A neural network to surrogate computational bone remodelling in the calcaneus

Abstract

This study proposes a data-driven approach using surrogate models based on Multi-Layer Perceptrons to predict bone remodelling outcomes in the calcaneus, both with and without fractures. The objective is to develop and train a neural network that accurately captures the biomechanical factors influencing the problem and predicts the resulting bone density distribution in the calcaneus. Given the complexity of bone healing processes, a comprehensive dataset was collected to train and validate the models under two distinct scenarios: an intact calcaneus and a fractured calcaneus treated with a surgical screw.

Key parameters of the surrogate model, namely, the number of hidden layers, hidden layer size, and activation function, were optimized to enhance model performance. Additionally, training parameters such as learning rate and batch size were tuned. The hyperbolic tangent activation function was found to yield a lower mean squared error compared to the rectified linear units. Larger batch sizes and learning rates were found to improve model performance. The neural network designed to predict bone density in the intact model outperformed the one used for the fractured calcaneus with a screw, largely due to the increased variability in the fractured data. When the fracture did not significantly alter the trabecular distribution, prediction accuracy improved.

Finally, the structural response of the models was evaluated, and it was observed that the trabecular arrangement inferred by the neural network tended to produce less stiff responses compared to those from the finite element method, likely due to the smoother density field predicted by the network.