### Objectives

To improve birth weight estimation in fetuses weighing ⩽ 1600 g at birth by deriving a new formula including measurements obtained using three-dimensional (3D) sonography.

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Original Paper# Weight estimation by three-dimensional ultrasound imaging in the small fetus

## Authors

### R. L. Schild,

Corresponding author- E-mail address: ralf.schild@uk-erlangen.de

- Department of Obstetrics and Gynecology, University Women's Hospital, Erlangen, Germany

- Frauenklinik, Universitätsklinikum, Universitätsstraße 21–23, 91054 Erlangen, Germany

### M. Maringa,

- Institute for Medical Informatics, Biometry and Epidemiology, Friedrich-Alexander University Erlangen-Nuremberg, Erlangen, Germany

### J. Siemer,

- Department of Obstetrics and Gynecology, University Women's Hospital, Erlangen, Germany

### B. Meurer,

- Department of Obstetrics and Gynecology, University Women's Hospital, Erlangen, Germany

### N. Hart,

- Department of Obstetrics and Gynecology, University Women's Hospital, Erlangen, Germany

### T. W. Goecke,

- Department of Obstetrics and Gynecology, University Women's Hospital, Erlangen, Germany

### M. Schmid,

- Department of Obstetrics and Fetal Medicine, University Women's Hospital, Bonn, Germany

### T. Hothorn,

- Department of Obstetrics and Fetal Medicine, University Women's Hospital, Bonn, Germany

### M. E. Hansmann

- Institute for Medical Informatics, Biometry and Epidemiology, Friedrich-Alexander University Erlangen-Nuremberg, Erlangen, Germany

- First published: Full publication history
- DOI: 10.1002/uog.6111 View/save citation
- Cited by (CrossRef): 12 articles Check for updates
- Funding Information

To improve birth weight estimation in fetuses weighing ⩽ 1600 g at birth by deriving a new formula including measurements obtained using three-dimensional (3D) sonography.

In a prospective cohort study, biometric data of 150 singleton fetuses weighing ⩽ 1600 g at birth were obtained by sonographic examination within 1 week before delivery. Exclusion criteria were multiple pregnancy, intrauterine death as well as major structural or chromosomal anomalies. A new formula was derived using our data, and was then compared with currently available equations for estimating weight in the preterm fetus.

Different statistical estimation strategies were pursued. Gradient boosting with component- wise smoothing splines achieved the best results. The resulting new formula (estimated fetal weight = 656.41 + 1.8321 × *volABDO* + 31.1981 × *HC* + 5.7787 × *volFEM* + 73.5214 × *FL* + 8.3009 × *AC* − 449.8863 × *BPD* + 32.5340 × *BPD*^{2}, where volABDO is abdominal volume determined by 3D volumetry, HC is head circumference, volFEM is thigh volume determined by 3D volumetry, FL is femur length and BPD is biparietal diameter) proved to be superior to established equations in terms of mean squared prediction errors, signed percentage errors and absolute percentage errors.

Our new formula is relatively easy to use and needs no adjustment to weight percentiles or to fetal lie. In fetuses weighing ⩽ 1600 g at birth it is superior to weight estimation by traditional formulae using two-dimensional measurements. Copyright © 2008 ISUOG. Published by John Wiley & Sons, Ltd.

Most of the currently available fetal weight formulae were first described more than two decades ago at a time when a very small fetus was often considered to be previable. As a consequence, only few cases with very low birth weight were included in formula descriptions1. Furthermore, none of the established formulae2–5 considers soft tissue thickness despite evidence that abnormal tissue content may be a reliable indicator of fetal growth aberrations6–8. Catalano *et al.* demonstrated that neonatal fat mass, although representing only 14% of weight at birth, explains 46% of its variance9. Recent advances in neonatal medicine have lowered the threshold of survival to a gestational age of 23–24 weeks and to a birth weight of approximately 500 g. As neonatal risks of morbidity and mortality are highest in the lowest weight range, diagnostic assessment of the small fetus should be as precise as possible10. The present study was undertaken to determine whether the addition of upper arm volume, thigh volume and abdominal volume to standard two-dimensional (2D) measurements could improve the accuracy of fetal weight estimation in the small fetus. As in a previous biometry study published by our group, birth weight of ⩽ 1600 g was chosen as the cut-off11.

