Does the Position of Foot-Mounted IMU Sensors Influence the Accuracy of Spatio-Temporal Parameters in Endurance Running?

able sensor technology already has a great impact on the endurance running community. Smartwatches and heart rate monitors are heavily used to evaluate runners' performance and monitor their training progress. Additionally, foot-mounted inertial measurement units (IMUs) have drawn the attention of sport scientists due to the possibility to monitor biomechanically relevant spatio-temporal parameters outside the lab in real-world environments. Researchers developed and investigated algorithms to extract various features using IMU data of different sensor positions on the foot. In this work, we evaluate whether the sensor position of IMUs mounted to running shoes has an impact on the accuracy of different spatio-temporal parameters. We compare both the raw data of the IMUs at different sensor positions as well as the accuracy of six endurance running-related parameters. We contribute a study with 29 subjects wearing running shoes equipped with four IMUs on both the left and the right shoes and a motion capture system as ground truth. The results show that the IMUs measure different raw data depending on their position on the foot and that the accuracy of the spatio-temporal parameters depends on the sensor position. We recommend to integrate IMU sensors in a cavity in the sole of a running shoe under the foot's arch, because the raw data of this sensor position is best suitable for the reconstruction of the foot trajectory during a stride. Keywords:wearable computing; foot kinematics; sensor position; zero velocity update; inertial measurement unit; sport science; running 1. Introduction Wearables have become increasingly important

integrate IMU sensors in a cavity in the sole of a running shoe under the foot's arch, because the raw data of this sensor position is best suitable for the reconstruction of the foot trajectory during a stride. Keywords:wearable computing; foot kinematics; sensor position; zero velocity update; inertial measurement unit; sport science; running 1. Introduction Wearables have become increasingly important in many elds of our everyday life. Among applications in medicine, workplaces, and many others, the sports domain was one of the early adopters of wearable technology. The reasons for the quick spread of small body-worn sensors in sports was due to the manifold advantages of the technology for athletes, researchers, and the sports industry. Using wearables, athletes can utilize low-cost sensor technologies in order to enhance their performance, prevent injuries, and improve their motivation [1]. Sports research bene ts from the fact that wearables allow in eld data acquisitions, whereas many studies in the sports domain were traditionally laboratory bound [2]. Furthermore, the sports industry can, on the one hand, offer innovative and more attractive sports products with integrated sensor technology, and, on the other hand, gather consumer data which they can use to improve their products. Sensors2020,20, 5705; doi:10.3390/s20195705

Sensors2020,20, 5705 2 of 21 One sport where wearable technology already has a great impact is endurance running. Both professional and recreational runners track themselves and use online platforms like Runtastic (Runtastic GmBH,Pasching, Austria) or Strava (Strava, San Francisco, CA, USA) to monitor their training progress and performance. Three heavily used sensor technologies in endurance running are Global Positioning System (GPS) trackers, heart rate monitors, and inertial measurement units (IMUs). While GPS trackers like smartwatches or smartphones are utilized for visualizing the running track and providing real-time feedback on pace and distance [3], heart rate monitors are used to evaluate the physical effort of runs and provide real-time feedback on exercise intensity and training effect [4]. However, these two sensor modalities are not capable of revealing insights into the biomechanics of runners. IMUs are low-cost sensors which consist of 3D-accelerometers measuring linear acceleration as well as 3D-gyroscopes measuring angular velocity. By attaching those sensors to different parts of the human body, various endurance running-related biomechanical parameters can be computed and evaluated. In this context, IMUs can be used in various ways. Researchers developed body sensor networks with multiple sensors in order to reconstruct the movement of different extremities in a synchronized manner [5]. The advantage of those sensor networks is the holistic evaluation of runners' movements. However, attaching all the sensors requires a lot of time which recreational runners are often not willing to spend for everyday runs. That is why researchers also investigated single sensors at speci c positions on the human body which can easily and quickly be attached. Apart from placing sensors on the lower back [6,7], the tibia [8,9], or the ankle [10], a popular sensor position used in literature is the foot or the running shoe [2,11–15]. One reason for the popularity of this sensor position is the amount of different spatio-temporal parameters that can be computed. Falbriard et al. [16] showed that foot-mounted IMUs can be used to accurately segment running strides into their sub-phases (ground contact phase and swing phase) and thus allow computing stride time and ground contact time. Apart from that,

