Using a meshless method to assess the effect of mechanical loading in angiogenesis

Although it is known that blood vessels can be found in mechanically active environments, less is known about the effect of mechanical stimulus in angiogenesis. Therefore, understanding how endothelial cells respond to a mechanical stimulus is essential to improve tissue vascularization and to promote wound healing and tissue engineering development. In this work, a meshless method is used to combine an elasticity formulation with a capillary growth algorithm. The final numerical model is capable to simulate the effect of compressive loading in angiogenesis, using three strain magnitudes (5, 10 and 30% strain). In this proposed model, the vascular endothelial growth factor gradient regulates the endothelial cell migration and the compressive loading affects the branching process. The numerical results showed that all the compressive loadings tested increased the vascular network length and the number of branches, being 5% strain magnitude the most effective one. The capillary network obtained resembles the one presented in experimental assays and the obtained numerical results coincided to the experimental ones. Nevertheless, this study possesses some limitations since the viscoelastic properties of the tissue, the dynamic loading effect and the effect of the time variable were not considered. In the future, the combination of computational and experimental studies will be very useful to understand and to define which are the mechanical cues that promote angiogenesis, allowing to improve tissue vascularization and, consequently, the wound healing process.