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Estimation of fetal weight from ultrasonic measurements
FETUS, PLACENTA, AND NEWBORN
Estimation of fetal weight from ultrasonic measurements W. D. McCALLUM, M.D., M.R.C.O.G., F.A.C.O.G.
J.
F. BRINKLEY, M.D.
Smttle, Washington Ultrasonic measurements were made on 65 fetuses within 48 hours of delivery. Multiple regression analysis of birth weight and the natural logarithm of birth weight against several measured variables were obtained. The formula giving the best correlation was a polynomial regression of the natural logarithm of birth weight vs. trunk circumference, circumterence, 2 and a long axis measurement. The correlation was improved by excluding the first 15 patients but was not improved further by excluding the next 15. The best correlation was 0.944, giving a predicted birth weight error of :t103 Gm. (1 S.D.). (AM. J. 0BSTET. GYNECOL 133:195, 1979.)
THE ASSESSMENT of fetal size (weight) is a significant part of prenatal care. Clinical methods of estimation are inaccurate, especially for growth-retarded and growth-accelerated fetuses. 1- 3 There is a need therefore to develop more accurate techniques. There are now several reports of weight estimation derived from measurements made on ultrasonic Bmode scans. Among these are measurements of the fetal thoracic diameter, 4 abdominal circumference.~- 7 combinations of skull and thoracic measurements. 8 skull and abdominal circumference, 9 skull, thoracic. and longitudinal trunk measurements, 10 skull and longitudinal trunk measurements, 11 and multiple parallel scans. 12 It is the purpose of this paper to compare the weight predictions of several of these and other fetal meaFrom the Departments of Obstetrin and Gvnecology and Bio-Engineering, University of Washington. ReceiFedfor publication March 6, 1978. Accepted Apnl27, 1978. Reprint requRsts: W. D. McCallum, M.D., Department of G_i-necology and Obstetric.1, Stanford Universil)• Medical Cmter, Stanford. California 94305.
0002-9378/79/020195+06$00.60/0
©
1979 The C. V. Mosby Co.
surements singly and in combination and to determine which measurement errors, if any, could be reduced. Our working hypothesis in beginning this study was that fetal volume is a good indicator of weight, since the density of fetal tissues is nearly constant. 12 Therefore, we felt that the most likely predictors of weight would be measurements which approximate volume, and that among these the ones which utilize the most information would give the most accurate volume and hence weight. For this reason several derived measurements were obtained from the original measurements in order to arrive at a closer theoretical approximation to fetal volume.
Methods Patients used and scans obtained. Sixty-five patients were scanned with a Sonograph III B-mode scanner (Unirad Corporation) 48 hours before delivery. Ten patients were examined prior to elective cesarean section or induction oflabor; the remainder either were in early spontaneous labor or had spontaneous rupture of membranes. The following scans were obtained on each patient: (I) three to five scans perpendicular to the fetus at the level of the umbilical/ portal vein (trans195
196 McCallum and Brinkley
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January 15, 1979 Obstet. Gynecol.
J.
FULL CIRCUMFERENCE and FULL AREA
:
AREA and _/CIRCUMFERENCE
VOLUME (by Simpson's Rule) and SUM OF CIRCUMFERENCES
Fig. 1. Measurements made on transverse scans.
Fig. 2. Measurements made on longitudinal scans.
verse scans); (2) three to five scans along the axis of the fetus (longitudinal scans); (3) a series of parallel scans at 2 em. intervals between the fetal neck and the end of the trunk (Fig. 1). The fetal head was not included because it was not possible to obtain complete parallel scans across a head \vhich \Vas \Vithin the pelvis. The scans were recorded on video tape and later displayed on a video graphics terminal interfaced with a PDP 10 computer. The various measurements were entered into the computer by means of a light pen associated with the terminal; for each patient the proper scale factor was established by using the light pen to indicate calibration marks recorded at the time of scanning. Measurements from scans. The capitals in brackets are the variables from Figs. 1 and 2. The birth weight (WEIGHT) and the following measurements were entered into the computer with the light pen (for the transverse and longitudinal scans the measurements were taken as the average of the three to five scans obtained): l. From the transverse scans (Fig. 1): The area and circumference of the fetai trunk (AREA and CIRCUMFERENCE) 2. From the longitudinal scans (Fig. 2): (a) The distance from the base of the skull to the end of the rump (BASE). The end of the rump was defined by the bladder base and/or the convergence of the anterior abdomina! wall with the fetal back. (b) The length of the dorsal arc outline between the same two points used to define the base (ARC).
