Our proposed gait analysis system is illustrated in Figure 1A. For gait analysis, we used two IMUs (TSND121, ATR-Promotions, Kyoto, Japan; Figure 1B) with a triaxial accelerometer (±8 G range), triaxial gyroscope (±1,000° per range), and Android OS tablet (ZenPad10, ASUSTeK Computer Inc., Taipei, Taiwan; Figure 1C). Raw accelerometer and gyroscope signals were sampled at 100 Hz (16 bits per sample). The size of the IMU is 37 mm × 46 mm × 12 mm and its weight is about 22 g. IMUs are attached on the shanks (just above the ankles) with bands (Figure 1B). The inertial coordinate system used to represent foot orientation and position is shown in Figure 1B. Acceleration and angular velocity data of both the shanks measured during walking are transmitted to the tablet through Bluetooth.

Our proposed method comprises two steps: dissociation of continuous gait data into multiple steps and three-dimensional trajectory estimation in a stepwise manner. Each process is described as follows.

We dissociated the signals into four steps: (1) smoothing and finding the local maximums; (2) finding the heel-strike (HS) and toe-off (TO) points; (3) quadratic regression; and (4) calculating the split point. One walking cycle is defined as a single step, and the starting point of each cycle is defined as the split point between HS and immediate TO points. We identify the split point in each cycle based on raw angular velocity data in the z-axis ω_z of the gyroscope (right-handed; Figure 1B, left).

The foot trajectory in each cycle can be calculated by integrating the acceleration between each segmentation point. Two coordinate systems are applied: a laboratory coordinate system (e) and a sensor coordinate system (s). Because the raw data from the sensor are represented by the time-variant sensor coordinates, we need to transpose them into time-invariant laboratory coordinates. Acceleration in the laboratory coordinates can be converted from measured sensor acceleration using a rotational matrix:

where θ, ϕ, and ψ are the Euler angles around the x-, y-, and z-axes.

We divide the estimation process of the foot trajectory into five steps: (1) calculate the initial Euler angles; (2) calculate the time derivative of the Euler angles; (3) calculate the Euler angles using the integral; (4) transpose the accelerations using a rotational matrix; and (5) calculate the trajectory using the double integral.

Integration may drift because of IMU sensor error, and the calculations of velocity and trajectory are corrected by the constraint condition. In each cycle, both the initial value and the end value of the velocity in three directions and the trajectory in the vertical direction can be assumed as 0. The algorithm below shows how to estimate velocity.

First, the forward integral and back integral are calculated separately from linear acceleration a_e,i:

where the superscripts f and b mean forward and backward, respectively. The correction result can then be derived by the weighted average of the forward and backward integral:

where w_i is the weight and w_i ∈ [0, 1].

Because ve,if is more accurate near the starting point and ve,ib is more accurate near the end point, the function for calculating w_i should increase monotonically. Here, we choose the sigmoid function to calculate w_i:

where N is the number of points in the current cycle and m is a hyperparameter calculated from experiment, which we choose as m = 0.1. The trajectory in the vertical direction can also be calculated using the algorithm above.

The gait events included the HS and TO points, which were extracted first. The HS and TO events detection algorithm was based on the peak detection of the raw angular velocity in sagittal plane ω_z. At the end of the swing period, several of negative peaks can be observed in ω_z and the first one is associated with the HS instant (Salarian et al., 2004). Before the swing period, a negative peak is associated with the TO instant (Salarian et al., 2004).

For the definition of each gait event search region, the pattern of shank tilt angle, which was inspired from an instep-based previous study (Tunca et al., 2017) was introduced. At the end of the swing period, the shank will rotate around the knee axis caused by knee extension and reach the maximum forward. Then, the rotation of the shank around the ankle axis will start and the foot contact with the ground will produce the HS instant. In this process, θ_z will appear to increase first and then decrease. Thus a positive peak will appear in θ_z before the HS instant where θ_z was computed via the integration of ω_zwith the sampling interval Δt. For the convenience of the description, we refer to this instant where peak occurrence as shank-max-forward (SMF). Similarly, after the TO instant, the ankle will lift slightly and rotate until reaching a certain height. Then it will start to rotate and present a negative peak in θ_z. We refer to this instant as the shank-max-backward (SMB) for convenience. As a result, SMF and SMB of θ_z can be used to define a proper search interval of the HS and TO. We found the SMF and SMB via a peak search algorithm signal.find_peaks in SciPy (version 1.2.0) which can find proper peaks via the prominence (define intrinsic height of a peak) and the distance (define the distance between peaks) properties. Then, SMFs are the positive peaks and SMBs are the negative peaks whose prominence is larger than 0.2 [rad] and the distance is at least 0.4 [s]. Finally, HS is defined as the first peak appears after each SMF instant, and the TO is the minimum of angular velocity in the interval (SMB − 0.3 [s], SMB).

