An investigation-of-fetal-growth-in-relation-to-pregnancy-characteristics

AN INVESTIGATION OF FETAL
GROWTH IN RELATION TO
PREGNANCY CHARACTERISTICS
by
Joe Max Mongelli
MB BS, B Sc (Sydney) MRCOG
Thesis submitted to the University of Nottingham for the
degree of Doctor of Medicine, November 1994

2
CONTENTS
Title page 1
Contents 2
Abstract 3
Acknowledgements 4
Abbreviations 5
Part I - Literature Review
Chapter 1 The Determinants of Birth Weight 6
Chapter 2 Adjustable Birth Weight Standards 15
Chapter 3 Ultrasonic Methods of Fetal Weight Estimation 22
Chapter 4 Models of Fetal Growth 29
Chapter 5 Screening Strategies for Abnormal Fetal Growth 37
Part II- Development of Research Techniques
Chapter 6 Principles of the Customised Growth Chart 49
Chapter 7 Methods of Gestational Age Estimation 57
Chapter 8 Forward Projection of Fetal Weight Estimate 64
Chapter 9 Selection of Ultrasonic Weight Formula 68
Chapter 10 Ultrasonic Study of Fetal Growth: Patients and
Methods.
76
Part III - Clinical Findings
Chapter 11 An Ultrasound Standard for Fetal Weight Gain 83
Chapter 12 Symphysis-fundus Height in Relation to
Gestational Age and Fetal Weight
95
Chapter 13 Fetal Growth Kinetics in Relation to Pregnancy
Characteristics
102
Chapter 14 Customised Growth Charts in Relation to
Neonatal Outcome
115
Chapter 15 The Prediction of Birth Weight 126
Part IV - General Discussion
Chapter 16 Comments and Conclusions 143
References 156

6
1. THE DETERMINANTS OF BIRTH WEIGHT
1.1 Introduction
Birth weight is one of the most important measures we have of the
health status of a population, being a strong predictor of both mortality
and morbidity, and reflecting nutritional status and growth rates. Yet
the estimation of the normal growth potential -and hence the definition
of growth retardation - for a given individual has remained an elusive
objective.
Neonatal size can be influenced by a large number of variables.
Kramer (1987), in a lengthy review on low birth weight, listed 43
potential causes, subdivided into 7 groups, while admitting that his
literature search may not have been complete. For the purposes of our
discussion, we will attempt to classify them as pathological or
physiological, depending whether or not they are associated with
adverse perinatal outcome. This classification will be arbitrary for
many of these factors, because of our limited knowledge in this field.
1.2 Pathological Factors
A large number of pregnancy complications are associated with
reduced birth weight. Classically, growth retardation has been
classified as either symmetric or asymmetric (Pearce & Campbell,
1985), depending on whether the fetal body dimensions are
proportionately reduced, or whether some degree of ‘head sparing’ has
occurred. In practice, asymmetric IUGR is associated with either pre-
eclamptic toxaemia or recurrent abruption, while most other causes
lead to symmetric IUGR.

7
Hypertensive Disease.
Essential, uncomplicated hypertension poses little or no risk to the
fetus. In early onset or severe pre-eclampsia birth weight may be
reduced by 300-500g and birth length by 1-3 cm, whereas late onset or
mild pre-eclampsia has no such association (Fedrick &
Adelstein,1978; Long et al, 1980). Reduced utero-placental blood flow
is considered to be responsible for reduced growth.
Chronic Maternal Illness
Maternal cyanotic heart disease is associated with fetal growth
retardation in up to 52% of pregnancies, as opposed to 9% in the
acyanotic group (Shime et al, 1987).
Diabetes has complex effects on fetal growth, with a tendency towards
larger babies unless associated with vascular disease and advanced
maternal age, when growth retardation is more likely. It is the main
pathological cause of fetal macrosomia.
Severe chronic respiratory diseases such as poorly controlled asthma
(Greenberger and Patterson, 1983), cystic fibrosis (Palmer et al, 1983)
and bronchiectasis (Thaler et al, 1986) may lead to reduced fetal
growth.
In the case of anaemia, it is difficult to separate the effects of
anaemia per se from the underlying nutritional problems. However,
women with sickle cell disease, sickle-thalassaemia and sickle
haemoglobin-C disease have an increased incidence of growth
retarded infants (Powers et al, 1986).This is most likely due to
placental micro-infarcts resulting from episodes of sickling, leading to
placental insufficiency.
Chronic renal disease of moderate severity is associated with IUGR in
up to 24% of cases (Katz et al, 1989), although some of this effect
may be related to hypertension.

