Full-scale, three-dimensional simulation of early-stage tumor growth: The onset of malignancy

Malignant tumors have the ability to trigger the growth of new vasculature towards them through a complex process called tumor angiogenesis. These new blood vessels provide cancerous cells with sufficient nutrients for growth and a means to escape the primary tumor and invade other tissues. This paper proposes a three-dimensional model that aims at predicting how the tumor and its associated vasculature grow during the onset of malignancy. The cellular growth equations of our model are derived using the phase-field method. We use standard reaction-diffusion equations to model the transport of chemicals. The model resolves the tumor-induced vasculature explicitly, considering capillaries with a diameter of up to ∼25  μm. We propose a suitable computational method based on isogeometric analysis. We present several numerical examples to test the model, including a macroscopic simulation (∼1 cm3) on a geometry taken from a histopathological image of a human colon. The proposed model naturally predicts the angiogenic switch. Our computations show realistic patterns of tumor and vascular growth.