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Predictive Behavior of a Computational Foot/Ankle Model through Artificial Neural Networks

View Article: PubMed Central - PubMed

ABSTRACT

Computational models are useful tools to study the biomechanics of human joints. Their predictive performance is heavily dependent on bony anatomy and soft tissue properties. Imaging data provides anatomical requirements while approximate tissue properties are implemented from literature data, when available. We sought to improve the predictive capability of a computational foot/ankle model by optimizing its ligament stiffness inputs using feedforward and radial basis function neural networks. While the former demonstrated better performance than the latter per mean square error, both networks provided reasonable stiffness predictions for implementation into the computational model.

No MeSH data available.


Training process, feedforward network. The flowchart depicts the nested  for loop structure of feedforward network training, which ultimately chooses the optimal network of those tested based upon minimum mean square error (MSE). Along with this minimum error, the number of hidden neurons and seed value corresponding to the minimum error is output.
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fig2: Training process, feedforward network. The flowchart depicts the nested  for loop structure of feedforward network training, which ultimately chooses the optimal network of those tested based upon minimum mean square error (MSE). Along with this minimum error, the number of hidden neurons and seed value corresponding to the minimum error is output.

Mentions: Because the task of predicting ligament stiffness is considered a curve-fitting problem, both feedforward and radial basis function networks were explored in the current work. Using MATLAB R2015a (The MathWorks, Inc., Natick, MA), multiple FFNs with a single hidden layer, two inputs (i.e., kinematic angles), and fourteen outputs (i.e., ligament stiffness elements) were created, each with varying hidden layer sizes and weight initializations. Hidden and output layer neurons included tan-sigmoid (steepness parameter of 1) and linear transfer functions, respectively. Beginning with a single hidden neuron, the size of the hidden layer was incrementally increased by one to a maximum of ten hidden neurons in order to determine the ideal network size (Figure 2). Determination of the optimal number of hidden neurons and the seed value of the random number generator (rng), the latter of which guaranteed reproducibility of results and effectively established optimal weights for the FFN, was accomplished using a series of nested “for” loops. Furthermore, 10-fold cross-validation was implemented to facilitate network selection. Generally, cross-validation is a methodology in which the known dataset is first divided into a given number of folds (in this case 10). A single fold is left out as test data, while the remaining folds of data are pooled together to train the network. Following training, the network is tested with the previously left out fold and the ANN's performance is assessed. Then, the data fold is placed back into the training subset while a second fold is left out as test data. This process is repeated until each of the folds is left out once as test data; finally, the overall performance of the network is determined by averaging all folds' test performances.


Predictive Behavior of a Computational Foot/Ankle Model through Artificial Neural Networks
Training process, feedforward network. The flowchart depicts the nested  for loop structure of feedforward network training, which ultimately chooses the optimal network of those tested based upon minimum mean square error (MSE). Along with this minimum error, the number of hidden neurons and seed value corresponding to the minimum error is output.
© Copyright Policy
Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC5304311&req=5

fig2: Training process, feedforward network. The flowchart depicts the nested  for loop structure of feedforward network training, which ultimately chooses the optimal network of those tested based upon minimum mean square error (MSE). Along with this minimum error, the number of hidden neurons and seed value corresponding to the minimum error is output.
Mentions: Because the task of predicting ligament stiffness is considered a curve-fitting problem, both feedforward and radial basis function networks were explored in the current work. Using MATLAB R2015a (The MathWorks, Inc., Natick, MA), multiple FFNs with a single hidden layer, two inputs (i.e., kinematic angles), and fourteen outputs (i.e., ligament stiffness elements) were created, each with varying hidden layer sizes and weight initializations. Hidden and output layer neurons included tan-sigmoid (steepness parameter of 1) and linear transfer functions, respectively. Beginning with a single hidden neuron, the size of the hidden layer was incrementally increased by one to a maximum of ten hidden neurons in order to determine the ideal network size (Figure 2). Determination of the optimal number of hidden neurons and the seed value of the random number generator (rng), the latter of which guaranteed reproducibility of results and effectively established optimal weights for the FFN, was accomplished using a series of nested “for” loops. Furthermore, 10-fold cross-validation was implemented to facilitate network selection. Generally, cross-validation is a methodology in which the known dataset is first divided into a given number of folds (in this case 10). A single fold is left out as test data, while the remaining folds of data are pooled together to train the network. Following training, the network is tested with the previously left out fold and the ANN's performance is assessed. Then, the data fold is placed back into the training subset while a second fold is left out as test data. This process is repeated until each of the folds is left out once as test data; finally, the overall performance of the network is determined by averaging all folds' test performances.

View Article: PubMed Central - PubMed

ABSTRACT

Computational models are useful tools to study the biomechanics of human joints. Their predictive performance is heavily dependent on bony anatomy and soft tissue properties. Imaging data provides anatomical requirements while approximate tissue properties are implemented from literature data, when available. We sought to improve the predictive capability of a computational foot/ankle model by optimizing its ligament stiffness inputs using feedforward and radial basis function neural networks. While the former demonstrated better performance than the latter per mean square error, both networks provided reasonable stiffness predictions for implementation into the computational model.

No MeSH data available.