Mathematical Modeling of the Capillary-Like Pattern Generated by Adrenomedullin-Treated Human Vascular Endothelial Cells In Vitro

A recently proposed approach was used to model the self-organization into capillary-like structures of human vascular endothelial cells cultured on Matrigel. The model combines a Cellular Potts Model, considering cell adhesion, cytoskeletal rearrangement and chemotaxis, and a Partial Differential Equation model describing the release and the diffusion of a chemoattractant. The results were compared with the data from real in vitro experiments to establish the capability of the model to accurately reproduce both the spontaneous self-assembly of unstimulated cells and their self-organization in the presence of the pro-angiogenic factor adrenomedullin. The results showed that the model can accurately reproduce the self-assembly of unstimulated cells, but it failed in reproducing the adrenomedullin-induced self-organization of the cells. The extension of the model to include cell proliferation led to a good match between simulated and experimental patterns in both cases with predicted proliferation rates in agreement with the data of cell proliferation experiments.