Sonographic fetal weight estimation in prolonged pregnancy: comparative study of two- and three-dimensional methods




To compare two-dimensional (2D) and three-dimensional (3D) ultrasound techniques, including volumetry of fetal thigh, for fetal weight (FW) estimation in prolonged pregnancy, and to develop a new FW estimation formula.


This prospective comparative study initially included 176 pregnant women. FW estimation was performed at ≥ 287 days of gestation within ≤ 4 days of delivery. Fetal head, abdomen and femur were measured using 2D ultrasound techniques, and fetal thigh volume was estimated using 3D techniques. The formula of Persson and Weldner (2D) was compared with two 3D formulae published by Lee and colleagues. In a subgroup of 63 fetuses, volumetry of the abdomen was performed and a new formula was developed; this formula was tested prospectively, along with the previously published formulae, on a further 50 women (Test Group).


In the initial group of 176 pregnancies, the SD of the mean percentage error (MPE) was 6.3% for both the 2D Persson and Weldner formula and for the better performing 3D formula of Lee et al., but the MPE of this Lee formula differed significantly from zero. Significantly more FW estimations were within ± 10% of the birth weight when the 2D formula was used than when the 3D formulae were applied. The new formula gave a SD of MPE of 5.6% when applied to the data from which it was derived. In the Test Group, the SD of MPE was similar for the 2D formula, the second formula of Lee et al. and the new formula, with values of 7.0, 7.0 and 7.1, respectively, but only the Persson and Weldner formula showed a MPE that did not differ significantly from zero.


FW in prolonged pregnancies can be estimated using 2D sonography with the same accuracy as with 3D sonography. 3D ultrasound techniques require technically advanced and expensive equipment, special operator training and skills, and are time consuming. It does not seem reasonable to abandon the 2D ultrasound methods in favor of 3D ultrasound imaging for FW estimation. Copyright © 2009 ISUOG. Published by John Wiley & Sons, Ltd.


One of the main tasks of antenatal care is the early detection of fetal growth abnormalities. In pregnancies with intrauterine growth restriction (IUGR) the fetus is at increased risk of hypoxia and perinatal death, and delivery of macrosomic fetuses is associated with increased rate of Cesarean section, postpartum hemorrhage, and maternal and fetal injury. The injuries commonly sustained by macrosomic fetuses during delivery—clavicular fracture and brachial plexus injury—are often a result of shoulder dystocia1. Knowledge of fetal size is of great clinical importance in order to minimize the risks associated with abnormal fetal growth. If diagnosed antenatally, an IUGR fetus can be submitted to intensified surveillance and, for both IUGR and macrosomic fetuses, antenatal diagnosis can enable the optimization of delivery mode and timing2.

For many years two-dimensional (2D) sonography has been used for fetal weight (FW) estimation and it has proved to be useful in detecting IUGR fetuses3. However, when used for the detection of fetal macrosomia, ultrasound biometry is characterized by low sensitivity and low positive predictive value4, and most of the 2D formulae have a tendency to underestimate large fetuses5. The early approach to estimation of fetal size was based on the reported correlation between fetal abdominal circumference and birth weight (BW)6. Numerous subsequent attempts have combined various fetal biometric variables in regression equations or volumetric formulae, with varying degrees of accuracy. Several of these methods have significant systematic errors, and SD of errors < 7% is rarely reported2.

Hadlock et al. developed several formulae for FW estimation based on various combinations of fetal biparietal diameter (BPD), head circumference (HC), abdominal circumference (AC) and femur length (FL)7. In 1986, Persson and Weldner developed a formula for estimating FW based on BPD, mean abdominal diameter (AD) and FL8. They reported a SD estimation error of 7.1%. In Sweden the Persson and Weldner formula is used nationwide for FW estimation as part of antenatal care.

