Strategies to enhance capillary formation inside biomaterials: a computational study

Control over angiogenesis (formation of new capillaries from preexisting vessels) is often a crucial requirement for implantable porous biomaterials serving as scaffolds for tissue regeneration. Angiogenesis is influenced by the transport of chemoattractants such as vascular endothelial growth factor (VEGF) through the implant. To investigate this influence, we developed a computational model of capillary formation based on endothelial cell migration by modeling the random motion of sprout tips biased along spatially and temporally evolving concentration gradients of VEGF. The model focuses on the effect of diffusive VEGF transport inside a 2D domain on the directed migration of sprouts to test several chemical and physical strategies to stimulate and control angiogenesis. We considered a 2D porous membrane that is located between the primary vessel and a line source of VEGF. We assess the vascular network formed in 2 cases of a high and zero VEGF degradation rates applying 3 strategies of VEGF production: (1) only a line source; (2) a line source plus controlled release from a small number of VEGF sources that are randomly dispersed on the pore boundaries; and (3) a line source plus controlled release of VEGF from the pore boundaries themselves. Results show that in the limiting cases where VEGF degradation rate is relatively high, strategies 2 and 3 lead to a substantial increase in the number of vessels. This increase depends on the relative rates at which the line source and embedded sources or solid boundaries produce VEGF. Using strategy 2 results in a newly formed capillary network that is highly localized around the embedded sources. However, using strategy 3 leads to a more uniformly distributed vessel network and a higher degree of vessel ingrowth inside the porous membrane. In addition, the duration at which we engineer the embedded sources or pore boundaries to release VEGF determines the morphology of the capillary network. Although a higher release duration leads to a dense network of newly formed vessels near the primary vessel, it hinders further vessel penetration inside the porous membrane. Therefore, in applying both strategies 2 and 3, there is an optimum release duration that leads to a deeper penetration of vessels inside the membrane. It is hoped that insights from this study will aid in the design of materials with optimal structural and chemical properties to facilitate controlled angiogenesis.