We owe the comeback of the lobular concept to Matsumoto
We owe the “comeback” of the lobular concept to Matsumoto . His “unit-concept” divides the portal venous tree into upstream “conducting” and downstream parenchymal (“delivering”) portions with a higher branching frequency (see section on Couinaud's segmental liver model). Typically, ~6 such terminal parenchymal portal twigs, accompanied by arterial and ductular twigs, embrace a piece of parenchyma that has a terminal hepatic vein as its central axis. The terminal portal twigs in the portal tracts typically form three portal venules (“septal” branches) that feed the sinusoids via inlet sinusoids. Because the sinusoids near the terminal portal tracts are more tortuous, whereas those originating from the distal ends of the septal portal venules and those surrounding the central (hepatic) veins are relatively straight, Matsumoto postulated an “inflow (perfusion) front” towards the central vein. The boundary between vital and lethally damaged hepatocytes after controlled digitonin perfusion of the liver [81,82] have underscored the concept of an inflow front. The redox ratio-scanning technique  showed, in addition, that the tortuous sinusoids characterize the metabolically robust periportal zone, whereas the straight sinusoids characterize the metabolically sensitive zone. We have hypothesized that the tortuous periportal sinusoids are also responsible for the ability of blood to flow from the portal to the central vein, but not vice versa, whereas a cell-free solution allows bidirectional perfusion [83,84].
The liver lobule has been further subdivided in some concepts, but also combined into 6-NBDG lobules. In Matsumoto's unit-concept, the classic (≈ “secondary”) lobule consists of ~6 “primary” lobules. A primary lobule represents the part of the secondary lobule that is perfused by a single terminal branch of a parenchymal portal vein . The even smaller “microcirculatory unit” represents the fraction of a lobule that is perfused by one inlet sinusoid . Because the bile that is produced in that microcirculatory unit usually drains into a bile ductule that leaves the hepatic parenchyma near the inlet sinusoid, the microcirculatory unit is also known as “cholehepaton” . Compound parenchymal units, on the other hand, include all lobules served by a parenchymal portal branch . In support of this compound model, we showed that the first 2–4 generations of terminal or “collecting” hepatic veins are surrounded by a rim of glutamine synthetase-containing hepatocytes, whereas the more downstream, larger “conducting” hepatic veins are not , probably because their wall is thicker and blocks the transmission of an endothelial signal necessary to express glutamine synthetase . The presence of sinusoid-draining terminal hepatic veins is, therefore, another feature of the compound liver lobule. In our view, the classic lobule is the most versatile functional unit.
Two aspects of lobular architecture that differ quantitatively between small and large mammals are the portocentral distance (vide supra) and the amount of connective tissue that is present in the portal tracts. Furthermore, liver lobules in small mammals like the mouse are more tortuous cylindrical structures  than those in pig and human liver [90,91], but too few examples are available to conclude that this is a general feature of size. It is well established that the amount of connective tissue in the portal tract is lowest in rodents, sparse in healthy human liver, better developed in ruminant and equine livers [92,93], and pronounced in pig liver, where it already reaches near-adult levels shortly after weaning . The amount of connective tissue determines the tissue stiffness and “fracture toughness” [94,95], but the adaptive value remains to be established.
Lobular perfusion The reported allometric constant of the relation between mammalian body weight and liver size (0.89) is similar to that between body weight and hepatic blood flow (0.85–0.91; [1,96]), showing that liver perfusion increases concomitantly with liver size. As shown above, the portocentral distance between species also increases with body weight, but the few species for which information could be obtained produce an allometric constant of only ~0.10 (Fig. 4A), which implies that the portocentral distance increases only slowly with liver size. Similarly, the allometric constant of the relation between body size and the number of hepatocytes on the portocentral axis is only ~0.10 (Fig. 4B). For most organs the allometric constant for the relation between body weight and cell size, including that of (diploid) hepatocytes, is not different from zero , that is, invariant with body size. However, the volume of hepatocytes increases with the degree of ploidy  and rodents have a higher percentage of polyploid hepatocytes than larger mammals [, , , ], so that fewer rodent hepatocytes fit on the same portocentral distance. For that reason, 0.1 is a high estimate for the allometric constant. The direct relation between liver size and perfusion is, therefore, accomplished by generating more rather than larger lobules. While blood pressure in the hepatic artery is ~120 mm Hg and independent of animal size , that in the portal vein is only 6–11 mm Hg and also similar for mice [107,108], rats [108,109], cats , dogs [110,111], and humans [112,113]. Hence, we hypothesize that one of the structural limitations for an increase in size of the lobule is its perfusion.