The Optimal Prepregnancy Body Mass Index for Lactation in Japanese Women with Neonatal Separation as Analyzed by a Differential Equation

We used a differential equation to identify the biological relationship between the maternal prepregnancy body mass index (BMI) and lactation on postpartum day 4 in Japanese women with neonatal separation. This retro-spective observational study included 252 mothers (135 primiparas, 117 multiparas) whose singleton neonates were admitted to a neonatal ICU. We formulated hypotheses based on breast anatomy to analyze the relation-ship between the expressed milk obtained on postpartum day 4 and the maternal prepregnancy BMI with the following differential equation: y'(x) = k y(x)/x, where k is the constant, x is the prepregnancy BMI, and y is the expressed milk volume. The formula was then obtained as y(x) = axk, where a is the constant. The Akaike information criterion (AIC) was used to estimate the regression equation with the maximum likelihood for primiparas and multiparas. The best criteria for BMI determined by the AIC were 20.89 kg/m2 in primiparas and 20.19 kg/m2 in multiparas. These were the optimal BMI values for lactation, coinciding with the median prepregnancy BMI in the study population (20.78 kg/m2 in primiparas and 20.06 kg/m2 in multiparas). The formula based on biomathematics might help establish the biological relationship between prepregnancy BMI and breastmilk volume.