrm{T}}_{\mathrm{s}}+\mathrm{position}\left(\mathrm{t}-1\right)}$ for each instant t, with T_s = 1/sample frequency

Note that the initial position at the start of the measurement (t = 0) was set at zero.

Stride time was defined as the time between two consecutive IC events: (5)${\displaystyle {\text{stride time}}_{\mathrm{n}}=\text{time at}{\mathrm{IC}}_{\mathrm{n}}-{\text{time at IC}}_{\mathrm{n}-1}}$

Stride length was defined as the distance traveled by the foot during the stride time (IC till following IC) in the horizontal plane: (6)${\displaystyle {\text{stride length}}_{\mathrm{n}}=\text{sqrt}\left({\left(\text{position}{\mathrm{X}}_{\mathrm{ICn}}-{\text{position X}}_{\mathrm{ICn}-1}\right)}^{\text{2}}+{\left({\text{position Y}}_{\mathrm{ICn}}-{\text{position Y}}_{\mathrm{ICn}-1}\right)}^{\text{2}}\right)}$

Stride velocity was calculated as the stride length divided by the stride time: (7)${\displaystyle {\text{stride velocity}}_{\mathrm{n}}={\text{stride length}}_{\mathrm{n}}/{\text{stride time}}_{\mathrm{n}}}$

Gait event detection in the OMCS data was performed according to the validated velocity based method of Zeni, Richards & Higginson (2008). This method defines TC at the instant that the velocity vector in anterior-posterior direction of the toe marker crosses zero in the anterior direction. IC is defined at the instant that the velocity vector in the anterior-posterior direction of the heel marker crosses zero in the posterior direction. For treadmill walking, the position of the toe and heel markers in the global coordinate system were used whereas the position of toe and heel markers were calculated relative to the pelvis for overground walking. Stride time and stride velocity were calculated according to the same definitions as used for the sensor algorithm (Eqs. (5) and (7)). Stride length for OMCS data during treadmill walking was calculated as the average velocity of the ankle on the contralateral side during flat foot (Eqs. (8) and (9)), multiplied by the stride time and added to the difference in position between IC and the following IC along the Y-axis, which is the axis in line with the walking direction (Eq. (10)). In overground walking the stride length was calculated as the difference in position between two consecutive IC events of the heel marker (Eq. (11)). (8)${\displaystyle {\mathrm{swing time}}_{\mathrm{n}}={\mathrm{IC}}_{\mathrm{n}}-{\mathrm{TC}}_{\mathrm{n}-1}}$ (9)${\displaystyle {\mathrm{velocity}}_{\mathrm{n}}^{\mathrm{treadmill}}=\left({\mathrm{position Y}}_{\mathrm{TC}+0.1\ast \mathrm{swing time}}^{\mathrm{contralateral foot}}-{\mathrm{position Y}}_{\mathrm{TC}+0.6\ast \text{swing time}}^{\mathrm{contralateral foot}}\right)/\left(0.5\ast \mathrm{swing time}\right)}$ (10)${\displaystyle {\mathrm{stride length}}_{\mathrm{n}}\mathrm{OMCS treadmill walking}=\left({\mathrm{position Y}}_{\mathrm{ICn}}-{\mathrm{position Y}}_{\mathrm{ICn}-1}\right)+{\mathrm{velocity}}_{\mathrm{n}}^{\mathrm{treadmill}}\ast {\mathrm{stride time}}_{\mathrm{n}}}$ (11)${\displaystyle {\mathrm{stride length}}_{\mathrm{n}}\mathrm{OMCS overground walking}=\left({\mathrm{position Y}}_{\mathrm{ICn}}-{\mathrm{position Y}}_{\mathrm{ICn}-1}\right)}$

Post-hoc analysis

Two methods are frequently used in literature to identify gait events: the OMCS-based method used in this study and a method based on force plate data (Pacini Panebianco et al., 2018; Behboodi et al., 2019; Mariani et al., 2010; El-Gohary et al., 2014). The benefit of OMCS-based gait event detection is that multiple strides per stretch in the overground lab can be analyzed against only one stride per stretch on force plates. To maximize the number of strides for analysis in the overground lab and be consistent in the methods used, the IMU-based algorithm was validated against OMCS in both settings. Nevertheless, during treadmill walking trials, force data was collected by the embedded force plates of the GRAIL. We checked the magnitude of the difference, including limits of agreement (LoA) at 1.96 standard deviation (SD), in gait event detection between the OMCS-based method and force plate data as ground truth.

