Emergence of Vascular Networks

The formation of vascular networks is a long-standing problem that has been the subject of intense research in recent decades. One of the main reasons for this is the wide range of applications in tissue regeneration, wound healing, cancer treatment, and many other areas.

The mechanisms involved in the formation of vascular networks are complex, and despite the large amount of research devoted to it, many of the mechanisms involved remain poorly understood. Our goal is to provide insight into the study of vascular networks by defining heuristic rules as simple as possible and simulating them numerically to test their relevance in the vascularization process. We will present a hybrid agent-based/continuum model that couples blood flow, oxygen flow, capillary network dynamics, and tissue dynamics. We will also show some simulations that demonstrate the ability of our model to capture the main features of vascular networks.

Bio
https://mathandparents.math.arizona.edu/people/pedroas