# Method for Estimating Temporal Gait Parameters Concerning Bilateral Lower Limbs of Healthy Subjects Using a Single In-Shoe Motion Sensor through a Gait Event Detection Approach

^{*}

## Abstract

**:**

## 1. Introduction

_{tr}) and symmetry index of stance phase time (SIS

_{ta}) between the two limbs. These GPBLLs are important because they capture the interaction of the two feet and are essential predictors for estimating certain deep gait parameters, such as gait asymmetry, lower limb muscle strength, and muscle strength transition ability from one limb to the other [5,6,9]. Furthermore, these deep gait parameters are significant predictors for metabolic monitoring, fatigue assessment, walking ability, body functions, and alcohol monitoring [5,6,7,9,10,11,12]. To expand the potential use of IMSs in healthcare or daily activity monitoring applications for healthy subjects, we believe it is necessary to conduct automatic measurement of these GPBLLs by an IMS.

_{tr}, and SIS

_{ta}can be captured well by a single IMS mounted on the right foot. In this case, hardware connection of two sensors would no longer be necessary to assess the interaction of two feet. We refer to this idea as the “gait event detection approach”, which requires an IMS to have a real-time gait event detection method.

## 2. Materials and Methods

#### 2.1. Participants

#### 2.2. Experimental Setup

^{3}. (Figure 2a). It included a 6-axis IMU, microprocessor, Bluetooth module, and control circuit. We assumed that the midfoot–hindfoot was a rigid body and that the shoe fit tightly on the foot, so that the signal from the IMS could be treated as the foot-motion signal. To verify the feasibility of the proposed estimation method, we mounted the IMS on the right foot to estimate the motion of the left foot (Figure 2b). The IMS signal comprised nine types of signal: the three directly measured axes of acceleration, A

_{x}(medial: +; lateral: −), A

_{y}(posterior: +; anterior: −), and A

_{z}(superior: +; inferior: −); the three angular velocity components, G

_{x}(plantarflexion: +; dorsiflexion: −), G

_{y}(eversion: +, inversion: −), and G

_{z}(adduction: +, abduction: −); and the three sole-to-ground angles (SGAs), namely, the roll (E

_{x}), pitch (E

_{y}), and yaw (E

_{z}). The SGA directions were defined in the same way as for the angular velocity, and the SGAs were calculated internally using a Madgwick filter [27]. The acceleration values from the IMS signal were corrected to inertial coordinates (Figure 2c).

_{HS}). The traced trajectory of the toe marker was used to specify the toe’s movement, so that the minimum of the trajectory specified the timestamp of a TO (T

_{TO}) event. Finally, the timestamps of the minima of the left heel trajectory (T

_{OHS}) and left toe trajectory (T

_{OTO}) were treated as the reference timestamps for OHS and OTO detection.

#### 2.3. Experimental Protocol

_{s}) was set to 100 Hz for both the IMS and Vicon measurement systems. The measurement range was ±16 g for acceleration and ±2000°/s for angular velocity in the IMS.

#### 2.4. Feature Selection for OHS and OTO Detection from Foot Motion through Biomechanical Analysis

#### 2.4.1. Foot Motion near OHS

_{ω_L}).

_{ω_sh}) in the anterior direction, which is appended to the foot through the ankle joint. Combined with the existing foot rotation, the foot’s total rotation motion suddenly becomes larger, and we can thus assume that this part of foot motion shifts to high-rotation motion (A

_{ω_H}) during PS.

_{TO}. Here, we refer to the points where the signal gradient suddenly changes as “gradient turning points” (GTPs), and we decided to use these GTPs in the foot motion signals in the sagittal plane, i.e., A

_{y}, A

_{z}, and G

_{x}, as the candidate feature points for OHS detection.

#### 2.4.2. Foot Motion near OTO

_{HS}in the sagittal plane. Accordingly, we decided to use these GTPs in the foot motion signals, A

_{y}, A

_{z}, and G

_{x}, as the candidate feature points for OTO detection.

#### 2.5. Data Processing for Analysis

_{HS}and T

_{TO}values could be detected by searching for local minima in the trajectories of the heel and toe in the Z direction (black and blue curves, respectively), while the HS and TO timestamps in the IMS signal A

_{y}(orange curve) could be detected by the peak detection algorithm described in our previous study [18]. Then, the synchronized data were divided into strides at two reference T

_{HS}points. We originally obtained a total of 679 strides. Before applying the OHS and OTO detection methods, the first and last two strides of each trial were excluded. Furthermore, some strides existed in the dataset that had a different waveform shape, which was probably induced by, for example, sensor error or accidental events disturbing the walking motion. These outliers may need to be removed from the dataset in order to retain the strides that can represent the true gait characteristics of participants [30] from the remaining strides. We removed these outliers, leaving a total of 342 effective strides that were recorded.