(c) The area between (a) and (b) (HALF AREA). (d) The area and the circumference of the fetus from the base of the skull to the end of the trunk (FULL AREA and FULL CIRCUtvfFERENCE). 3. From the series of parallel scans (Fig. 1): (a) The sum of circumferences of all the scans (SUM OF CIRCUMFERENCES). (b) The volume obtained by using Simpson's formula on the area of each scan and the known distance (2 em.) between scans (SIMPSON'S SUM). If the number of scans was even the trapezoidal rule was used to add the volume enclosed by the last two scans to the total since Simpson's Sum is only valid for an odd number of scans (this procedure was tested by us on simulated prolate ellipsoids and shown to give less than 1 per cent error from actual volumes obtained by integration). Derived measurements and statistical analysis. The computer program, "Statpack," from Western Michigan University was used to further analyze the data. For those measurements which were obtained as the mean of measurements made on the longitudinal and transverse scans, the individual coefficients of variation were computed, where coefficient of variation is defined as the mean divided by the standard deviation times I 00. This statistic is a normalized way of indicating the amount of variation among the three to five scans used to determine the given measurements. The mean coefficient of variation for all patients was then determined from the individual coefficient of variation, to be used as an indicator of the variability (and
Volume 133 Number 2
Estimation of fetal weight from ultrasonic measurements
hence repeatability) of a given measurement for a single patient. Several derived variables were obtained from the original measurements, in most cases to obtain a closer theoretical approximation to volume. For example, the cube of the abdominal circumference should be a closer approximation to volume than the circumference alone, since volume is a cubic measurement. The natural log of birth weight was derived in the hope of reducing scatter.~' Multiple linear regression was then carried out on various combinations of both the direct and derived measurements, where the general equation used was:
Table I. Coefficients of variation (n = 65)
y
bo + btx, + b2x2+ ... +l:>i
with y the dependent variable (weight or natural log of weight) and x 1 •.• x11 the independent variables. Results
The birth weights ranged from 1,200 to 4,420 grams, with a mean of 3,150 grams. Table I shows the mean coefficient of variation for those variables which were determined as the average of measurements made on three to five scans. Linear measurements such as circumference, base, and arc show a higher degree of repeatability than area measurements, which is understandable since areas tend to square any errors. Thus, on this basis alone regressions employing linear measurements such as circumference might be expected to give a closer correlation with weight than those employing quadratic measurements such as area. Table II shows some of our multiple regressions involving both measured and derived variables in order by correlation coefficient. Several points are of note . 1. Correlations were higher with the natural logarithm of birth weight than with birth weight alone, a result similar to that found by Campbell and Wilkin;; and Warsof and associates. 9 2. For R values >0.90 the transverse abdominal circumference and its square (C,C 2 ) were always included, which was also in accord with the findings of Campbell and Wilkin." 3. One longitudinal variable added to the transverse circumference improved the correlation (compare regressions 4 and 6). This improvement was found to be statistically significant (p < 0.01) by the F test. 4. Additional variables did not significantly improve the result (compare regressions l and 4). 5. It did not seem to matter which additional longitudinal variable was used (compare regressions 3, 4, and 5). 6. Simpson's Sum correlated reasonably well with weight but was still not as good as a single circumferen-
Measured variable
Mean coefficient of variatioo (9%)
CIRCUMFERENCE FULL CIRCUMFERENCE BASE ARC AREA FULL AREA HALF AREA
2.4 3.5 4.0 4.1 4.8 7.1 l 0.6
197
Table II. Multiple regressions (n = 65)
No.I 1
2 3 4 5 6
7 8 9 10 11 12 13 14 15 16
Regressioo variables* Ln (W) Ln (W) Ln (W) Ln {W) Ln (W) Ln (W) Ln (W) W W
w
W W W W W W
I
= f{C, CZ, AC, ACZ, C x AC) f(A, C, C2 , BA, AC, HA, FA, FC) = f{C, CZ, HA) = f(C, C2 , AC) = f(C, CZ, FC) f(C, CZ) = f(A, C, BA, AC, HA, FA, FC) f(A, C, BA, AC, HA, FA, FC) = f(SIM) f(C) F(A) = f(A X AC) = F(SOC) = f(A 312 ) f(CZ) = f(AC)
Correlatioo coeffioent 0.924 0.924 0.920 0.920 0.920 0.906 0.896 0.871 0.845 0.839 0.828 0.824 0.823 0.806 0.797 0.714
*Key: W =WEIGHT, A= AREA (transverse scans). C = CIRCUMFERENCE (transverse scans). BA = BASE (longitudinal scans), AC = ARC (longitudinal s~:ans), HA = HALF AREA (longitudinal scans), FA= FULL AREA (longitudinal scans), FC FULL CIRCUMFERENCE (longitudinal scans), SOC = SUM OF CIRCUMFERENCES (parallel scans), SIM SIMPSON'S SUM (parallel scans).
tial measurement (compare regressions 6 and 9) for fetuses <3,000 grams. This was somewhat surprising since Simpson's Sum should give the best estimation of volume (and therefore presumably of weight) because it utilized the maximum amount of information. 7. In general, any multiplication or exponentiation of variables (the derived variables) produced poorer correlation than the original variables, even though the derived variables were expected to be linearly related to volume. Evidently, the fact that repeatability errors were multiplied or exponentiated more than offset any increase in linearity (compare regressions 10 and 15, and regressions 11 and 14). To test the effect of experience in outlining the scans on the repeatability errors, the regressions were recomputed after deleting groups of observations for three representative formulas (Table Ill). In all three cases deleting the first 15 patients improved the correlation, whereas, no further improvements were seen
198
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January 15, 1979 Obstet. Gynecol.
