The use of a neural network for the ultrasonographicestimation of fetal weight in the macrosomic fetus

Richard M. Farmer, MD, PhD, Arnold L. Medearis, MD, Greigh I. Hirata, MD, andLawrence D. Platt, MD

Los Angeles, California

The error associated with regression analysis methods for the ultrasonographic estimation of fetal weightin the suspected macrosomic fetus, approximately 10%, is clinically unacceptable. This study was

undertaken to evaluate the applicability of an emerging technique, biologically simulated intelligence, to

this problem. One hundred patients with suspected macrosomic fetuses underwent ultrasonographic

measurements of biparietal diameter, head and abdominal circumference, femur length, abdominalsubcutaneous tissue, and amniotic fluid index. The biologically simulated intelligence model included

gestational age, fundal height, age, gravidity, and height. The model was then compared with results

obtained from previously published formulas relying on the abdominal circumference and femur length.

The biologically simulated intelligence yielded an average error of 4.7% from actual birth weight,

statistically better (p = 0.001) than the results obtained from regression models. (AM J OBSTET GVNECOL1992;166:1467-72.)

Key words: Ultrasonography, macrosomia, estimation of fetal weight, neural network,biologically simulated intelligence

Accurate estimation of fetal weight in the clinicallysuspected macrosomic fetus continues to be an area inevolution. Perinatal and maternal morbidity increaseswith larger birth weights.':" making correct identifica­tion of the macrosomic infant essential. Once the fetusat risk has been identified, clinical decisions and pre­cautions can be used to reduce morbidity! Clinical es­timation of fetal weight by means of the Leopold ma­neuvers has not been shown to be accurate.' Roent­genographic and computed tomographic examinationsof the fetus have also not been useful, because the pre­dictive value offers no advantage over ultrasonographyand it has the concern of fetal roentgenographic ex­posure." Ultrasonography continues to be consideredthe most reliable means of estimating fetal weight.Regression analysis of standard measured parametersgenerated in nonmacrosomic populations by Hadlocket al." and Shepard et al." has yielded the most commonformulas for the estimation of fetal weight. Hirata et

From the Division of Maternal-Fetal Medicine, Department of Ob­stetrics and Gynecology, University of Southern California School ofMedicine, Los Angeles County-University of Southern CaliforniaMedical Center, Women's Hospital.Presented at the Eleventh Annual Meeting of the Society ofPerinatalObstetricians, San Francisco, California, january 28-February 2,1991.Received for publication April 29, 1991,. revised October 17, 1991,.accepted November 7,1991.Reprint requests:Arnold L. Medearis, MD, Department of Obstetricsand Gynecology, University of Southern California School of Medi­cine, Los Angeles County-University ofSouthern California MedicalCenter, Women's Hospital, Room 5K40, 1240 N. Mission Road, LosAngeles, CA 90033.6/1 /34896

al." found that Hadlock's model performs best in themacrosomic population, in spite of the fact that esti­mated fetal weights calculated from these formulas canvary from the actual birth weight by ~ 10%. Using astudy population of suspected macrosomic fetusesrather than the general population to generate regres­sion curves has not yielded significantly better results."

An emerging technique for data analysis is biologi­cally simulated intelligence or neural network. Theforte of the neural network is pattern recognition,which can be likened to regression analysis where inputvariables are associated with outcomes according to aspecified relationship to obtain a predictive model. Theactual data reduction is unique to the neural network,which is derived from models of the human pattern ofthinking. The technique excels in correlating manyvariables that, when taken alone, may not be statisticallysignificant but as a group provide added informationto best model an outcome. This technique uses a non­linear system of variable weighting to best model inputdata.

The purpose of the current study was to determinethe applicability of a biologically simulated intelligenceto the estimation of fetal weight in the clinically sus­pected macrosomic fetus. This model was then pro­spectively tested against the Hadlock and Shepardmodels.

Material and methods

The study population consisted of 102 patients seenat Los Angeles County-University of Southern Cali­fornia Women's Hospital, either in the clinic population

1467

1468 Farmer et al.

or in the labor and delivery suite, with a clinically sus­pected macrosomic fetus. Excluded from the studywere the fetuses of women with diabetes, anomalousinfants, multiple gestations, and women whose ad­vanced labor precluded an accurate ultrasonographicexamination. All ultrasonographic measurementswere conducted within 72 hours of delivery. Measure­ments were made with an ATL Ultramark-4 (Bothell.Wash.), a GE RT 3000 or GE RT 3600 (Milwaukee,Wis.), or a Corometrics Aloka 620 (Wallingford, Conn.).All measurements were made with a 3.5 MHz lineararray transducer.