A study by Mongelli and Benzie, using computer modeling techniques, estimated the rate of sonographic diagnosis of macrosomia (fetal weight > 4500 g) for 18 ultrasound weight formulae reported in the literature4. The frequency of diagnosis of macrosomia increased with advancing gestational age at the time of ultrasound scan, a large increase occurring between 40 and 41 weeks. The type of weight formula used had a profound influence on the results, and the diagnosis of macrosomia was dependent on the population from which the formulae were developed and/or on the properties of the formulae. In general, sonographic weight estimation was more accurate in smaller fetuses at 34–37 weeks of gestation than in large fetuses at term.

Fetal growth is a complex developmental process that involves anatomical changes over time, suggesting that more complex measurements than diameters and circumferences might be needed to achieve greater precision in weight estimation, especially in macrosomic fetuses. In 1997, Lee at al. examined the feasibility of using fetal volume measurements obtained with three-dimensional (3D) sonography, including thigh volume and abdominal volume, in the prediction of BW9. The 3D-based formulae showed good precision in predicting BW.

The first aim of the present study was to compare, in prolonged pregnancies, FW estimation using 2D sonography with that using 3D sonography, including volumetry of the fetal thigh, using formulae described in the literature. The second aim was to develop a new formula based on a Swedish population of prolonged pregnancies using 3D ultrasound techniques, and to compare the accuracy of BW prediction using the new formula with that of previously published formulae.


From April 2005 to November 2006, 296 pregnant women, mostly of Caucasian origin (97%), participated in a prospective comparative study. The study was approved by the Regional Research Ethics Committee and all women gave their informed consent to participation. Inclusion criteria were: singleton pregnancy, ultrasound dating before 20 weeks of gestation, no fetal malformations, gestational age ≥ 287 days, and delivery ≤ 4 days following the ultrasound estimation of FW. One hundred and seventy-six women fulfilled the above criteria and constituted the Study Group (Group 1). Their data were used for a comparison of three previously published formulae8, 10, 11. While the study was ongoing, we decided to perform measurement of fetal abdominal volume as well. Therefore, only the last consecutive 63 women of the Study Group had abdominal volumetry performed and the new formula was based on these data (Subgroup 1a, Formula Group). Subsequently, another 50 women who fulfilled the study criteria were included to prospectively test all of the formulae (Group 2, Test Group) (Table 1).

Table 1. Demographic data of the study population
 Group 1 (Study Group, n = 176)Subgroup 1a (Formula Group, n = 63)Group 2 (Test Group, n = 50)
  • Values are median (range) or n (%).

  • *

    n = 160,

  • **

    n = 55,

  • ***

    n = 47; maternal weight was not available in all women.

  • Deviation from the expected birth weight according to the Swedish growth standard (of which 1 SD = 11%)24.

  • Birth weight > 2 SD below mean of standard population.

  • §

    Birth weight > 2 SD above mean of standard population.

 Age (years)32 (17–43)33 (17–42)32 (21–45)
 Nulliparous86 (48.9)31 (49.2)26 (52.0)
 Body mass index (kg/m2)24 (18–40)*24 (18–40)**27 (19–55)***
 Amniotic fluid index (mm)125 (12–350)117 (27–264)108 (5–293)
 Gestational age at examination (days)290 (287–294)290 (289–292)290 (288–293)
 Gestational age at delivery (days)292 (289–298)292 (289–295)291 (289–296)
 Birth weight (g)3938 (2740–5470)3901 (2750–5470)3968 (2875–5296)
 Birth weight deviation (%)1 (− 30 to + 39)0 (− 30 to + 37)2 (− 27 to + 30)
 Small-for-gestational age8 (4.5)5 (7.9)1 (2.0)
 Large-for-gestational age§7 (4.0)4 (6.3)2 (4.0)
 Macrosomia (birth weight > 4500 g)17 (9.7)5 (7.9)5 (10.0)
 Male gender103 (58.5)38 (60.3)30 (60.0)