Tabie iii. Effect of deleting observations on correlation coefficient Correlation coefficients
No.
Regression (see Table II)
Original (n = 65)
4 6 9
Ln (W) = f(C, C2 , AC) Ln (W) = f(C. C2 ) W = f(SIM)
0.920 0.906 0.845
I
First 15 deleted
I
l
First30 deleted
0.943 0.927 0.871
0.946 0.926 0.895
Last 30 deleted
0.887 0.873 0.836
l
Last 15 deleted
0.901 0.885 0.829
Table IV. 95 per cent confidence intervals tor three predictors of weight (n = 50)
Predicted weight (Gm.)
LL (%)
1,500 2,000 2,500 3,000 3,500
-285(-20) -390(-19) -470(-18) -550(-18) -640(-18)
Estimated "Standard error"
I
No. 9: W = j(S/M)
No. 6: Ln(W) = j(C, C 2)
No. 4: Ln(W) = j(C, C 2 , AC)
I
UL (%)
LL (%)
+355(24) +480(23) +580(23) +670(22) +780(2?)
-330(-2i) -415(-20) -520(-20) -600(-20) -700(-20)
LL (%)
+430(26) +522(26) +650(25) +760(25) +880(25)
-730(-47) -720(-33) -700(-28) -690(-23) -690(-20)
UL (%)
+730(47) +720(33) +700(28) +690(23) +690(20)
340 Gm.
116 Gm./Kg.
103 Gm./Kg.
I
UL (%)
Table V. Other attempts at predicting weight No. of
Authors
Lunt and Chard8 Higgenbottom et al." Morrison and McLennan 12 Campbell and Wilkin 15 Warsof and associates• Present study
Error
Parameters
Weight vs. skull area x thoracic area Weight vs. abdominal circumference" Weight vs. sum of a series of parallel scans (2 series) Ln (Weight) vs. abd. circumference, abd. circumference2 Log10 (Weight) vs. several combinations of abd. circumference, biparietal diameter Ln(Weight) vs. abd. circumference2 , length
when the second 15 were also deleted or when the last 15 or 30 were deleted. We therefore concluded that the 1st 15 patients more or less represented the number required to learn repeatable methods of outlining the scans. Table IV shows 95 per cent confidence limits fi>r these three formulas with the first 15 patients deleted. The confidence limits for Nos. 4 and 6 were computed by multiplying the predicted weight by e±to.o.>sy where t0.05 is the 95 per cent t value (two-tailed test) and Sy is the standard error for an individual predicted weight. This exponentiation means that the limits are a constant percentage of weight, so the limits increase with increasing weight. Thus our best method (No. 4) is most accurate for small fetuses and less accurate for larger ones. The equation found for No. 4 (n=50) is: In (W) = 2.19 + 0.29C - 0.004C 2 + 0.02l(AC).
69 50 21 20 140
I I I I I
S.D.= S.D. = S.D. = S.D.= S.D.=
215 Gm. 97 Gm. 230 Gm. 106 Gm. 91 Gm./Kg.
85
I S.D.= 106 Gm./Kg.
50
I S.D. = I 03 Gm./Kg.
