Preliminary analysis of the liver lobular architecture in porcine and human livers by our group suggested a relationship between the general lobular organization of liver tissue and Voronoi diagrams-further understanding of which could prove useful for the study of liver development, microanatomy, and various disease processes. Voronoy (1868–1908) and referred to thereafter as Voronoi diagrams-a principle which is now widely utilized across a wide variety of disciplines, from natural sciences and medicine to engineering and computational geometry 10, 11, 12, 13, 14, 15, 16, 17, 18. The mathematical basis for this method would later be described in detail by the Russian mathematician Georgy F. Recently, our group has fortuitously observed a striking similarity between the pattern of geometric partitioning of the universe illustrated by early astronomers in the seventeenth century (René Descartes, in Principia philosophiae 9, supplement figure S1) and the classic lobular architecture of the liver. Other unit models have been described, including the “portal lobule” 5 (in which the portal tracts represent the center of the lobule), the “single-sinusoid” model by Bloch 6 and McCuskey 7 and the cholehepaton model by Ekataksin and Wake 8, but have not been as widely adopted as the other aforementioned models. The Matsumoto’s “primary lobule” model 3, 4, which is based on the angio-architecture of the portal venous tree and proposes the subdivision of the classic lobules (termed “secondary lobule” in this model) into 6–8 primary lobules, has also received increasing attention and acceptance in recent decades. These proposed regions, although 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. 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. The boundaries of the classic liver lobules are easily recognized in some animal species (most notably in pigs-as they are often used in scientific studies-but also in camels, raccoons, and polar bears) due to the presence of well-defined fibrous septa delineating the periphery of individual normal lobules. This model would later be known as “classic” or “Kiernan” lobule, whereby the basic histologically-defined units of the liver are depicted as polygonal-shaped structures containing a central vein in the middle and portal tracts at the vertices. In 1833, Kiernan 1 described and illustrated the microscopic anatomy of the liver lobules. Different models of the hepatic microarchitecture and their corresponding anatomic and functional units were subsequently proposed (Fig. Wepfer examining pig livers in 1665 and shortly thereafter by Malpighi in his celebrated work “ De Viscerum Structura Exercitatio Anatomica” (cited by Kiernan 1), in which several species were studied. The microanatomy of the liver was first described by J.J. 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. We have also designed a Voronoi-based algorithm of hepatic zonation, which also showed an overall zonal accuracy of nearly 90%. The Voronoi diagram model described the organization of the hepatic classic lobules with overall accuracy nearly 90% based on known histologic landmarks. We examined the histology of normal porcine and human livers and analyzed the geometric relationships of various microanatomic structures utilizing digital tools. Our aim was to evaluate whether Voronoi diagrams can be used to describe the classic liver lobular architecture. 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.
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