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.
Highlights
The liver is the largest organ in the body and 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
The deterministic structure of the body fluid networks was highlighted in the early twentieth century by respectively Hess[27] and Murray[28] who came to the conclusion that the diameter ratio between mother and daughter branches has a unique value
We demonstrated previously that beyond the value of 6 connected branches, radial networks should be replaced by tree-shaped ones with optimized diameter ratios (Eq 3) and length ratios (Eq 6) in order to spend less pumping power for the same fluid volume[26]
Summary
Detailed measurements of the geometrical features of the human liver blood network are scarce. As the splitting number is n = 3 on an average, Eq 3 predicts that the corresponding diameter ratio should be 3–1/3 ≅ 0.69 in order to minimize the pumping power needed to push the blood in and out the liver. This result is in good agreement with the anatomical data. Each square element receives the blood from each of its 4 corners This means that √in this configuration, the central vein would be connected to 4 radial branches of diameter dc and length Lc = 2LS through which the mass flow rate is mh/4.
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