2D simulation and visualization of tumour growth based on discrete mathematical models

The aim of this paper is to present a two-dimensional simulation tool based on several mathematical models, visualizing the growth and development of a solid tumour in avascular growth phase, vascular growth phase and the progress of angiogenesis. The avascular tumour remains in a diffusion-limited state of a few millimeters in diameter, while during vascularized phase, tumour cell proliferating rapidly and being able to invade the surrounding host tissue and blood system. Tumour-induced angiogenesis, the growth of a capillary network of blood vessels from a pre-existing vasculature, provides the crucial link between the two stages. Under different molecular mechanisms, this discrete model demonstrates several important factors affecting tumour growth at each stage. The simulation results are presented in two-dimensional combined with quantitatively surveyed. The long-term goal of this work is to develop a multicellular engine for precisely simulating and visualizing the insight into cancer biology.