Resilience of three-dimensional sinusoidal networks in liver tissue

Abstract

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 multiobjective 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.

Myostatin Knockout Regulates Bile Acid Metabolism by Promoting Bile Acid Synthesis in Cattle

“…The liver is the largest internal organ and controls organism metabolism [ 42 ]. Myostatin inhibits proliferation and insulin-stimulated glucose uptake in liver cells [ 43 ].…”

Quantification of nematic cell polarity in three-dimensional tissues

“…We can analyze nematic order of cell polarity not only within an ensemble of cells, but also quantify the mutual alignment between cell polarity and auxiliary anisotropic structures such as transport networks. As example, we analyze co-orientational order between apical nematic cell polarity of hepatocytes, and the local anisotropy of the blood-transporting sinusoidal network [ 15 , 26 ]. Sinusoids are specialized blood vessels forming a network within the liver lobule [ 10 ].…”

“…Furthermore, we found co-alignment between nematic cell polarity of hepatocytes and the local anisotropy of the sinusoidal network. This mutual alignment is not uniaxial, but of phase-biaxial type, i.e., its description requires two reference axes, a preferred axis of the sinusoidal network (approximately parallel to the direction of blood flow [ 26 , 34 ]), and a plane axis, which characterizes local layered order of the sinusoidal network. Specifically, we observe signatures of layered organization of the sinusoidal network, characterized by a distinguished plane axis ( s 2 ), normal to layers enriched in sinusoids.…”

On biological flow networks: Antagonism between hydrodynamic and metabolic stimuli as driver of topological transitions

“…and subsequently the local Peclet numbers. The impact of the simultaneously given dissipation-volume constraints, as in (16), is tuned via the coupling parameters α 0 , α 1 . Increased volume penalties α 0 naturally lead to smaller vessel structures, simultaneously increasing P e and therefore hindering solute uptake.…”

“…A recurring problem in these studies is to identify stimuli causing the complex topology of capillary networks, i.e. resilient, space-filling meshes containing hydrodynamically favorable 'highways', defying Murray's law [16][17][18]. Subsequently, more complex stimuli such as growth, noisy flow patterns and hemodynamical complications have been rigorously discussed in computational studies, and have been found to account for complex topological changes in the respective networks [19][20][21][22][23][24].…”