Vascular networks continuously reorganize their morphology by growing new or shrinking existing veins to optimize function. Flow shear stress on vein walls has been set forth as the local driver for this continuous adaptation. Yet, shear feedback alone cannot account for the observed diversity of network dynamics -- a puzzle made harder by scarce spatio-temporal data. Here, we resolve network-wide vein dynamics and shear during spontaneous reorganization in the prototypical vascular networks of Physarum polycephalum. Our experiments reveal a plethora of vein dynamics (stable, growing, shrinking) that are not directly proportional to local shear. We observe (a) that shear rate sensing on vein walls occurs with a time delay of 1 to 3 min and (b) that network architecture dependent parameters -- such as relative pressure or relative vein resistance -- are key to determine vein fate. We derive a model for vascular adaptation, based on force balance at the vein walls. Together with the time delay, our model reproduces the diversity of experimentally observed vein dynamics, and confirms the role of network architecture. Finally, we observe avalanches of network reorganization events which cause entire clusters of veins to vanish. Such avalanches are consistent with architectural feedback as the vein connections perpetually change with reorganization. As these network architecture dependent parameters are intrinsically connected with the laminar fluid flow in the veins, we expect our findings to play a role across flow-based vascular networks.

Veins in vascular networks, such as in blood vasculature or leaf networks, continuously reorganize, grow or shrink, to minimize energy dissipation. Flow shear stress on vein walls has been set forth as the local driver for a vein's continuous adaptation. Yet, shear feedback alone cannot account for the observed diversity of vein dynamics - a puzzle made harder by scarce spatiotemporal data. Here, we resolve network-wide vein dynamics and shear rate during spontaneous reorganization in the prototypical vascular networks of Physarum polycephalum. Our experiments reveal a plethora of vein dynamics (stable, growing, shrinking) where the role of shear is ambiguous. Quantitative analysis of our data reveals that (a) shear rate indeed feeds back on vein radius, yet, with a time delay of 1-3 min. Further, we reconcile the experimentally observed disparate vein fates by developing a model for vein adaptation within a network and accounting for the observed time delay. The model reveals that (b) vein fate is determined by parameters - local pressure or relative vein resistance - which integrate the entire network's architecture, as they result from global conservation of fluid volume. Finally, we observe avalanches of network reorganization events that cause entire clusters of veins to vanish. Such avalanches are consistent with network architecture integrating parameters governing vein fate as vein connections continuously change. As the network architecture integrating parameters intrinsically arise from laminar fluid flow in veins, we expect our findings to play a role across ow-based vascular networks.

Understanding and controlling transport through complex media is central for a plethora of processes ranging from technical to biological applications. Yet, the effect of micro-scale manipulations on macroscopic transport dynamics still poses conceptual conundrums. Here, we demonstrate the predictive power of a conceptual shift in describing complex media by local micro-scale correlations instead of an assembly of uncorrelated minimal units. Specifically, we show that the non-linear dependency between microscopic morphological properties and macroscopic transport characteristics in porous media is captured by transport statistics on the level of pore junctions instead of single pores. Probing experimentally and numerically transport through two-dimensional porous media while gradually increasing flow heterogeneity, we find a non-monotonic change in transport efficiency. Using analytic arguments, we built physical intuition on how this non-monotonic dependency emerges from junction statistics. The shift in paradigm presented here broadly affects our understanding of transport within the diversity of complex media.

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