Allometric metabolic scaling and fetal and placental weight
  We tested the hypothesis that the fetal-placental relationship scales allometrically and identified modifying factors.   Among women delivering after 34 weeks but prior to 43 weeks gestation, 24,601 participants in the Collaborative Perinatal Project (CPP) had complete data for placental gross proportion measures, specifically, disk shape, larger and smaller disk diameters and thickness, and umbilical cord length. The allometric metabolic equation was solved for alpha and beta by rewriting PW= alpha(BW)^beta as Log (PW) = Log(alpha) + beta*Log(BW).   Mean beta was 0.78+ 0.02 (range 0.66, 0.89), 104% of that predicted by a supply-limited fractal system (0.75). Gestational age, maternal age, maternal BMI, parity, smoking, socioeconomic status, infant sex, and changes in placental proportions each had independent and significant effects on alpha. Conclusions: In the CPP cohort, the placental - birth weight relationship scales to approximately 3/4 power. 
Carolyn M. Salafia, Dawn P. Misra, Michael Yampolsky, Adrian K.   Charles, Richard K. Miller