8
Systemic lupus erythematosus has been implicated in fetal growth
retardation (Carlson,1988), though this may be a result of the
underlying renal disease or drug therapy.
Maternal Addictions
Smoking mothers have babies that are 150 - 200g lighter than those of
non-smokers (Wilcox et al,1993a); this appears to be caused by
smoking in itself rather than other factors associated with the smoker
(Doughterty,1982).
Excessive alcohol intake may result in small babies with shortened
palpebral fissures and a small head - the fetal alcohol syndrome
(Lemoine P et al, 1968). Fetal weights are reduced by 165-200 grams
among mothers who drink the equivalent of more than 50 ml of
absolute alcohol per day (Ouellette et al, 1977).
Heroin addiction has also been associated with reduced fetal growth
(Naeye et al, 1973).
High Altitude
Babies born at high altitude are lighter than those born at ground level
(Lubchenko, 1963); this appears to be a 'dose-response' effect related
to chronic hypoxia, with smaller babies being born at higher altitude
(Yip, 1987). Interestingly, both of these studies showed higher rates of
preterm delivery.
Malnutrition
Maternal malnutrition, when severe, may result in adverse neonatal
outcome. Stein and Susser (1975) analysed the birth statistics in
Holland during the famine of 1944-1945; they found that birth weights
declined by about 10% only when under-nutrition occurred in the third
trimester with caloric intake below 1500 g. This is to be expected,
since the period of greatest absolute growth is in the last 10 weeks of

9
gestation, when the average fetus gains about 2000g during this
interval (Hadlock et al, 1991).
Placental Disorders.
Recurrent antepartum haemorrhages in the first and second trimesters
is strongly related to reduced fetal growth, possibly due to impaired
development of the utero-placental circulation (Fedrick & Adelstein,
1978). Other placental anomalies associated with SGA infants include
circumvallate placenta, and large chorioangiomas.
Infection
Viral infections, particularly rubella and cytomegalovirus, may reduce
fetal weight and length to 80-85% of normal values ( Miller, 1981;
Naeye, 1967). In fatal cases of rubella, the growth restriction is
associated with markedly reduced cell numbers in the fetal organs
(Naeye, 1965). Listeriosis is sometimes associated with IUGR.
In global terms, malaria is probably the most important infectious
agent associated with growth restriction on a world-wide basis. This is
related to haemolytic anaemia and placental insufficiency related to
placental infestation. The pathological changes observed in the
placenta include perivillous fibrinoid deposits, syncytiotrophoblast
necrosis and partial loss of microvilli. A brownish discoloration may
be observed (plasmodial placental pigmentation), and these cases are
associated with significantly lower birth weights (Garin et al, 1985;
Walter et al,1982).
Chromosomal Defects
Most chromosomal and genetic disorders are associated with impaired
fetal growth of varying severity. In Downs’ syndrome the birthweight
is 80-90% of normal, while for trisomy 13 and Turner’s syndrome it is

10
80% and 84% respectively (Polani, 1974). More severe growth
restriction is observed in foetuses with trisomy 18, with an average
birth weight of only 62% of normal. Some genetic disorders such as
the Seckel and Russell-Silver syndromes are associated with severe
dwarfing apparent at birth.
On the opposite side of the spectrum, we find a group of genetic
disorders that are associated with fetal growth acceleration. These
include the Beckwith-Wiedemann syndrome, in which trisomy for the
IGF-II gene has been implicated, and ‘stood’ conditions associated
with a dramatic increase of fibrous tissue (Elejalde et al, 1977).
In Sotos’ syndrome, characterised by cerebral gigantism , the birth
weight is not significantly increased but the birth length is increased to
a mean of 55.2 cm.
1.3 Physiological Factors
Duration of pregnancy.
The length of gestation is the most important determinant of birth
weight (Wilcox et al,1993b), and also of perinatal mortality and
morbidity in the pre-term period (Allen et al, 1993). The 'terminal
flattening’ seen in birth weight standards based on menstrual data is
artefactual; it is much less marked in standards derived from
ultrasound-dated populations (Wilcox et al, 1993a).
Parental size.
The relationships between birth weight and parental size have been
studied extensively, both in humans and in animals. The classic
studies by Walton and Hammond (1938) on crosses between the Shire
horse and the Shetland pony showed that the birth weights of foal born
to Shetland dams of Shire sires were close to those of pure Shetlands;
conversely, foals of shire dams by Shetland sires were close to those

11
of the pure breed. Evidence in humans on the preponderance of the
maternal effects on fetal growth has been presented by Cawley (1954)
and Ounsted (1966). Both maternal height and weight have positive
correlations with birth weight, the latter being the stronger factor.
Low maternal pre-pregnancy weight is significantly correlated with
both preterm delivery and low birth weight (Garn 1990).
Obesity, as measured by the body mass index, is only weakly
correlated (Abrams, 1986; Wilcox et al, 1993b). The parents' own
birthweight is significantly correlated with that of their offspring
(Alberman et al, 1992).
Parity.
The positive effect of parity on birth weight has been documented in
most races and many mammalian species (Ounsted, 1973; Bantje,
1985), suggesting that its mechanism may have an evolutionary
advantage. Garn (1990) has argued, on epidemiological grounds, that
the effect of parity is a result of the increase in the maternal pre-
pregnancy weight seen in developed countries, rather than an
independent factor. This does not agree with multiple regression
analysis of birth weight, which shows parity to be a factor independent
of mid-pregnancy weight (Wilcox et al, 1993b); this may be because
the mid-pregnancy weight is a compound variable, dependent on both
the pre-pregnancy weight and the maternal weight gain.
There is some evidence that the effect is partner-specific, i.e. a change
in partner may be associated with a reduction in the birth weight of the
first born of the new relationship (Warburton & Naylor, 1971).
It may be argued that because of the significant increase in the
perinatal mortality of first-born infants and those of mothers of high
parity, this factor should be classified as a pathological variable. The
odds ratios, however are only slightly elevated (Kirkup &
Welch,1990), and do not justify this re-classification.

