A multiscale model for tumoral vascular growth: blood flow and cell dynamics

Vascularization is a fundamental factor in the progression of tumor growth. The vascular phase is characterized by angiogenesis, responsible for the growth of new blood vessels in tumor direction from an original vascular network. Through an additional supply of nutrients, the tumor acquires unlimited resources for its uncontrolled progress. Besides, the risk of metastasis increases with the eventual invasion of blood vessels by cancer cells. In this work, we developed a multiscale model to represent the growth of vascular tumors, integrating angiogenesis and blood flow dynamics. Dynamics on the cell scale are represented discretely using agent-based modeling, while oxygen dispersions and pro-angiogenic factors are modeled using partial diffusion-reaction equations. Blood flow is obtained by solving Kirchhoff's circuit equations for flow in a connected network. The new blood vessels are formed through a set of rules based on stimuli of factors secreted by cancer cells submitted to the oxygen structure. The coupling between the models can capture phenomena that occur at the cellular and tissue scales, qualitatively representing the growth of vascular tumors. The computational model was developed using PhysiCell, an open-source C ++ framework that allows the construction of multicellular models at various scales in 2D and 3D.