_{OHS}and T

_{OTO}from the trajectories measured by the Vicon system, and we obtained all the candidate points mentioned in Section 2.4.1 from each effective stride. Because we did not previously know which candidate point was the best for OHS and OTO detection, before calculating GPBLLs in the final step, the candidate whose timestamp had the best synchronicity and agreement with the reference was judged as the best one, by comparing the synchronicities between the candidate points and the reference data. Then, the best candidates in the IMS signals were chosen for constructing OHS and OTO detection algorithms. In the final step, the GPBLLs were calculated from the Vicon and IMS signals as reference and estimated values, respectively, and they were compared to evaluate the effectiveness of our proposed method.

#### 2.6. Candidate Feature Points for OHS and OTO Detection

_{y}, A

_{z}, and G

_{x}, and the trajectories of the markers in the superior–inferior (Z) direction on the left and right heels and toes, which contain all the information in one GC. In this case, HS occurred around 1200 ms and TO occurred around 1720 ms. The aforementioned candidate feature points for OHS and OTO detection are indicated by red triangles. These GTPs are detected from the waveform via the triangle thresholding algorithm (TTA) [31]. Please note that the TTA is applied independently on each signal from the sensor and then validated using the Vicon’s measurement. We use this algorithm because, if the reference points (P

_{A}and P

_{B}in the figure) are appropriately chosen, a partial waveform in the region of interest can be treated as a monotonic curve without inflection points when tiny fluctuations are ignored. This type of curve is then suitable for application of the TTA.

_{A}can be selected at the moment when the amplitude of the foot motion signal exceeds the baseline level in a foot-flat state before TO, and P

_{B}can be selected at the local maximum (or minimum for A

_{y}) before TO. For OTO detection, P

_{A}can be selected at 20% of the GC after HS, because most people are in a foot-flat state at that time, and P

_{B}can be selected at the nearest local maximum to 20% of the GC after HS. Here, to obtain the length of a GC, the duration between an HS and the previous HS is also recorded. HS and TO event detection in the IMS signal is performed by the peak detection algorithm in our previous study [19].

_{A}(t

_{1}, u

_{1}) and P

_{B}(t

_{2}, u

_{2}), which are located in front of and behind the target point, respectively. Then, a straight line U(T) passing through P

_{A}and P

_{B}is constructed via Equation (1):

_{GTP}, is the furthest point on the curve of interest, Q(T), which is the partial waveform between t

_{1}and t

_{2}. The distance D(T) between the points on Q(T) and the line U(T) is expressed by Equation (2), and the GTP is then obtained by Equation (3):

_{B}, and the 20% location is selected as P

_{A}. The waveform between P

_{A}and P

_{B}is sent to a buffer, and T

_{GTP}for OTO detection is then obtained from the calculated D(T). Next, within one GC after entering a foot-flat state, the data stream is monitored to check whether it exceeds the baseline, as judged by a threshold. In this study, the thresholds for A

_{y}, A

_{z}, and G

_{x}were 0.15 g, 1.15 g, and 30 deg/s, respectively, which were considered higher than the noise levels. For OHS detection, the point exceeding the threshold is selected as P

_{A}, and another local maximum is selected as P

_{B}. Finally, T

_{GTP}for OHS detection is detected by the TTA.

_{HS_ref}, indicating the true HS timestamp in every stride as determined by the Vicon system. Then, we express the Vicon and IMS measurements in terms of the relative OHS and OTO time in one stride, T

_{OHS_}

_{0}and T

_{OTO_}

_{0}, via Equations (4) and (5):

_{OHS}and T

_{OTO}are the OHS and OTO timestamps in the data stream, respectively.

#### 2.7. Temporal GPBLL Estimation through Gait Event Detection Approach

_{1}) and PS (DST

_{2}). Here, DST

_{t}is defined as the total of DST

_{1}and DST

_{2}and can be expressed by Equation (6):

_{sta_l}) and stride time (T

_{str_l}) of the left foot and the stance phase time (T

_{sta_r}) and stride time (T

_{str_r}) of the right foot can be expressed by Equations (7)–(10):

_{HS}and T’

_{OHS}denote the timestamps of HS and OHS in the next stride, respectively. Additionally, the symmetry indexes of the stance phase time (SIS

_{ta}) and the stride time (SIS

_{tr}) can be expressed by Equations (11) and (12), which are modified from the definitions given in [5,11]:

_{ta}and SIS

_{tr}to express both the symmetry and the magnitude relationship of the temporal gait parameters between the left and right feet.

_{HS}in Equations (6), (9), and (10) is different from that in Equations (4) and (5). For the Vicon measurements, T

_{HS}was equivalent to T

_{HS_ref}, whereas for the IMS measurements, T

_{HS}was determined from the IMS signal using the peak detection algorithm [18].

