Fractal geometry of mosaic pattern demonstrates liver regeneration is a self-similar process

Abstract

Partial hepatectomy causes compensatory, nonneoplastic growth and regeneration in mammalian liver. Compensatory liver growth can be used to examine aspects of patterns of cell division in regenerating tissue. Chimeric animals provide markers of cell lineage which are independent of growth and can be used to follow cell division patterns. Previous experimental evidence suggests that compensatory liver growth is uniform, without focal centers of proliferation. In this study we have extended that observation to include genes important in regeneration and cell cycle control in order to establish that nascent growth centers are not present in regenerating liver. There is a uniform spatial distribution of expression of these genes which is not related to mosaic pattern in the chimeras. While these genes may help regulate hepatocyte proliferation they do not appear to regulate patch pattern in the chimeras. With this information confirming uniform growth it was possible to use fractal analysis to test various hypothesized patterns of regenerative growth in the liver. The results of this analysis indicate that mosaic pattern does not change substantially during the regenerative process. Patch area and perimeter (the area occupied by or perimeter around cells of like lineage) increase during compensatory liver growth in chimeric rats without alteration of the geometric complexity of patch boundaries (boundaries around cells of like lineage). These tissue findings are consistent with previously reported computer models of growth in which repetitive application of simple decisions assuming uniform growth created complex mosaic patterns. They support the notion that an iterating (repeating), self-similar (a pattern in which parts are representative of, but not identical to the whole) cell division program is sufficient for the regeneration of liver tissue following partial hepatectomy. Iterating, self-similar cell division programs are important because they suggest a way in which complex patterns (or morphogenesis) can be efficiently created from a small amount of stored information.