Scaling of the surface vasculature on the human placenta

The networks of veins and arteries on the chorionic plate of the human placenta are analyzed in terms of Voronoi cells derived from these networks. Two groups of placentas from the United States are studied: a population cohort with no prescreening, and a cohort from newborns with an elevated risk of developing autistic spectrum disorder. Scaled distributions of the Voronoi cell areas in the two cohorts collapse onto a single distribution, indicating common mechanisms for the formation of the complete vasculatures, but which have different levels of activity in the two cohorts.

Figure 1

(a) Digital image of the chorionic plate of a placenta from the NCS cohort with the hand-tracing of the arteries and their thicknesses. The regular shape and near-central umbilical cord insertion (indicated by the blue circle) are expected of a “normal” placenta. (b) Representation of each blood vessel as a seed at its midpoint, indicated by filled circles. (c) Voronoi cells obtained from the seeds in (b). (d) Generations of Voronoi cells according to the adjacent color bar. The same color coding for generations is used in (a) and (b).

Figure 2

Histograms of core Voronoi cell areas for (a) NCS arteries (b) EARLI arteries, (c) NCS veins, and (d) EARLI veins. The cumulative contributions for the first three and first six generations are indicated by darker and lighter shading, respectively, in each panel.

Figure 3

Voronoi constructions of placentas from the [(a),(b)] NCS and [(c),(d)] EARLI cohorts. Core and boundary cells are shown as unshaded and shaded regions, respectively. The umbilical cord insertions are indicated by light blue circles.

Figure 4

Scaling plots of the data in Fig. 2 for the (a) NCS and (b) EARLI cohorts. The similarity of the two best-fit distributions (Table 2) points to a collapse of all data into a single scaling function. Bin widths in $(0,3]$ have comparable numbers of data points, while those in $(3,6]$ each have at least 30 data points. Comparisons are made between the data points and the best fit gamma (solid black curve), best fit lognormal (broken blue curve), and random gamma (dot-dashed red curve) distributions. The insets show magnifications for the fits to the tails of the distributions. See text and Table 2 for details.

Figure 5

Scaling plots of Voronoi core cell areas for arteries of the (a) NCS and (b) EARLI chorionic vasculatures resolved according to generation $g$ for the first ten generations. The tighter data collapse for NCS is likely due to the larger number of placentas in that cohort (Table 1).