12
Race.
Meredith (1970) published an extensive description of the variations
in birth weight among different ethnic groups. Of the 78 groups
considered, the largest newborns were found in Anguilla and Nevis,
weighing a mean of 3.88 Kg. The smallest babies were those of the
Lumi tribe in the Toricelli mountains in New Guinea, with a mean
birth weight of 2.4 Kg. These ethnic differences clearly persist in
mixed populations from the same location (Cheng et al, 1972; Wilcox
et al, 1993b). Birth weight variations do not always correlate with
trends in perinatal mortality. In Singapore, Malay babies have a much
higher perinatal mortality than Indian babies even though their
percentage of low-birthweight (<2500) is significantly smaller
(Hughes, 1984), both groups living in similar socio-economic
conditions with total health care coverage. Similarly, Californian black
babies under 3001g have much lower mortality rates than whites, even
though their birthweights are lower (Williams et al, 1982).
Sex
The female newborn weighs on the average 118 g less than the male
(Wilcox et al, 1993b), and this has been observed in most ethnic
groups studied (Meredith, 1970).Animal studies suggest that the XY
embryo has a growth advantage at the earliest stages of organogenesis
(Snow, 1989); hormonal differences are not responsible, since the sex
differences are noted even in anencephalic foetuses. It is of interest
that in spite of this, females born preterm have lower mortality and
morbidity than males (Allen et al, 1993). This may be due to female
infants having relatively more energy stores in adipose tissue than
males (Oakley et al, 1977).

13
Others
Women with a history of SGA infants are more likely to give birth to
small babies. It is not clear whether this is due to genetic factors, or
recurrence of genetic/pathological factors. Work performed by
Ounsted (1965,1966) has shown that mothers who have borne SGA
infants had themselves lower than average birth weights, although
their adult height did not differ significantly from that of women who
had given birth to babies of normal weight.
Consanguinity in parents has been shown to cause a significant
reduction in birth weight in Pakistan (Shami et al, 1991), Japan
(Morton, 1958) and Norway ( Magnus et al, 1985).
A seasonal trend has been observed in birth weights, with significantly
lower values in summer and a peak in winter/early spring (Matsuda,
1992). These fluctuations are rather minor, occurring within a 100g
band.
1.4 Discussion
The distinction between 'pathological ' and 'physiological' factors is
to some extent arbitrary, with a significant 'grey zone' of uncertainty.
In terms of defining normal growth potential, the genetic components
of the physiological factors are probably more important, and this was
stressed by Lazar and colleagues (1975). This distinction is, however,
an important exercise in order to develop valid adjustable growth
standards. It is likely that fetal development is under the control of
inhibitory and stimulatory growth factors, and that some physiological
and pathological factors may well act through common pathways.
Animal studies have shed some light on the relative importance of
fetal genome and maternal effect; these have been reviewed by Snow
(1989). There is good evidence to suggest that maternal effects operate

14
late in gestation, whereas early fetal growth is controlled by fetal
genetic mechanisms. Winick (1971) studied the cellular basis of fetal
growth using animal models. Three phases of growth were identified:
cellular hyperplasia, followed by both hyperplasia and hypertrophy,
and then predominantly hypertrophy. Depending on the timing and
duration of experimental insults, different forms of growth restriction
were observed. Disturbances in early pregnancy restricted the total
cell number, so that no 'catch-up' growth was possible, whereas later
in pregnancy cell size was predominantly affected with minimal
reduction in cell numbers , and post-natal recovery was possible with
adequate nutrition. This points to the heterogeneous nature of growth
disturbances and to the need for using appropriate standards.
It is difficult to determine how much of the differences observed
among different ethnic groups are due to genetic factors, as opposed to
environmental factors such as nutrition and socio-economic
conditions. Hence customising for ethnicity can only be justified when
the adjustment factors are derived from sub-populations in the same
location and ideally living under similar socio-economic conditions.
The observed differences in neonatal morbidity between different
sub-populations do not always agree with the birth weight differences.
This lends weight to the argument that, for optimal performance, fetal
weight for gestation as an index of morbidity needs to be evaluated in
relation to other pregnancy characteristics.

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2. ADJUSTABLE BIRTH WEIGHT STANDARDS
2.1 Introduction
Birth weight on its own is only a crude indicator of neonatal welfare,
being a retrospective measure from which it is difficult to make
accurate inferences about prenatal growth kinetics. The definition of
'low birth weight infant' as being a newborn weighing below 2500g
was used as an index of prematurity until the 60's, when it was
realised that a considerable proportion of these cases were in fact
growth restricted (Ounsted, 1970). It has been nevertheless a
convenient tool for epidemiologists, since reliable data on the
duration of gestation is often difficult to obtain, particularly in
developing countries. This, however, fails to make the important
distinction between infants who are small because they were born
preterm and those term babies who are small because of constitutional
or pathological factors.
2.2 Pathological Implication of Abnormal Birth Weight
This has prompted the search for birth weight for gestation standards,
so that given the appropriate variables this distinction can be made.
When birth weight is analysed as a function of gestation, some
important relationships with poor perinatal outcome emerge. In a large
study by Patterson et al (1986) of a database of 44 811 cases, a
U-shaped relationship was found between birth weight centile and the
incidence of morbidity , with minimal morbidity near the middle
ranks of birth weight ; the percentage of the total poor perinatal
outcome occurring below the tenth or above the 90th centiles
increased linearly from 16% at 28-29 weeks to 57% at 40-41 weeks.
There is mounting evidence that being small for gestational age has
pathological implications extending into childhood and adulthood.
Hill et al (1984) , in a small study, related the outcome of term infants

