An adaptive semi-implicit finite element solver for brain cancer progression modeling

Glioblastoma is the most aggressive and infiltrative glioma, classified as Grade IV, with the poorest survival rate among patients. Accurate and rigorously tested mechanistic in silico modeling offers great value to understand and quantify the progression of primary brain tumors. This paper presents a continuum-based finite element framework that is built on high performance computing, open-source libraries to simulate glioblastoma progression. We adopt the established proliferation invasion hypoxia necrosis angiogenesis model in our framework to realize scalable simulations of cancer, and has demonstrated to produce accurate and efficient solutions in both two- and three-dimensional brain models. The in silico solver can successfully implement arbitrary order discretization schemes and adaptive remeshing algorithms. A model sensitivity analysis is conducted to test the impact of vascular density, cancer cell invasiveness and aggressiveness, the phenotypic transition potential, including that of necrosis, and the effect of tumor-induced angiogenesis in the evolution of glioblastoma. Additionally, individualized simulations of brain cancer progression are carried out using pertinent magnetic resonance imaging data, where the in silico model is used to investigate the complex dynamics of the disease. We conclude by arguing how the proposed framework can deliver patient-specific simulations of cancer prognosis and how it could bridge clinical imaging with modeling.