Based on the data of 150 predominantly Caucasian women in a prospective cohort study, collected during a 9-year period (1998–2002, Department of Obstetrics and Fetal Medicine, University of Bonn; 2003–2006, Department of Obstetrics and Gynecology, University of Erlangen), and for whom a complete set of data was available, a new formula for optimized fetal weight prediction in the small fetus was generated. The study was approved by the local ethics committees of the universities of Bonn and Erlangen, Germany, and informed consent was obtained before study entry.

Ultrasound examinations were performed specifically for the purpose of the study. Inclusion criteria were a singleton live fetus at the time of study entry, estimated birth weight of ⩽ 2000 g using the Hadlock formula1, and fetal biometry within 7 days before delivery. Multiple pregnancies, intrauterine fetal death at presentation and infants with major structural or chromosomal anomalies were excluded as were those pregnancies with incomplete information, with actual birth weight above 1600 g or where delivery occurred more than 7 days after the last ultrasound examination. In cases where fetal growth or condition had been followed serially the last examination before delivery was considered; each fetus was included only once. All measurements were performed by the principal investigator (R.L.S.) using a Voluson 530D, Voluson 530 MT or Voluson Expert ultrasound machine (GE Medical Systems, Solingen, Germany). Gestational age determined from the last menstrual period and confirmed by first- or second-trimester biometry was given in days. Gestational age was based on crown–rump length obtained in the first trimester if there was uncertainty about the true gestational age.

Biparietal diameter (BPD) measurements were taken from the outer edge of the proximal fetal skull bone to the outer edge of the distal bone2. No correction was made for different shapes of the fetal head in non-vertex presentations. The head circumference (HC) was calculated from the measurement of the occipitofrontal diameter and the BPD using the formula 2.325 × (d_{1}^{2} + d_{2}^{2})^{1/2}, where d_{1} and d_{2} were the two diameters2. The transverse diameter and circumference of the fetal abdomen (AC) were measured in standard transverse planes at the levels of the stomach and umbilical vein–ductus venosus complex. The circumference was calculated by derivation from the measurement of the transverse and anteroposterior diameters using the formula π × (d_{1} + d_{2})/212. Femur length (FL) was measured from the proximal end of the greater trochanter to the distal metaphysis.

Details of the three-dimensional (3D) ultrasound system used and the principles of fetal upper arm and thigh volumetry have been described elsewhere13–15. In brief, with the fetus at rest the transducer was placed to display the femur closest to the transducer in the traditional plane for measuring the FL. Care was taken that the whole contour of the thigh could be clearly seen on the screen. This demonstrated the area of interest with the size of the volume box adjusted accordingly. Sweep speed was set on medium to avoid motion artifacts. The transducer was then initiated to perform an automated volume sweep through the outlined object. The rendered volume was displayed in three orthogonal planes on the screen and subsequently stored on a magneto-optical disc for later analysis.

After retrieval from storage the dataset was rotated to a standard anatomical orientation with the sagittal, transverse and frontal view positioned in upper left, upper right and lower left plane, respectively. For final review, the area of interest was rotated into the optimal position. Subsequent volume measurements were performed in the upper right plane with the femur in the transverse plane. Starting from the left to the right end of the femur shaft, the contour of the thigh was outlined with a cursor and stored. The contouring procedure was repeated whenever the shape of the thigh visually changed or every 3 mm, whichever condition was met first. The built-in computer calculated the volume of the thigh (volFEM) automatically by integrating the area and thickness of each slice. Volumetry of the upper arm was performed accordingly. Measurements of fetal limb circumferences were not performed.

