Speaker
Description
Predicting tumor dynamics in biological systems under physiologically relevant conditions remains a challenging problem for mathematical and computational modeling. Among the various approaches proposed to describe tumor dynamics, phase-field (diffuse-interface) formulations provide an attractive continuum modeling framework to capture the spatiotemporal evolution of interfaces separating phases and integrate multiple physical processes and interacting species into a unified description of complex multiphysics phenomena. Within this framework, this work presents a Cahn–Hilliard (CH) equation-based tumor growth model that governs tumor–healthy tissue interactions under the influence of nutrient concentration. The formulation involves a fourth-order differential operator that imposes higher continuity requirements on approximation spaces for a well-defined primal variational formulation. We use isogeometric analysis (IGA), which inherently satisfies this requirement through spline-based basis functions within a unified geometric and analysis framework. Furthermore, a locally adaptive IGA scheme with truncated hierarchical B-splines is used to reduce computational cost while maintaining accuracy, since phase-field models often demand fine meshes to resolve steep gradients at phase interfaces. The model is first validated on standard benchmark cases and subsequently applied to a patient-specific, organ-scale breast model reconstructed from magnetic resonance imaging (MRI) data. The results capture the characteristic tumor morphologies, ranging from a spheroidal pattern to fingered growth. A series of numerical experiments also shows the diversity of tumor dynamics produced by different model parameter choices. Taken together, the findings demonstrate the predictive potential of the CH phase-field tumor growth model integrated with a locally adaptive IGA framework.