Predicting facial deformation during respiratory mask fitting with semi-supervised graph neural networks

Respiratory masks are necessary to protect against airborne contaminants in both medical and industrial environments. However, prolonged use remains uncomfortable and frequently causes pressure sores. This problem usually related to poor fit not only compromises user comfort but also reduces protection effectiveness and compliance with recommendations. The objective is to predict facial deformation and pressure distribution when wearing a mask, based on a limited set of annotated biomechanical data, in order to provide an optimum fit. We designed a semi-supervised graph neural network that represents facial geometries as graph structures. The proposed framework leverages 45 labeled and 120 unlabeled facial datasets employing a variational graph autoencoder constrained by Hertzian contact theory and incorporates an XGBoost-based module for deformation zone classification. Our approach achieves 0.164 mm deformation RMSE (R2=0.9896) and 0.0492 kPa pressure RMSE (R2=0.9517), representing 34.27% improvement over Random Forest, 20.62% improvement over PointNet++ baselines and 10.01% improvement over TPSNET in terms of<i>R</i>². Five-fold cross-validation confirms robust generalization with minimal overfitting and sub-2-second inference time. This study introduces a real-time personalized respiratory mask model, achieving precise prediction of facial deformation and contact pressure. The approach ensures generalization from limited labeled data, thereby improving comfort, safety, and compliance in medical and industrial applications.