#### 2.8. Statistical Analysis

_{2.5%}and P

_{97.5%}) [33]. Next, the significance of the correlation coefficient r between the differences (D) and averages (A) of the two systems’ measurements was used to check for proportional bias. When both the differences and the averages followed a normal distribution, Pearson’s correlation test was applied, and the LoA was corrected by a parametric approach via linear regression, as expressed by Equations (13)–(16) [33]:

## 3. Results

#### 3.1. Evaluation of Signal Features for Gait Event Detection

_{2.5%}and P

_{97.5%}. Note that, because the temporal resolution was 10 ms, the graphs include many overlapping points.

#### 3.1.1. Best Candidate Signal Feature for OHS Detection

_{gx1}had the best synchronicity with the reference OHS value, with a median difference of 0 ms. However, according to the Wilcoxon signed-rank test, the null hypothesis that the median value was 0 was rejected (p < 0.001). This result indicated that there was still a fixed bias between F

_{gx1}and the reference OHS value. Additionally, we compared the precisions between the two sets of measurements in terms of the QD and Kendall’s W. From this comparison, F

_{gx1}had the best performance for OHS detection (better than F

_{z1}and F

_{y1}), with the best Kendall’s W value of 0.966. This result suggested almost perfect agreement when using this feature to detect OHS. The F

_{gx1}were the concave GTPs in a monotonically increasing waveform that appeared after heel rise in G

_{x}, which suggested that, at the moment of OHS, the foot rotation shifted from a low angular acceleration to a high angular acceleration in the plantarflexion direction. According to the Spearman’s correlation analysis for the Bland–Altman plots, there was no correlation between the averages and differences of the two systems’ measurements (r = −0.022, p = 0.614). Therefore, there was no proportional bias between the two systems.

#### 3.1.2. Best Candidate Signal Feature for OTO Detection

_{gx2}+ 2% GC most closely approached the reference OTO value, with a median difference of 0 ms. Moreover, the Wilcoxon signed-rank test suggested that there was no fixed bias between the two systems (p = 0.151). Additionally, the Kendall’s W of F

_{gx2}+ 2% GC was 0.837, the best value among the three candidates, which suggested strong agreement. Accordingly, this feature was considered the most suitable for OTO detection. Specifically, it indicated that OTO occurs at 2% GC after the foot ends its rotation motion and has landed completely. According to the Spearman’s correlation analysis for the Bland–Altman plots, there was a correlation between the averages and differences of the two systems’ measurements (r = −0.372, p < 0.001). Moreover, the Bland–Altman plots showed a tiny proportional bias between the two systems, such that when the average became larger, the difference became larger in the negative direction. This result suggested that when the average becomes larger, the IMS value of OTO becomes earlier than the reference OTO value.

#### 3.2. Evaluation of Using GPBLL Measurements for Gait Event Detection

#### 3.2.1. Results for One-Stride Measurement

_{str_L}, T

_{str_R}, T

_{sta_L}, and T

_{sta_R}had very high values near the “perfect agreement” level. All the temporal parameters had precisions no higher than 25 ms, i.e., a deviation of no more than 3 units of 100 Hz measurement, although some of them had a slight proportional bias. Moreover, the precisions of the two symmetry indexes, SIS

_{tr}and SIS

_{ta}, were 0.014 and 0.032, respectively. The Wilcoxon signed-rank test showed no fixed biases in DST

_{2}, T

_{str_L}, T

_{str_R}, SIS

_{tr}, and SIS

_{ta}, and the Spearman’s correlation test showed no proportional biases in T

_{str_L}and T

_{str_R}.

#### 3.2.2. Results for Multiple-Stride Measurement

_{2}, DST

_{t}, T

_{str_L}, T

_{str_R}, T

_{sta_L}, and T

_{sta_R}had excellent agreement. Although there were fixed biases for DST

_{1}, DST

_{t}, and T

_{sta_R}, the precisions of all the temporal parameters were no higher than 10 ms, i.e., a deviation of less than 1 unit of 100 Hz measurement; accordingly, we concluded that there were no fixed biases under the condition of 100 Hz measurement. In contrast, there were still proportional biases for DST

_{1}, DST

_{2}, DST

_{t}, T

_{sta_R}, and SIS

_{ta}. Moreover, the precisions of the two symmetry indexes, SIS

_{tr}and SIS

_{ta}, were 0.010 and 0.030, respectively. Comparison of the SD with the QD suggests that there was no obvious improvement in precision from averaging five continuous effective strides; however, the Bland–Altman plots show that the LoA ranges of SIS

_{tr}and SIS

_{ta}became narrower, which means that their precision was improved through averaging.

## 4. Discussion

_{HS_half}and T

_{TO_half}. Because the OHS and OTO of a healthy person are very near these halfway points, it may be doubtful that the best candidate IMS signal features for OHS and OTO detection, as described above, may have only matched T

_{HS_half}and T

_{TO_half}occasionally, rather than representing the true OHS and OTO points.