shoe [2,11–15]. One reason for the popularity of this sensor position is the amount of different spatio-temporal parameters that can be computed. Falbriard et al. [16] showed that foot-mounted IMUs can be used to accurately segment running strides into their sub-phases (ground contact phase and swing phase) and thus allow computing stride time and ground contact time. Apart from that, researchers developed algorithms to reconstruct the trajectory, that is, orientation and translation, of the foot during a stride. A popular approach for the computation of the trajectory is strapdown integration using a zero-velocity assumption during midstance [17]. From the resulting foot translation, stride length and average stride velocity was calculated with a mean error of 2 cm and 0.03 m/s, respectively [15]. Additionally, the orientation can be used to compute angular foot kinematic parameters like the sole angle in the sagittal plane or the range of motion in the frontal plane [12,14]. However, publications using foot-mounted IMUs differ not only in the computed spatio-temporal parameters, but also in the position of the IMU sensors on the running shoes. Shiang et al. [11], Falbriard et al. [12], and Strohrmann et al. [2] mounted the IMU sensors on the instep of the foot on top of the shoelaces, whereas Lederer et al. [13] and Koska et al. [14] mounted the sensors on the heel. Other sensor positions presented in literature are on the lateral side of the running shoe below the ankle [17] and inside the sole of the running shoe [18,19]. To our knowledge, the effect of the IMU sensor position on the foot with respect to raw data quality and accuracy of spatio-temporal parameters has not been evaluated yet. Peruzzi et al. [20] evaluated the best possible IMU sensor position for algorithms using zero-velocity updates and found a lateral mounting below the ankle to be the best sensor location. They evaluated the quality of the sensor position using a motion capture system by investigating the motion of the retrore ective markers at different locations. However, they did not include IMU raw data or spatio-temporal parameters to evaluate the sensor position.

for algorithms using zero-velocity updates and found a lateral mounting below the ankle to be the best sensor location. They evaluated the quality of the sensor position using a motion capture system by investigating the motion of the retrore ective markers at different locations. However, they did not include IMU raw data or spatio-temporal parameters to evaluate the sensor position. We contribute an in-depth analysis by comparing different sensor positions with respect to the raw signals as well as their suitability for the computation of spatio-temporal parameters. We base our evaluation on a study with 29 subjects, which wore running shoes with IMUs attached to the instep, the heel, the lateral side of the foot, and within the cavity of the running shoe. We compare the similarity of IMU raw data at different sensor positions by computing Pearson's correlation coef cients between the individual sensor positions' raw data. Besides, we compute and evaluate temporal stride features

Sensors2020,20, 5705 3 of 21 based on state-of-the-art event detection algorithms and spatial features using a zero-velocity-based strapdown integration algorithm. 2. Methods 2.1. De nition of Spatio-Temporal Parameters The temporal parameters we evaluated were stride time t strideand ground contact timetgc(Figure). One stride was de ned by two consecutive initial ground contacts (ICs) of the same foot. The duration between those time instances is the stride time. One stride could be further segmented into ground contact phase and swing phase by nding the toe off (TO) event where the foot leaves the ground. The duration of the ground contact phase is called ground contact time. One further important phase during ground contact time is midstance (MS). It subdivides the ground contact phase into absorption and propulsion phase. We used the MS for the zero-velocity update in the strapdown integration algorithm.Initial ground contact Midstance Toe o Ground contact phase Swing phase Initial ground contact Stride time , Stride length Ground contact time Figure 1.Visualization of the running gait cycle. The spatial parameters based on the translation of the foot were stride lengthd strideand the average stride velocityv stride. The stride length is de ned as the translation of the foot during one stride. The average stride velocity can be computed by dividing the stride length by stride time. We used the sole angle and the range of motion as spatial parameters based on the orientation to evaluate the sensorpositions (Figure). The sole angle is de ned as the angle between the sole of the running shoe and the ground in the sagittal plane at IC. The range of motion describes the eversion movement of the foot during ground contact. Runners land on the lateral side of their foot and rotate inwards after IC. The angle describing the amount of inward rotation is the range of motion in the frontal plane.Sole angle Range of motion Sagial plane Frontal plane lateralmedial Figure 2.Visualization of sole angle and range of motion.

after IC. The angle describing the amount of inward rotation is the range of motion in the frontal plane.Sole angle Range of motion Sagial plane Frontal plane lateralmedial Figure 2.Visualization of sole angle and range of motion.

Sensors2020,20, 5705 4 of 21 2.2. Data Set We collected data of 29 amateur runners (23 male; 6 female) with a mean age of24.9 2.4years. All subjects were informed about related risks and gave written consent to participate in the study and for the collected data to be published. The data was acquired in a laboratory with a motion capture system (Vicon Motion Systems Inc., Oxford, UK) as reference. All subjects wore the same kind of running shoes (adidas Response Cushion 21, Adidas AG, Herzogenaurach, Germany). Both the left and the right shoe were equipped with four IMU sensors. The sensors were located in a cavity in the sole of the running shoe, laterally under the ankle, at the heel, and on the instep (Table; Figure). Table 1.Naming of the sensor position and details on the mounting of the sensors. Name Mounting Cavity Cavity cut in the sole of the shoe under the arch Instep Mounted with suiting clip to laces of the shoe Lateral Mounted with tape laterally under ankle Heel Mounted with tape on heel capHeel Lateral Cavity Instep Figure 3. Visualization of sensor positions on the running shoes, the global coordinate system (xg,yg,zg), the shoe coordinate system(xs,ys,zs), and the individual sensor coordinate systems. When the foot is at on the ground, the global and the shoe coordinate system are aligned. For the study, we used miPod IMU sensors [21]. The accelerations~a[n]and angular rates~w[n]at samplenmeasured with those sensors will be denoted as ~a[n] = 0 B B @ ax[n] ay[n] az[n] 1 C C A and ~w[n] = 0 B B @ wx[n] wy[n] wz[n] 1 C C A , (1) where indicesx,y, andzdenote the vector components along the axis of the respective sensor (Figure). The sensors sampled accelerations and angular rates with a frequency offs=200Hz and a resolution of 16 bit. According to Potter et al. [22], we set the range of the accelerometer to 16g and the range of the gyroscope to 2000 /s. Prior to the data acquisition, the miPod sensors were calibrated using the calibration routine introduced byFerraris et al. [23]. Additionally, a functional

