2.1. Subjects and Data Acquisition
24 healthy subjects were included in the study (12 female, 12 male). The study was approved by the ethical committee of the Technische Universität Kaiserslautern (TUK) and meets the criteria of the declaration of Helsinki. After receiving all relevant study information, the participants signed an informed consent to the study including a permission to publish data. Each participant conducted two test sessions on two different days with approximately seven days in between. The subjects were instrumented by means of seven IMUs (MTW Awinda, Xsens Technologies BV, Enschede, The Netherlands) attached to the segments of the lower body and pelvis. The pelvis IMU was attached to the segment roughly at half the distance between the left and right spinae illiacae posteriores superiores. Each thigh IMU was attached to the segment approximately at half the distance between the greater trochanter and the lateral epicondyle. Each shank IMU was attached roughly at half the distance between the lateral epicondyle and the lateral malleolus. Each foot IMU was attached roughly at three-fourth the distance between the calcaneus and the head of the second metartarsal. Further, 32 retroreflective markers were attached to bony landmarks according to Leardini et al. [34
] (Figure 1
). In the present study only the markers attached to the calcaneus (CA), the first distal phalanx (DP1) and the four markers creating the pelvic segment were considered.
A test session consisted of one 6-min walk test. Prior to the main test a variation of the two-step-calibration poses described by Palermo et al. [35
] was conducted. The participants had to maintain a slightly inclined standing position for several seconds and then stand in a neutral zero position for another several seconds (Figure 2
). The underlying assumptions are: in the neutral zero pose, all segments are aligned with gravity, the feet are parallel and pointing forward in the sagittal plane, i.e., they are neither outward nor inward rotated. Moreover, it is assumed that between the two poses every segment and IMU is rotated around the frontal body axis only, while the amounts of rotation can differ between segments. Subjects then were asked to walk along a straight line of about 5 m. On both ends of the line, the subjects had about 1 m additional space to turn sharply and then walk the line straight back again. The areas including the turning phases were omitted for the evaluation.
IMU and OMC data were hardware-synchronized, using a standard 5V transistor-transistor-logic signal, and recorded at 60 Hz using Xsens MVN Biomech (Version 4.3.7, Xsens Technologies BV, Enschede, The Netherlands) and OptiTrack Motive (Version 1.10.0, NaturalPoint, Inc., Corvallis, OR, USA).
The sensor-fusion method for obtaining the 6 degrees of freedom segment kinematics from the IMU data is summarized in [33
] and based on [36
]. Note, the segment kinematics serve as basis for the gait event-detection as well as for calculating the STP. The magnetometer-free kinematics estimation method fuses gyroscope and accelerometer measurements with assumptions from a per-segment motion model, biomechanical model constraints and environmental constraints in an iterated extended Kalman filter framework. For this, the state contains IMU-centered kinematics (global position, velocity, acceleration, orientation, angular velocity) of all seven lower body segments, which are all jointly estimated. These are related to the segment kinematics via the IMU-to-segment calibrations, which are assumed known and rigid. Note, the resulting coupled estimation of the complete lower body movement was already shown to provide drift-free joint kinematics estimates even without using magnetometer information in [33
]. The biomechanical constraints model the fact that the body segments are connected at the joints. For this, the segment lengths are assumed known. The joints are all modeled with 3 degrees of freedom. The environmental constraints consist of estimated ground contacts at virtual foot contact points suggesting zero height and zero velocity pseudo measurements, since a level ground is currently assumed (Figure 3
). The probabilistic ground contact estimation method is carried out in parallel to the kinematics estimation for a set of potential ground contact points as shown in Figure 3
, without making any assumptions concerning the type of movement (see [37
] for more details). Hence, the segment kinematics estimation method as well as the calculation of the spatio-temporal parameters given the events are generally applicable, while only the chosen event-detection method is specific for gait. Compared to the description in [33
], only the noise settings of the connected segments, the zero height and the zero velocity pseudo measurements were changed (
). Note that the virtual contact points of the IMU system represent the marker positions in the OMC system projected on the foot soles [37
] (Figure 1
). The DP1 marker was omitted for the foot model in the IMU system, since no inertial information is available to estimate the orientations of the proximal and distal phalanges.
], the biomechanical model (including the segment lengths), the IMU-to-segment calibrations and the tracking initialization were extracted from the OMC data. In the present study, the biomechanical model was obtained from the Twente Lower Extremity Model (TLEM) 2.0 dataset [38
] which was scaled based on the subject’s gender and height using anthropometric tables [39
]. The IMU-to-segment orientations were obtained from the above mentioned calibration poses according to [35
] and the tracking process was initialized from inertial data only by assuming a neutral zero position. The IMU-to-segment positions were assumed fixed in the kinematic model. The assumed positions along the segments coincide with the description of the actual IMU positioning at the beginning of Section 2.1
. The distances out of the segments were all assumed with 3 cm to roughly account for the tissue lying between bones and sensor origins. More specifically, the pelvis IMU position was assumed at 3 cm along the negative
-axis (see Figure 1
), the IMUs attached to thighs and shanks were assumed at 3 cm along the positive (left) or negative (right)
-axis (pointing laterally, see [33
]), and the IMUs attached to the feet were assumed at 3 cm along the positive
-axis (see Figure 3
The real-time detection of IC and TC events, as mentioned above, uses a kinematics based algorithm. It is a modification of the coordinate-based treadmill algorithm described in Zeni et al. [40
] for over-ground walking. The general idea of the base algorithm is that the IC corresponds to the heel having maximal distance to the pelvis center in walking direction, while the TC corresponds to the toe having maximal distance to the pelvis center against the walking direction. In the present study, this algorithm was applied to both the OMC data (optical markers on pelvis and feet) and the IMU data (estimated pelvis pose and virtual foot markers in the biomechanical model). Note, an offline version was used for deriving the events from the OMC data, while an online version was developed for obtaining real-time event-detections. The required modifications (compared to [40
]) for over-ground walking and real-time detection are described in the following.