Because the confidence limits are a constant percentage of predicted weight, an indication of the standard error per kilogram may be obtained by multiplying 1,000 by es-1 where sis the over-all standard error of the estimate (after '\A/arsof and associates 9). Based on this estimate the standard errors for the three methods are shown at the bottom of Table IV. (These estimates are useful only for comparing different studies since a true confidence interval, as calculated in the upper part of Table IV, must take into account the number of cases and the deviation of the predicted weight from the mean measured weight). Comment In this study the best predictor of fetal weight for fetuses under 3,000 grams was the polynomial regression natural log of weight versus transverse circum-
Volume 133 Number 2
Estimation of fetal weight from ultrasonic measurements
ference, transverse circumference squared, and arc length, giving an approximate standard error of 103 Gm. per kilogram. This method is essentially that proposed by Campbell and Wilkin," with the addition of a length measurement which we have shown in· creased our accuracy by a statistically significant (although small) amount. The fact that measurements of arc length were not as repeatable as those of abdominal circumference (Table I) suggests that further improvement in fetal weight prediction could be achieved if a more accurate length measurement could be found. A length measurement added to the abdominal circumference improves the accuracy of the prediction and makes sense if weight is related to volume. However, in this study, we have also shown that certain methods im·olving powers of measurements, which should theoretically give a better measurement of volume than single measurements alone, are not as accurate in predicting weight (for example, abdominal circumference cubed was less accurate than abdominal circumference alone). It seems that even in as accurate a measure as abdominal circumference the repeatability error offsets the gain in predictability expected by cubing this measurement. It may be that these repeatability errors could be improved somewhat as we gain experience (Table III), but we feel that until ultrasonic image quality becomes better the errors will remain large, and hence measurements which do not compound these errors should be used. The method which we expected to be most accurate was Simpson's Sum over a series of parallel scans, because that method should give the closest approximation to volume. There are several possible explanations for the relative inaccuracy of this method: (1) fetal weight is not linearly related to trunk volume; (2) the contributions of the head and limbs (which are not included in Simpson's Sum) add a nonlinear amount to the actual volume of the fetus; (3) our inability to adequatelv define the fetal trunk at the endpoints of the
parallel scans contributes a large amount to the repeatability error; (4) fetal movement is a factor. Of these reasons we believe that the third contributes the most to the error although the others may also play a part. By requiring that the scans be parallel the ultrasound transducer could not be at right angles to the fetal skin surface throughout the length of the fetus, a factor which made it very difficult to identify the fetal endpoints. It seems reasonable that if a similar volume method could be used which did not require the use of parallel scans and which included the skull, it might be possible to significantly improve the results obtainable with this technique. Table V compares our best method with several others using similar kinds of measurements, the basis of comparison being the standard error. As mentioned in the Results section, these errors do not reflect true confidence limits since confidence limits depend on the number of patients studied and the range of weights observed. Nevertheless, they provide some basis for comparison among studies and show that the errors involved for all those in Table V are roughly similar. The method proposed by Higgenbottom and associates,6 corresponds to our regression No. 15, that proposed by Morrison and McLennan 12 roughly corresponds to our regression No. 9 (although our method does not include head or limbs), and that proposed by Campbell and Wilkin" corresponds to our regression No. 6. The fact that several of these methods give better predictability than seems indicated by our results simply points out the difficulty in making comparisons between studies done at different times on different groups of patients. In conclusion, it appears that the accuracy achieved by any of these methods is no better than ±200 grams per kilogram (2 S.D.). Further improvement in our ability to predict fetal weight seems unlikely until we are able to reduce the repeatability error in longitudinal measurements or are able to find more accurate ways of assessing volume.
199
REFERENCES 1. Loeffler, F. E.: Clinical foetal weight prediction, J. Obstet. Gvnaecol. Br. Commonw. 74: 675, 1967. 2. Niswander, K. R., Capraro, V. J., and Van Coevering, R. J: Estimation of birth weight by quantified external uterine measurements, Obstet. Gynecol. 36: 294, 1970. 3. Ong, H. C., and Sen, D. K.: Clinical estimation of fetal weight, AM. J. OssTET. GYNECOL. 112: 877. 1972. 4. Issei. E. P., Prenslau, P., Bayer, H., Luder, R., Schulte, R., Wohlfahrth, G., Weight, M., and Acker, R.: The measurement of fetal growth during pregnancy by ultrasound (B-scan). J. Perinat. Med. 3: 269, 1975.
5. Campbell, S., and Wilkin, D.: Ultrasonic measurement of fetal abdomen circumference in the estimation of fetal weight, Br. J. Obstet. Gynecol. 82: 689, I 975. 6. Higgenbottom, J, Slater, J., Porter, G., and Whitfield, C. R.: Estimation of fetal weight from ultrasonic measurement of trunk circumference, Br. J. Obstet. Gynecol. 82: 698, 1975. 7. Kurjak, A., and Breyer, B.: Estimation of fetal weight by ultrasonic abdorninometry, AM . .J. 0BSTET. GYNECOL. 125: 962, 1976. 8. Lunt, R., and Chard, T.: A new method for estimation of
200 McCallum and Brinkley Am.
fetal weight in late pregnancy by ultrasonic scanning, Br. J. Obstet. Gynaecol. 83: 1, 1976. 9. Warsof, S. L., Gohari, P., Berkowitz, R. L., and Hobbins, J. C.: The estimation of fetal weight by computer-assisted analysis, AM. J. OBSTET. GYNECOL. 128: 881, 1977. 10. Issei, E. P., Prenzlau, P., and Laag. F.: Problems in using linear ultrasound parameters for the determination of fetal weight, J. Perinat. Med. 4: 26, 1976.
January 15, 1979 Obstet. Gynecol.
J.
II. Picker, R. H., and Saunders, D. M.: A simple geometric method for determining fetal weight in utero with the compound gray scale ultrasonic scan. AM. J. 0BSTET. GYNECOL. 124: 493, 1976. 12. Morrison,]., and McLennan, M.J.: The theory, feasibility and accuracv of an ultrasonic met hoc! of Pstim~tino- fpt~l weight, Br. j. Obstet. Gy~ae~ol. 83S~
83:
1976.-----" ------
Estimation of fetal weight from ultrasonic measurements W. D. McCALLUM, M.D., M.R.C.O.G., F.A.C.O.G.