_{gx1}had a median of 560 ms and an upper-to-lower quartile range of 520–590 ms, whereas the reference T

_{HS_half}had a median of 540 ms with an upper-to-lower quartile range of 510–580 ms. Similarly, F

_{gx2}had a median of 120 ms with an upper-to-lower quartile range of 110–130 ms, whereas the reference T

_{TO_half}had a median of 130 ms with an upper-to-lower quartile range of 110–150 ms. According to the Wilcoxon signed-rank test, the null hypotheses that the IMS system’s measured OHS and OTO timings were similar to T

_{HS_half}and T

_{TO_half}, respectively, were both rejected (p < 0.001, p < 0.001), which means that our proposed features from IMS signals did not represent T

_{HS_half}and T

_{TO_half}.

_{gx1}and F

_{gx1}+ 2% GC had Kendall’s W values of 0.966 and 0.837, respectively. Moreover, the Kendall’s W of 0.602 for SIS

_{ta}, which relied on the precision of both the OTO and OHS measurements, suggested that even if only weak asymmetries were found in the healthy participants, they were still evaluated well. Accordingly, we conclude that our proposed feature points could capture changes in the participants’ gait asymmetry well, which further suggests that the proposed method is reliable for detection of OHS and OTO events from IMS signals. Nevertheless, the method still requires testing on participants whose gait is obviously asymmetric.

## 5. Conclusions

_{x}signal, which appears after a foot-flat state, with a precision of 15 ms. OTO can be specified by a concave GTP induced by the G

_{x}waveform returning to zero after HS in one GC, with a precision of 10 ms.

