Cardiovascular networks span the body by branching across many generations ofvessels. The resulting structure delivers blood over long distances to supplyall cells with oxygen via the relatively short-range process of diffusion atthe capillary level. The structural features of the network that accomplishthis density and ubiquity of capillaries are often called space-filling. Thereare multiple strategies to fill a space, but some strategies do not lead tobiologically adaptive structures by requiring too much construction material orspace, delivering resources too slowly, or using too much power to move bloodthrough the system. We empirically measure the structure of real networks (18humans and 1 mouse) and compare these observations with predictions of modelnetworks that are space-filling and constrained by a few guiding biologicalprinciples. We devise a numerical method that enables the investigation ofspace-filling strategies and determination of which biological principlesinfluence network structure. Optimization for only a single principle createsunrealistic networks that represent an extreme limit of the possible structuresthat could be observed in nature. We first study these extreme limits for twocompeting principles, minimal total material and minimal path lengths. Wecombine these two principles and enforce various thresholds for balance in thenetwork hierarchy, which provides a novel approach that highlights thetrade-offs faced by biological networks and yields predictions that bettermatch our empirical data.
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