| Abstract | We present a hybrid continuum-discrete mathematical multiscale modeling framework for vascular solid tumor growth. A continuum model based on mixture theory is used to describe the evolution of volume fractions of multiple tumor cell clones, extracellular matrix (ECM), host cells, nutrients and water. The continuum model is coupled to an agent-based, lattice-free model that describes the evolution of discrete tumor cell clones. The models couple through mass and momentum exchange. In addition, a model for tumor-induced angiogenesis and vascular growth is incorporated. Simulations are presented that demonstrate the effectiveness of the hybrid approach in describing hypoxia-induced transitions from collective to individual based motion and vice-versa when cells are in oxygen-rich environments near the flowing, dynamic neovasculature network. |
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