A similar principle was used for the technique of abdominal volumetry (volABDO measurement). After abdominal volume sampling in the traditional plane for conventional 2D measurements the dataset was rotated to a transverse, sagittal and frontal view in the upper left, upper right and lower left plane, respectively. In the sagittal plane an arbitrary distance of 50 mm from the dome of the diaphragm to the distal part of the abdomen was marked with arrows. In a subsequent step, the circumference of the fetal abdomen was traced manually in the transverse plane, with the contouring procedure repeated whenever the shape of the abdomen changed. Area tracing was performed between the marked endpoints in the upper right plane and the final volume of the sampled area was calculated as described above. Total time spent on volume determinations was 10–15 min. Even though the number of cases with oligohydramnios was not further specified, it was our subjective impression that a small amount of amniotic fluid did not significantly impede volume determination. All cases fulfilling our inclusion criteria were entered into the final statistical analysis. 2D ultrasound measurements were expressed in centimeters, 3D volumetric results in milliliters and weight in grams. Birth weight and length were obtained within 1 h of delivery by our nursing staff.

To derive the best-fit formula for weight estimation, four statistical estimation techniques were applied:

- 1.Gradient boosting with component-wise smoothing splines (gamboost)16–18. This technique fits an additive regression model where the response variable (i.e. birth weight) is a sum of smooth functions of the covariates. The former are represented as splines, which can either be non-linear or linear functions of the covariates. When fitting the additive model, gradient boosting automatically selects a subset of relevant covariates out of the total of all covariates.
- 2.Linear modeling using stepwise variable selection (lm). This technique fits a linear regression model where the response variable is a weighted sum of the covariates. The covariates are not transformed. The selection of relevant covariates is done in a stepwise fashion19.
- 3.Multiple fractional polynomial models (mfp)20, 21. This technique fits an additive regression model where the response variable is a sum of transformed covariates. The transformation functions of the covariates are not represented as splines as with gradient boosting but are restricted to be either power functions (of various degrees between − 2 and 3) or logarithmic transformations. The mfp method has a built-in variable selection mechanism which is similar to that of lm.
- 4.Random forests (rforest)22. This technique is an extension of the well known classification and regression tree (CART) method22. With the CART method a decision tree based on binary splits is fitted to the data. The rforest method is an improvement over CART because its prediction is based on a combination of several decision trees, where each tree is built from a different set of predictor variables. In addition to being computationally efficient, the rforest method is known to produce highly accurate prediction results22.

All four methods use the squared error loss, which is well known from linear modeling (lm) as the main loss criterion to be minimized. Whereas lm is a standard estimation technique, gradient boosting, mfp and rforest are relatively new approaches leading to a more flexible determination of regression models. We employed the latter techniques as they allowed both estimation of transformation functions of the covariates and selection of relevant covariates.

To determine the predictive power of the four techniques (i.e. to assess which performed best), the following strategy was applied. First, 100 bootstrap samples with a size of 150 each were drawn from the complete dataset. These samples were then used as training samples, i.e. each of the four estimation techniques was applied to each of the 100 bootstrap samples. For each bootstrap sample the observations included in the complete dataset but *not* in the bootstrap sample were used as a test sample for predicting birth weight. The rationale behind this testing strategy was that it allowed a much more accurate estimation of prediction errors than splitting the complete dataset into one training and one test sample only23.

In order to compare the four estimation techniques, the mean squared prediction error (MSE) was computed for each of the 100 test samples and for each of the four estimation techniques. MSE, which is a standard measure for summarizing the distribution of the prediction errors of a test sample, is defined in the following way:

where the index *k* = 1, …4 denotes the number of the estimation technique, the index *p* = 1, …100 the number of the test sample, the index *i* the observation number in the test sample, *N*_{p} the number of observations in the test sample *p*, bw the true birth weight and the predicted birth weight. For each of the four estimation techniques we obtained 100 MSE values. In general, MSE takes *both* bias and variance of the prediction errors into account. To take *relative* prediction errors into account, we additionally computed the mean absolute percentage predictive error (MAE) from the 100 test samples. MAE is defined as follows:

MSE and MAE values from the 100 test samples were also computed for standard weight estimation formulae (Schild 2D11, Hadlock1, Scott24, Weiner A and Weiner B25, Mielke 126 and Mielke 227). To allow a comparison of the four estimation techniques with standard weight estimation formulae, we re-estimated the coefficients of the standard weight estimation formulae in each of the 100 training samples by means of multiple regression analysis.

