A mathematical model of chemotactic endothelial cell migration in a fibrin-based hydrogel extracellular matrix*

The formation of new vasculature from existing blood vessels, or angiogenesis, occurs as a multistep process driven by an extensive collection of pro- and anti-angiogenic factors. In this process, the extracellular matrix (ECM) plays a crucial role due to its structural function, the store of mediators, such as vascular endothelial growth factor (VEGF), and matrix-cell interactions. The scenario of the remodelling of the ECM and matrix-cell interactions during angiogenesis is intricate. A standard approach to study angiogenesis is to explore the underlying cellular mechanisms focusing on endothelial cell (EC) motility regulated by chemotactic stimulus, ignoring mechanotactic stimuli. In cultured ECs, it is possible to easily analyze, separately, the concentration of growth factors, namely VEGF, and the structure of the culture substrate, mimicking ECM material.

Here, we present a phase-field model and experiments to study the collective EC migration considering the chemotactic and the mechanotactic stimuli. By using fluorescence microscopy images of the fibrin-based hydrogel, mimicking the ECM, we integrated its structure together with a growth factor distribution to the model to describe the combined effect in ECs directed migration. The numerical integration of our mathematical model agrees with our experimental results.