J.
F. BRINKLEY, M.D.
Smttle, Washington Ultrasonic measurements were made on 65 fetuses within 48 hours of delivery. Multiple regression analysis of birth weight and the natural logarithm of birth weight against several measured variables were obtained. The formula giving the best correlation was a polynomial regression of the natural logarithm of birth weight vs. trunk circumference, circumterence, 2 and a long axis measurement. The correlation was improved by excluding the first 15 patients but was not improved further by excluding the next 15. The best correlation was 0.944, giving a predicted birth weight error of :t103 Gm. (1 S.D.). (AM. J. 0BSTET. GYNECOL 133:195, 1979.)
THE ASSESSMENT of fetal size (weight) is a significant part of prenatal care. Clinical methods of estimation are inaccurate, especially for growth-retarded and growth-accelerated fetuses. 1- 3 There is a need therefore to develop more accurate techniques. There are now several reports of weight estimation derived from measurements made on ultrasonic Bmode scans. Among these are measurements of the fetal thoracic diameter, 4 abdominal circumference.~- 7 combinations of skull and thoracic measurements. 8 skull and abdominal circumference, 9 skull, thoracic. and longitudinal trunk measurements, 10 skull and longitudinal trunk measurements, 11 and multiple parallel scans. 12 It is the purpose of this paper to compare the weight predictions of several of these and other fetal meaFrom the Departments of Obstetrin and Gvnecology and Bio-Engineering, University of Washington. ReceiFedfor publication March 6, 1978. Accepted Apnl27, 1978. Reprint requRsts: W. D. McCallum, M.D., Department of G_i-necology and Obstetric.1, Stanford Universil)• Medical Cmter, Stanford. California 94305.
0002-9378/79/020195+06$00.60/0
©
1979 The C. V. Mosby Co.
surements singly and in combination and to determine which measurement errors, if any, could be reduced. Our working hypothesis in beginning this study was that fetal volume is a good indicator of weight, since the density of fetal tissues is nearly constant. 12 Therefore, we felt that the most likely predictors of weight would be measurements which approximate volume, and that among these the ones which utilize the most information would give the most accurate volume and hence weight. For this reason several derived measurements were obtained from the original measurements in order to arrive at a closer theoretical approximation to fetal volume.
Methods Patients used and scans obtained. Sixty-five patients were scanned with a Sonograph III B-mode scanner (Unirad Corporation) 48 hours before delivery. Ten patients were examined prior to elective cesarean section or induction oflabor; the remainder either were in early spontaneous labor or had spontaneous rupture of membranes. The following scans were obtained on each patient: (I) three to five scans perpendicular to the fetus at the level of the umbilical/ portal vein (trans195
196 McCallum and Brinkley
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January 15, 1979 Obstet. Gynecol.
J.
FULL CIRCUMFERENCE and FULL AREA
:
AREA and _/CIRCUMFERENCE
VOLUME (by Simpson's Rule) and SUM OF CIRCUMFERENCES
Fig. 1. Measurements made on transverse scans.
Fig. 2. Measurements made on longitudinal scans.
verse scans); (2) three to five scans along the axis of the fetus (longitudinal scans); (3) a series of parallel scans at 2 em. intervals between the fetal neck and the end of the trunk (Fig. 1). The fetal head was not included because it was not possible to obtain complete parallel scans across a head \vhich \Vas \Vithin the pelvis. The scans were recorded on video tape and later displayed on a video graphics terminal interfaced with a PDP 10 computer. The various measurements were entered into the computer by means of a light pen associated with the terminal; for each patient the proper scale factor was established by using the light pen to indicate calibration marks recorded at the time of scanning. Measurements from scans. The capitals in brackets are the variables from Figs. 1 and 2. The birth weight (WEIGHT) and the following measurements were entered into the computer with the light pen (for the transverse and longitudinal scans the measurements were taken as the average of the three to five scans obtained): l. From the transverse scans (Fig. 1): The area and circumference of the fetai trunk (AREA and CIRCUMFERENCE) 2. From the longitudinal scans (Fig. 2): (a) The distance from the base of the skull to the end of the rump (BASE). The end of the rump was defined by the bladder base and/or the convergence of the anterior abdomina! wall with the fetal back. (b) The length of the dorsal arc outline between the same two points used to define the base (ARC).