All statistical analyses were performed using the statistical software package R, version 2.4.1 (mboost, version 0.6–228, 29; mfp, version 1.3.2; randomForest, version 4.5–18). For all techniques we used the standard tuning parameters provided by the respective R package. A previous repeatability study for all volume estimations demonstrated a statistically significant degree of agreement between different measurements (*n* = 10) taken by the principal observer15. To detect differences in the MSE and MAE values between the four estimation techniques and traditional formulae, Friedman's test procedure was applied. Pairwise comparisons between the four estimation techniques were performed using the Wilcoxon–Nemenyi–McDonald–Thompson test30. The prediction errors obtained from the resulting new formula were additionally summarized by means of signed percentage errors and absolute percentage errors obtained from all 100 test samples.

The clinical data of our study patients and their infants are shown in Table 1. Applying Friedman's test to the 100 MSE and MAE values of the four estimation techniques resulted in *P* < 0.001 for both MSE and MAE. The means and medians of the MSE and MAE values, as well as pairwise comparisons between the MSE and MAE values, showed that gamboost performed significantly better than did the other estimation techniques, and also better than standard weight formulae (Tables 2–4).

Parameter | Mean ± SD (range) or % |
---|---|

- *
According to Voigt *et al.*45.
| |

Gestational age at ultrasound (weeks) | 28.5 ± 3.6 (18.6–36.4) |

< 24 + 0 | 8.6 |

24 + 0 to 30 + 0 | 57.4 |

> 30 + 0 | 34.0 |

Parity | 0.8 ± 1.5 (0–10) |

Birth weight (g) | 960 ± 357 (260–1580) |

< 500 | 8 |

500–1000 | 47.3 |

> 1000 | 44.7 |

Birth weight centile* | |

< 10^{th} | 42.8 |

> 90^{th} | 0 |

Fetal gender | |

Female | 45.3 |

Male | 54.7 |

Birth length (cm) | 34.8 ± 4.5 (25–45) |

Technique | Median MSE | Mean MSE | Median MAE | Mean MAE |
---|---|---|---|---|

lm | 7238.912 | 7698.600 | 8.371 | 8.418 |

mfp | 6927.573 | 7602.537 | 7.893 | 8.015 |

rforest | 6628.042 | 7083.351 | 8.014 | 8.014 |

gamboost | 6193.017 | 6700.216 | 7.624 | 7.671 |

Technique | MSE predictions | MAE predictions | ||||
---|---|---|---|---|---|---|

lm | mfp | rforest | lm | mfp | rforest | |

Values are *P*-values for pairwise comparisons.*P*< 0.001 in Friedman's test for both MSE and MAE predictions.- *
Significant differences at the 0.05 level. gamboost, gradient boosting with component-wise smoothing splines16–18; lm, linear modeling using stepwise variable selection19; mfp, multiple fractional polynomial models20, 21; rforest, random forests22.
| ||||||

gamboost | < 0.001* | < 0.001* | 0.013* | < 0.001* | < 0.001* | < 0.001* |

lm | 0.038* | < 0.001* | 0.061 | 0.227 | ||

mfp | 0.202 | 0.934 |

Formula | Hadlock1 | Scott24 | Weiner A25 | Weiner B25 | Mielke 126 | Mielke 227 | Schild 2D11 |
---|---|---|---|---|---|---|---|