First of all, the walking direction, which changed with each turn in the present study (in contrast to the treadmill walking in [40
]), was extracted from the captured data by filtering the estimated
-axis of the pelvis segment. The latter is a three dimensional unit vector lying in the sagittal plane and pointing in anterior direction for both the biomechanical model used to process the OMC and the IMU data (see Figure 1
). The filtering was applied to compensate for small internal and external rotations which naturally appear around the direction of movement during walking. It was based on an autoregressive model of first order (AR 1). After each filtering operation the axis was renormalized to unit length. In the offline version (for extracting the events from the OMC data), the filter was used in a zero-lag manner to avoid the introduction of a delay.
To obtain the IC and TC events, the relative positions of the respective real or virtual foot markers with respect to the sacrum were computed. These distances were then projected onto the estimated walking direction using the dot product. As in the original algorithm, the gait events were then extracted by finding the peaks of the projected distances. The maxima in the projected distances
between the CA marker positions and the pelvis center positions defined the ICs and the minima in the projected distances
between the DP1 marker positions (for the OMC data) or the FM marker positions (for the IMU data) and the pelvis center positions defined the TCs. An exemplary course of the projected distances
for both systems with filtered and unfiltered
-axis is illustrated in Figure 4
In the offline version, the Matlab function was used and the median of the complete sequence was used as a threshold for the minimal peak height.
In the online version, the extrema were detected as zero-crossings of differences of subsequent values of the projected distances with event . Instead of using the median as threshold for peak detection, the online version validates each found peak using the following conditions:
1. At the found peak, or , i.e., the IC occurs in anterior and the TC in posterior direction.
2. After an event has been detected, a subsequent event of the same type cannot occur within a given amount of time (0.42 s in our experiments).
3. In addition to the previous temporal condition and in order to increase the robustness of the algorithm to false positive detections, a spatial condition based on the distance between two subsequent events has to be fulfilled. The absolute value of the projected distances between the current event and the last event can be interpreted as the distance between the marker positions associated to IC and TC or vice versa with respect to the pelvis segment center. We assume this distance to be , where indicates a threshold.
For the update of the threshold, we again use a filter based on a AR 1 model to compensate for greater fluctuations of the distances over time. After a valid event-detection the threshold is updated according to . Here denotes the threshold of the previous event and the value is computed as . To ensure that also smaller strides are detected after several bigger strides, the scaling factor was introduced. In our setting it was chosen to be . The threshold was initialized with 1.2 times the foot size. Note, these parameters were empirically determined during pilot experiments and then used for the present study. The pilot experiments showed that the detection is not sensitive to the exact choice of the parameters.
Based on the detected events and estimated real/virtual foot marker positions, the STP parameters described in Table 1
were calculated and the combined average of both lower limbs was considered for evaluation.
2.2. Statistical Analysis
To evaluate the performance of the event-detection algorithm all erroneous detections of the IMU system were captured (surplus and missing events compared to the OMC system) and the relative error compared to the OMC system was calculated. Further, the average detection offset (time difference between events in the IMU and OMC system) for all subjects was calculated for IC and TC. Therefore, the detection offsets over all subjects were averaged and converted from frames per second (fps) to seconds according to the data acquisition frame rate of 60 Hz. Additionally, the detection offset of IC and TC was graphically represented.
To validate the results of the STP the mean error, the root mean square error (RMSE) plus 95% confidence interval (CI), the relative RMSE and Bland-Altman (BA) analysis were calculated. In the present evaluation the left and right side were combined.
The chi-square goodness-of-fit test was used to check for normal distribution in the data. Consequently, a paired sample t-test or the non-parametric Wilcoxon rank sum test was calculated to find significant differences in the STP between the IMU and OMC system. The critical p-value was set to α = 0.05.
To evaluate the test-retest reliability of the STP the intraclass correlation coefficient (ICC) was estimated. In this study a two way random effect model was used to calculate the reliability of the average of two measurements according to McGraw and Wong [41
]. ICC values below 0.40 were rated poor, values between 0.41 and 0.59 fair, between 0.60 and 0.74 good and above 0.74 excellent [42
All statistics, the calculation of the events from the OMC data and the calculation of the STP were conducted in Matlab 2017 (Mathworks Inc., Natick, MA, USA). The real-time event-detection from IMU based kinematics data was implemented in C++.