(c) The area between (a) and (b) (HALF AREA). (d) The area and the circumference of the fetus from the base of the skull to the end of the trunk (FULL AREA and FULL CIRCUtvfFERENCE). 3. From the series of parallel scans (Fig. 1): (a) The sum of circumferences of all the scans (SUM OF CIRCUMFERENCES). (b) The volume obtained by using Simpson's formula on the area of each scan and the known distance (2 em.) between scans (SIMPSON'S SUM). If the number of scans was even the trapezoidal rule was used to add the volume enclosed by the last two scans to the total since Simpson's Sum is only valid for an odd number of scans (this procedure was tested by us on simulated prolate ellipsoids and shown to give less than 1 per cent error from actual volumes obtained by integration). Derived measurements and statistical analysis. The computer program, "Statpack," from Western Michigan University was used to further analyze the data. For those measurements which were obtained as the mean of measurements made on the longitudinal and transverse scans, the individual coefficients of variation were computed, where coefficient of variation is defined as the mean divided by the standard deviation times I 00. This statistic is a normalized way of indicating the amount of variation among the three to five scans used to determine the given measurements. The mean coefficient of variation for all patients was then determined from the individual coefficient of variation, to be used as an indicator of the variability (and
Volume 133 Number 2
Estimation of fetal weight from ultrasonic measurements
hence repeatability) of a given measurement for a single patient. Several derived variables were obtained from the original measurements, in most cases to obtain a closer theoretical approximation to volume. For example, the cube of the abdominal circumference should be a closer approximation to volume than the circumference alone, since volume is a cubic measurement. The natural log of birth weight was derived in the hope of reducing scatter.~' Multiple linear regression was then carried out on various combinations of both the direct and derived measurements, where the general equation used was:
Table I. Coefficients of variation (n = 65)
y
bo + btx, + b2x2+ ... +l:>i
with y the dependent variable (weight or natural log of weight) and x 1 •.• x11 the independent variables. Results
The birth weights ranged from 1,200 to 4,420 grams, with a mean of 3,150 grams. Table I shows the mean coefficient of variation for those variables which were determined as the average of measurements made on three to five scans. Linear measurements such as circumference, base, and arc show a higher degree of repeatability than area measurements, which is understandable since areas tend to square any errors. Thus, on this basis alone regressions employing linear measurements such as circumference might be expected to give a closer correlation with weight than those employing quadratic measurements such as area. Table II shows some of our multiple regressions involving both measured and derived variables in order by correlation coefficient. Several points are of note . 1. Correlations were higher with the natural logarithm of birth weight than with birth weight alone, a result similar to that found by Campbell and Wilkin;; and Warsof and associates. 9 2. For R values >0.90 the transverse abdominal circumference and its square (C,C 2 ) were always included, which was also in accord with the findings of Campbell and Wilkin." 3. One longitudinal variable added to the transverse circumference improved the correlation (compare regressions 4 and 6). This improvement was found to be statistically significant (p < 0.01) by the F test. 4. Additional variables did not significantly improve the result (compare regressions l and 4). 5. It did not seem to matter which additional longitudinal variable was used (compare regressions 3, 4, and 5). 6. Simpson's Sum correlated reasonably well with weight but was still not as good as a single circumferen-
Measured variable
Mean coefficient of variatioo (9%)
CIRCUMFERENCE FULL CIRCUMFERENCE BASE ARC AREA FULL AREA HALF AREA
2.4 3.5 4.0 4.1 4.8 7.1 l 0.6
197
Table II. Multiple regressions (n = 65)
No.I 1
2 3 4 5 6
7 8 9 10 11 12 13 14 15 16
Regressioo variables* Ln (W) Ln (W) Ln (W) Ln {W) Ln (W) Ln (W) Ln (W) W W
w
W W W W W W
I
= f{C, CZ, AC, ACZ, C x AC) f(A, C, C2 , BA, AC, HA, FA, FC) = f{C, CZ, HA) = f(C, C2 , AC) = f(C, CZ, FC) f(C, CZ) = f(A, C, BA, AC, HA, FA, FC) f(A, C, BA, AC, HA, FA, FC) = f(SIM) f(C) F(A) = f(A X AC) = F(SOC) = f(A 312 ) f(CZ) = f(AC)
Correlatioo coeffioent 0.924 0.924 0.920 0.920 0.920 0.906 0.896 0.871 0.845 0.839 0.828 0.824 0.823 0.806 0.797 0.714
*Key: W =WEIGHT, A= AREA (transverse scans). C = CIRCUMFERENCE (transverse scans). BA = BASE (longitudinal scans), AC = ARC (longitudinal s~:ans), HA = HALF AREA (longitudinal scans), FA= FULL AREA (longitudinal scans), FC FULL CIRCUMFERENCE (longitudinal scans), SOC = SUM OF CIRCUMFERENCES (parallel scans), SIM SIMPSON'S SUM (parallel scans).
tial measurement (compare regressions 6 and 9) for fetuses <3,000 grams. This was somewhat surprising since Simpson's Sum should give the best estimation of volume (and therefore presumably of weight) because it utilized the maximum amount of information. 7. In general, any multiplication or exponentiation of variables (the derived variables) produced poorer correlation than the original variables, even though the derived variables were expected to be linearly related to volume. Evidently, the fact that repeatability errors were multiplied or exponentiated more than offset any increase in linearity (compare regressions 10 and 15, and regressions 11 and 14). To test the effect of experience in outlining the scans on the repeatability errors, the regressions were recomputed after deleting groups of observations for three representative formulas (Table Ill). In all three cases deleting the first 15 patients improved the correlation, whereas, no further improvements were seen
198
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January 15, 1979 Obstet. Gynecol.