The coefficients of the traditional formulae were re-estimated for each of the 100 training samples by means of multiple linear regression analysis. Values are *P*-values for pairwise comparisons.*P*< 0.001 in Friedman's test for both MSE and MAE. Hadlock formula used: Log(EFW) = 1.5662 − 0.0108(HC)+ 0.0468(AC)+ 0.171(FL)+ 0.00034(HC)^{2}− 0.003685(AC × FL)^{1}.- *
Significant differences at the 0.05 level. AC, abdominal circumference; 2D, two dimensional; EFW, estimated fetal weight; FL, femur length; HC, head circumference.
| |||||||

MSE predictions | |||||||

gamboost | < 0.001* | < 0.001* | < 0.001* | < 0.001* | < 0.001* | < 0.001* | < 0.001* |

Hadlock1 | 0.999 | 0.413 | < 0.001* | < 0.001* | < 0.001* | 0.832 | |

Scott24 | 0.707* | < 0.001* | < 0.001* | < 0.001* | 0.561 | ||

Weiner A25 | < 0.001* | < 0.001* | < 0.001* | 0.008* | |||

Weiner B25 | 1.000 | 1.000 | < 0.001* | ||||

Mielke 126 | 1.000 | < 0.001* | |||||

Mielke 227 | < 0.001* | ||||||

MAE predictions | |||||||

gamboost | < 0.001* | < 0.001* | < 0.001* | < 0.001* | < 0.001* | < 0.001* | < 0.001* |

Hadlock1 | 0.999 | 0.777 | < 0.001* | < 0.001* | < 0.001* | 0.824 | |

Scott24 | 0.865 | < 0.001* | < 0.001* | < 0.001* | 0.726 | ||

Weiner A25 | < 0.001* | < 0.001* | < 0.001* | 0.051 | |||

Weiner B25 | 0.999 | 0.999 | < 0.001* | ||||

Mielke 126 | 1.000 | < 0.001* | |||||

Mielke 227 | < 0.001* |

After determining gamboost to be the best performing estimation technique we carried out a detailed analysis of the function estimates obtained with this technique. The results of this analysis are shown in Figure 1, where the function estimates obtained from the complete dataset are illustrated. Function estimates of HC, volABDO, volFEM, FL and AC were approximately linear, whereas the function estimate of BPD was approximately quadratic (Figure 1). Other covariates were not selected by the gamboost technique (data not shown). On the basis of these results, we obtained our final formula by estimating a linear regression model with the covariates HC, volABDO, volFEM, FL, AC and BPD, the latter after quadratic transformation. To assess the predictive power of our model we estimated its coefficients from the 100 training samples and computed signed percentage errors and absolute percentage errors from the respective test samples. Mean, SD and quartile values of the signed and absolute percentage errors of the pooled distribution of all 100 test samples are shown in Tables 5 and 6, along with the signed and absolute percentage errors obtained from standard formulae for weight estimation. Although the mean signed percentage errors of the new method and of the standard formulae for weight estimation did not differ significantly in all cases (which is due to the use of sample-specific coefficients), a test on the corresponding variances of the signed percentage errors proved that the new method had a significantly smaller variance than did standard formulae (Tables 5 and 7). Table 8 further characterizes the distribution of absolute percentage errors. Error distributions of the new method and of traditional formulae differed significantly (Chi-square test, *P* < 0.001). Prediction accuracy between the formulae, within 5% of actual birth weight, was also examined for frequency differences by Cochran's Q test (*P* < 0.001). Tables 5–8 demonstrate that the new 3D formula performed better than standard formulae for weight estimation. Finally, estimating the coefficients of the final model from the complete dataset yielded the following best-fit formula for weight estimation:

Formula | Mean | Median | SD | 25% quartile | 75% quartile |
---|---|---|---|---|---|

