Accurate birth weight prediction from fetal biometry using the Gompertz model

Monitoring of fetal growth and estimation of birth weight is of clinical importance. During pregnancy, ultrasound fetal biometry values including femur length, head circumference, abdominal circumference, biparietal diameter are measured and used to place fetuses on "growth charts". There is no simple growth-model-based, predictive formula in use for fetal biometry. Estimation of fetal weight at birth currently depends on ultrasound data taken a short time before birth.

Our cohort ("Seethapathy cohort") consists of ultrasound biometry measurements and other data for 774 pregnant women in Chennai, India, 2015-2017. We use the Gompertz model, a standard model for constrained growth, with just three intuitive parameters, to model the growth of fetal biometry, and a machine learning (ML) model trained on these parameters to predict birth weight (BW).

The Gompertz model convincingly fits the growth of fetal biometry values. Two Gompertz parameters- $t_0$ (inflection time) and $c$ (rate of decrease of growth rate)-seem universal to all fetuses, while the third, $A$ , is an overall scale specific to each fetus, capturing individual variation. On the Seethapathy cohort we can infer $A$ for each fetus from ultrasound data available by the 24 or 35 weeks. Our ML model predicts birth weight with < 8 % error, outperforming published methods that have access to late-term ultrasound data. The same model gives an 8.4 % error in BW prediction on an independent validation cohort of 365 women.

The Gompertz model fits fetal biometry growth and enables birth weight estimation without need of late-term ultrasounds. Aside from its clinical predictive value, we suggest its use for future growth standards, with almost all variation described by a single scale parameter $A$ .