Cancer is a complex, multi-scale disease marked by unchecked cellular growth and proliferation. As a tumor grows, it is known to lose its capacity to maintain a compact structure. This stage of development, known as invasion, is marked by the disaggregation and dispersion of peripheral cells, and the formation of finger-like margins. This thesis provides an overview of three multi-scale models of tumor growth and invasion. The hybrid discrete-continuum (HDC) model couples a cellular automaton approach, which is used to direct the behavior and interactions of individual cells, with a system of reaction-diffusion-chemotaxis equations that describe the micro-environment. The evolutionary hybrid cellular automaton (EHCA) model maintains the core of the HDC approach, but employs an artificial response network to describe cellular dynamics. In contrast to these two, the immersed boundary (IBCell) model describes cells as fully deformable, viscoelastic entities that interact with each other using membrane bound receptors. As part of this thesis, the HDC model has been modified to examine the role of the ECM as a barrier to cellular expansion. The results of these simulations will be presented and discussed in the context of tumor progression.

Cancer is a complex, multi-scale disease marked by unchecked cellular growth and proliferation. As a tumor grows, it is known to lose its capacity to maintain a compact structure. This stage of development, known as invasion, is marked by the disaggregation and dispersion of peripheral cells, and the formation of finger-like margins. This thesis provides an overview of three multi-scale models of tumor growth and invasion. The hybrid discrete-continuum (HDC) model couples a cellular automaton approach, which is used to direct the behavior and interactions of individual cells, with a system of reaction-diffusion-chemotaxis equations that describe the micro-environment. The evolutionary hybrid cellular automaton (EHCA) model maintains the core of the HDC approach, but employs an artificial response network to describe cellular dynamics. In contrast to these two, the immersed boundary (IBCell) model describes cells as fully deformable, viscoelastic entities that interact with each other using membrane bound receptors. As part of this thesis, the HDC model has been modified to examine the role of the ECM as a barrier to cellular expansion. The results of these simulations will be presented and discussed in the context of tumor progression.