Ultrasound examinations (both 2D and 3D) were performed using a Voluson Expert 730 ultrasound system (GE Kretztechnik, Zipf, Austria) with a real-time 4–8-MHz abdominal probe (RAB4-8L H48621Z). All measurements were performed by one operator (G.L.) and each fetus was examined on a single occasion. Three measurements of each fetal parameter (BPD, HC, AD, AC and FL) were performed in frozen images of subsequent scans and the means of the three values were used for further analysis. The fetal BPD was measured in the standard projection of the fetal head12, from the outer edge of the proximal parietal bone to the inner edge of the distal parietal bone. HC was measured in the same image as BPD, with an ellipse measurement tool from the frontal to the occipital part of the outer contour of the skull bone. The abdomen was measured in the standard cross-sectional plane at the level of the stomach and umbilical vein/ductus venosus complex. The AD was taken as the mean value of the anteroposterior and transverse diameters measured from the outer aspects of the abdominal contour. The same image was used for the measurement of AC by placing an ellipse around the outer border of the abdomen. FL was measured from the proximal end of the major trochanter to the distal metaphysis.

Subsequently, 3D ultrasound scans were performed to measure the volumes of the fetal thigh and abdomen according to the techniques described by Lee et al.10 and Schild et al.13, respectively. The 3D scan sweep of fetal thigh was taken from the projection corresponding to FL measurements, and the 3D scan sweep of the abdomen was performed from the plane used for AD measurements. Three volume datasets of the abdomen and thigh were acquired and stored. All measurements were obtained from images taken during periods without fetal movements and breathing movements. While the 3D sweep was running, for around 5–10 s, the mother was asked to hold her breath. Each volume acquisition took approximately 1 min.

Volume data of the abdomen and thigh were analyzed offline on the ultrasound machine using 4DView software version (GE Kretztechnik). Fractional thigh volume was measured as described previously, using a volume including 50% of the femoral diaphysis length centered on the midpoint14. This midpart of the volume was split into four equal sections and each of the five cross-sectional images was traced manually. Limb circumference measurements were performed in the five sections on the outer skin margin to include the subcutaneous fat and skin. Transverse, sagittal and frontal views were used to obtain an optimal image of the abdomen. In the sagittal plane, an arbitrary distance of 50 mm from the dome of the diaphragm towards the distal part of the abdomen was marked. In five transverse projections, 10 mm apart, the images were optimized to visualize the borders as clearly as possible, and the circumference of the outer border of the fetal abdomen was then traced manually13. Each offline measurement of the thigh volume and the abdominal volume took approximately 2–3 min.

For calculation of FW based on 2D measurements, the Persson and Weldner formula was used8, and for FW estimation based on 3D measurements, including fetal thigh volumetry, the two formulae by Lee et al. (Lee 110; Lee 211) were applied (Table 2).

Table 2. Fetal weight (FW) estimation formulae
FormulaReferenceRegression equation
  1. Abdvol, fractional abdominal volume; AC, abdominal circumference; AD, mean abdominal diameter; BPD, biparietal diameter; FL, femur length; HC, head circumference; Tvol, fractional thigh volume.

Persson and WeldnerPersson and Weldner 19868FW = BPD0.972 × AD1.743 × FL0.367 × 10−2.646
Lee 1Lee et al. 200110FW = 20.953 × Tvol + 113.571 × AC − 2375.068
Lee 2Lee et al. 200611Log FW = 11.1372 × BPD2 − 67.2281 × BPD + 1.2175 × AC2 − 17.3004 × AC − 0.0490 × Tvol2 + 25.3052 × Tvol + 285.429
New formulaCurrent studyFW = 2088.4904 + 81.0519 × HC − 0.1214 × HC2 − 69.0966 × AD + 0.4741 × AD2 + 6.4044 × Tvol + 0.0534 × Abdvol

The repeatability and reproducibility of thigh volume measurements were evaluated offline using images acquired by the first examiner in 20 randomly chosen fetuses included in the study. Three stored ultrasound volumes were used for each fetus and the examiners were blinded to the previous results, the estimated FW and the actual BW. The results for each single examiner and between the two examiners were evaluated using intraclass and interclass correlation coefficients. Both examiners had similar training and skills in calculating 3D volume measurements.

