The Voronoi theory of the normal liver lobular architecture and its applicability in hepatic zonation

C Lau,R P Graham,B Kalantari,Roger K Moreira,L D Ferrell,K P Batts,S L Nyberg

doi:10.1038/s41598-021-88699-2

Abstract

The precise characterization of the lobular architecture of the liver has been subject of investigation since the earliest historical publications, but an accurate model to describe the hepatic lobular microanatomy is yet to be proposed. Our aim was to evaluate whether Voronoi diagrams can be used to describe the classic liver lobular architecture. We examined the histology of normal porcine and human livers and analyzed the geometric relationships of various microanatomic structures utilizing digital tools. The Voronoi diagram model described the organization of the hepatic classic lobules with overall accuracy nearly 90% based on known histologic landmarks. We have also designed a Voronoi-based algorithm of hepatic zonation, which also showed an overall zonal accuracy of nearly 90%. Therefore, we have presented evidence that Voronoi diagrams represent the basis of the two-dimensional organization of the normal liver and that this concept may have wide applicability in liver pathology and research.

Highlights

The precise characterization of the lobular architecture of the liver has been subject of investigation since the earliest historical publications, but an accurate model to describe the hepatic lobular microanatomy is yet to be proposed
The classic lobular architecture of the liver largely overlapped with Voronoi diagrams obtained through any of our five methods, which showed a surface overlap area ranging from 86.7% to 88.6% of all 203 porcine lobules by digital analysis (P = 0.007, but no statistically significant difference among trial and error, modified edge, and centroid methods)
The classic liver lobule—most clearly visualized in the normal porcine liver, in which dense and well-delineated interlobular fibrous septa linking portal tracts establish an identifiable boundary to each classic lobule—has traditionally been characterized and illustrated as uniform hexagonal structures, with portal tracts positioned in each of the six vertices and a central vein located in its center (Fig. 1)

Summary

Introduction

The precise characterization of the lobular architecture of the liver has been subject of investigation since the earliest historical publications, but an accurate model to describe the hepatic lobular microanatomy is yet to be proposed. The “hepatic acinus” model was put forth by Rappaport and colleagues[2] in 1954, according to which the liver is subdivided in units based on terminal portal circulation—with zones 1 being closest to portal tracts, zones 3 closest to central veins, and zones 2 located between zones 1 and 3 These proposed regions, not defined by histologic landmarks in any species, have been widely adopted in hepatology and hepatopathology due to their broad correlation with zonal patterns of expression of different cellular products, cell metabolism, as well as with zonal susceptibility to various disease processes. We investigate various aspects of the microanatomy of the human liver and whether the mathematical properties of Voronoi diagrams and its geometric/graph theoretical dual, Delaunay triangulation, can be used to more precisely describe classic hepatic lobules and to determine whether this mathematical tool can offer further insights to our understanding of the liver microarchitecture that could be useful in the emerging era of computational histopathology

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Conclusion