Voronoi diagram description of the maternal surface of the placenta: preliminary report

Voronoi diagram is defined as a diagram of a collection of geometric points that defines a partition of space into cells, each of which consists of the points closer to one particular point than to any other. The distinctive feature of a placentone is the fetomaternal circulatory unit which is composed of one villous tree with a corresponding, centrifugally perfused portion of the intervillous space. Based on this placental architecture, in this study we generated Voronoi diagram from the photographic images of the maternal surface of the placenta and compared them with the shapes of the actual placentones.

We simulated the placentones of 12 placentas based on Voronoi diagram using a computer program, and compared them with the photographic images of the actual maternal surface of the placentas. The point was carefully selected and adjusted so that the generated Voronoi diagram could represent the actual maternal surface of the placenta.

Voronoi diagram simulated satisfactorily the borders of placentones in 10 placentas. However, we could not succeed in the simulation in two cases.

It seems that development and formation of placentones are not only theoretically and physiologically explainable by Voronoi diagram, but also actually achieved by this mechanism. We believe that mathematical Voronoi diagram holds a promise for evaluating physiological and pathological development of the placenta.