The BW prediction of each formula was evaluated by calculating the absolute error, the mean percentage error (MPE) calculated as:

equation image

and the number (%) of fetuses with an estimated FW within ± 5% and ± 10% of their BW.

Statistical analyses were performed using the statistical packages MedCalc version (MedCalc Software, Mariakerke, Belgium), Analyse-it (Analyse-it Software Ltd, Leeds, UK) and Statistical Package for the Social Sciences (SPSS Inc., Chicago, IL, USA).


Comparisons between the BW and estimated FW in Group 1 (Study Group) using the three published formulae are shown in Table 3. Of the two 3D formulae, the Lee 2 formula performed better than the Lee 1 formula. The accuracy of BW prediction using the 2D Persson and Weldner formula was similar to or even better than the accuracy obtained using 3D ultrasound volumetry. The SD of the MPE was equal, at 6.3%, for the Persson and Weldner and Lee 2 formulae, but the mean MPE of the Lee 2 formula differed significantly from zero. Significantly more FW estimations were within ± 10% of the BW when the Persson and Weldner formula was used than when the Lee 1 or Lee 2 formula was applied.

Table 3. Comparison between the fetal weight (FW) estimated by the three formulae and birth weight (BW) in Group 1 (Study Group, n = 176)
FormulaR2Absolute error (g)MPE (%)FW vs. BW agreement
FW within ± 5% of BWFW within ± 10% of BW
Mean (95% CI)SDMean (95% CI)SDn (%)95% CI (%)n (%)95% CI (%)
  1. MPE, mean percentage error (100 × (estimated FW − BW)/BW).

Persson and Weldner0.72− 121 (−160 to − 84)253.5− 2.7 (−3.6 to 1.7)6.388 (50)43–57151 (86)80–90
Lee 10.67− 42 (−97 to 12)366.2− 1.3 (−2.9 to 0.1)9.373 (41)34–48129 (73)66–79
Lee 20.71− 243 (−282 to − 205)259.6− 6.0 (−6.9 to − 5.0)6.370 (40)33–47125 (71)64–77

A new formula was developed based on the measurement of fetal BPD, HC, AD, FL, thigh volume and abdominal volume in the last consecutive 63 women of the study group (Subgroup 1a, Formula Group). For each variable, the regression against true weight was studied using equations of one to three exponential functions in all possible combinations (1st to 3rd degree polynomials) and the formula was selected which gave the best fit to the observed BW. The new formula is presented in Table 2, and the results of its application to the data of the subgroup from which it was derived are shown in Table 4.

Table 4. Agreement between the fetal weight (FW) estimated using the new formula and birth weight (BW) in Subgroup 1a (Formula Group, n = 63)
FormulaR2Absolute error (g)MPE (%)FW vs. BW agreement
FW within ± 5% of BWFW within ± 10% of BW
Mean (95% CI)SDMean (95% CI)SDn (%)95% CI (%)n (%)95% CI (%)
  1. MPE, mean percentage error (100 × (estimated FW − BW)/BW).

