Multiscale Modeling of Tumor Angiogenesis and Resistance Evolution: A Hybrid PDE–ABM Framework for Cancer Prediction and Therapy Planning

Tumor drug resistance involves intrinsic cellular mechanisms, microenvironmental regulation, and epigenetic alterations. Hypoxia, drug distribution, and microvascular heterogeneity critically mediate resistance within the tumor microenvironment (TME). We develop a hybrid discrete–continuous (HDC) model coupling agent-based tumor and endothelial cell dynamics with partial differential equations (PDEs) governing oxygen, cytotoxic drug, and tumor angiogenic factor (TAF) evolution. This framework integrates hypoxia-driven angiogenesis and resistance dynamics to address how microenvironmental feedback shapes resistant phenotype emergence and spatial distribution during chemotherapy. Our system models tumor cells stochastically proliferating, migrating, and mutating in response to local oxygen and drug concentrations. Endothelial tip cells remodel vasculature via TAF-gradient-driven chemotaxis. Simulations indicate that hypoxia-induced angiogenesis causes uneven drug penetration and creates niches that support resistant subclones. These findings highlight a complex interplay between vascularization and resistance evolution. This work bridges reaction-diffusion-chemotaxis PDEs and agent-based modeling to capture tumor-vascular interactions and microenvironmentally mediated resistance, providing spatial predictions for intervention design.