16
with nutritional parameters. Malnutrition in the newborn was defined
in terms of subcutaneous tissue thickness. About 45% of the 33
malnourished infants had birth weights below the 10th centiles; in this
group, poor outcome included reduced educational achievement up to
the age of 14. Rantakallio(1985) studied a cohort of 12,000 children
in Finland followed up to 14 years; it was found that the incidence of
neuro-behavioural disturbances was significantly higher in weight
percentile classes below the median. Most of these and similar studies
are flawed by the use of menstrual dates in determining gestation . As
the error tends to be towards overestimation (Gardosi & Mongelli,
1993), more babies would be classified incorrectly as below the 10th
centile than those assigned above the 90th centile.
2.3 Assignment of Gestational Age
With very few exceptions, gestation is usually estimated from
menstrual dates, rounded down to 'completed weeks'. Typically, when
birth weight is plotted against gestation, the resulting standard curves
show considerable flattening near term, and this has been attributed
either to placental ageing/insufficiency, or to physical restriction of
growth. More recent standards in which gestational age has been
calculated on the basis of early ultrasound measurements show a
much more linear relationship between duration of pregnancy and
birth weight (Lindgren, 1988; Wilcox et al,1993a). This inaccuracy in
the estimation of gestational age is also likely to lead to a greater
apparent variance in the birthweight distribution for any given week of
gestation.
2.4 Preterm Delivery and Birth Weight Standards
Birth weight standards have in the past been referred to as 'fetal
growth curves'. Apart from the fact that these are cross-sectional
studies, values derived from preterm deliveries cannot be regarded as

17
representative of normal growth. Furthermore, unless the population
sample is very large, the number of babies born preterm is relatively
small, leading to a greater incidence of sampling errors. Preterm
delivery may be associated with growth restriction , and birth weight
norms at these gestations may be well below those derived from serial
ultrasound weight estimations (Ott, 1993). An experimental model of
growth retardation supporting this epidemiological data was described
by Alexander (1964). He, and subsequent workers, found that the
excision of endometrial caruncles in the sheep (before pregnancy)
resulted not only in an increased rate of growth retardation, but also in
increased preterm labour rates and intrauterine death.
Another indicator of pathology in the preterm period is the statistical
distribution of birth weights. Whereas the distribution of birth weights
at term shows a significant positive skewness, in the preterm period
this becomes negative (Wilcox et al, 1993a), most likely because of
the greater number of growth-retarded babies born at these gestations.
It has also been shown that preterm babies delivered electively are
significantly lighter than those born spontaneously, yet even when the
former are excluded from the analysis the negative skewness is
reduced but not entirely eliminated (Yudkin, 1987).
2.5 Effect of Environment
Reference standards may also be strongly affected by the environment
and population characteristics. For example, Lubchenko's (1962) birth
weight chart has been used widely in the United States and elsewhere.
This was derived from a population in Denver, Colorado, at an altitude
of about 10000 ft. Not only did this high altitude result in lower birth
weights for all gestations than any other published standard, but also
the percentage of births occurring preterm was much higher than
expected. There is also some evidence that birth weight standards may

18
change historically as living standards and social characteristics vary
(Alberman 1991; Ulizzi & Terrenato, 1992).
2.6 Adjustable Standards
The realisation that these genetic or physiological effects are in
operation led to attempts to introduce adjustment factors to allow for
maternal characteristics. Thomson and colleagues (1968) published
birth weight for gestation tables allowing for sex, parity and inclusive
of correction factors for maternal weight . Altman and Coles (1980)
produced nomograms for the calculation of birth weight centiles based
on this data that included correction factors for parity, maternal height
and weight, and fetal sex.
Lazar and colleagues (1975) used multiple regression analysis to
derive correction factors for both maternal and paternal weight and
height, claiming that paternal weight is as important as maternal
weight; they believed that the effect of these variables is largely of
genetic origin, and in order to improve their predictive power they
estimated what the parental values of height and weight would be at
the age of 20 before entering them in their regression model. Parity
and ethnic group were not considered in their analysis, and their model
was not tested prospectively.
Voigt (1989) and Mamelle(1989) published elaborate tables to allow
adjustment for these variables, but the fact that they are not in general
use attests to their complexity.
Some interesting similarities among different birth weight standards
were described by Dunn (1989). When the centile cut-off points were
expressed as percentages above or below the population median and
plotted against gestation, virtually identical values were obtained for
all the standards. This remarkable correspondence led to the
construction of the Bristol Perinatal Growth Chart, a method that
would allow the production of antenatal and post-natal growth

