A Cahn-Hilliard model of vascularized tumor growth in a complex evolving confinement using a diffuse domain approach

Understanding the spatiotemporal evolution of tumor growth is essential for developing effective strategies to treat cancers. Various studies have suggested that spatial heterogeneity during tumors growth is a key factor associated with subsequent tumor invasion and the effectiveness of chemotherapy. Spatial heterogeneity may arise due to morphological instability of the tumors and the complex tissue structure surrounding the tumors. In previous works, we have used a Cahn-Hilliard tumor growth model to study the morphological instability for tumors in non-resisting tissues. However, most tumors are surrounded by complex tissue structures and confined in the capsules of some organs or between certain basement membranes. The capsules and basement membranes may be distorted by interacting with the evolving tumors, affecting the morphological instability. Here we adopt a novel diffuse domain approach to adapt our previous Cahn-Hilliard model for tumor growth in such complex evolving environments. As an example, we apply the model to simulate the evolution of lymphoma in a lymph node, incorporating also the tumor-induced angiogenesis.