## Supplementary Materials

_{x}waveform signals.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

- Rast, F.M.; Labruyère, R. Systematic review on the application of wearable inertial sensors to quantify everyday life motor activity in people with mobility impairments. J. NeuroEng. Rehabil.
**2020**, 17, 148. [Google Scholar] [CrossRef] - Jagos, H.; Pils, K.; Haller, M.; Wassermann, C.; Chhatwal, C.; Rafolt, D.; Rattay, F. Mobile gait analysis via eSHOEs instrumented shoe insoles: A pilot study for validation against the gold standard GAITRite
^{®}. J. Med. Eng. Technol.**2017**, 41, 375–386. [Google Scholar] [CrossRef] - Gokalgandhi, D.; Kamdar, L.; Shah, N.; Mehendale, N. A Review of Smart Technologies Embedded in Shoes. J. Med. Syst.
**2020**, 44, 150. [Google Scholar] [CrossRef] - Eskofier, B.M.; Lee, S.I.; Baron, M.; Simon, A.; Martindale, C.F.; Gaßner, H.; Klucken, J. An overview of smart shoes in the internet of health things: Gait and mobility assessment in health promotion and disease monitoring. Appl. Sci.
**2017**, 7, 986. [Google Scholar] [CrossRef] [Green Version] - Mariani, B.; Rochat, S.; Büla, C.J.; Aminian, K. Heel and toe clearance estimation for gait analysis using wireless inertial sensors. IEEE Trans. Biomed. Eng.
**2012**, 59, 3162–3168. [Google Scholar] [CrossRef] - Ellis, R.G.; Howard, K.C.; Kram, R. The metabolic and mechanical costs of step time asymmetry in walking. Proc. R. Soc. B-Biol. Sci.
**2013**, 280, 20122784. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Zhang, G.; Wong, D.W.-C.; Wong, I.K.-K.; Chen, T.L.-W.; Hong, T.T.-H.; Peng, Y.; Wang, Y.; Tan, Q.; Zhang, M. Plantar Pressure Variability and Asymmetry in Elderly Performing 60-Minute Treadmill Brisk-Walking: Paving the Way towards Fatigue-Induced Instability Assessment Using Wearable In-Shoe Pressure Sensors. Sensors
**2021**, 21, 3217. [Google Scholar] [CrossRef] - Park, E.; Lee, S.I.; Nam, H.S.; Garst, J.H.; Huang, A.; Campion, A.; Arnell, M.; Ghalehsariand, N.; Park, S.S.; Chang, H.J.; et al. Unobtrusive and continuous monitoring of alcohol-impaired gait using smart shoes. Methods Inf. Med.
**2017**, 56, 74–82. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Scarborough, D.M.; Krebs, D.E.; Harris, B.A. Quadriceps muscle strength and dynamic stability in elderly persons. Gait Posture
**1999**, 10, 10–20. [Google Scholar] [CrossRef] - Taylor, M.E.; Delbaere, K.; Mikolaizak, A.S.; Lord, S.R.; Close, J.C. Gait parameter risk factors for falls under simple and dual task conditions in cognitively impaired older people. Gait Posture
**2013**, 37, 126–130. [Google Scholar] [CrossRef] - Kim, C.M.; Eng, J.J. Symmetry in vertical ground reaction force is accompanied by symmetry in temporal but not distance variables of gait in persons with stroke. Gait Posture
**2003**, 18, 23–28. [Google Scholar] [CrossRef] - Nagano, H.; James, L.; Sparrow, W.A.; Begg, R.K. Effects of walking-induced fatigue on gait function and tripping risks in older adults. J. NeuroEng. Rehabil.
**2014**, 11, 155. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Anwary, A.R.; Yu, H.; Vassallo, M. An Automatic Gait Feature Extraction Method for Identifying Gait Asymmetry Using Wearable Sensors. Sensors
**2018**, 18, 676. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Han, S.H.; Kim, C.O.; Kim, K.J.; Jeon, J.; Chang, H.; Kim, E.S.; Park, H. Quantitative analysis of the bilateral coordination and gait asymmetry using inertial measurement unit-based gait analysis. PLoS ONE
**2019**, 14, e0222913. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Rhee, I.K.; Lee, J.; Kim, J.; Serpedin, E.; Wu, Y.C. Clock Synchronization in Wireless Sensor Networks: An Overview. Sensors
**2009**, 9, 56–85. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Sichitiu, M.L.; Veerarittiphan, C. Simple, accurate time synchronization for wireless sensor networks. In In Proceedings of the 2003 IEEE Wireless Communications and Networking, New Orleans, LA, USA, 16–20 March 2003; Volume 2, pp. 1266–1273. [Google Scholar] [CrossRef]
- Neumann, D.A. Kinesiology of the Musculoskeletal System: Foundations of Physical Rehabilitation, 2nd ed.; Mosby: St Louis, MO, USA, 2010; pp. 627–676. [Google Scholar]
- Huang, C.; Fukushi, K.; Wang, Z.; Kajitani, H.; Nihey, F.; Nakahara, K. Initial Contact and Toe-Off Event Detection Method for In-Shoe Motion Sensor. In Activity and Behavior Computing. Smart Innovation, Systems and Technologies; Ahad, M.A.R., Inoue, S., Roggen, D., Fujinami, K., Eds.; Springer: Singapore, 2021; Volume 204. [Google Scholar] [CrossRef]
- Caldas, R.; Mundt, M.; Potthast, W.; de Lima Neto, F.B.; Markert, B. A systematic review of gait analysis methods based on inertial sensors and adaptive algorithms. Gait Posture
