A new mathematical formula for predicting long bone length in early pregnancy

To propose new mathematical formulae to estimate fetal long bone biometry in early pregnancy and to establish their efficacy in comparison to previously constructed mathematical formulae.

A study population of 1960 singleton euploid fetuses was referred for transvaginal ultrasound examinations between 71 and 112 days of gestation prior to genetic amniocentesis. To determine the relationship between the biparietal diameter and long bone length, a sample group of 400 randomly chosen normal fetuses was evaluated. Regression equations were derived, then tested in the remaining 1560 control fetuses and compared with previously reported mathematical formulae by other authors. Mean absolute error, mean absolute percentage error and mean systematic error with their standard deviations were calculated.

The relationships between femur or humerus length vs. biparietal diameter (BPD) and gestational age (GA) were, respectively: expected femur length = -16.92108 + 0.4569402 x BPD + 0.171617 x GA (P < 0.001) and expected humerus length = -16.28531 + 0.4283019 x BPD + 0.1696017 x GA (P < 0.001). The confidence intervals of the predicted values for different values of biparietal diameter and gestational age and confidence intervals for the regression coefficients, such as the distribution of the residuals, are given. All previous formulae obtained by transabdominal ultrasound demonstrated an overestimation of expected long bones measurements; this was reduced using different formulae obtained in early pregnancy. Using our mathematical formulae, the mean absolute percentage error and the mean systematic error in estimating femur and humerus length were very low (11.15% and -2.02%; 10.59% and -1.74%, respectively).

The new ultrasonographic morphometric models derived from transvaginal measurements in early pregnancy show a good reliability in estimating fetal long bone length.