A predictive model of a growing fetus

Fetal growth is monitored periodically during pregnancy via ultrasound measurements of fetal dimensions such as femur length (FL), head circumference (HC), abdominal circumference (AC), and biparietal diameter (BPD). Multiple growth standards have been published for each of these, which are clinically used to place a fetus on a "growth chart". These consist of percentile tables varying by weeks of gestation, computed from cohorts of "low-risk" women with healthy lifestyles, living conditions, and clinical parameters. Such charts are prescriptive of ideal growth, but not necessarily descriptive of diverse real-world populations where they may be used. Moreover, they are constructed by pooling all fetal measurements across the cohort, not based on a growth model, and therefore not necessarily predictive of growth of an individual fetus. We show that the Gompertz model, a standard model for constrained growth, with just three intuitive parameters, convincingly fits the growth of fetal ultrasound biometries. Two of these parameters - t0 (the inflection time) and c (the rate of decrease of growth rate) - can be treated as universal to all fetuses, while the third parameter A can be modeled as an overall scale parameter specific to each fetus, which captures the individual variation in growth. On our cohort of 817 pregnant women ("Seethapathy cohort"), we show that not only can the value of A for each fetus be inferred from ultrasound data available by the second or the third trimester, but the weight of the baby at delivery can also be predicted with remarkable accuracy using these inferred Gompertz parameters. A model trained on the Seethapathy cohort performs well in estimating the birth weight in an independent validation cohort of 365 women, demonstrating the predictive power of the model. Moreover, we find that deviation from Gompertz-like growth is linked to neonatal complications. Finally, we show that the Gompertz growth curve is a close fit to the standards from WHO, NICHD and INTERGROWTH, with the optimal t0 and c close to that in the Seethapathy cohort. We propose that the Gompertz formula be a basis for future growth standards, with almost all variation described by a single scale parameter A, which can serve either as a descriptor of mean or variance in population, or as a descriptor for growth of an individual fetus. Indeed, the formula is descriptive of typical growth, predictive of future growth, and may be used in prescriptive standards.