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. 2020 Oct 1;10(1):16194.
doi: 10.1038/s41598-020-73208-8.

The liver, a functionalized vascular structure

Sylvie Lorente  1 , Mathieu Hautefeuille  2 , Aczel Sanchez-Cedillo  3
Affiliations

The liver, a functionalized vascular structure

Sylvie Lorente et al. Sci Rep. .

Abstract

The liver is not only the largest organ in the body but also the one playing one of the most important role in the human metabolism as it is in charge of transforming toxic substances in the body. Understanding the way its blood vasculature works is key. In this work we show that the challenge of predicting the hepatic multi-scale vascular network can be met thanks to the constructal law of design evolution. The work unveils the structure of the liver blood flow architecture as a combination of superimposed tree-shaped networks and porous system. We demonstrate that the dendritic nature of the hepatic artery, portal vein and hepatic vein can be predicted, together with their geometrical features (diameter ratio, duct length ratio) as the entire blood flow architectures follow the principle of equipartition of imperfections. At the smallest scale, the shape of the liver elemental systems-the lobules-is discovered, while their permeability is also predicted. The theory is compared with good agreement to anatomical data from the literature.

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Conflict of interest statement

The authors declare no competing interests.

Figures

Figure 1
Figure 1
The measured diameters (blue dots) and lengths (red squares) ratios inside the liver as a function of the splitting generation number, for the hepatic artery HA, the portal vein PV and the hepatic vein HV. The data are from Refs,,.
Figure 2
Figure 2
The shape of the liver as a hemisphere of radius R.
Figure 3
Figure 3
The canopy-to-canopy view of the liver vascular system. The inlet vasculature is made of the hepatic artery and the portal vein, the outlet vasculature is made of the hepatic vein. The lobules area porous medium located between the tree canopies.
Figure 4
Figure 4
Lobules of the liver paving the entire available domain. The inlet flow comes from the hepatic artery and the portal vein constituting the triad (the third element being the bile canal). The outlet flow (hepatic vein) is located at the center of each lobule.
Figure 5
Figure 5
Sketch of hexagonal (left side) and square configurations (right side). The blood flow path is represented by the arrows.
Figure 6
Figure 6
River basin in a liver lobule. The blood distribution within the lobule is similar to a reverse river basin connecting rivulets to a central sink.
See this image and copyright information in PMC

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