Patient-specific Prediction of Glioblastoma Growth via Reduced Order Modeling and Neural Networks
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Glioblastoma (GBL) is among the most aggressive brain tumors in adults, characterized by patient-specific invasion patterns driven by the underlying brain microstructure. In this work, we present a proof-of-concept for a mechanistic learning framework for patient-specific prediction of GBL growth. The approach integrates a diffuse-interface mathematical model to describe the tumor evolution with machine learning techniques to enable real-time prediction and parameter identification from longitudinal neuroimaging data. A reduced-order modeling strategy, based on proper orthogonal decomposition (POD), is trained on synthetic data generated from patient-specific brain anatomies reconstructed from magnetic resonance imaging (MRI) and diffusion tensor imaging (DTI). A neural network surrogate learns the inverse mapping from tumor evolution to model parameters, achieving a computational speed-up of 99\% while maintaining an accuracy of 96\% in forecasting tumor volume. To ensure model robustness and interpretability, we perform both global and local sensitivity analyses to identify the dominant parameters governing tumor dynamics and assess the stability of the inverse problem. This hybrid methodology bridges mechanistic modeling and data-driven learning, addressing both the direct and inverse problems of GBL evolution and offering a practical solution for time-sensitive clinical scenarios. The current contribution focuses on methodological innovation, providing a rigorous computational foundation for the future clinical deployment of patient-specific digital twins in neuro-oncology. In conclusion, our approach represents a significant step toward the development of interpretable, scalable, and efficient computational tools for precision medicine in the management of Glioblastoma.