Estimation of Vertical Ground Reaction Forces and Sagittal Knee Kinematics During Running Using Three Inertial Sensors

Abstract

Analysis of running mechanics has traditionally been limited to a gait laboratory using either force plates or an instrumented treadmill in combination with a full-body optical motion capture system. With the introduction of inertial motion capture systems, it becomes possible to measure kinematics in any environment. However, kinetic information could not be provided with such technology. Furthermore, numerous body-worn sensors are required for a full-body motion analysis. The aim of this study is to examine the validity of a method to estimate sagittal knee joint angles and vertical ground reaction forces during running using an ambulatory minimal body-worn sensor setup. Two concatenated artificial neural networks were trained (using data from eight healthy subjects) to estimate the kinematics and kinetics of the runners. The first artificial neural network maps the information (orientation and acceleration) of three inertial sensors (placed at the lower legs and pelvis) to lower-body joint angles. The estimated joint angles in combination with measured vertical accelerations are input to a second artificial neural network that estimates vertical ground reaction forces. To validate our approach, estimated joint angles were compared to both inertial and optical references, while kinetic output was compared to measured vertical ground reaction forces from an instrumented treadmill. Performance was evaluated using two scenarios: training and evaluating on a single subject and training on multiple subjects and evaluating on a different subject. The estimated kinematics and kinetics of most subjects show excellent agreement (ρ>0.99) with the reference, for single subject training. Knee flexion/extension angles are estimated with a mean RMSE <5°. Ground reaction forces are estimated with a mean RMSE < 0.27 BW. Additionaly, peak vertical ground reaction force, loading rate and maximal knee flexion during stance were compared, however, no significant differences were found. With multiple subject training the accuracy of estimating discrete and continuous outcomes decreases, however, good agreement (ρ > 0.9) is still achieved for seven of the eight different evaluated subjects. The performance of multiple subject learning depends on the diversity in the training dataset, as differences in accuracy were found for the different evaluated subjects.

Keywords: artificial neural networks; inertial motion capture; kinetics; machine learning; reduced sensor set; running.

Figure 1

The measurement setup, (A) shows a front and back view of the sensor and retroreflective marker placement (B) shows the measurement setup (only 2 cameras are visible in this angle). Subjects wore a Lycra suit to hold the IMUs in place, which was customized with holes to accommodate the placement of retroreflective markers on the subject's skin. In this manner it was possible to measure kinematics simultaneously using both an inertial and optical motion capture system. The retroreflective markers were placed according to the Plug-in Gait protocol. To ensure retroreflective marker placement during the whole measurements, tapes were placed around these markers. Note that written informed consent was provided for use of these images.

Figure 2

The IMU in the top left represents the sensors strapped to the lower legs and pelvis. Information from these sensors is used by two concatenated Artificial Neural Networks (ANNs) to estimate kinematics and kinetics. ANN₁ maps the relative orientations of the lower legs (with respect to the pelvis) to lower body joint angles (hip, knee and ankle). ANN₂ is trained to map the estimated kinematics in combination with the vertical (after transformation to the global frame) sensor accelerations to the reference ground reaction forces.

Figure 3

Mean (and standard deviation band) of the flexion/extension knee joint angle (in degrees) estimates are presented (normalized to the stride cycle) compared to their respective references (IMU and Plug-In Gait output). These estimates were obtained from training (using running data at 10 and 14 km/h) and evaluating (using running data at 12 km/h) on a single subject, similar results were obtained for the other subjects. The top row shows the angles of the left side and the bottom row presents the right side. At the top of each graph Pearson's correlation coefficient, root mean square error (RMSE) and the standard deviation (between the brackets) are specified, which were calculated for the estimate compared to its respective reference kinematics.

Figure 4

The left side shows the correlation plot of the discrete outcome measures: maximal knee flexion angle during stance (A), peak vGRF (B), and loading rate (C). The right side shows the corresponding difference plots of those three discrete outcome measures. Approximately 4,000 data points are shown, where different subjects are represented by the various colors.

Figure 5

Mean (and standard deviation band) of the estimated ground reaction forces (in BW) are presented (normalized to the stance phase) compared to their respective references (IMU and Plug-In Gait joint angle output). These estimates were obtained from training and evaluating on a single subject, similar results were obtained for the other subjects. The top row shows the forces of the left contacts and the bottom row presents the right contacts. At the top of each graph Pearson's correlation coefficient, root mean square error (RMSE) and the standard deviation (between the brackets) are specified, which were calculated for the estimate compared to its respective reference kinematics.

Figure 6

Accuracy of the estimated vertical ground reaction force (vGRF) and knee flexion/extension (F/E) angle for different evaluated speeds, hence the other speeds are part of the training dataset, using single subject training and evaluation, as described in section 2.4. The artificial neural networks were trained with and evaluated relative to a full-body inertial kinematic measurement (Table 1, training scheme 1). The results for a representative subject are shown in this graph. The Root Mean Squared Error (RMSE) is calculated over all stride/stance phases and averaged over approximately 200 strides for each different evaluated speed (10, 12, and 14 km/h).

Figure 7

Mean (and standard deviation band) of the flexion/extension knee joint angle (in degrees) estimates are presented (normalized to the stride cycle) compared to their respective references (IMU and Plug-In Gait joint angle output). These estimates were obtained from training on multiple subjects and evaluating on a different subject, and were comparable to the other evaluated subjects. The top row shows the angles of the left side and the bottom row presents the right side. At the top of each graph Pearson's correlation coefficient, root mean square error (RMSE) and the standard deviation (between the brackets) are specified, which were calculated for the estimate and its respective reference kinematics.

Figure 8

Mean (and standard deviation band) of the estimated vertical ground reaction forces (in BW) are presented (normalized to the stance phase) compared to the measured reference. These estimates were obtained from training on multiple subjects and evaluating on a different subject, and were comparable to the other evaluated subjects. The top row shows the forces of the left contacts and the bottom row presents the right contacts. At the top of each graph Pearson's correlation coefficient, root mean square error (RMSE) and the standard deviation (between the brackets) are specified, which were calculated for the estimate and its respective reference kinematics.