The biparietal diameter, occipitofrontal diameter,transverse abdominal diameter, anteroposterior ab­dominal diameter. and femur length were measuredwith standard techniques. Circumferences of the headand abdomen were calculated with the equation for acircle: Circumference = (Diameter 1 + Diameter 2) .1.57. An assessment of the subcutaneous tissue wasmade by measuring the distance from the bony spineto the skin in the anteroposterior orientation at the levelof the abdominal circumference. The amniotic fluidindex was measured as previously described." Calcu­lated values were the head circumference/abdominalcircumference and the femur length/abdominal cir­cumference ratios. The other measured variable wasthe fundal height, which was measured in centimetersfrom the symphysis pubis to the fundus. Demographicvariables included in the analysis included gestationalage, gravidity, parity, and height of the patient.

The biologically simulated intelligence used to modelthe data was the Brainmaker software package (version1.5, California Scientific Software, Sierra Madre, Calif).The input variables were gestational age, fundal height,amniotic fluid index, biparietal diameter, head circum­ference, abdominal circumference, subcutaneous tissuemeasurement, femur length, head circumference/ab­dominal circumference, femur length/abdominal cir­cumference, gravidity, parity, and patient height. Dataused to develop the network were taken from a pre­viously published set of 146 patients from this insti­tution.' The model was then successively iterated untilthe estimated fetal weight (the output variable) agreedwith the actual birth weight within specified tolerance.Adjustments with respect to the number of neurons,neuron gain, and training tolerance were made to ob­tain maximal performance on a training subset. Pro­spective evaluation of the trained network was thenconducted on the 102 patients described above.

Data analysis was conducted on a personal com­puter-based system with the CRUNCH statistical soft­ware package (Crunch Software Corp., Oakland,Calif.). The error in the estimated fetal weight is ex­pressed as a percentage of the actual birth weight" asfollows: Error (%) = (Estimated fetal weight - Actualbirth weight)/ Actual birth weight x 100. An estimated

May 1992Am J Obstet Gynecol

fetal weight was calculated for each patient with theneural network model, the Hadlock formula, and theShepard formula. The Hadlock estimated fetal weightwas calculated with the model: LogJO estimated fetalweight = 1.304 + 0.05281 (abdominal circumference)+ 0.1938(femur length) - 0.004(abdominal circum­ference)(femur length). The Shepard estimated fetalweight was calculated from: LogJO estimated fetalweight = -1.7492 + 0.166(biparietal diameter) +0.046(abdominal circumference) - [2.646(abdominalcircumference)(biparietal diameter)]/1000. Paired ttests were used to compare the difference in the meanpercent error derived from the Hadlock, Shepard, andneural network models. Significance was defined asp < 0.05.

Results

The average birth weight in the study population was4250 ± 350 gm, with a range of 3360 to 5260 gm.Seventy of the 101 infants (69.3%) had a birth weight2=4000 gm, whereas 24 (23.8%) weighed 2=4500 gm atbirth. The distribution of actual fetal weights whenthere was a clinical suspicion of macrosomia is displayedgraphically in Fig. 1. A total of 62.4% (631101) infantswere 2=41 weeks' gestation. There were no anomaliesor neonatal deaths in the study population.

The mean error from the actual birth weight ob­tained with the neural network was 4.7% ± 3.9%,whereas the Shepard and Hadlock formulas' errorswere 6.5% ± 4.6% and 6.8% ± 5.0%, respectively(Table I). The neural network results were calculatedwith the input variables outlined in Material and Meth­ods. Another neural network was generated with onlyabdominal circumference and femur length used asinput variables, with a resultant mean error of6.1% ± 4.5%.

The performance of each model over the weightrange studied is shown graphically in Fig. 2. The pointsshown are the mean percent deviation from the actualbirth weight within the weight range specified.

