Modeling Lymphoma Growth in an Evolving Lymph Node Using a Diffuse Domain Approach

Tumor growth often poses as a multiphase free-boundary problem as tumor cells aggregate into distinct subdomains due to differentiated cell-cell and cell-matrix adhesion. In ``Three-dimensional multispecies nonlinear tumor growth - I Model and numerical method'' [Wise et al., J. Theor. Biol. 253, pp. 524-543 (2008)], we have developed a multiphase Cahn-Hilliard model to study morphological patterns of tumor growth in a homogeneous open environment, and the results resembled in-vitro experiments. In living tissues, however, tumors are often confined in a closed environment of an organ, where the tissue geometry can also evolve in response to the pressure of tumor growth. Here we adapt our previous Cahn-Hilliard tumor growth model to an evolving geometry using a recently developed diffuse domain approach. We use the model to study the growth of lymphoma in a lymph node that swells during the process. An angiogenesis model for tumor-induced vasculature is also adapted to investigate substrate distribution and drug delivery within the lymph node.