19
standard for population sub-groups. The method assumes that the
latter are normally distributed.
2.7 The Birth Weight Ratio
An alternative variable to describe size for gestation , the 'birth weight
ratio' , was described by Brooke and colleagues (1989) in order to
analyse factors affecting birth weight. This is simply the observed
weight divided by the weight expected for a given gestation. Morley
and colleagues (1990) described a relationship between birthweight
ratio and the need for mechanical ventilation and post-neonatal
mortality in preterm infants; this, however, was not observed in the
study of Brownlee et al (1991). More recently, Wilcox and colleagues
(1993b) analysed a large database of 31 561 computerised records of
term deliveries in order to develop a multiple regression model to
predict birth weight. The variables included gestation, sex, maternal
height, weight, parity and ethnic group. The ratio of the observed
birth weight to predicted weight ('individualised birth weight ratio',
IBR) can then be calculated by a computer program and expressed as a
centile value. This method has been reported to identify a higher
proportion of truly growth retarded infants, as defined by neonatal
ponderal index and skinfold thickness measurements (Sanderson,
1994). The drawback of Wilcox's program is that in its present form it
is only applicable to babies born at term, and cannot be used for
screening purposes in the antenatal period.
It can be shown that when birth weight ratios are transformed into
centile values, these are very similar to the corresponding birth weight
centiles, provided the reference standards used to obtain the mean and
standard deviation are similar (chapter 16).
2.8 Discussion
The large number of birth weight standards in existence is a reflection
of the importance given to this parameter, as well as the need to relate

20
birth weight to local conditions. In the English literature alone,
Goldenberg and colleagues (1989) were able to review 13 such
standards published since 1963. Large differences were noted in the
10th centile cut-off point, greater than 500g for some gestational ages.
These discrepancies are partly due to inconsistencies in methodology.
For example, McKeown and Gibson (1951) included both live and
still births in their analysis of the Birmingham data, whereas most
investigators have restricted their samples to live born infants. The
treatment of outliers in the data can vary between studies. A variety of
corrections for bimodal or skew birthweight distributions have also
been adopted (Gruenwald, 1966; Milner & Richards, 1974). A number
of studies are also limited by small sample sizes, making it difficult to
estimate centile distributions of birthweight with any degree of
accuracy.
Another major source of error is gestational age assignment.
Assessment of fetal well-being, by whatever means, requires an
accurate estimate of gestational age. The introduction of routine early
ultrasound scanning in the United Kingdom has eliminated large
errors, but the use of '10-day' or '7-day' rules whereby menstrual dates
are used in preference to ultrasound determined dates if in agreement,
may lead to some loss of accuracy (see Chapter 7). Those women who
book late tend to have poorer outcomes, and ultrasonography may be
of special benefit in this group. Although algorithms have been
developed for the accurate determination of gestational age up until 32
week's gestation (Sabbagha et al, 1978), these have not gained
widespread acceptance.
All of the adjustable standards of fetal growth are limited by their use
of cross-sectional birth weight data. While they may be valid for the
assessment of relative size, they are not suitable for assessing serial
weight estimates, i.e. growth (Altman, 1994).

21
With the exception of the IBR, the correction factors are usually
presented in tabular form, and do not take into account gestation-
dependent variations. Thomson and colleagues (1968) stated that these
adjustments should not be made for gestations under 37 weeks, since
their numbers was limited in that range. Nevertheless, their parity
differences were statistically different even at 32 weeks. Even if there
were sufficient numbers, it is doubtful that these adjustment factors
would be applicable to intrauterine fetal weight estimates. In practice
most clinicians do not adjust beyond sex and parity, probably because
of the inconvenience in using complex tables or graphs. In the
standard published by Yudkin and colleagues (1987) - widely used in
paediatric units in the UK-, no adjustment is made apart from fetal
sex.
Although the importance of accurate and valid fetal growth standards
has long been acknowledged, the validity of specific growth standards
when applied to a particular population or study sample is seldom
tested. As a result, the assessment of growth retardation and evaluation
of screening procedures may be inaccurate and biased.

22
3. ULTRASONIC METHODS OF FETAL WEIGHT
ESTIMATION
3.1 Introduction
Fetal weight estimation plays an important part in clinical obstetrics
decision-making, often used in screening for IUGR, the management
of diabetes in pregnancy and pregnancy complicated by breech
presentation. In current practice, ultrasonography remains the most
accurate method for determining the estimated fetal weight (EFW).
Although newer imaging techniques such as computerised tomography
and nuclear magnetic resonance are likely to be much more accurate
(Baker et al, 1994), their cost will prevent widespread use; their main
role in the immediate future will remain as research tools. Three-
dimensional ultrasound equipment, on the other hand, is now
affordable, and the better, more reliable definition of anatomical
planes (Kuo, 1991) should lead to reduced operator error and
hopefully to better performance of the existing formulae.
3.2 Fetal Weight Estimation Formulae
The equations for fetal weight estimation in terms of given ultrasound
parameters are usually derived by applying a model of fetal weight
composition to a source population examined shortly before delivery.
The measured ultrasound parameters and the birth weights, are entered
and the relevant coefficients are estimated by multiple regression
analysis. The performance of the formula in term of its prediction
errors is then tested on a separate sample, and 'target' population. One
of the first such formulae to be developed was that of Campbell &
Wilkin (1975 ); this was based on the fetal abdominal circumference
(AC), and it is still in common use in the UK A considerable number
of other formulae that usually employ more than one ultrasound
parameter have since been published. A sample of these are listed in

