Estimating Running Ground Reaction Forces from Plantar Pressure during Graded Running
<p>Center−of−Mass (COM) power components for running at 3.0 m/s on level ground. The three different components of the COM power were computed respectively from the anterior/posterior (A/P), medial/lateral (M/L), and vertical components of the ground reaction force. The sagittal plane components (i.e., vertical and A/P) have the greatest contribution to the COM power. Presented data are from one representative subject.</p> "> Figure 2
<p>Vertical and anterior−posterior (A/P) ground reaction force prediction using plantar pressure. The plantar pressure was segmented into five different regions (indicated by the different colors). Example plantar pressure curves are shown in the same color to the right of the respective region. Additional inputs to the machine learning algorithms include running speed, running slope, and subject mass. Model performance was then evaluated using statistical parametric mapping, time continuous error (study mean ± standard deviation), root mean square error (not shown here), and correlation coefficients (not shown here).</p> "> Figure 3
<p>Linear and recurrent neural network model architecture for computing vertical (vert) and anterior–posterior (A/P) ground reaction forces (GRF). The linear models predicted vertical and A/P GRFs from five different pressure regions (PR<sub>1–5</sub>) divided by subject−specific body mass (BM). The coefficients (A<sub>1–5</sub>, B<sub>1–5</sub>) were computed using a least−square regression. The recurrent neural network predicted GRFs based on eight different inputs: PR<sub>1–5</sub>, body mass, speed and slope. The bidirectional long short−term memory (LSTM) layers utilized information from the current sample (x<sub>t</sub>) and from the future (x<sub>t+1</sub>) and previous samples (x<sub>t-1</sub>). For example, the GRF at 1% of the step is informed from the input at 0%, 1%, and 2% of the step. Both models were cross−validated using a leave−one subject out approach.</p> "> Figure 4
<p>Average (N = 18) summary metrics for vertical and anterior/posterior (A/P) ground reaction force (GRF) prediction. Downhill and uphill running was performed at 6° (10.5% grade). Error bars represent standard deviations.</p> "> Figure 5
<p>Average (N = 18) ground reaction forces (GRFs), model predictions, and model errors for running at 3.0 m/s. Top row shows average vertical GRF from the force platform (FP) along with average linear model (LM) and recurrent neural network (RNN) predictions. Areas shaded red are where there were significant differences between the FP and LM (<span class="html-italic">p</span> < 0.05). There were no significant differences between the FP and the RNN (<span class="html-italic">p</span> > 0.05). The second row shows the mean absolute percent error plus/minus one standard deviation for each model in the vertical direction. The third row shows average anterior/posterior (A/P) GRF from the FP along with LM and RNN predictions. Areas shaded red are where there were significant differences between the FP and LM (<span class="html-italic">p</span> < 0.05). There were no significant differences between the FP and the RNN (<span class="html-italic">p</span> > 0.05). The last row shows the mean absolute percent error plus/minus one standard deviation for each model in the A/P direction. Downhill and uphill running was performed at 6° (10.5% grade).</p> "> Figure 6
<p>Subject−averaged (N = 18) ground reaction forces (GRFs), model predictions, and model errors for running at 3.0 m/s on level ground. The top row shows average vertical GRF from the force platform (FP) along with average recurrent neural network (RNN) predictions. Each column represents a different subject that either had the lowest, near average, and highest average errors in the RNN prediction of vertical GRF. Areas shaded green are where there were significant differences between the FP and RNN (<span class="html-italic">p</span> < 0.05). The second row shows the mean absolute percent error plus/minus one standard deviation for the RNN in the vertical direction. The third row shows average anterior/posterior (A/P) GRF from the FP and average RNN predictions. Each column represents a different subject that either had the lowest, near average, and highest average errors in the RNN prediction of A/P GRF. Areas shaded green are where there were significant differences between the FP and RNN (<span class="html-italic">p</span> < 0.05). The bottom row shows the mean absolute percent error plus/minus one standard deviation for the RNN in the A/P direction.</p> "> Figure 7
