Resilience of three-dimensional sinusoidal networks in liver tissue

PLoS Comput Biol. 2020 Jun 29;16(6):e1007965. doi: 10.1371/journal.pcbi.1007965. eCollection 2020 Jun.


Can three-dimensional, microvasculature networks still ensure blood supply if individual links fail? We address this question in the sinusoidal network, a plexus-like microvasculature network, which transports nutrient-rich blood to every hepatocyte in liver tissue, by building on recent advances in high-resolution imaging and digital reconstruction of adult mice liver tissue. We find that the topology of the three-dimensional sinusoidal network reflects its two design requirements of a space-filling network that connects all hepatocytes, while using shortest transport routes: sinusoidal networks are sub-graphs of the Delaunay graph of their set of branching points, and also contain the corresponding minimum spanning tree, both to good approximation. To overcome the spatial limitations of experimental samples and generate arbitrarily-sized networks, we developed a network generation algorithm that reproduces the statistical features of 0.3-mm-sized samples of sinusoidal networks, using multi-objective optimization for node degree and edge length distribution. Nematic order in these simulated networks implies anisotropic transport properties, characterized by an empirical linear relation between a nematic order parameter and the anisotropy of the permeability tensor. Under the assumption that all sinusoid tubes have a constant and equal flow resistance, we predict that the distribution of currents in the network is very inhomogeneous, with a small number of edges carrying a substantial part of the flow-a feature known for hierarchical networks, but unexpected for plexus-like networks. We quantify network resilience in terms of a permeability-at-risk, i.e., permeability as function of the fraction of removed edges. We find that sinusoidal networks are resilient to random removal of edges, but vulnerable to the removal of high-current edges. Our findings suggest the existence of a mechanism counteracting flow inhomogeneity to balance metabolic load on the liver.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Humans
  • Liver / anatomy & histology*
  • Liver / blood supply
  • Microvessels / anatomy & histology
  • Models, Biological*

Grant support

JK, MZ and BMF were supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany´s Excellence Strategy – EXC-1056 – 194636624– Cluster of Excellence cfaed of TU Dresden. MZ and BMF were supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany´s Excellence Strategy – EXC-2068 – 390729961– Cluster of Excellence Physics of Life of TU Dresden. This work was further financially supported by the German Federal Ministry of Education and Research (BMBF) (LiSyM: grant #031L0038 to MZ), European Research Council (ERC) (grant #695646 to MZ) and the Max Planck Society (MPG) (YK and MZ). JW acknowledges funding by the DAAD RISE program. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.