Tabie iii. Effect of deleting observations on correlation coefficient Correlation coefficients
No.
Regression (see Table II)
Original (n = 65)
4 6 9
Ln (W) = f(C, C2 , AC) Ln (W) = f(C. C2 ) W = f(SIM)
0.920 0.906 0.845
I
First 15 deleted
I
l
First30 deleted
0.943 0.927 0.871
0.946 0.926 0.895
Last 30 deleted
0.887 0.873 0.836
l
Last 15 deleted
0.901 0.885 0.829
Table IV. 95 per cent confidence intervals tor three predictors of weight (n = 50)
Predicted weight (Gm.)
LL (%)
1,500 2,000 2,500 3,000 3,500
-285(-20) -390(-19) -470(-18) -550(-18) -640(-18)
Estimated "Standard error"
I
No. 9: W = j(S/M)
No. 6: Ln(W) = j(C, C 2)
No. 4: Ln(W) = j(C, C 2 , AC)
I
UL (%)
LL (%)
+355(24) +480(23) +580(23) +670(22) +780(2?)
-330(-2i) -415(-20) -520(-20) -600(-20) -700(-20)
LL (%)
+430(26) +522(26) +650(25) +760(25) +880(25)
-730(-47) -720(-33) -700(-28) -690(-23) -690(-20)
UL (%)
+730(47) +720(33) +700(28) +690(23) +690(20)
340 Gm.
116 Gm./Kg.
103 Gm./Kg.
I
UL (%)
Table V. Other attempts at predicting weight No. of
Authors
Lunt and Chard8 Higgenbottom et al." Morrison and McLennan 12 Campbell and Wilkin 15 Warsof and associates• Present study
Error
Parameters
Weight vs. skull area x thoracic area Weight vs. abdominal circumference" Weight vs. sum of a series of parallel scans (2 series) Ln (Weight) vs. abd. circumference, abd. circumference2 Log10 (Weight) vs. several combinations of abd. circumference, biparietal diameter Ln(Weight) vs. abd. circumference2 , length
when the second 15 were also deleted or when the last 15 or 30 were deleted. We therefore concluded that the 1st 15 patients more or less represented the number required to learn repeatable methods of outlining the scans. Table IV shows 95 per cent confidence limits fi>r these three formulas with the first 15 patients deleted. The confidence limits for Nos. 4 and 6 were computed by multiplying the predicted weight by e±to.o.>sy where t0.05 is the 95 per cent t value (two-tailed test) and Sy is the standard error for an individual predicted weight. This exponentiation means that the limits are a constant percentage of weight, so the limits increase with increasing weight. Thus our best method (No. 4) is most accurate for small fetuses and less accurate for larger ones. The equation found for No. 4 (n=50) is: In (W) = 2.19 + 0.29C - 0.004C 2 + 0.02l(AC).
69 50 21 20 140
I I I I I
S.D.= S.D. = S.D. = S.D.= S.D.=
215 Gm. 97 Gm. 230 Gm. 106 Gm. 91 Gm./Kg.
85
I S.D.= 106 Gm./Kg.
50
I S.D. = I 03 Gm./Kg.