**2017**, 57, 204–210. [Google Scholar] [CrossRef] [PubMed] - Taborri, J.; Palermo, E.; Rossi, S.; Cappa, P. Gait Partitioning Methods: A Systematic Review. Sensors
**2016**, 16, 66. [Google Scholar] [CrossRef] [Green Version] - González, I.; Fontecha, J.; Hervás, R.; Bravo, J. An Ambulatory System for Gait Monitoring Based on Wireless Sensorized Insoles. Sensors
**2015**, 15, 16589–16613. [Google Scholar] [CrossRef] [Green Version] - Liu, T.; Inoue, Y.; Shibata, K. Development of a wearable sensor system for quantitative gait analysis. Measurement
**2009**, 42, 978–988. [Google Scholar] [CrossRef] - Mannini, A.; Genovese, V.; Sabatini, A.M. Online decoding of hidden Markov models for gait event detection using foot-mounted gyroscopes. IEEE J. Biomed. Health
**2013**, 18, 1122–1130. [Google Scholar] [CrossRef] - Kidziński, Ł.; Delp, S.; Schwartz, M. Automatic real-time gait event detection in children using deep neural networks. PLoS ONE
**2019**, 14, e0211466. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Rueterbories, J.; Spaich, E.G.; Andersen, O.K. Gait event detection for use in FES rehabilitation by radial and tangential foot accelerations. Med. Eng. Phys.
**2014**, 36, 502–508. [Google Scholar] [CrossRef] [PubMed] - Endo, K.; Herr, H. Human walking model predicts joint mechanics, electromyography and mechanical economy. In Proceedings of the 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems, St. Louis, MO, USA, 10–15 October 2009; pp. 4663–4668. [Google Scholar] [CrossRef]
- Madgwick, S.O.H.; Harrison, A.J.L.; Vaidyanathan, R. Estimation of IMU and MARG orientation using a gradient descent algorithm. In Proceedings of the 2011 IEEE International Conference on Rehabilitation Robotics, Zurich, Switzerland, 29 June–1 July 2011; pp. 1–7. [Google Scholar] [CrossRef]
- Houglum, P.A.; Bertoti, D.B. Brunnstrom’s Clinical Kinesiology, 6th ed.; FA Davis: Philadelphia, PA, USA, 2011; pp. 533–585. [Google Scholar]
- Perry, J. Gait Analysis: Normal and Pathological Function, 2nd ed.; Slack: Thorofare, NJ, USA, 2010; pp. 19–46. [Google Scholar]
- Sangeux, M.; Polak, J. A simple method to choose the most representative stride and detect outliers. Gait Posture
**2015**, 41, 726–730. [Google Scholar] [CrossRef] [PubMed] - Nilufar, S.; Morrow, A.A.; Lee, J.M.; Perkins, T.J. FiloDetect: Automatic detection of filopodia from fluorescence microscopy images. BMC Syst. Biol.
**2013**, 7, 66. [Google Scholar] [CrossRef] [Green Version] - Bland, J.M.; Altman, D. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet
**1986**, 327, 307–310. [Google Scholar] [CrossRef] - Bland, J.M.; Altman, D.G. Measuring agreement in method comparison studies. Stat. Methods Med. Res.
**1999**, 8, 135–160. [Google Scholar] [CrossRef] - Chen, L.A.; Kao, C.L. Parametric and nonparametric improvements in Bland and Altman’s assessment of agreement method. Stat. Med.
**2021**, 40, 2155–2176. [Google Scholar] [CrossRef] - Cicchetti, D.V. Guidelines, criteria, and rules of thumb for evaluating normed and standardized assessment instruments in psychology. Psychol. Assess.
**1994**, 6, 284. [Google Scholar] [CrossRef] - Moslem, S.; Ghorbanzadeh, O.; Blaschke, T.; Duleba, S. Analysing stakeholder consensus for a sustainable transport development decision by the fuzzy AHP and interval AHP. Sustainability
**2019**, 11, 3271. [Google Scholar] [CrossRef] [Green Version] - Wilson, C.M.; Kostsuca, S.R.; Boura, J.A. Utilization of a 5-meter walk test in evaluating self-selected gait speed during preoperative screening of patients scheduled for cardiac surgery. Cardiopulm. Phys. Ther. J.
**2013**, 24, 36. [Google Scholar] [CrossRef] - Kirtley, C.; Whittle, M.W.; Jefferson, R.J. Influence of walking speed on gait parameters. J. Biomed. Eng.
**1985**, 7, 282–288. [Google Scholar] [CrossRef] - Kaczmarczyk, K.; Błażkiewicz, M.; Wit, A.; Wychowański, M. Assessing the asymmetry of free gait in healthy young subjects. Acta Bioeng. Biomech.
**2017**, 19, 101–106. [Google Scholar] [CrossRef] [PubMed] - Lai, P.P.; Leung, A.K.; Li, A.N.; Zhang, M. Three-dimensional gait analysis of obese adults. Clin. Biomech.
**2008**, 23, S2–S6. [Google Scholar] [CrossRef] - Montero-Odasso, M.; Casas, A.; Hansen, K.T.; Bilski, P.; Gutmanis, I.; Wells, J.L.; Borrie, M.J. Quantitative gait analysis under dual-task in older people with mild cognitive impairment: A reliability study. J. Neuroeng. Rehabil.
**2009**, 6, 35. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Lemke, M.R.; Wendorff, T.; Mieth, B.; Buhl, K.; Linnemann, M. Spatiotemporal gait patterns during over ground locomotion in major depression compared with healthy controls. J. Psychiat. Res.
**2000**, 34, 277–283. [Google Scholar] [CrossRef] - Lobet, S.; Hermans, C.; Bastien, G.J.; Massaad, F.; Detrembleur, C. Impact of ankle osteoarthritis on the energetics and mechanics of gait: The case of hemophilic arthropathy. Clin. Biomech.
**2012**, 27, 625–631. [Google Scholar] [CrossRef] [PubMed] - Wiszomirska, I.; Błażkiewicz, M.; Kaczmarczyk, K.; Brzuszkiewicz-Kuźmicka, G.; Wit, A. Effect of drop foot on spatiotemporal, kinematic, and kinetic parameters during gait. Appl. Bionics Biomech.
**2017**, 2017, 3595461. [Google Scholar] [CrossRef] - Boudarham, J.; Roche, N.; Pradon, D.; Bonnyaud, C.; Bensmail, D.; Zory, R. Variations in kinematics during clinical gait analysis in stroke patients. PLoS ONE
**2013**, 8, e66421. [Google Scholar] [CrossRef]

