Smooth and accurate predictions of joint contact force time-series in gait using over parameterised deep neural networks

Abstract

Alterations in joint contact forces (JCFs) are thought to be important mechanisms for the onset and progression of many musculoskeletal and orthopaedic pain disorders. Computational approaches to JCFs assessment represent the only non-invasive means of estimating in-vivo forces; but this cannot be undertaken in free-living environments. Here, we used deep neural networks to train models to predict JCFs, using only joint angles as predictors. Our neural network models were generally able to predict JCFs with errors within published minimal detectable change values. The errors ranged from the lowest value of 0.03 bodyweight (BW) (ankle medial-lateral JCF in walking) to a maximum of 0.65BW (knee VT JCF in running). Interestingly, we also found that over parametrised neural networks by training on longer epochs (>100) resulted in better and smoother waveform predictions. Our methods for predicting JCFs using only joint kinematics hold a lot of promise in allowing clinicians and coaches to continuously monitor tissue loading in free-living environments.

Keywords: deep learning; locomotion; machine learning; musculoskeletal modelling; running biomechanics; walking biomechanics.

FIGURE 1

(A) General workflow of the deep learning modelling approach, with the three-dimensional joint kinematics used as the predictors, and joint contact forces as outcomes; (B) Data organisation of the multivariate time-series predictors and univariate outcomes; and (C) High-level overview of the XCM model architecture.

FIGURE 2

Observed (black) and predictedthree-dimensional joint contact forces of (A) ${\mathit{M}\mathit{o}\mathit{d}\mathit{e}\mathit{l}}_{\mathit{T}\mathit{e}\mathit{s}\mathit{t}=\mathit{w}\mathit{a}\mathit{l}\mathit{k}}^{\mathit{T}\mathit{r}\mathit{a}\mathit{i}\mathit{n}=\mathit{w}\mathit{a}\mathit{l}\mathit{k}}$ across the walking stride and (B) ${\mathit{M}\mathit{o}\mathit{d}\mathit{e}\mathit{l}}_{\mathit{T}\mathit{e}\mathit{s}\mathit{t}=\mathbf{r}\mathbf{u}\mathbf{n}}^{\mathit{T}\mathit{r}\mathit{a}\mathit{i}\mathit{n}=\mathbf{r}\mathbf{u}\mathbf{n}}$ across the running stride. The x-axis of (A) reflects 100 data points reflecting a walking stride, and (B) 50 data points reflecting a running stance. Waveforms represent the average across all test samples.

FIGURE 3

Observed (black) and predicted three-dimensional joint contact forces of (A) ${\mathit{M}\mathit{o}\mathit{d}\mathit{e}\mathit{l}}_{\mathit{T}\mathit{e}\mathit{s}\mathit{t}=\mathit{w}\mathit{a}\mathit{l}\mathit{k}}^{\mathit{T}\mathit{r}\mathit{a}\mathit{i}\mathit{n}=\mathit{r}\mathit{u}\mathit{n}}$ across the walking stride and (B) ${\mathit{M}\mathit{o}\mathit{d}\mathit{e}\mathit{l}}_{\mathit{T}\mathit{e}\mathit{s}\mathit{t}=\mathbf{r}\mathbf{u}\mathbf{n}}^{\mathit{T}\mathit{r}\mathit{a}\mathit{i}\mathit{n}=\mathbf{w}\mathbf{a}\mathbf{l}\mathbf{k}}$ across the running stride. The x-axis of (A) reflects 100 data points reflecting a walking stride, and (B) 50 data points reflecting a running stance. Waveforms represent the average across all test samples.

FIGURE 4

Observed (black) and predicted three-dimensional joint contact forces of (A) ${\mathit{M}\mathit{o}\mathit{d}\mathit{e}\mathit{l}}_{\mathit{T}\mathit{e}\mathit{s}\mathit{t}=\mathit{w}\mathit{a}\mathit{l}\mathit{k}}^{\mathit{T}\mathit{r}\mathit{a}\mathit{i}\mathit{n}=\mathit{c}\mathit{o}\mathit{m}\mathit{b}}$ across the walking stride and (B) ${\mathit{M}\mathit{o}\mathit{d}\mathit{e}\mathit{l}}_{\mathit{T}\mathit{e}\mathit{s}\mathit{t}=\mathbf{r}\mathbf{u}\mathbf{n}}^{\mathit{T}\mathit{r}\mathit{a}\mathit{i}\mathit{n}=\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{b}}$ across the running stride. The x-axis of (A) reflects 100 data points reflecting a walking stride, and (B) 50 data points reflecting a running stance. Waveforms represent the average across all test samples.

FIGURE 5

Prediction performances of machine learning models involving different training epochs and gait types, using the models ${\mathit{M}\mathit{o}\mathit{d}\mathit{e}\mathit{l}}_{\mathit{T}\mathit{e}\mathit{s}\mathit{t}=\mathit{w}\mathit{a}\mathit{l}\mathit{k}}^{\mathit{T}\mathit{r}\mathit{a}\mathit{i}\mathit{n}=\mathit{w}\mathit{a}\mathit{l}\mathit{k}}$ for walking and ${\mathit{M}\mathit{o}\mathit{d}\mathit{e}\mathit{l}}_{\mathit{T}\mathit{e}\mathit{s}\mathit{t}=\mathbf{r}\mathbf{u}\mathbf{n}}^{\mathit{T}\mathit{r}\mathit{a}\mathit{i}\mathit{n}=\mathbf{r}\mathbf{u}\mathbf{n}}$ for running. (A) Root mean squared error, (B) relative root mean squared error, and (C) correlation.

FIGURE 6

Prediction performances of machine learning models involving different training epochs and gait types, using the models ${\mathit{M}\mathit{o}\mathit{d}\mathit{e}\mathit{l}}_{\mathit{T}\mathit{e}\mathit{s}\mathit{t}=\mathit{w}\mathit{a}\mathit{l}\mathit{k}}^{\mathit{T}\mathit{r}\mathit{a}\mathit{i}\mathit{n}=\mathit{r}\mathit{u}\mathit{n}}$ for walking and ${\mathit{M}\mathit{o}\mathit{d}\mathit{e}\mathit{l}}_{\mathit{T}\mathit{e}\mathit{s}\mathit{t}=\mathbf{r}\mathbf{u}\mathbf{n}}^{\mathit{T}\mathit{r}\mathit{a}\mathit{i}\mathit{n}=\mathbf{w}\mathbf{a}\mathbf{l}\mathbf{k}}$ for running. (A) Root mean squared error, (B) relative root mean squared error, and (C) correlation.

FIGURE 7

Prediction performances of machine learning models involving different training epochs and gait types, using the models ${\mathit{M}\mathit{o}\mathit{d}\mathit{e}\mathit{l}}_{\mathit{T}\mathit{e}\mathit{s}\mathit{t}=\mathit{w}\mathit{a}\mathit{l}\mathit{k}}^{\mathit{T}\mathit{r}\mathit{a}\mathit{i}\mathit{n}=\mathit{c}\mathit{o}\mathit{m}\mathit{b}}$ for walking and ${\mathit{M}\mathit{o}\mathit{d}\mathit{e}\mathit{l}}_{\mathit{T}\mathit{e}\mathit{s}\mathit{t}=\mathbf{r}\mathbf{u}\mathbf{n}}^{\mathit{T}\mathit{r}\mathit{a}\mathit{i}\mathit{n}=\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{b}}$ for running. (A) Root mean squared error, (B) relative root mean squared error, and (C) correlation.