Evolving complex flow networks

During embryonic development, the cardiovascular system already functions, even while it is still growing. From an initially more or less unstructured network of capillaries, a branching network starts to form. This network keeps evolving and finally results in a branching pattern that appears to share many similarities between species. For example, Murray's law states that when a blood vessel bifurcates, the ratio of parent and 'daughter' branch diameter is 1:1.26. This relationship is thought to originate in an optimization between energy consumption to maintain the network and energy consumption to drive the flow (i.e. overcome viscous resistance).In this project, we will start with a simple "1D" flow model, which consists of nodes that are connected in a hexagonal pattern. In each of the connections between nodes, we assume that the flow obeys Poiseuille's law. By setting up simple rules, e.g. "a blood vessel diameter should increase if the local flow is above a certain threshold", we can study the evolution of the network (see figure above). Other rules could be based on e.g. nutrient/waste diffusion as the blood flow passes through the network. The main aim of this project is to find if it is possible to create complex (physiologically meaningful) networks from a simple set of rules. During the project, experimental data will become available that describes real vascular networks during development.

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