Allometric Metabolic Scaling and Fetal and Placental Weight

Abstract

Background We tested the hypothesis that the fetal-placental relationship scales allometrically and identified modifying factors of that relationship. Materials and Methods 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, placental weight (PW), disk shape, larger and smaller disk diameters and thickness, and umbilical cord length. The allometric metabolic equation was solved for α and β by rewriting PW = α (BW)^β as ln (PW) = lnα + β [ln(BW)]. αɩ was then the dependent variable in regressions with p<0.05 significant. Results Mean β was 0.78± 0.02 (range 0.66, 0.89), which is consistent with the scaling exponent 0.75 predicted by Kleiber's Law.. Gestational age, maternal age, maternal BMI, parity, smoking, socioeconomic status, infant sex, and changes in placental proportions each had independent and significant effects on α. Conclusions We find an allometric scaling relation between the placental weight and the birth weight in the CPP cohort with an exponent approximately equal to 0.75, as predicted by Kleiber's Law. This implies that: 1) Placental weight is a justifiable proxy for fetal metabolic rate when other measures of fetal metabolic rate are not available; and 2) The allometric relationship between placental and birth weight is consistent with the hypothesis that the fetal-placental unit functions as a fractal supply limited system. Furthermore, our data suggest that the maternal and fetal variables we examined have at least part of their effects on the normal balance between placental weight and birth weight via effects on gross placental growth dimensions.

Use of a Bayesian hierarchical model to study the allometric scaling of the fetoplacental weight ratio

“…Another advantage is that it allows for the incorporation of a priori information that the researcher has about model parameters. 9 In the present study β was estimated to be 0.71, a value close to 3/4 and to that found by Salafia et al, 6 of 0.78. The coefficients associated with the co-variables PA, ESP, GA, sex and the interaction between PA, ESP and GA were not significant, possibly due to the small sample size, although the model achieved a reasonable fit.…”

“…These settings were determined from the evidence available in the literature. 6,8 Table 1 shows the point estimates of the parameters for β, ψ, σ 2 and σα and their respective confidence intervals of 95%. Table 1 Bayesian estimates of the parameters for β, ψ, σ 2 and σα : mean and quartiles of the pos terior dis tribution.…”

“…7 The value of β is often reported to lie within the range of 3/4 to 2/3. 7,8 These findings led, in the second half of the twentieth century (as cited in a previous study 6 ) to the suggestion that the fetoplacental weight ratio could be modeled as (PP) =α(PRN) β (PP: Placental weight; PRN: Birth weight). α would be a constant, in this case perhaps representing factors that may influence the metabolic efficiency of the placenta, for example.…”

“…5 Relationships between mass (M) and biological variables can be studied using allometric principles. 6,7 This approach was adopted by Max Kleiber to explore the relationship between baseline metabolic rate (BMR) and mass (BMR = BMR 0 M β ). 7 In this equation, β is called the allometric exponent, which must necessarily be different from 1.…”

“…In step 2, values for log(α) i are estimated using the expression log(α) i = log(PP) i -β log(PRN) i and then a new multiple regression model is estimated to assess the association of covariates, such as characteristics of the mother, the child and the placenta, through log(α). 6 The need for two steps in this analysis increases the probability of errors in the estimation of the model. The aim of the present study was therefore to use a hierarchical Bayesian model to improve the modeling of the relationship between PP and PRN.…”