accelerations and angular rates with a frequency offs=200Hz and a resolution of 16 bit. According to Potter et al. [22], we set the range of the accelerometer to 16g and the range of the gyroscope to 2000 /s. Prior to the data acquisition, the miPod sensors were calibrated using the calibration routine introduced byFerraris et al. [23]. Additionally, a functional calibration routine was performed to align the individual sensors' coordinate systems with the shoe coordinate system(xs,ys,zs) . The functional calibration routine (Figure) was performed for each subject and generated two vector pairs for each sensor. Each vector pair consisted of one vector in the sensor frame and one vector in the shoe frame: 1. Vector pair superior/inferior direction: The subjects were asked to stand still with both feet on the ground. Thus, the accelerometer of all sensors measured the gravitational acceleration in the sensor frame. Thezs-axis was de ned as the corresponding vector in the shoe frame.

Sensors2020,20, 5705 5 of 21 2. Vector pair medial/lateral direction: The subjects rotated their feet on a balance board, which only allowed for a rotation in the shoe frame's sagittal plane. A gyroscope in the shoe frame measures the angular rate of the rotation on the medial/lateral axis. The medial/lateral axis of the shoe frame corresponds to the principle component of the angular rate data during rotation in the sensor frame. Thexs-axis was de ned as the medial/lateral axis in the shoe frame. Using these vector pairs, we computed a subject dependent rotation matrix for each sensor location, which rotated the IMU-data in the sensor frame into the shoe frame using an adapted version of the Whaba algorithm [24,25]. After applying this rotation matrix to the sensor data, all sensor frames were aligned with the shoe frame, which makes the raw IMU data comparable on each axis. Besides, the functional calibration offers the possibility to run the same algorithms on each sensor due to the same alignment of the sensors and thus enable a fair comparison between the sensor positions. For the simplicity of the notation in this work, we keep the convention for acceleration~a[n]and gyroscope~w[n] de ned in Equation, but use x,y, andzas the axis in the shoe coordinate system from now on. Figure 4. Visualization of the functional calibration procedure. The rst part of the functional calibration consisted of standing still with the foot at on the ground in order to measure gravity. During the second part the subjects rotated their feet on a balance board to compute the medial/lateral axis using a principal component analysis. The motion capture ground truth system consisted of 16 infrared cameras and sampled the positional data of the retrore ective markers with a sampling rate offs=200Hz. The running shoes were equipped with a subset of the marker setup described by Michel et al. [26]. For our study, we only used the six markers attached to each foot. Using these markers and the marker-based stride segmentation method for IC and TO using motion capture data introduced by Maiwald et al. [27], the reference

a sampling rate offs=200Hz. The running shoes were equipped with a subset of the marker setup described by Michel et al. [26]. For our study, we only used the six markers attached to each foot. Using these markers and the marker-based stride segmentation method for IC and TO using motion capture data introduced by Maiwald et al. [27], the reference values for the spatio-temporal stride features could be estimated. The sensors and the motion capture system were synchronized using an adapted version of the wireless trigger introduced by Kugler et al. [28]. Due to small differences in the IMUs sampling rates, this procedure only allowed for a stride-to-stride synchronization, not a sample-to-sample synchronization. In the described set-up, each subject was asked to run 50 times through the motion capture volume. We controlled for speed by capturing different number of trials in different velocity ranges of 2–6 m/s (Table). Using the described study set-up, we were able to collect data of 2426 strides.

Sensors2020,20, 5705 6 of 21 Table 2. Number of trials and recorded strides per velocity range. During the data acquisition, we controlled for speed and the subjects only changed the velocity range, if the required number of trials in the previous (slower) velocity range was reached. Velocity Range (m/s) Number of Trials Number of Strides 2–3 10 962 3–4 10 558 4–5 15 544 5–6 15 362 An example stride for the four IMU sensors, which was segmented from IC to IC, is depicted in Figure. 00.20.40.6 50050ax[t]in m/s 2 CavityHeelInstepLateral00.20.40.6 5000500wx[t]in deg/s00.20.40.6 100 500ay[t]in m/s 2 00.20.40.6 400 2000200wy[t]in deg/s00.20.40.6 150 100 500t in saz[t]in m/s 2 00.20.40.6 2000200t in swz[t]in deg/s Figure 5. Exemplary IMU data of one stride segmented from IC to IC for the four different sensor positions.

Study evaluates the impact of IMU sensor position on accuracy of spatio-temporal parameters in running.