Multi-scale model of lumen formation via inverse membrane blebbing mechanism during sprouting angiogenesis process

Abstract

Cancer is one of the leading causes of mortality and morbidity among people worldwide. Cancer appears as solid tumors in many cases. Angiogenesis is the growth of blood vessels from the existing vasculature and is one of the imperative processes in tumor growth. Another vital phenomenon for formation and functionality of this vasculature network is lumen formation. The results of recent studies indicate the importance of blood pressure in this mechanism. Computational modeling can study these processes in different scales. Hence, wide varieties of these models have been proposed during recent years. In this research, a multi-scale model is developed for the angiogenesis process. In the extracellular scale, the growth factor concentration is calculated via the reaction diffusion equation. At the cellular scale, growth, migration, and the adhesion of endothelial cells are modeled by the Potts cellular model. At the intra-cellular scale by considering biochemical signals, a Boolean network model describes migration, division, or apoptosis of endothelial cells. A stochastic model developed for lumen formation via inverse membrane blebbing mechanism. A CFD simulation was also used to investigate the role of pulsated blood pressure in the inverse membrane blebbing mechanism. The lumen formation model shows stochastic behavior in blebs expansion and lumen expansion. Comparing the stochastic model's results with the CFD simulation also shows the vital role of pressure pulse and the topology of the blebs in bleb retraction.

Keywords: Angiogenesis process; Boolean network model; Computational modeling; Inverse membrane blebbing; Lumen formation; Multi-scale model; Potts cellular model; Stochastic model.