Joint Torque Prediction via Hybrid Neuromusculoskeletal Modelling during Gait Using Statistical Ground Reaction Estimates: An Exploratory Study

Abstract

Joint torques of lower extremity are important clinical indicators of gait capability. This parameter can be quantified via hybrid neuromusculoskeletal modelling that combines electromyography-driven modelling and static optimisation. The simulations rely on kinematics and external force measurements, for example, ground reaction forces (GRF) and the corresponding centres of pressure (COP), which are conventionally acquired using force plates. This bulky equipment, however, hinders gait analysis in real-world environments. While this portability issue could potentially be solved by estimating the parameters through machine learning, the effect of the estimation errors on joint torque prediction with biomechanical models remains to be investigated. This study first estimated GRF and COP through feedforward artificial neural networks, and then leveraged them to predict lower-limb sagittal joint torques via (i) inverse dynamics and (ii) hybrid modelling. The approach was evaluated on five healthy subjects, individually. The predicted torques were validated with the measured torques, showing that hip was the most sensitive whereas ankle was the most resistive to the GRF/COP estimates for both models, with average metrics values being 0.70 < R2 < 0.97 and 0.069 < RMSE < 0.15 (Nm/kg). This study demonstrated the feasibility of torque prediction based on personalised (neuro)musculoskeletal modelling using statistical ground reaction estimates, thus providing insights into potential real-world mobile joint torque quantification.

Keywords: centre of pressure; gait; ground reaction force; inverse dynamics; joint torque; machine learning; neuromusculoskeletal modelling.

Figure 1

The schematic flowchart of the entire investigating paradigm for each subject. Prior to both GRF/COP estimation and torque computation, statistical and hybrid biomechanical models are calibrated using measured data from three train trials. After statistical model calibration, a set of optimal features as inputs to the ANN model are selected by NCA from the measured data of the test trial for the GRF/COP estimation. After the hybrid model calibration, GRF/COP estimates are fed into the biomechanical models (musculoskeletal and hybrid models) for joint torque prediction.

Figure 2

Measured (blue) and estimated (red) GRF (top row) and COP (bottom row) averaged across all the trials and subjects. GRF was normalised with respect to BW and COP illustrated in mm. Shaded area represents one standard deviation of the subject means.

Figure 3

Distribution of $$R^2$$ (top row) and RMSE (bottom row) for GRF (left column) and COP (right column) for all the trials. RMSE for GRF and COP in % BW and in mm, respectively.

Figure 4

Measured (blue) and estimated (red) joint torques via musculoskeletal modelling for hip (left column), knee (middle column) and ankle (right column) for three conditions: estimated both GRF and COP (EGEC-M) (top row), estimated GRF only (EGMC-M) (middle row) and estimated COP only (MGEC-M) (bottom row) averaged across all the trials and subjects. Torques were normalised with respect to body mass. Data were plotted in percent of stance phase from heel strike to toe-off. Shaded area represents one standard deviation of the subject means.

Figure 5

Measured (blue) and estimated (red) joint torques via neuromusculoskeletal modelling for hip (left column), knee (middle column) and ankle (right column) for three conditions: estimated both GRF and COP (EGEC-N) (top row), estimated GRF only (EGMC-N) (middle row) and estimated COP only (MGEC-N) (bottom row) averaged across all the trials and subjects. Torques were normalised with respect to body mass. Data were plotted in percent of stance phase from heel strike to toe-off. Shaded area represents one standard deviation of the subject means.

Figure 6

$$R^2$$ (left column) and RMSE (right column) for hip (top row), knee (middle row) and ankle (bottom row) for each of the following conditions: (i) estimated GRF and COP with muscu-loskeletal model (EGEC-M), (ii) estimated GRF and COP with neuromusculoskeletal model (EGEC-N), (iii) estimated GRF and measured COP with musculoskeletal model (EGMC-M), (iv) estimated GRF and measured COP with neuromusculoskeletal model (EGMC-N), (v) measured GRF and estimated COP with musculoskeletal model (MGEC-M), (vi) measured GRF and estimated COP with neuromusculoskeletal model (MGEC-N). Asterisk indicates statistically significant difference (p < 0.05).