Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
Phys Rev E. 2019 Jan;99(1-1):012321. doi: 10.1103/PhysRevE.99.012321.
The structure of flow networks determines their function under normal conditions as well as their response to perturbative damage. Brain vasculature often experiences transient or permanent occlusions in the finest vessels, but it is not clear how these microclots affect the large-scale blood flow or to what extent they decrease functionality. Motivated by this, we investigate how flow is rerouted after the occlusion of a single edge in networks with a hierarchy in edge conductances. We find that in two-dimensional networks, vessels formed by highly conductive edges serve as barriers to contain the displacement of flow due to a localized perturbation. In this way, the vein provides shielding from damage to surrounding edges. We show that once the conductance of the vein surpasses an initial minimal value, further increasing the conductance can no longer extend the shielding provided by the vein. Rather, the length scale of the shielding is set by the network topology. Upon understanding the effects of a single vein, we investigate the global resilience of networks with complex hierarchical order. We find that a system of veins arranged in a grid is able to modestly increase the overall network resilience, outperforming a parallel vein pattern.
流网络的结构决定了它们在正常情况下的功能，以及它们对微扰损伤的反应。大脑脉管系统在最细的血管中经常经历短暂或永久性的阻塞，但尚不清楚这些微栓如何影响大尺度血流，或者它们在多大程度上降低了功能。出于这个原因，我们研究了在具有边缘电导层次结构的网络中，单个边缘阻塞后，流是如何重新路由的。我们发现，在二维网络中，由高导电边缘形成的血管充当屏障，以阻止由于局部扰动引起的流的位移。通过这种方式，静脉为周围边缘的损伤提供了屏蔽。我们表明，一旦静脉的电导超过初始最小值，进一步增加电导就无法再扩展静脉提供的屏蔽。相反，屏蔽的长度尺度由网络拓扑决定。在了解了单个静脉的影响之后，我们研究了具有复杂层次结构的网络的全局弹性。我们发现，以网格形式排列的静脉系统能够适度提高整体网络弹性，优于平行静脉模式。
