Modeling the Variability of Shapes of a Human Placenta☆

Abstract 

Background

Placentas are generally round/oval in shape, but “irregular” shapes are common. In the Collaborative Perinatal Project data, irregular shapes were associated with lower birth weight for placental weight, suggesting variably shaped placentas have altered function.

Methods

(I) Using a 3D one-parameter model of placental vascular growth based on Diffusion Limited Aggregation (an accepted model for generating highly branched fractals), models were run with a branching density growth parameter either fixed or perturbed at either 5–7% or 50% of model growth. (II) In a data set with detailed measures of 1207 placental perimeters, radial standard deviations of placental shapes were calculated from the umbilical cord insertion, and from the centroid of the shape (a biologically arbitrary point). These two were compared to the difference between the observed scaling exponent and the Kleiber scaling exponent (0.75), considered optimal for vascular fractal transport systems. Spearman's rank correlation considered p<0.05 significant.

Results

(I) Unperturbed, random values of the growth parameter created round/oval fractal shapes. Perturbation at 5–7% of model growth created multilobate shapes, while perturbation at 50% of model growth created “star-shaped” fractals. (II) The radial standard deviation of the perimeter from the umbilical cord (but not from the centroid) was associated with differences from the Kleiber exponent (p=0.006).

Conclusions

A dynamical DLA model recapitulates multilobate and “star” placental shapes via changing fractal branching density. We suggest that (1) irregular placental outlines reflect deformation of the underlying placental fractal vascular network, (2) such irregularities in placental outline indicate sub-optimal branching structure of the vascular tree, and (3) this accounts for the lower birth weight observed in non-round/oval placentas in the Collaborative Perinatal Project.

Keywords: Placental growth, Placental shape, Placental vasculature, Fractal, Diffusion limited aggregation