Statistical analysis

Groups were compared on gender distribution by the Chi-square test, and on age, height and weight by the Mann–Whitney-U test. The validity of the gait algorithm was evaluated on a stride-by-stride basis, quantifying the agreement of the instant of IC and TC, stride time, stride length, and stride velocity, with OMCS-derived outcomes as reference (Zeni, Richards & Higginson, 2008). For stride time and length variability, we calculated the coefficient of variation (CoV) for each participant, defined as the SD over all strides divided by the mean of all strides within a participant. Differences between sensor and OMCS-derived timing of IC and TC were visualized in histograms. For stride time, stride length and stride velocity, we created Bland-Altman-like plots to reflect the agreement between the IMU-based and OMCS-based analysis. Because the difference between methods for stride length and velocity showed a downward trend with increasing means of the value (non-uniformity), evaluated using linear regression models, we did not calculate the limits of agreement. To evaluate variance within and between subjects, we constructed Bland-Altman-like plots based on the mean over strides within a participant, as well as based on all separate strides (except for CoV measures which can only be calculated per participant).

To evaluate the algorithm’s performance in irregular walking, we compared differences between methods for regular with irregular conditions in healthy controls and for regular with irregular conditions in stroke participants using a linear mixed model with the difference between methods for each gait parameters as dependent measure, condition as fixed effect and participant ID as random effect. We also tested differences between methods comparing healthy versus stroke participants during regular walking. For this comparison, we constructed linear mixed models with the difference between methods of each gait parameter as dependent variable, group (healthy vs stroke) as fixed effect and participant ID as random effect. For CoV measures, we compared regular vs irregular walking in healthy participants using a paired t-test and compared healthy and stroke participants during regular walking using an unpaired t-test.

The significance level was set at alpha 0.05. Differences between overground and treadmill walking in the differences between methods were described by mean differences and SD. All statistical analysis was done in RStudio (R version 2022.02.0; RStudio Team, 2022), using the lme4 package (version 1.1-29; Bates et al., 2015).

Treadmill walking

All participants performed all regular and irregular walking conditions except for one individual with stroke (participant ID: STR_03), whose walking capacity was insufficient to perform the target stepping task. Therefore, only a fixed-speed trial representing regular walking from this participant was included for further analysis. One other stroke participant (participant ID: STR_09) had to perform the regular walking task at a fixed treadmill speed. All other participants performed the regular walking condition in self-paced mode. Stride time varied between 0.71 and 2.58 s, stride length between 0.26 and 1.83 m, and stride velocity between 0.14 and 1.73 m/s across all participants and conditions (Table 2).

Gait event detection

Detection of IC when collapsing groups and conditions was on average 9-17 ms later based on IMU compared to OMCS (Figs. 2A, 2E). TC was on average 15–24 ms earlier for the IMU-based method (Figs. 2B, 2F). For both gait events, the variance of difference between methods (SD for each individual) was limited in healthy participants, and more apparent in stroke participants (Figs. 2C, 2D and 2G, 2H).

When comparing regular with irregular walking in healthy participants, the difference between methods for IC was 2.5 (95% CI [2.2–2.8]) ms smaller in the regular condition (t = 15.76, p < 0.001, Table 3). The difference between methods for TC was 3.4 (95% CI [3.0–3.8]) ms smaller in the irregular compared to regular condition (t = 18.06, p < 0.001, Table 3). The second operationalization of the effect of irregular walking, comparing stroke with healthy participants, showed that the difference between methods for IC was 7.6 (95% CI [−14.0 to −1.1]) ms smaller for stroke than healthy participants (t = −2.30, p = 0.029, Table 3), while TC did not differ significantly between groups (95% CI [−21.2–3.5], t = −1.41, p = 0.169, Table 3). The third operationalization of the effect of irregular walking, comparing regular with irregular walking conditions in stroke participants, showed that the difference between methods for IC was 2.6 ms (95% CI [−4.9 to −0.3]) lower for the irregular than regular condition (t = −2.17, p = 0.030, Table 3). The difference between methods for TC was 2.2 ms (95% CI [−4.2 to −0.1], t = −2.05 p = 0.040, Table 3).

