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Probability distributions for measures of placental shape and morphology

Weight at delivery is a standard cumulative measure of placental growth. But weight is a crude summary of other placental characteristics, such as the size and shape of the chorionic plate and the location of the umbilical cord insertion. Distributions of such measures across a cohort reveal information about the developmental history of the chorionic plate that is unavailable from an analysis based solely on the mean and standard deviation. Various measures were determined from digitized images of chorionic plates obtained from the Pregnancy, Infection, and Nutrition Study, a prospective cohort study of preterm birth in central North Carolina between 2002 and 2004. The centroids (the geometric centers) and umbilical cord insertions were taken directly from the images. The chorionic plate outlines were obtained from an interpolation based on a Fourier series, while eccentricity (of the best-fit ellipse), skewness, and kurtosis were determined from a shape analysis using the method of moments. The distribution of each variable was compared against the normal, lognormal, and Levy distributions. We found only a single measure (eccentricity) with a normal distribution. All other placental measures required lognormal or "heavy-tailed" distributions to account for moderate to extreme deviations from the mean, where relative likelihoods in the cohort far exceeded those of a normal distribution. Normal and lognormal distributions result from the accumulated effects of a large number of independent additive (normal) or multiplicative (lognormal) events. Thus, while most placentas appear to develop by a series of small, regular, and independent steps, the presence of heavy-tailed distributions suggests that many show shape features which are more consistent with a large number of correlated steps or fewer, but substantially larger, independent steps.