Estimating 3D ground reaction forces in running using three inertial measurement units

Abstract

To understand the mechanisms causing running injuries, it is crucial to get insights into biomechanical loading in the runners' environment. Ground reaction forces (GRFs) describe the external forces on the body during running, however, measuring these forces is usually only possible in a gait laboratory. Previous studies show that it is possible to use inertial measurement units (IMUs) to estimate vertical forces, however, forces in anterior-posterior direction play an important role in the push-off. Furthermore, to perform an inverse dynamics approach, for modelling tissue specific loads, 3D GRFs are needed as input. Therefore, the goal of this work was to estimate 3D GRFs using three inertial measurement units. Twelve rear foot strike runners did nine trials at three different velocities (10, 12 and 14 km/h) and three stride frequencies (preferred and preferred ± 10%) on an instrumented treadmill. Then, data from IMUs placed on the pelvis and lower legs were used as input for artificial neural networks (ANNs) to estimate 3D GRFs. Additionally, estimated vertical GRF from a physical model was used as input to create a hybrid machine learning model. Using different splits in validation and training data, different ANNs were fitted and assembled into an ensemble model. Leave-one-subject-out cross-validation was used to validate the models. Performance of the machine learning, hybrid machine learning and a physical model were compared. The estimated vs. measured GRF for the hybrid model had a RMSE normalized over the full range of values of 10.8, 7.8 and 6.8% and a Pearson correlation coefficient of 0.58, 0.91, 0.97 for the mediolateral direction, posterior-anterior and vertical direction respectively. Performance for the three compared models was similar. The ensemble models showed higher model accuracy compared to the ensemble-members. This study is the first to estimate 3D GRF during continuous running from IMUs and shows that it is possible to estimate GRF in posterior-anterior and vertical direction, making it possible to estimate these forces in the outdoor setting. This step towards quantification of biomechanical load in the runners' environment is helpful to gain a better understanding of the development of running injuries.

Keywords: ensemble model; estimation; ground reaction force; machine learning; running.

Figure 1

Overview of the different models. A ensemble artificial neural network (ensANN) was used to estimate 3-dimensinal ground reaction force (3D eGRF directly). Also, a hybrid model was created by adding the physical estimate as additional input for the ensANN. The estimates of the models were then compared with measured GRF (mGRF) to evaluate the performance.

Figure 2

The leave-one-subject-out cross-validation process to create an ensemble model with 7 random validation-test splits per subject, with four subjects for validation and 7 for training. Every combination is used as an ensemble-member and combined in the ensemble model. After 7 models were trained for one subject, the test subject was changed and repeated until seven different models were fitted for every test to have a leave-one-subject-out cross validation.

Figure 3

Relative root mean squared error (rRMSE) for each axis per model per subject. The exact data can be seen in Supplementary material Table S1. The error bars indicate the standard deviation.

Figure 4

Pearon's r for each axis per model per subject. The exact data can be seen in Supplementary material Table S2. The error bars indicate the standard deviation.

Figure 5

The estimated ground reaction curves for the different axes during stance for all models at 12 km/h preferred stride frequency. With the direct model in blue, hybrid in green, physical in red and reference in orange. Stance phase is replaced by a fixed gap in the data. Note that the y-axis is not the same scale for the different sub-plots.

Figure 6

The estimated ground reaction curves for the different axes during stance from the direct model at 12 km/h preferred stride frequency. The shading indicates the average over the ensemble-members plus/minus one standard deviation. Also, the maximum and minimum values are plotted. Stance phase is replaced by a fixed gap in the data. Note that the y-axis is not the same scale for the different sub-plots.

Figure 7

Comparison between performance of the hybrid models and ensemble models with relative root mean squared error (rRMSE) as performance metric. Performance of the single models is shown as the boxplot, the box indicates the lower to upper quartile values of the data, with an orange line at the median. The whiskers show the range of the values, with the black circles as outliers. The ensemble models are indicated with a blue circle. Models were fitted using a leave-one-subject-out cross-validation structure. The average, range and ensemble values can be found in Supplementary material Table S3.