Spatiotemporal parameters

Figure 3 shows the Bland-Altman-like plots for the spatiotemporal gait parameters averaged per subject (left panels) and on a stride-by stride basis (middle and right panels). The stride time difference between methods did not vary as a function of the value of the method itself in both healthy and stroke participants. Differences between methods for stride time were on average 0 ms, with low between-subject variance for all conditions in healthy participants (SD = 0.01 s) and 0.04 s during regular walking and 0.05 s during irregular walking in stroke participants (Table 4).

In healthy participants, the difference between methods on stride time was not different between regular and irregular walking (t = 0.153, p = 0.878, Table 3), and not different between healthy participants and stroke participants during regular walking (t = −0.111, p = 0.912, Table 3). Also, no differences between methods were found between the regular and irregular walking condition on stride time in stroke participants (t = 0.618, p = 0.537, Table 3). Differences between methods for CoV of stride time did not significantly differ between regular and irregular walking in healthy participants (t = 1.189, p = 0.249, Table 5 and Fig. 4), or between healthy and stroke participants during regular walking (t = −1.909, p = 0.089, Table 5 and Fig. 4), or between regular and irregular walking conditions in stroke participants (t = −1.038, p = 0.330, Table 5). However, a larger mean CoV of stride time and stride length in the irregular trials, suggests that the proposed method to induce irregularity seemed to work.

In both conditions, stride length in healthy participants was 0.03 m (SD regular: 0.04 m, SD irregular: 0.05 m) smaller when based on IMUs compared to OMCS (Table 4 and Fig. 3). In stroke participants, the stride length difference between methods was 0.00 m (SD regular: 0.06 m, SD irregular: 0.04 m, Table 4 and Fig. 3). Comparing regular vs irregular walking in healthy participants, resulted in larger differences between methods for the regular walking condition (0.003 m, t = 4.500, p < 0.001, Table 3). The difference between methods for stride length during regular walking was closer to zero for stroke patients compared to healthy participants (0.038 m, t = 3.422, p = 0.002, Table 3). The difference between methods for CoV of stride length was larger in irregular walking compared to regular walking (−0.44%, t = −4.198, p < 0.001, Table 5). Differences between methods for CoV of stride length in stroke participants (0.7% higher in IMU vs OMCS) was not different from healthy participants during regular walking (0.2% lower in IMU vs OMCS; t = −1.186, p = 0.266, Table 5). There were also no differences found between methods for CoV of stride length in irregular walking compared to regular walking in stroke participants (t = −1.165, p = 0.278, Table 5).

Stride velocity in healthy participants was 0.03 m/s (SD = 0.04) lower when based on IMUs compared to OMCS (Table 4). In stroke participants, stride velocity difference between methods was 0.00 m/s (SD = 0.03, Table 4). Comparing regular vs irregular walking in healthy participants, resulted in smaller differences in regular walking (0.004 m/s, t = 5.951, p < 0.001, Table 3). Differences between methods were larger for healthy participants compared to stroke participants during regular walking (0.034 m/s, t = 3.313, p = 0.003, Table 3).

Details of the statistical output can be found in Tables 3 and 5. A table including the mean differences and SDs for each subject, for each walking condition can be found in the supplementary materials.

Overground walking

Spatiotemporal parameters per subject ranged between 0.94 and 1.28 (median = 1.01) s for stride time, 1.18 and 1.64 (median = 1.40) m for stride length and 1.05 and 1.70 (median = 1.36) m/s for stride velocity. Table 6 shows differences in gait event detection and spatiotemporal parameters between IMU-based and OMCS-based analysis during overground walking.

Post-hoc analysis

OMCS detected IC 0.03 s [LoA: −0.01; 0.07] and TC 0.01 s [LoA: −0.03; 0.05] after the force plates. See Supplementary Materials for full details of this analysis and histograms (Fig. S1) of the mean differences.