Comment

The ultrasonographic estimation of fetal weight inthe clinically suspected macrosomic fetus is an area thatcontinues to evolve. Previous efforts in this area havefocused on correlating a few morphometric parame­ters, i.e., the biparietal diameter, abdominal circum­ference, or femur length, with birth weight. However,the error associated with these methods has been im­perfect. Because most of the permutations of thesemorphometric measurements have been explored, itmight seem reasonable to postulate that inclusion ofmore parameters would add to the predictive value ofa model. Although a given parameter, when takenalone, does not statistically contribute to a model, anaggregate of parameters related to macrosomia may

Volume 166Number 5

Ultrasonographic weight estimation in macrosomic fetus 1469

Frequency30 -

~

r----

-

~

r----

-r----

~

n

20

10

o< 3800 3800 ­

40004000·4200

4200 - 4400 - 4600 -4400 4600 4800

Birthweight in grams

4800 ­5000

> 5000

Fig. 1. Actual birth weight distribution in clinically suspected macrosomic infants.

Table I. Mean percent deviation from actual birth weight of several models for estimating fetal weight inmacrosomic infants

Model

HadlockShepardNeural networkNeural network (abdominal circumference and femur

length only)

*Neural network used as a comparison.

Deviation fromactual birth

weight(%, mean ± SD)

6.8 ± 5.06.5 ± 4.64.7 ± 3.96.1 ± 4.5

Significance*

p< 0.001P< 0.001

round out a model so that its performance best predictsthe actual birth weight. The problem with such an ap­proach in the past has been the unwieldy nature of thedata analysis with multiple parameters.

The analysis of multiple parameters to develop a pre­dictive model is the forte of the neural network orbiologically simulated intelligence. A neural networkmodel was first used as a research tool to model humanthinking. The computer sets up a miniature model thatsimulates the biologic architecture of the human brain,with the terminology of the network borrowed fromneurobiology (Fig. 3). The biologically simulated in­telligence relies on a training data set as input, with thenumber of variables corresponding to the number ofinput neurons. The input layer is then connected to aprespecified number of neurons in the hidden layer so

that all inputs are connected to all neurons in the hid­den layer. Similarly, all neurons of the hidden layer areconnected to an output layer, the result(s) to be mod­eled. The training set, matched data and outcome, isthen run through the network. The network then at­tempts to vary the interconnections between the input­hidden layers and the hidden-output layers until thespecified outcome is obtained for each input. The pro­cess is iterative, with the entire data set run throughthe network numerous times until all inputs match alloutputs. The model is then ready for use as a predictivetool.

The neural network model is statistically moreaccurate than the Hadlock or Shepard formula(P < 0.05). The standard deviation of the percent erroris minimized with the neural network model, an indi-

1470 Farmer et al.

mean percent error20 -

May 1992Am J Obstet Gynecol

10 - *.

-- Neuralnetwork

-4- Hadlockformula

.* Shepard formula

0-

-10 -

·20 -< 3800 3800 ­

40004000·4200

Birthweightin grams

4200· 4400· 4600 •4400 4600 4800

4800·5000

> 5000

Fig. 2. Performance of various models for estimating fetal weight in clinically suspected macrosomicfetus.

MeasurementVariables

input layer hidden layer

OutcomeVariables

outputlayer

Fig. 3. Schematic representation of neural network architecture.

cation of the method's precision and accuracy. With theuse of only the abdominal circumference and femurlength the network model yielded results that were notstatistically different from either the Hadlock and theShepard model.

The performance of a model over the study weightrange is shown in Fig. 2. It is of interest that all modelshave a diminished performance at the extremes of the

weight range, especially when the birth weight is <3800gm. A possible explanation for this may be operatorbias on the basis of referral indication. A clinical sus­picion of macrosomia existed for inclusion in the study.This clinical impression may have carried over into abias in the measurement of morphometric parameters,particularly abdominal circumference. The resultwould be the systematic overestimation of fetal weight

Volume 166Number 5

Ultrasonographic weight estimation in macrosomic fetus 1471

Mean percent error15 -

10 -

5-

Neural network

-+- AC and FL network

o-------"--'-'~~~~,..,.----='""""--------------

-5 -

-10 -

-15 'I-----,-------,------,---------,---------r------,

3800-4000 4000-4200 4200-4400 4400-4600 4600-4800

Birthweight in gramsFig. 4. Performance of two neural network models over weight range of clinical interest. AC, Ab­dominal circumference; FL, femur length.