23
table 3.1. They can be broadly classified as exponential or non-
exponential, depending on the type of mathematical expression.
Exponential formulae take the form of:
EFW = exp[F(P1,..Pn)]
where F(p1,..pn) is a polynomial function of the ultrasound parameters
P1 to Pn.
Other approaches to weight prediction have been explored. A
computer neural network program has been developed specifically to
estimate weights in foetuses at risk of macrosomia (Farmer et al,
1992); ultrasound parameters were combined with clinical
measurements such as fundal height, with a reported accuracy of
around 5%. Birnholz (1986) published an algorithmic method for
weight estimation, whereby one of two formulae are chosen by a
computer program depending on the body proportions of the
individual. About 90% of cases had an error less than 80 g/Kg . This
method requires regression analysis of the fetal ultrasound parameters
in the population under study.
3.3 Clinical Performance of Weight Estimation Formulae
This is usually assessed by the statistical analysis of the errors. They
may be expressed as signed or absolute percentage errors, absolute
error in grams, errors in grams per Kg of fetal weight, and percent of
errors beyond a given threshold. A typical weight formula employing
more than one parameter will estimate 75% of cases within 15% of the
actual weight (Thompson et al, 1990).The most common practice is to
report the mean error and its standard deviation (SD); the former gives
a measure of the tendency to under- or over-estimate (the systematic
error), whereas the latter indicates the spread of the errors. It has
recently been suggested that the standard deviation should be replaced

24
by the 95% confidence limit of the errors (Bland & Altman, 1986);
this is certainly preferable in situations when the distribution is not
Gaussian. There is general agreement that equations employing two or
more ultrasound parameters are more reliable than those using only
one (Hadlock et al, 1985; Guidetti et al, 1990). Formulae developed
within an institution tend to perform better than those from other
centres (Thompson et al, 1990), probably because of significant inter-
observer variability (Chang et al, 1993) and differences in equipment
and populations. For example, formulae derived from Chinese
populations perform better on Chinese patients than those developed
from European populations (Chang et al, 1991). It has been reported
that continual review of the results obtained by the methods used by an
obstetric ultrasound department may further enhance its performance
(Thompson et al, 1990). In Hadlocks' studies (1985), the prediction
errors of equations employing three or four ultrasound parameters
(BPD, HC, FL and AC) had a SD of around 8%. Slightly better values
were reported by Issel and colleagues (1991), a SD of about 7% by
measuring up to 7 ultrasound parameters. In clinical practice these
errors tend to be somewhat higher (Miller et al, 1988). The problem
of systematic over- or under-estimation of fetal weight is frequently
reported when such formulae are used by centres other than the one
where the formula originated (Robson et al, 1993). Some of this error
may be due to the variations in the lag times between ultrasound
examination and delivery, which is not usually allowed for by the
authors of the formulae; this means that a fetus examined some days
before delivery will be slightly lighter than at birth, and when the birth
weight is entered into the regression analysis without due
modification, a small but appreciable over-estimation will take place.
This problem was appreciated by Spinnato and colleagues (1993), who
introduced a time component into the established formulae, valid up to
35 days before delivery. A more serious and common problem is the

25
existence of trends in the errors. There may be significant and
negative correlation with the size of the fetus (Robson et al, 1993;
Miller et al, 1988); hence small babies tend to be overestimated while
large ones are under-estimated. This can lead to serious data distortion
when producing normal values in growth curves for fetal weight, and
may affect the performance of screening programs for small- and
large- for gestational age infants.
3.4 Discussion
Early retrospective studies on the detection of growth retarded
foetuses by measuring the biparietal diameter suggested that this
parameter could be helpful in defining groups of cases with higher
perinatal mortality and preterm delivery rates (Persson et al, 1978).
The technique, however, was subsequently found by Campbell &
Dewhurst (1971) to have a false positive rate for SGA of 25%. This is
not surprising, since the correlation coefficient of BPD with birth
weight is not as high as other ultrasound parameters such as the
abdominal circumference and femur length (Favre et al, 1993).
Several studies have been published on the performance of different
ultrasound parameters in the detection of the SGA fetus. Neilson and
colleagues (1984) measured a series of fetal parameters in the third
trimester; they found that the product of trunk area and crown-rump
length (as an index of fetal weight) was superior to the trunk diameter
alone. Dudley and colleagues (1990) showed that EFW was the best of
four ultrasound parameters in identifying the small-for-dates infant.
Similarly, Chang and colleagues (1993) reported that a single EFW
estimate based on multiple ultrasound parameters was superior to
abdominal circumference in predicting 2 out of 3 indices of neonatal
nutritional deprivation. The efficacy of growth screening programs
continues to be limited by the error of ultrasonic EFW and by the lack
of a uniform standard for fetal growth and growth velocity. The