Because the confidence limits are a constant percentage of predicted weight, an indication of the standard error per kilogram may be obtained by multiplying 1,000 by es-1 where sis the over-all standard error of the estimate (after '\A/arsof and associates 9). Based on this estimate the standard errors for the three methods are shown at the bottom of Table IV. (These estimates are useful only for comparing different studies since a true confidence interval, as calculated in the upper part of Table IV, must take into account the number of cases and the deviation of the predicted weight from the mean measured weight). Comment In this study the best predictor of fetal weight for fetuses under 3,000 grams was the polynomial regression natural log of weight versus transverse circum-
Volume 133 Number 2
Estimation of fetal weight from ultrasonic measurements
ference, transverse circumference squared, and arc length, giving an approximate standard error of 103 Gm. per kilogram. This method is essentially that proposed by Campbell and Wilkin," with the addition of a length measurement which we have shown in· creased our accuracy by a statistically significant (although small) amount. The fact that measurements of arc length were not as repeatable as those of abdominal circumference (Table I) suggests that further improvement in fetal weight prediction could be achieved if a more accurate length measurement could be found. A length measurement added to the abdominal circumference improves the accuracy of the prediction and makes sense if weight is related to volume. However, in this study, we have also shown that certain methods im·olving powers of measurements, which should theoretically give a better measurement of volume than single measurements alone, are not as accurate in predicting weight (for example, abdominal circumference cubed was less accurate than abdominal circumference alone). It seems that even in as accurate a measure as abdominal circumference the repeatability error offsets the gain in predictability expected by cubing this measurement. It may be that these repeatability errors could be improved somewhat as we gain experience (Table III), but we feel that until ultrasonic image quality becomes better the errors will remain large, and hence measurements which do not compound these errors should be used. The method which we expected to be most accurate was Simpson's Sum over a series of parallel scans, because that method should give the closest approximation to volume. There are several possible explanations for the relative inaccuracy of this method: (1) fetal weight is not linearly related to trunk volume; (2) the contributions of the head and limbs (which are not included in Simpson's Sum) add a nonlinear amount to the actual volume of the fetus; (3) our inability to adequatelv define the fetal trunk at the endpoints of the
parallel scans contributes a large amount to the repeatability error; (4) fetal movement is a factor. Of these reasons we believe that the third contributes the most to the error although the others may also play a part. By requiring that the scans be parallel the ultrasound transducer could not be at right angles to the fetal skin surface throughout the length of the fetus, a factor which made it very difficult to identify the fetal endpoints. It seems reasonable that if a similar volume method could be used which did not require the use of parallel scans and which included the skull, it might be possible to significantly improve the results obtainable with this technique. Table V compares our best method with several others using similar kinds of measurements, the basis of comparison being the standard error. As mentioned in the Results section, these errors do not reflect true confidence limits since confidence limits depend on the number of patients studied and the range of weights observed. Nevertheless, they provide some basis for comparison among studies and show that the errors involved for all those in Table V are roughly similar. The method proposed by Higgenbottom and associates,6 corresponds to our regression No. 15, that proposed by Morrison and McLennan 12 roughly corresponds to our regression No. 9 (although our method does not include head or limbs), and that proposed by Campbell and Wilkin" corresponds to our regression No. 6. The fact that several of these methods give better predictability than seems indicated by our results simply points out the difficulty in making comparisons between studies done at different times on different groups of patients. In conclusion, it appears that the accuracy achieved by any of these methods is no better than ±200 grams per kilogram (2 S.D.). Further improvement in our ability to predict fetal weight seems unlikely until we are able to reduce the repeatability error in longitudinal measurements or are able to find more accurate ways of assessing volume.
199
REFERENCES 1. Loeffler, F. E.: Clinical foetal weight prediction, J. Obstet. Gvnaecol. Br. Commonw. 74: 675, 1967. 2. Niswander, K. R., Capraro, V. J., and Van Coevering, R. J: Estimation of birth weight by quantified external uterine measurements, Obstet. Gynecol. 36: 294, 1970. 3. Ong, H. C., and Sen, D. K.: Clinical estimation of fetal weight, AM. J. OssTET. GYNECOL. 112: 877. 1972. 4. Issei. E. P., Prenslau, P., Bayer, H., Luder, R., Schulte, R., Wohlfahrth, G., Weight, M., and Acker, R.: The measurement of fetal growth during pregnancy by ultrasound (B-scan). J. Perinat. Med. 3: 269, 1975.
5. Campbell, S., and Wilkin, D.: Ultrasonic measurement of fetal abdomen circumference in the estimation of fetal weight, Br. J. Obstet. Gynecol. 82: 689, I 975. 6. Higgenbottom, J, Slater, J., Porter, G., and Whitfield, C. R.: Estimation of fetal weight from ultrasonic measurement of trunk circumference, Br. J. Obstet. Gynecol. 82: 698, 1975. 7. Kurjak, A., and Breyer, B.: Estimation of fetal weight by ultrasonic abdorninometry, AM . .J. 0BSTET. GYNECOL. 125: 962, 1976. 8. Lunt, R., and Chard, T.: A new method for estimation of
200 McCallum and Brinkley Am.
fetal weight in late pregnancy by ultrasonic scanning, Br. J. Obstet. Gynaecol. 83: 1, 1976. 9. Warsof, S. L., Gohari, P., Berkowitz, R. L., and Hobbins, J. C.: The estimation of fetal weight by computer-assisted analysis, AM. J. OBSTET. GYNECOL. 128: 881, 1977. 10. Issei, E. P., Prenzlau, P., and Laag. F.: Problems in using linear ultrasound parameters for the determination of fetal weight, J. Perinat. Med. 4: 26, 1976.
January 15, 1979 Obstet. Gynecol.
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II. Picker, R. H., and Saunders, D. M.: A simple geometric method for determining fetal weight in utero with the compound gray scale ultrasonic scan. AM. J. 0BSTET. GYNECOL. 124: 493, 1976. 12. Morrison,]., and McLennan, M.J.: The theory, feasibility and accuracv of an ultrasonic met hoc! of Pstim~tino- fpt~l weight, Br. j. Obstet. Gy~ae~ol. 83S~
83:
1976.-----" ------