Table II. Mean percent deviation from actual birth weight of several models for estimating fetal weight inthe birth weight age of 3800 to 4800 gm

Model

Hadlock

Shepard

Neural networkNeural network (abdominal circumference and femur

length only)

Deviation fromactual birth

weight(%, mean ± SD)

6.5 ± 4.5

6.4 ± 4.2

4.2 ± 3.54.9 ± 3.2

Significance*

p < 0.005*P< 0.005tP< 0.005*P< 0.004t

*Neural network used as a comparison.tNeural network with only abdominal circumference and femur length used as a comparison.

when the actual birth weight was <3800 gm. All modelswould be expected to perform poorly because the datawas biased before calculation of estimated fetal weight.

At the other end of the scale infants >4800 gm rep­resent technical problems in the estimation of abdom­inal circumference because the entire abdomen maynot fit on the display. This would result in estimationsof abdominal circumference that would tend to favorthe bias of the observer. In this study it resulted in asystematic bias toward underestimation of fetal weightin the larger weight ranges. The problems of bias existfor all the models studied. However, the underesti-

mation of fetal weight for infants with a birth weight>4800 gm appears greater for the neural networkmodel than for the regression models. A possible ex­planation for this lies in the method of data analysisparticular to the neural network. The network relieson past experience with a subset of the range for ac­curate prediction. The model will deteriorate signifi­cantly when there are not enough data in a given area.In particular, there are only seven infants with birthweights >4800 gm. The model's predictive abilitywould probably be significantly enhanced by the inclu­sion of more infants in this weight category. Finding

1472 Farmer et al.

such study cand idates would be the major impedimentto the improvement of the model in this weight range.

Exclusion of infants at the weight extremes of birthweights <3800 and > 4800 gm results in the exclusionof 16 patients. The resultant mean percent error ofeach estimated fetal weight from the actual birthweight , with its standard deviation, is shown in TableI I. The p values for the results of a paired t test com­paring the neural network model with the other modelsare also shown in Table II. The predictive value of theneural network is significantly better than the regres­sion models of Hadlock and Shepard. The perfor­mance of the network over the weight range from>3800 to <4800 mg is shown in Fig. 4. Inclusion ofparameters other than biparietal diameter, abdominalcircumference, and femur length (gestational age, fun­dal height, amniotic fluid index, head circumference,subcutaneous tissue measurement, head circumfer­ence/abdominal circumference, femur length/abdom­inal circumference, sex, age, and gravidity, parity, andheight) tends to have a smoothing effect on the esti­mated fetal weight because the errors are less systematicthan with the Hadlock or Shepard formulas.

Data analysis with the neural network is not restrictedto the reduction of large numbers of variables. Whenonly the abdominal circumference and femur lengthare considered, as was done in the Hadlock model, thenetwork performed as well as the Hadlock and Shepardformulas (Table I). If the weight range is restricted to>3800 and <4800 gm (because of the previous argu­ments) the resultant model has a statistically greater(p < 0.005) predictive value than either regression for­mula in the macrosomic weight range. The perfor­man ce of this network model, however, is not as con­sistent over the entire weight range as the full networkmod el (Fig. 3).

Another interesting observation from the study is theconfirmation of the inaccuracy of Leopold examina­tions for the estimation of fetal weight. All infants, aspart of the inclusion criteria, were estimated to be> 4000 gm . Only 69 .3% ofthe infants actually had birthweights > 4000 gm.

We conclude that the neural network method of dataana lysis is a new technique that deserves further eva1-

May 1992Am J Obstet Gynecol

uation. Its ability to integrate numerous variables todevelop a predictive model offers significant potentialadvantages over regression anal ysis. Its performancein the estimation of fetal weight in the clincially sus­pected macrosomic fetus is better than the traditionalregression analysis used by Hadlock and Shepard ifmultiple parameters are considered. If the parametersare restricted to the abdominal circumference and fe­mur length, as was done with the Hadlock formula , thenetwork still predicts the estimated fetal weight signif­icantly better than a regression formula does. The ma­jor drawback to this form of analysis is the necessity ofincluding a sufficient number of patients over the entirerange of birth weights, with the predictive value de­grading significantly when this is not done.

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