<p>Subject−averaged (N = 18) ground reaction forces (GRFs), model predictions, and model errors for running downhill and level ground at 3.4 m/s for a single subject. The left two columns represent a generic model that was trained on the other 17 subjects in the study. The right two columns represent a subject−specific model that is trained on 17 subjects plus ≈10% of the data from the subject illustrated. The top row shows the average vertical GRF from the force platform (FP) along with average recurrent neural network (RNN) predictions. Areas shaded green are where there were significant differences between the FP and RNN (<span class="html-italic">p</span> < 0.05). The second row shows the mean absolute percent error plus/minus one standard deviation for the RNNs in the vertical direction. The third row shows average anterior/posterior (A/P) GRF from the FP and average RNN predictions. Areas shaded green are where there were significant differences between the FP and RNN (<span class="html-italic">p</span> < 0.05). The bottom row shows the mean absolute percent error plus/minus one standard deviation for the RNNs in the A/P direction.</p> "> Figure A1
<p>Root mean squared errors (RMSE) of ground reaction force (GRF) prediction with increasing number of subjects included in training the models. Present data are means (solid line) of all subjects and conditions evaluated and standard deviations (clouds). The model errors for each subject were evaluated such that the values of 17 training subjects (the right−hand side of each plot) corresponds to the average leave−one−subject−out error across all conditions.</p> ">
Abstract
:1. Introduction
- The first running study to predict multiple ground reaction force components during running for different speeds and slopes
- We introduce a new combination of tools to understand the performance of time−continuous model predictions during gait
- GRF predictions with plantar pressure do not need a priori knowledge of the speed or slope
- Subject−specific training can enhance GRF predictions, such that these predictions could be confidently used outside of the laboratory
2. Materials and Methods
2.1. Participants and Protocol
2.2. Data Processing
2.3. Model Development: Linear Model
2.4. Model Development: Recurrent Neural Network
2.5. Validation
3. Results
3.1. Model Ability to Predict Average Ground Reaction Forces
3.2. Model Ability to Predict Step−Average Ground Reaction Forces
3.3. Effect of Speed and Slope
4. Discussion
Anecdotes from Model Building
- The five plantar pressure regions examined here were based on data exploration and preliminary linear model fitting. We explored as little as three regions and some explorations looked at regions that were unequal in size/length. The five regions used here worked relatively well. We did explore using all 99 pressure sensors as inputs to the recurrent neural network; however, it did not improve performance enough to justify the added complexity and reduced applicability to other pressure sensing modalities.
- The GRFs were aligned parallel/perpendicular to the gravity vector as preliminary exploration demonstrated that such an orientation enabled better linear model predictions in contrast to GRFs aligned parallel/perpendicular to the running surface.
- Including a binary predictor variable for left/right foot was explored; however, it did not affect model performance
- The recurrent neural network sequence input layer was responsible for normalizing the predictor variables. We found that ‘Z−Score’ normalization resulted in the best performance. During network development we also experimented with four other methods, which did not perform as well:
- ○
- ‘zerocenter’; Subtract the mean
- ○
- ‘Rescale−symmetric’; Rescale range to [−1 1]
- ○
- ‘Rescale−zero−one’; Rescale range to [0 1]
- ○
- ‘none’; Raw inputs
- We applied a dropout function to each of the bidirectional LSTM layers of the recurrent neural network that set randomly selected nodes to 0. This was done to prevent overfitting and the dropout probability was 30% and 20% for the first and second bidirectional LSTM layer, respectively. During development, we experimented with lower (up to 0%) and higher (up to 80%) dropout probabilities. Generally, higher probabilities resulted in worse performances, while lower dropout probabilities created better training results but worse testing results.
- For the first two fully connected layers of the recurrent neural network we applied the hyperbolic tangent as activation function, while the last fully connected layer was not exposed to an additional transfer function. We experimented with the rectified liner unit transfer function as an alternative but found no substantial differences within the network performances.
5. Conclusions
6. Patents
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
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Honert, E.C.; Hoitz, F.; Blades, S.; Nigg, S.R.; Nigg, B.M. Estimating Running Ground Reaction Forces from Plantar Pressure during Graded Running. Sensors 2022, 22, 3338. https://doi.org/10.3390/s22093338
Honert EC, Hoitz F, Blades S, Nigg SR, Nigg BM. Estimating Running Ground Reaction Forces from Plantar Pressure during Graded Running. Sensors. 2022; 22(9):3338. https://doi.org/10.3390/s22093338
Chicago/Turabian StyleHonert, Eric C., Fabian Hoitz, Sam Blades, Sandro R. Nigg, and Benno M. Nigg. 2022. "Estimating Running Ground Reaction Forces from Plantar Pressure during Graded Running" Sensors 22, no. 9: 3338. https://doi.org/10.3390/s22093338