**Figure 1.**Illustration of the definitions of a GC, gait phases, gait events, and certain temporal gait parameters, and information on the foot acceleration in the anterior–posterior direction, the knee joint angle, and the ankle joint angle in one GC.

**Figure 2.**(

**a**) Schematic of an IMS embedded in an insole. (

**b**) Schematic of the insole inserted in an athletic shoe. (

**c**) Definition of the coordinate axes and corresponding planes.

**Figure 3.**Foot motion analysis based on standard kinesiology knowledge: (

**a**) foot motion near OHS, and (

**b**) foot motion near OTO.

**Figure 5.**Example showing how to divide data into strides. Black and blue curves represent the trajectories of the heel and toe in the Z direction, and the orange curve represents IMS signal A

_{y}.

**Figure 6.**Examples of the foot motion signals, (

**a**) A

_{y}, (

**b**) A

_{z}, and (

**c**) G

_{x}, with candidate feature points for OHS and OTO detection and the marker trajectories in the superior−inferior (Z) direction on the left and right heels and toes.

**Figure 9.**(

**a**) Agreement plots for the candidate features for OHS detection, and (

**b**) agreement plots for the candidate features for OTO detection. The red dotted lines represent the PA lines.

**Figure 10.**Detailed characteristics and Bland–Altman plots of the best candidates for (

**a**) OHS and (

**b**) OTO detection. The upper and lower LoAs (ULoA and LLoA, black dotted lines) are shown around the PA (black dashed line) for comparison of the IMS and Vicon gait event detection results. The LoAs for OTO were corrected by a nonparametric approach via quantile regression.

**Figure 11.**(

**a**) Agreement plots between the IMS and Vicon results for gait parameters measured from one stride, including DST

_{1}, DST

_{2}, DST

_{t}, T

_{str_L}, T

_{str_R}, SIS

_{tr}, T

_{sta_L}, T

_{sta_R}, and SIS

_{ta}. (

**b**) Bland–Altman plots and LoAs of the 95% confidence interval around the PA line for comparison of the one-stride IMS and Vicon gait parameter measurement results. The black dashed lines are the PA lines, and each pair of black dotted lines represents the ULoA and LLoA. The LoAs of the parameters judged as having a proportional bias were corrected by a nonparametric approach via quantile regression.

**Figure 12.**(

**a**) Agreement plots between the IMS and Vicon results for gait parameters measured from five continuous effective strides, including DST

_{1}, DST

_{2}, DST

_{t}, T

_{str_L}, T

_{str_R}, SIS

_{tr}, T

_{sta_L}, T

_{sta_R}, and SIS

_{ta}. (

**b**) Bland–Altman plots and LoAs of the 95% confidence interval around the PA line for comparison of the multiple-stride IMS and Vicon gait parameter measurement results. The black dashed lines are the PA lines, and each pair of black dotted lines represents the ULoA and LLoA. The LoAs of the parameters judged as having a proportional bias were corrected by a parametric approach via linear regression.

Gait Event | Feature | Relative Time to HS (ms) | Temporal Difference (ms) | Kendall’s W | ||||
---|---|---|---|---|---|---|---|---|

Vicon (Median (Lower–Upper Quartile)) | IMS (Median (Lower–Upper Quartile)) | Accuracy (Median) | Precision (QD) | Fixed Bias? (p-Value) | Proportional Bias? (r, p-Value) | |||

OHS | F_{y1} | 550 (520–590) | 620 (570–670) | 60 | 20 | p < 0.001 | r = 0.279, p < 0.001 | 0.943 |

F_{z1} | 570 (530–605) | 10 | 15 | p < 0.001 | r = 0.095, p = 0.028 | 0.963 | ||

F_{gx1} | 560 (520–590) | 0 | 15 | p < 0.001 | r = −0.022, p = 0.614 | 0.966 | ||

OTO | F_{y2} + 2%GC | 120 (100–140) | 110 (90–120) | −10 | 20 | p < 0.001 | r = −0.049, p = 0.250 | 0.618 |

F_{z2} + 2%GC | 110 (100–130) | −10 | 20 | p < 0.001 | r = −0.589, p < 0.001 | 0.727 | ||

F_{gx2} + 2%GC | 120 (110–130) | 0 | 10 | p = 0.151 | r = −0.372, p < 0.001 | 0.837 |

Gait Parameter | Median (Lower–Upper Quartile) | Temporal Difference | Kendall’s W | |||
---|---|---|---|---|---|---|

Vicon (ms) | IMS (ms) | Accuracy and Precision (Median (QD), ms) | Fixed Bias? (p-Value) | Proportional Bias? (r, p-Value) | ||

DST_{1} (ms) | 120 (107.5–140) | 110 (100–130) | −10 (15) | Y p < 0.001 | r = −0.279, p < 0.001 | 0.687 |

DST_{2} (ms) | 120 (110–140) | 120 (110–130) | 0 (10) | N p = 0.608 | r = −0.410, p < 0.001 | 0.814 |

DST_{t} (ms) | 240 (210–270) | 230 (210–250) | 0 (25) | Y p < 0.001 | r = −0.485, p < 0.001 | 0.794 |

T_{str_L} (ms) | 1080 (1020–1170) | 1070 (1020–1160) | 0 (10) | N p = 0.529 | r = 0.033, p = 0.549 | 0.985 |

