A Particle-Based Model of Endothelial Cell Dynamics in the Extracellular Matrix

Branching structures such as vascular networks are representative morphological patterns in living systems, and they often arise from collective cell migration. Angiogenesis, the sprouting of new blood vessels from pre-existing ones, is a fundamental process in development. Experimental and theoretical studies have demonstrated that sprout formation depends on the collective movements and shapes of endothelial cells, as well as the remodelling of the extracellular matrix. Many discrete models have been proposed to describe cell dynamics, successfully reproducing vascular patterns and collective behaviours. In this study, we present a two-dimensional mathematical model that represents each endothelial cell as an ellipse and incorporates the effects of the extracellular matrix. We performed computer simulations under two scenarios: invasion from a pre-formed sprout and collective advancement into an extracellular matrix region. The results show that the extracellular matrix helps maintain linear sprout extension and suppresses the formation of dispersed or curved branches, while elongated cell shapes promote sprouting more effectively than round cells. The model also reproduces experimentally observed behaviours such as tip-cell replacement and the mixing of cells within sprouts. These findings highlight the importance of integrating cell shape and extracellular matrix remodelling to understand early blood vessel formation.