2D, two dimensional.
| |||||

Schild 3D | 0.66 | 0.71 | 9.55 | − 4.93 | 5.91 |

Hadlock1 | 0.72 | 0.14 | 10.38 | − 6.04 | 6.58 |

Scott24 | 0.84 | 0.26 | 10.46 | − 5.98 | 6.40 |

Weiner A25 | 0.69 | 0.45 | 10.43 | − 6.15 | 6.19 |

Weiner B25 | 0.75 | − 0.11 | 11.17 | − 7.25 | 7.96 |

Mielke 126 | 0.97 | 0.32 | 12.50 | − 6.88 | 7.92 |

Mielke 227 | 0.97 | 0.32 | 12.50 | − 6.88 | 7.92 |

Schild 2D11 | 1.24 | 0.61 | 10.40 | − 5.37 | 7.01 |

Formula | Mean | Median | SD | 25% quartile | 75% quartile |
---|---|---|---|---|---|

2D, two dimensional.
| |||||

Schild 3D | 7.13 | 5.43 | 6.39 | 2.58 | 9.57 |

Hadlock1 | 7.97 | 6.32 | 6.69 | 2.93 | 11.33 |

Scott24 | 8.03 | 6.16 | 6.76 | 2.69 | 11.77 |

Weiner A25 | 8.01 | 6.17 | 6.72 | 3.12 | 11.10 |

Weiner B25 | 8.81 | 7.60 | 6.90 | 3.67 | 12.25 |

Mielke 126 | 9.26 | 7.33 | 8.46 | 2.98 | 12.87 |

Mielke 227 | 9.26 | 7.33 | 8.46 | 2.98 | 12.87 |

Schild 2D11 | 7.89 | 6.19 | 6.88 | 2.78 | 11.26 |

Formula | Hadlock1 | Scott24 | Weiner A25 | Weiner B25 | Mielke 126 | Mielke 227 | Schild 2D11 |
---|---|---|---|---|---|---|---|

- *
Significant differences at the Bonferroni-adjusted level 0.0071. 2D, two dimensional.
| |||||||

t-tests | 0.583 | 0.067 | 0.795 | 0.495 | 0.028 | 0.028 | < 0.001* |

Correlated variance tests | < 0.001* | < 0.001* | < 0.001* | < 0.001* | < 0.001* | < 0.001* | < 0.001* |

Formula | < 5% | < 10% | < 15% | < 20% |
---|---|---|---|---|

Values are percentages. A Chi-square test of the homogeneity of the distributions resulted in *P*< 0.001. Cochran's Q test on frequency differences between the formulae (smaller than 5% vs. larger than 5%) also resulted in*P*< 0.001. 2D, two dimensional.
| ||||

Schild 3D | 47.10 | 76.74 | 89.47 | 94.47 |

Hadlock1 | 40.61 | 69.85 | 86.90 | 94.53 |

Scott24 | 42.52 | 67.44 | 86.30 | 93.45 |

Weiner A25 | 41.75 | 69.90 | 86.72 | 94.66 |

Weiner B25 | 33.82 | 63.97 | 84.71 | 93.91 |

Mielke 126 | 38.53 | 63.39 | 81.07 | 90.30 |

Mielke 227 | 38.53 | 63.39 | 81.07 | 90.30 |

Schild 2D11 | 41.52 | 69.79 | 86.96 | 94.66 |

Most of the commonly used formulae for estimating fetal weight in the low weight range were derived from infants of appropriate size close to term. These calculations, including measurements of the head, abdomen and femur, are still widely used in predicting weight of the small fetus despite evidence that no single formula can provide reliable estimations across the whole fetal weight range26. Few weight formulae were designed specifically for the small fetus remote from term. Theoretically, these formulae can improve weight prediction by accounting for the altered head–abdomen ratio and for growth restriction often found in these fetuses24. Importantly, fetal weight correlates better with soft tissue content than with 2D measurements9. To this end several studies have used, with varying degrees of success, a variety of ultrasound measurements to account for the soft tissue content13, 14, 31–44. To the best of our knowledge, our study is the first to investigate the role of 3D ultrasound imaging in improving fetal weight estimates in the low birth weight range.

