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

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.

Figure 1

General structure for feedforward (FFN) and radial basis function (RBFN) networks. Sigmoidal and Gaussian transfer functions appear in the hidden layers' neurons for the FFN and RBFN, respectively. (x = input; w_in = nth weight in layer i; y = output; h_m = mth hidden neuron) (adapted from [1, 13]).

Figure 2

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.

Figure 3

Training process, radial basis function network. Similar to the feedforward network, the radial basis function network also includes a nested  for loop structure. Here, an optimal network is chosen based on minimum mean square error of each k, σ, and seed value combination.