Super-fast and accurate nonlinear foot deformation Prediction using graph neural networks.

Recently, there has been a significant increase in the number of foot diseases, highlighting the importance of non-surgical treatments. Customized insoles, tailored to an individual's foot morphology, have emerged as a promising solution. However, the traditional design process of the customized insole is both slow and expensive due to the high computational complexity of finite element analysis (FEA) required to predict deformations of the foot. This study explores the applicability of a graph neural network (GNN) based on the MeshGraphNet framework to predict the 3-D shape of the foot under load and test the performance of GNN depending on the number of datasets. A total of 186 3-D undeformed foot CAD geometries are obtained from a series of 2-D foot images with deformations predicted through FEA. This FEA data is then used to train the GNN model, which aims to predict foot displacement with high accuracy and computation speed. After optimization of the weights of the GNN, the model remarkably outperformed FEA simulations in speed, being approximately 97.52 times faster, while maintaining high accuracy, with R values above 95% in predicting foot displacement. This breakthrough suggests that GNN models can greatly improve the efficiency and reduce the cost of manufacturing customized insoles, providing a significant advancement in non-surgical treatment options for foot conditions.