Biomechanical modeling of glioblastoma progression: a comprehensive review from classic mathematical frameworks to...

Glioblastoma multiforme (GBM) remains a formidable challenge due to its aggressive proliferation, heterogeneity, and invasiveness. This review synthesizes biomechanical models for GBM prediction, from classic proliferation-invasion (PI) frameworks-based on reaction-diffusion equations-to continuum biomechanical models that quantify tumor-induced stress and tissue interactions. We highlight multiphysics approaches integrating fluid dynamics, nutrient transport, and solid mechanics to simulate the tumor microenvironment, alongside numerical methods like FEM and meshless techniques. Treatment modeling, including radiotherapy and emerging therapies, is critically evaluated for optimizing clinical strategies. Challenges in validation and parameterization are addressed, with a forward-looking emphasis on hybrid physics-informed and machine learning models to enable personalized prediction. By bridging biophysics, computation, and clinical needs, this work aims to guide future research toward improved GBM therapeutics.