New formula (present paper)0.811 (−53.2 to 54.6)2140.3 (−1.1 to 1.7)5.639 (62)50–7358 (92)83–97

The new formula and the three formulae from the literature were applied prospectively to Group 2 (Test Group) (Table 5). The SD of MPE was similar for the new formula, Persson and Weldner and Lee 2 formulae, all of which were lower than that for the Lee 1 formula. Only the Persson and Weldner formula showed a MPE that did not differ significantly from zero. The SD estimates of 7.0, 7.0 and 7.1 for the Persson and Weldner formula, new formula and Lee 2 formula, respectively, each have their own error of ± 0.6; therefore, the SD of MPE of 9.4 ± 0.8 for the Lee 1 formula differs significantly from the other three. A chi-square test including the Lee 1 formula showed a highly statistically significant difference between the formulae with respect to the frequency of ± 5% (chi-square = 17.8, P < 0.001) and ± 10% (chi-square = 41.9, P < 0.001) agreement between estimated FW and BW. After exclusion of the Lee 1 formula no significant difference between the three remaining formulae was found ( ± 5%, chi-square = 0.9, P = 0.65; ± 10%, chi-square = 1.1, P = 0.58).

Table 5. Comparison of fetal weight (FW) estimation using the new three-dimensional formula and the three previously published formulae in Group 2 (Test Group, n = 50)
FormulaR2Absolute error (g)MPE (%)FW vs. BW agreement
FW within ± 5% of BWFW within ± 10% of BW
Mean (95% CI)SDMean (95% CI)SDn (%)95% CI (%)n (%)95% CI (%)
  1. BW, birth weight; MPE, mean percentage error (100 × (estimated FW − BW)/BW).

New formula0.68169 (94–244)2644.6 (2.6–6.6)7.026 (52)39–6543 (86)74–93
Persson and Weldner0.58− 57 (−140 to 225)295− 1.0 (−3.0 to 1.1)7.022 (44)31–5841 (82)69–90
Lee 10.67564 (459–669)37014.2 (11.5–16.8)9.47 (14)7–2617 (34)22–48
Lee 20.65148 (70–225)2724.1 (2.1–6.1)7.122 (44)31–5839 (78)65–87

Neither the maternal body mass index (BMI) nor the amount of amniotic fluid showed a significant relationship with the measurement error of any of the tested formulae. With regard to the reproducibility analysis of fetal thigh volume measurements, the interclass correlation coefficient was 0.72 (95% CI, 0.51–0.87), indicating good interobserver reproducibility. The intraclass correlation coefficients were 0.92 (95% CI, 0.80–0.97) and 0.93 (95% CI, 0.85–0.97) for Examiners I and II, respectively. This suggests an excellent intraobserver repeatability of fetal thigh volume measurements15.


The main aim of antenatal care is to prevent maternal and fetal/neonatal mortality and morbidity. To achieve this it is important, among other things, to identify fetuses with abnormal growth patterns14. The FW needs to be estimated as accurately as possible, preferably within a few percent of BW, to enable proper management of delivery. Several studies have compared FWs estimated at term by clinical palpation and by ultrasound imaging, and most of these have shown that sonography is the most accurate technique for predicting FW. However, in fetuses of normal size, at term or post-term, the clinical and sonographic estimation of FW showed similar accuracy16–20.

The majority of the most commonly used formulae for sonographic estimation of FW include measurements of the fetal head, abdomen and femur, either alone or in combination. These measurements are obtained using 2D ultrasound techniques that are well established and familiar to the sonographers who perform obstetric ultrasound examinations. Dudley reviewed formulae used for FW estimation based on 2D ultrasound techniques and found a general tendency to underestimate the weight in fetuses with high BW (≥ 4000 g)2. Overall, the methods showed wide variation in their systematic and random errors. The variations between methods and centers were attributed to differences in the study populations, observers, measurement protocols and equipment, or a combination of these factors. Dudley concluded that maternal BMI and fetal sex did not seem to significantly influence the measurement error, but reported that there was conflicting evidence regarding the influence of amniotic fluid volume on FW estimation. Other authors have found that different characteristics, such as lower gestational age, higher BW, anterior placenta, higher gravidity and younger maternal age, reduced the accuracy of BW prediction18, 21, 22. Maternal BMI and the amount of amniotic fluid did not have any significant effect on the accuracy of estimated FW. This was also our experience in the present study.