T_{str_R} (ms) | 1070 (1020–1160) | 1070 (1020–1160) | 0 (10) | N p = 0.612 | r = 0.069, p = 0.206 | 0.988 |

T_{sta_L} (ms) | 650 (600–690) | 640 (610–690) | 0 (20) | Y p = 0.032 | r = −0.182, p < 0.001 | 0.925 |

T_{sta_R} (ms) | 665 (620–710) | 665 (620–700) | 0 (15) | Y p = 0.022 | r = −0.172, p < 0.001 | 0.967 |

SIS_{tr} | 0.000 (−0.011–0.010) | 0.000 (−0.017–0.017) | 0.000 (0.014) | N p = 0.379 | r = 0.250, p < 0.001 | 0.698 |

SIS_{ta} | −0.017 (−0.046–0.000) | −0.026 (−0.060–0.014) | 0.000 (0.032) | N p = 0.708 | r = 0.359, p < 0.001 | 0.708 |

**Table 3.**Accuracy and precision evaluation results for temporal gait parameters obtained by averaging five strides.

Gait Parameter | Accuracy (Average, ms) | Precision (SD, ms) | Fixed Bias? (p-Value) | Proportional Bias? (r, p-Value) | ICC(2,k) |
---|---|---|---|---|---|

DST_{1} (ms) | −6.9 | 18.9 | Y p = 0.003 | r = −0.530, p = <0.001 | 0.665 |

DST_{2} (ms) | −1.3 | 15.4 | N p = 0.493 | r = −0.410, p = <0.001 | 0.835 |

DST_{t} (ms) | −8.2 | 30.1 | Y p = 0.027 | r = −0.596, p = <0.001 | 0.800 |

T_{str_L} (ms) | 2.0 | 8.0 | N p = 0.707 | r = 0.160, p = 0.238 | 0.998 |

T_{str_R} (ms) | 0.1 | 6.5 | N p = 0.935 | r = −0.024, p = 0.864 | 0.998 |

T_{sta_L} (ms) | −5.4 | 21.8 | Y p = 0.045 | r = −0.216, p = 0.075 | 0.957 |

T_{sta_R} (ms) | −2.8 | 13.3 | N p = 0.081 | r = −0.273, p = 0.023 | 0.984 |

SIS_{tr} | 0.002 | 0.010 | N p = 0.186 | r = 0.250, p = 0.063 | 0.654 |

SIS_{ta} | −0.004 | 0.030 | N p = 0.297 | r = 0.263, p = 0.029 | 0.602 |

**Table 4.**Potential applications and required estimation precisions for gait parameters measured by an IMS.

Potential Application | Gait Parameter | Required Precision | Achieved Precision | Reference |
---|---|---|---|---|

Fall | DST_{total} | 80 ms | 18.9 ms | [10] |

Fatigue | DST_{total} | 2.00%GC or 17–26 ms | 18.9 ms | [12] |

Obesity | T_{sta_L} or T_{sta_R} | 1.70%GC or 15–24 ms | 8.0 or 6.5 ms | [40] |

DST_{total} | 3.48%GC or 30–45 ms | 18.9 ms | ||

Mild cognitive impairment | DST_{total} | 30 ms | 18.9 ms | [41] |

Depression | DST_{total} | 54 ms | 18.9 ms | [42] |

T_{sta_L} or T_{sta_L} | 65 ms | 8.0 or 6.5 ms |

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**MDPI and ACS Style**

Huang, C.; Fukushi, K.; Wang, Z.; Nihey, F.; Kajitani, H.; Nakahara, K.
Method for Estimating Temporal Gait Parameters Concerning Bilateral Lower Limbs of Healthy Subjects Using a Single In-Shoe Motion Sensor through a Gait Event Detection Approach. *Sensors* **2022**, *22*, 351.
https://doi.org/10.3390/s22010351

**AMA Style**

Huang C, Fukushi K, Wang Z, Nihey F, Kajitani H, Nakahara K.
Method for Estimating Temporal Gait Parameters Concerning Bilateral Lower Limbs of Healthy Subjects Using a Single In-Shoe Motion Sensor through a Gait Event Detection Approach. *Sensors*. 2022; 22(1):351.
https://doi.org/10.3390/s22010351

**Chicago/Turabian Style**

Huang, Chenhui, Kenichiro Fukushi, Zhenwei Wang, Fumiyuki Nihey, Hiroshi Kajitani, and Kentaro Nakahara.
2022. "Method for Estimating Temporal Gait Parameters Concerning Bilateral Lower Limbs of Healthy Subjects Using a Single In-Shoe Motion Sensor through a Gait Event Detection Approach" *Sensors* 22, no. 1: 351.
https://doi.org/10.3390/s22010351