Previous work by Medchill *et al.* compared the actual birth weight of 76 extremely low birth weight neonates (500 g–1000 g) with estimations derived from 20 published formulae10. None of the tested formulae estimated fetal weight significantly more accurately than any other. Weiner *et al.* developed a weight formula for the preterm fetus, including head, abdomen and FL measurements, and the results of their new formula compared favorably with those of other formulae25. One of the largest such studies to date, by Scott *et al.*, included 142 cases with a fetal weight of < 1000 g24. The newly generated best-fit formula was evaluated prospectively using data from 27 fetuses with a birth weight between 420 g and 1080 g, and it achieved the lowest mean percentage error compared with 10 other formulae available at the time. Mielke *et al.* described a new weight formula for infants delivered before 30 weeks of gestation, weighing between 400 g and 1680 g26. The data of 73 cases were used to develop a new best-fit formula. In cases of non-vertex fetal lie, BPD measurements were corrected using standard HC charts. Separate coefficients for different weight percentile groups further improved the accuracy of weight prediction. The same authors undertook another study to test the accuracy of their previously described formulae in a group of 62 premature infants of less than 30 weeks' gestation with a weight of ⩽ 1400 g27. Combining data from the two studies, the authors then calculated new coefficients for their different formulae. Using separate sets of coefficients fetal weight prediction could be further improved.

The measurement data of our previous study on fetal weight prediction in the very small fetus, containing one of the largest published series of such estimates for this group, were obtained by 2D ultrasound examination. The results demonstrated that the new formula allowed reliable weight prediction in the very small fetus of ⩽ 1600 g weight, irrespective of the weight percentile or the gestational age11. When we tested our published 2D formula11 against the newly developed 3D formula, weight determination by the latter proved to be superior (Tables 4–8).

We reported recently on the history of volumetric measurements for fetal weight prediction15. Attempts to assess fetal weight by volume determinations such as 3D head and trunk reconstruction33, ultrasound measurements based on neonatal specific gravities and volumes42, as well as modification of the latter two-compartment model of fetal volume34 have been described. The rationale behind these attempts was that fetal weight should be directly proportional to fetal volume34. In all of these formulae, however, results were obtained from reconstruction of 2D measurements rather than derived by direct volumetry33, 34, 42. With the advent of 3D ultrasound imaging, reproducible circumference and volumetric measurements have become feasible by simultaneous visualization of three orthogonal sections. These measurements were difficult to standardize with real-time 2D ultrasound examination36. Chang *et al.* and Liang *et al.* introduced fetal limb volumetry by 3D ultrasonography into clinical practice13, 14. In these studies single-parameter volumetry of the fetal arm and thigh achieved higher accuracy in predicting weight at delivery than conventional 2D equations based on several biometric parameters13, 13. In principle, these results were confirmed by our previous study of fetal volumetry, although application of the published 3D weight formulae13, 14 to our predominantly Caucasian population led to gross overestimation of fetal weight41, highlighting the need for population-specific weight formulations.

Lee *et al.* reported on a pilot 3D study assessing the volume of a specified abdominal and thigh cylinder. Although the former was defined as the volume 1.5 cm adjacent to the reference plane for abdominal measurements on each side, the latter was measured as a 2-cm cylinder of the midthigh region, in both cases including the subcutaneous tissue. Preliminary findings on 18 term fetuses suggested that accurate birth weight predictions by fetal volume parameters appeared feasible40.

The present study is unique in that it presents a new formula for predicting weight of the small fetus based on 2D and volumetric measurements. Average squared prediction errors and signed/absolute percentage errors of the newly generated formula were lower than those of all other tested traditional formulae. We are convinced that incorporating volumetric measurements into weight calculations may help to improve weight prediction in the fetus remote from term. Inclusion of all three volumetric measurements, albeit more time consuming, yielded better results than estimating fetal weight by traditional techniques.

Supported by the Deutsche Forschungsgemeinschaft (SCHI/552-1).