Formulae Based on Biomathematics to Estimate the Standard Value of Fetal Growth of Japanese

We devised biomathematics-based formulae to estimate the standard values of fetal growth of Japanese after 22 weeks' gestation. The growth rates of bi-parietal diameter (BPD), abdominal circumference (AC), femur length (FL), and estimated fetal body weight (EFBW) at the time of gestation were assumed to be proportional to the product of the value at the time and the rest value of an unknown maximum value, respectively. The EFBW was also assumed to follow a multiple logistic function of BPD, AC and FL to fit the standard values of Japanese fetuses published by the Japan Society of Ultrasonics in Medicine. The Mann-Whitney test was used for statistical analysis. The values as a function of gestational day, t, were as follows: BPD(t)=99.6/(1+exp (2.725−0.01837＊t)) (mm); AC(t)=39.7/(1+exp (2.454−0.01379＊t)) (cm); FL(t)=79.6/(1+exp (2.851−0.01710＊t)) (mm); EFBW(t)=8045.1/(1+exp (6.028−0.06582＊BPD(t)−0.1469＊AC(t)+ 0.07377＊FL(t))) (g). EFBW as a function of BPD, AC and FL was as follows: EFBW=8045.1/(1+exp (4.747+ 0.02584＊BPD+0.1010＊AC−0.1416＊FL)) (g). When the BPD, AC and FL were at −2 standard deviation (SD), −1SD, mean and + 2SD, the EFBW values calculated by the formula were statistically closer to the standard values than conventional formulas with p-values of 4.871×10−7, 4.228×10−7, 9.777×10−7 and 0.028, respectively. The formulae based on biomathematics might be useful to estimate the fetal growth standard values.