Estimated stride length SL is calculated by the trajectory in the y and z direction:

where pe,i=(px,i,py,i,pz,i)T. Estimated stride duration is calculated as the time from one HS to the next ipsilateral HS. Estimated gait speed is calculated as the value obtained by dividing stride length by stride duration. Estimated stance duration is calculated as the time from HS to ipsilateral TO. Estimated swing duration time is calculated as the time from TO to the next ipsilateral HS.

We conducted an experimental evaluation of our proposed method to validate the accuracy of the trajectory estimation of the shanks (just above the ankles) to verify whether it allows the analysis of gait for clinical purposes. Twenty healthy people participated in the experiment, and we used a motion capture system as the criterion standard for the evaluating gait in a clinical setting. We evaluated the accuracy of our proposed method for calculating the estimated trajectory and clinical gait parameters. We used an IMU attached on the shanks for the experimental evaluation.

An optical motion capture system (Nobby Tech. Ltd., Tokyo, Japan) was used as the reference system. We used 12 cameras, and the motion capture volume was about 2 m × 7 m × 1 m (width, length, and height; Figure 3A). The position error of the markers of the motion capture system during the calibration was <1 mm. The dimensions of the floor of the room were 18 m × 7 m (length and width; Figure 3A). Three optical markers were attached on each foot as shown in Figure 3B. Two of the three markers were attached on the heel and the toe (metatarsal head II) to assess gait parameters. The third marker was attached on the IMU to evaluate the trajectory estimation. To synchronize the IMU and the motion capture system, the participants hit their heel to the floor before the gait measurement. The peaks of the spike waveforms, that were caused by the heel hits of the participants, in both the IMU signals and the motion capture system data were used to define time 0.

We recruited 20 able-bodied volunteer participants, with no history of gait abnormalities, from the Tokyo Institute of Technology for the experimental evaluation. The Ethics Committee of Tokyo Institute of Technology approved the protocols for the evaluation, and all participants provided their written informed consent. Because of technical problems with the motion capture system, the data for one of the 20 volunteer participants were excluded from the analyses. Ultimately, we used data from 19 participants (mean age 23.9 years, 9 men and 10 women, mean height 1.66 ± 0.07 m and mean body mass index 20.2 ± 2.7).

As an example of the application of the proposed method to PD patients, we used the method to analyze gait in one healthy elderly participant and four patients with PD. The healthy elderly participant was recruited from a public interest incorporated association in Machida City, Tokyo that provides human resource services for elderly people. Patients with PD were recruited from Kanto Central Hospital, Tokyo. PD had been diagnosed by a physician. The exclusion criteria for this study were past history of other neurological or orthopedic disorders that can affect gait or posture (excluding PD). The healthy elderly participant and the four PD participants provided written informed consent in accordance with requirements of the Ethics Committee of Tokyo Institute of Technology. The Kanto Central Hospital Ethics Committee and the Ethics Committee of Tokyo Institute of Technology approved the protocol for the application of the proposed method.

To construct the spike waveforms for synchronization between the IMU and the motion capture system (for the synchronization method, see “Overview of the evaluation”), the participants hit their heel to the floor before the gait measurement. In two trials, the participants walked on a flat floor at their own self-selected natural pace and a slow pace. In each trial, the participants walk straight in the motion capture volume and turned outside of the motion capture volume. Thus, each trial comprised four straight walks (two round trips; Figure 3A, left). We used the gait data obtained as the participants walked in the motion capture volume and removed the gait data as the participants turned outside of the motion capture volume.

To consider the validity of the estimation of foot trajectory from IMUs attached on the shanks, we calculated correlations between stride length estimated with the proposed method, measured with a motion capture marker attached on the IMU, and measured with a motion capture marker attached on the heel.

The trajectories of our proposed method and the reference data are shown in Figure 4. The R value between displacement in the direction of forward movement calculated with the proposed method and measured with a marker attached on the IMU was 0.978 (Figure 5A, left). The R value between the maximum vertical displacement calculated with the proposed method and measured with a marker attached on the IMU was 0.925 (Figure 5A, right).

The R value between displacement in the direction of forward movement calculated with the marker attached on the IMU and that measured with the marker attached on the heel was 0.994 (Figure 5B).

The means and standard deviations (SD) of the gait parameters compared between the proposed method and the motion capture system are summarized in Table 1. Figure 6 shows the agreement between the proposed method and the motion capture system in Bland-Altman plots. The mean ±1 SD accuracy of stride length was 0.054 ± 0.031 m (Figure 6A). The R value between displacement in the direction of forward movement calculated with the proposed method and measured with a marker attached on the heel was 0.978 (Figure 6A). The mean ±1 SD accuracy were as follows: 0.034 ± 0.039 m/s for gait speed (Figure 6B); 0.002 ± 0.020 s for stride duration (Figure 6C); 0.000 ± 0.017 s for stance duration (Figure 6D); and 0.002 ± 0.024 s for swing duration (Figure 6E).

The shank trajectory over 15 steps for each participant is shown in Figure 7. The mean clinical gait parameters of the PD patients are summarized in Table 2.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.