Mathematical and computational modeling of head and neck cancer for personalized therapy

Abstract We present a coupled mathematical model for tumor progression and treatment-induced tissue remodeling in head and neck cancer. The framework links a reaction–diffusion equation for tumor cell density with finite-strain growth mechanics through a multiplicative decomposition of the deformation gradient. Radiation therapy enters the model as both a cytotoxic term in the kinetic equation and a remodeling stimulus altering the growth parameter. We develop the model systematically, provide nondimensionalisation, offer formal analysis including linear stability, and propose a staggered finite element scheme for numerical simulation. Numerical experiments on stylized head–neck geometries demonstrate qualitative behaviour consistent with clinical expectations and illustrate candidate model-derived indicators that may warrant future investigation as imaging biomarkers following patient-specific validation.