Use of a modified Michaelis-Menten equation to estimate growth from birth to 3 years in healthy full term babies.

Mathematical models that accurately describe growth in human infants are lacking. We used the Michaelis-Menten equation, initially derived to relate substrate concentration to reaction rate, and subsequently modified and applied to nonhuman vertebrate growth, to model growth in humans from birth to 36 months. We compared the model results to actual growth values from two pediatric cohorts. The modified Michaelis-Menten equation showed excellent fit for both infant weight (median RMSE: boys: 0.22kg [IQR:0.19; 90%<0.43]; girls: 0.20kg [IQR:0.32; 90%<0.39]) and height (median RMSE: boys: 0.93cm [IQR:0.53; 90%<1.0]; girls: 0.91cm [IQR:0.50;90%<1.0]). Using permutations of dropped data, few combinations of time points were critical to optimizing model fit. This modified Michaelis-Menten equation accurately describes growth in humans aged 0-36 months, allowing imputation of missing weight and height values in individual longitudinal measurement series. The pattern of growth in healthy babies raised in resource-rich environments mirrors the saturation curve of a basic enzymatic reaction.