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Abstract

Recent work on self-organized remodeling of vasculature in slime molds, leaf venation systems, and vesselsystems in vertebrates has put forward a plethora of potential adaptation mechanisms. All these share theunderlying hypothesis of a flow-driven machinery, meant to alter rudimentary vessel networks in order tooptimize the system’s dissipation, flow uniformity, or more, with different versions of constraints. Nevertheless,the influence of environmental factors on the long-term adaptation dynamics as well as the network structureand function have not been fully understood. Therefore, interwoven capillary systems such as those found inthe liver, kidney, and pancreas present a novel challenge and key opportunity regarding the field of coupleddistribution networks. We here present an advanced version of the discrete Hu-Cai model, coupling two spatialnetworks in three dimensions. We show that spatial coupling of two flow-adapting networks can control the onsetof topological complexity in concert with short-term flow fluctuations. We find that both fluctuation-inducedand spatial coupling induced topology transitions undergo curve collapse, obeying simple functional rescaling.Further, our approach results in an alternative form of Murray’s law, which incorporates local vessel interactionsand flow interactions. This geometric law allows for the estimation of the model parameters in ideal Kirchhoffnetworks and respective experimentally acquired network skeletons.