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
Am.
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:>i0.90 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
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
Am.
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:>i0.90 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
