The aim of this study was to propose simple mathematical formulae to estimate median values of fetal biometry including biparietal diameter (BPD), abdominal circumference (AC) and femur length (FL) at each gestational age (GA) easily without looking up the previously established reference values.
Simple mathematical formulae to estimate median values of fetal biometric values at each gestational week were inferred. To validate these formulae, three different linear equations were derived from previously reported reference values of median BPD, AC and FL using regression analysis at each gestational week. Finally, calculated data through the inferred formula were compared to retrospectively collected data (observed data).
The equation revealing the relationship between BPD and GA was: median BPD (cm)=GA (wk)/4. Using this simple mathematical formula, the absolute percentage error between observed data and calculated data ranged from 0.12% to 7.50%. The equation between AC and GA was: median AC (cm)=GA (wk)-5. Through this formula, the absolute percentage error was analyzed same as above and it ranged from 0.30% to 4.76%. Lastly the derived formula between FL and GA was: median FL (cm)=GA (wk)/5 and the absolute percentage error ranged from 4.52% to 16.75%.
The three simple formulae suggested in our study showed a significantly easy way to estimate the median values of fetal biometry at each gestational week with good reliability.
Ultrasound has become the essential tool of modern obstetric practice [
The aim of this study was to propose simple mathematical formulae to estimate median values of fetal biometry including BPD, AC and FL at each GA easily without looking up the previously established reference values.
We had an impression that the positive correlation between GA and median (defined as 50th percentile) biometric values could be expressed in simple mathematical formulae. Looking through the values of GA and biometric values in the references [
We retrospectively reviewed medical records of 832 pregnant Korean women who underwent serial ultrasound examinations and delivered at Seoul National University Bundang Hospital from January 2008 to December 2008. A cross-sectional study was performed among singleton pregnancies with available records of at least 3 or more ultrasound evaluations of fetal biometry after GA 20 weeks. Those who delivered at term (from GA 37 weeks) were included regardless of delivery mode. Patients with multifetal gestation, intrauterine growth restriction, hypertensive disorders such as preeclampsia, gestational diabetes mellitus, overt diabetes mellitus, major fetal anomalies (including heart, central nervous system, skeletal, gastrointestinal and genitourinary anomaly), systemic disease or medication history which might affect fetal growth and fetal death in utero cases were excluded. After excluding the aforementioned cases, a total of 194 cases and 1,157 sonographic measurements were selected for analysis. Prenatal visits were scheduled at 4-week intervals until 28 weeks, then every 2 weeks until 36 weeks, and weekly thereafter [
Simple linear regression was done using previously known reference values to validate the inferential equations between GA and each biometric value. Reference values were cited from
Simple linear regression analysis was performed. The results were analyzed using IBM SPSS ver. 21.0 (IBM Corp., Armonk, NY, USA). A
We came up with inferential mathematical formulae between GA (wk) and median fetal biometric values (cm). Median BPD=GA/4. Median AC=GA-5. Median FL=GA/5
In attempt to validate these inferential equations, we performed simple linear regression analysis with known reference values (
In addition to validating the inferential equations through known reference values, we applied the inferential equations to observed data to see how capable these formulae were in explaining real measurements. Observed data were collected from 194 cases, and the differences between observed and calculated data were analyzed. The calculated, observed and reference values are depicted in graph form in
Evaluating adequacy of fetal growth is one of the most essential part of prenatal care. Evaluation of not only estimated fetal weight but also each biometric parameter (BPD, FL, and AC) is also important. There have been several mathematical formulae proposed by different authors which estimate the relationship between GA and fetal biometric values [
Another significant finding of this study was discovering the coefficient of the formula for each biometric value. By knowing the gradient of each graph, the derived formulae let us take notice of other aspects of fetal growth rate and its prediction. For instance, through the equation BPD=GA/4, we can assume that fetal BPD increases approximately 1 cm every 4 weeks on average. In the same way, we can expect fetal AC to increase approximately 1 cm every week, and fetal FL to increase approximately 1 cm every 5 weeks on average. Knowledge of such biometric growth trends helps obstetricians in counseling patients by providing simple and easy explanations to those who are curious about their baby's growth trend. Also, in situations when the BPD plane is inevitably measured inadequately due to fetal position, by knowing the growth trend of fetal BPD, the examiner can have in mind the estimated value.
The limitation of this study is the relatively small number (n=194) of patients whose biometric values were used to validate our equations. Also, our observed data were limited to women who delivered at a single tertiary hospital which may not adequately represent the whole Korean population. Lastly, the proposed equations may seem oversimplified and thus not completely fit mathematically, especially if compared to other previously proposed models [
SE, standard error; BPD, biparietal diameter; AC, abdominal circumference; FL, femur length.
a)Coefficient of determinant.
BPD, biparietal diameter; AC, abdominal circumference; FL, femur length; SD, standard deviation.
a)Median value of difference; b)Mininum value of difference; c)Maximum value of difference.
GA, gestational age; BPD, biparietal diameter; AC, abdominal circumference; FL, femur length.
a)Absolute % error: [(calculated data-observed data)/calculated]×100.
GA, gestational age; FL, femur length; BPD, biparietal diameter; HL, humerus length.