Mongelli and Benzie showed that FW estimation formulae perform best in populations that are similar to those from which they were originally derived, and that most of the formulae tend to overdiagnose macrosomia at term4. In their comparative study, the formula of Persson and Weldner had one of the lowest false-positive rates, when predicting macrosomia in relation to gestational age (41 gestational weeks) and FW.

In the present study, performed post-term, the Persson and Weldner formula showed lower false-positive rates than did 3D formulae for FW estimation of fetuses in prolonged pregnancies (Table 3). Our SD of MPE for the Persson and Weldner formula (6.3% and 7.0% in the Study Group and Test Group, respectively) were comparable to the SD reported in the original study (7.1%)8. No systematic overestimation of FW was observed, the MPE for the Study Group and the Test Group being −2.7% and −1.0%, respectively. These results should be considered bearing in mind that the formula of Persson and Weldner was developed from a population similar to that of our own study, and that the examiner in the present study had many years of experience estimating FW using this formula.

By using 3D ultrasound imaging it is possible to generate volume data sets of the fetus. There is published evidence that fetal limb volume measurements and abdominal volume measurements may be valuable in estimating FW2, 9–14. Lee et al. have developed several BW prediction models using 3D volumetric measurements of thigh, arm and abdomen, including one or more parameters1, 9–11. The models yielding the best results were those including BPD, AC and thigh volume. Somewhat surprisingly, we found the 2D method of FW estimation to perform better than the Lee 1 formula10 and similarly to the Lee 2 formula11. It could be argued that this may have been due to the examiner lacking sufficient experience in the use of 3D ultrasound imaging. However, the study was performed after an intense 1.5-year period of training and the result obtained for the Lee 2 formula (SD of MPE, 6.3%) was within the range originally reported in the studies by Lee et al. (6.6% and 6.2%)10, 11.

In an attempt to improve the accuracy of FW estimation using 3D ultrasound examination we developed a new formula, which was based on HC, AD, thigh volume and abdominal volume, acquired from our own population of fetuses in prolonged pregnancies. When applied to a new, independent group of 50 patients (Group 2, Test Group), the new formula performed better than the Lee 1 formula, but was not significantly better than the Lee 2 and Persson and Weldner formulae. The Persson and Weldner formula had a smaller mean error (− 1.0%) than the other formulae, all of which used 3D measurements, when applied to this group (Table 5). The size of the Test Group was restricted to 50 individuals and it cannot be excluded that a larger sample might identify some advantage of 3D weight estimation techniques. It is possible that the use of 3D measurements could provide greater accuracy in only a specific subgroup, for example in macrosomic fetuses, of which there were few in our study population (Table 1).

Our results indicate that the currently available 3D ultrasound techniques that enable volume estimation of individual fetal body parts are not sufficient to achieve greater accuracy in FW estimation in prolonged pregnancies. An imaging technique that allows measurement of the entire fetal body volume might give better results. Magnetic resonance imaging has been used for this purpose23, but it is not generally available and would not be cost effective. Further technical development of 3D ultrasound imaging, allowing volume acquisition of the whole uterus, might be another way of improving accuracy.

In summary, the present prospective comparative study showed that FW can be estimated using a well established 2D ultrasound method with accuracy that is fully comparable to that obtained using 3D ultrasound techniques including volumetry of the fetal thigh and abdomen. This was true both for the recently published 3D formulae and for a new formula based on the 3D measurements of our own population. 3D ultrasound techniques require technically sophisticated and expensive ultrasound equipment, special training and extra skills for examiners, and are time consuming. Therefore, it does not seem reasonable, at least at present, to abandon the 2D ultrasound methods in favor of 3D ultrasound imaging for FW estimation in prolonged pregnancy.


The authors thank Professor Bengt Källén, Center for Reproductive Epidemiology, Tornblad Institute, Lund University, and Data manager Håkan Lövkvist, Competence Center for Clinical Research, Lund University, for expert statistical help, fruitful discussions and encouragement.