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Abstract

In this thesis, I study how vascular networks form, how they function in transporting flow, and how they remodel over time. I begin by introducing a stochastic model that mimics how blood vessel tips grow and branch, producing complex network structures. I convert these simulated structures into graphs and analyze their geometric and topological features under different parameter settings. Next, I use well-known graph-based methods such as maximum-flow and minimum spanning tree algorithms to study how effectively these networks can deliver flow from source nodes to sink nodes, and how resilient they are to damage or removal of vessels. I then develop a mathematical model that describes how networks remodel in response to internal flow conditions, such as the distribution of sources and sinks. I explore how this remodeling process changes under different assumptions, including the effects of external stressors like radiation. Finally, I design a practical image-processing pipeline to extract graph representations of real vascular structures from retinal images.