26
normal standards of EFW published to date show considerable
disagreement, and at least some of the differences may be attributable
to the choice of weight estimation formula. This is further discussed in
chapter 9.
Volumetric formulae for fetal weight estimation have been proposed
by several workers, including Combs (1993 ) and Birnholz (1986), on
the grounds that fetal volume is proportional to weight when the
specific gravity is constant. There are at least two theoretical
objections to this argument. Firstly, the gestational age-dependent
changes in specific gravity have not been described, and the magnitude
of error from this factor is unknown. Secondly, growth retarded babies
would have considerably less fat stores, increasing their specific
gravity and thus leading to underestimation of weight. That this may
be the case is suggested by the fact that Birnholz noted systematic
underestimation of fetal weight in the under-1000g group, for whom
he had to apply a recursive correction formula. In any case, the
claimed improvements in accuracy of their methods have not been
confirmed by independent workers.
Birnholz (1986) has suggested that , on the grounds of information
theory, averaging serial fetal weight estimates would improve the final
estimate, with the expected improvement being related to the square
root of the number of measurements. This makes the assumption that,
for a given individual, the error in fetal weight estimation on each
occasion is random, i.e. the signed error values are not correlated with
each other. This particular issue has not been reported on in the
literature.
All of the commonly used formulae place an emphasis on bony
landmarks and do not use any other soft tissue measurements apart
from the AC. While bony landmarks are accurate for the purposes of
estimating gestational age, the emphasis on these parameters could
explain their relative inaccuracy in estimating weight.

27
New weight estimation formulae should be explored that include
additional measures of soft tissue parameters. These were explored by
Favre and colleagues (1993), who reported better performance in the
small for dates group using the thigh circumference and femur length.
The standard deviation of the error was nevertheless fairly high at
15.9%, and they did not compare their formulae with older established
equations.
Other measures that should improve not only accuracy of fetal weight
estimation but also performance of other tasks include continual audit
and quality control, to ensure consistent techniques and peak
performance of equipment. Plastic ‘phantoms’ have been designed in
order check the technique and accuracy of the measurements
performed by ultrasonographers, but these are not in common use in
the UK.
The scope for making major errors in estimating growth velocity from
ultrasound fetal weight estimation has been pointed out in
correspondence by Gardosi (1994b). Substantial gains in accuracy will
be needed before abnormalities in growth velocity can be reliably
detected.

28
Table 3.1 Ultrasound fetal weight estimation formulae.
Authors Exponential formulae
Campbell & Wilkin
(1975)
wt=1000*exp(-4.564 +0.282*fac -0.00331*fac*fac)
Hadlock et al (1985) wt=exp(2.695 +0.253*fac -0.00275*fac*fac)
Hadlock et al (1985) log10(wt)=1.3598 +0.051*fac +0.1844*fl -0.0037*fac*fl
Hadlock et al (1985) log10(wt)= 1.4787 -0.003343*fac*fl +0.001837*bpd*bpd
+0.0458*fac +0.158*fac
Hadlock et al (1985) log10(wt)=1.3596 -0.00386*fac*fl +0.0064*hc
+0.00061*bpd*fac +0.0424*fac +0.174*fl
Shepard et al (1982) wt=1000*exp(-1.7492 +0.166*bpd +0.046*fac -
0.002646*fac*bpd)*(ln(10))
Warsof et al (1977) wt=1000*exp(2.302585*(-1.599 +0.144*bpd +0.032*fac
-0.000111*bpd*bpd*fac))
Persson et al (1986) wt=exp(ln(10)*(0.972*ln(bpd)/ln(10) +1.743*ln(ad)/ln(10)
+0.367*ln(fl)/ln(10) -2.646))
Balouet et al (1992) wt=0.1135exp(0.739*ln(fac) +1.179*ln(ethc) -0.041*ln(ithc))
Non-exponential formulae
Combs et al (1993) wt=0.23718*fac*fac*fl +0.03312*hc*hc*hc
Dudley et al (1990) wt=4.1*fl*apa +0.86*fl*hpa
Shinozuka (1987) wt=0.23966*fac*fac*fl +1.6230*bpd*bpd*bpd
Birnholz (1986) wt=(3.42928*bpd*ad*ad/1000) +41.218)
Birnholz (1986) wt=1.0206*{1.88496*[0.01*fl*ad+0.01667*bpd*ad +
0.01*bpd*bpd]*[(((-0.0069558*fl) +1.7394)*fl/10)
-3.3626]} -61.537

29
4. MODELS OF FETAL GROWTH
4.1 Introduction
Awareness of the limitations of birth weight standards as indicators of
fetal growth have led to the pursuit of ultrasound-defined intrauterine
growth standards. But while it is relatively easy to obtain birthweight
data from large populations, to derive ultrasound-defined standards
requires considerable effort in manpower, logistics and equipment.
Usually this data originates from ultrasound departments, and often
does not contain the clinical details of individual cases. As a result, all
of the fetal weight standards published to date have been derived from
relatively small samples.
The norms for commonly measured ultrasound parameters such as the
AC, FL and BPD are well established, yet relatively few studies
specifically address the issue of intrauterine weight gain. This is
partly because for the purposes of growth monitoring, most
ultrasound departments plot the individual measurements rather than
weight estimates. This in spite of several studies suggesting that the
EFW is at least as good as the AC for the detection of IUGR (Chang et
al, 1993; Hedriana & Moore,1994). Here we review the literature on
intrauterine weight curves, and describe an 'average' growth curve,
based on published data.
4.2 Comparative Analysis of Ultrasound-Derived Growth Curves
A total of seven studies describing intra-uterine weight gain were
retrieved .Studies on the growth of linear ultrasound parameters
without weight estimations were excluded, since derived fetal weight
curves can differ markedly depending on the weight equation being
used (see chapter 8 ). The characteristics of these studies are

