Fractal geometry in mosaic organs: a new interpretation of mosaic pattern

Abstract

Fractal geometries have been widely observed in nature. The formulation of mathematical treatments of non-Euclidean geometry has generated models of highly complex natural phenomena. In the field of developmental biology, branching morphogenesis has been explained in terms of self-similar iterating branching rules that have done much toward explaining branch patterns observed in a range of real tissue. In solid viscera the problem is more complicated because there is no readily available marker of geometry in parenchymal tissue. Mosaic pattern provides such a marker. The patches observed in mosaic liver are shown to be fractal, indicating that the pattern may have arisen from a self-similar process (i.e., a process that creates an object in which small areas are representative of, although not necessarily identical to, the whole object). This observation offers a new analytical approach to the study of biologic structure in organogenesis.