30
summarised in table 4.1; these include population samples, weight
estimation formulae, mean birth weight and the methods of data
analysis. The fetal growth kinetics described by each study are
displayed in table 4.2. In order to describe the shape of the growth
curves independently of the predicted term weight, growth can be
expressed as a percentage of the predicted 280-day fetal weight, and
plotted as fractional growth curves. This allows comparisons in terms
of arbitrary descriptive landmarks such as gestation at which 50% of
the term weight is reached (G50), and the percentage of term weight
that is expected at 28, 37 and 42 weeks (P28, P37, P42). Figure 4.1
shows the medians of the ultrasound EFW curves plotted to 42 weeks
and also the corresponding birth weight data derived from the East
Midlands Obstetric Database (Wilcox et al, 1993a). Figure 4.2 shows
the derived fractional growth curves, as a percentage of term weight.
The equation for average fractional curve was obtained by taking the
arithmetic average of the coefficients of the derived growth functions
listed in table 4.1. This is plotted in figure 4.3; only a minimal degree
of deceleration is noted at term.
4.3. Alternative models of fetal growth
Rossavik and Deter (1986) proposed a sigmoid function to describe
fetal growth of any parameter, including weight. This function is of
the form:
P= c(t) k+st
where P is the ultrasound parameter, t is the duration of growth, k a
fixed coefficient determined by the anatomical characteristics, c and s
constants related to growth regulatory processes. This function allows
the prediction of individual 'normal' growth channels based on two

31
separate ultrasonic examinations before 27 weeks. This model was
applied prospectively by Simon et al (1989) to a number of parameters
including fetal weight. They found a small but significant systematic
error of overestimation for most of the parameters and fetal weight;
the standard deviation of the errors for fetal weight ranged from 6.7 %
to 9.4% , depending on gestation. This is well within the range of the
published errors of weight estimation formulae. The advantage of this
model is that reference charts are no longer needed; instead, growth
disturbances may be detected as deviations from the individually
projected standard. The main drawbacks are the need for two
ultrasound examinations before 27 weeks' gestation, spaced at least 5
weeks apart, and the need for appropriate computer equipment and
software to carry out complex calculations.
4.4 Discussion
Most of the differences between the published ultrasound growth
curves become apparent during the term period. They agree within a
100g band up to about 36 weeks gestation (figure 4.1). Beyond this
point, Jeanty's curve shows marked deceleration, whereas Deter's and
Otts display moderate acceleration. The remaining four curves
continue a linear trend evident from about 28 weeks. Jeanty's
abdominal circumference values are markedly below other standards
in late pregnancy, and this probably accounts for the deceleration in
his weight curve. The overall fractional average curve (figure 4.3)
shows only minimal deceleration at term, and this is in contrast to
birth weight standards based on menstrual data. Another approach to
deriving this curve would have been to use a weighted average; the
problem here is that two of the studies are cross-sectional. In any case,
the largest studies are included in the middle five curves, and thus it is

32
doubtful that a weighing procedure would change the shape of the
curve significantly.
On the basis of their published birth weight data, Ott's and Deter's
weight formulae overestimate fetal weight at term by 255g and 471 g
respectively, and this may account for the steeper slopes of their
curves. Larsen's study is the only one to use birth weight in order to
select the optimal growth model; yet even here there is a systematic
overestimation at term of about 170g. This contrasts with Hadlock's
study, of similar (cross-sectional) design, where an overestimation of
only about 20g was observed, probably because of better performance
of the weight estimation formula.
Of the five studies whose weight formula was not developed locally,
none compares more than 3 different weight formulas in order to
select the best. As will be discussed in chapter 8, the type of weight
equation selected may result in differences of more than 300g at term.
Hence, when producing standards of intrauterine weight gain,
measures should be taken to correct any systematic error due to the
weight estimation formula, since other centres will not necessarily
employ the same formula.
It is unlikely that the method of gestational dating makes a significant
contribution to the observed differences among these studies. This is
because, with the exception of Ott's study, menstrual dates were used
only if in close agreement with early ultrasound measurements; if they
did not agree, gestation age was estimated from the early ultrasound
measurements of the biparietal diameter .
The study by Larsen and colleagues is the only one to produce separate
standards for males and females; they describe a mean weight
difference between the sexes of 3.8%, but do not elaborate on whether
this holds true for all gestations or only for part of pregnancy.
It is apparent from figure 4.1 that all of the ultrasound derived medians
are higher than the birth weight data, by an average of about 100g.

33
Systematic weight estimation errors may account for some of this
difference, but other factors may be at play , since the differences
persist in the studies where this error was minimal, such as Hadlock's
or even negative, as in Jeanty's. The most likely explanation is that
infants born preterm are more likely to be growth retarded, and
preterm delivery in these cases is an escape mechanism from an
adverse intra-uterine environment.
Complex mathematical models such as Rossavik's, irrespective of
their validity, are unlikely to improve birth weight prediction in view
of the magnitude of ultrasound error. A recent study by Shields and
colleagues (1993) has shown that serial plotting of fetal measurements
on normal curves is as accurate in this respect as complicated
mathematical modelling. This would also be expected on the basis of
information theory (Birnholz, 1986).

34
Figure 4.1. Ultrasound-derived fetal growth standards compared with
Nottingham’s birth weight standard. The continuous curves represent the ultrasound-derived
standards published by Hadlock et al, Gallivan et al, Ott, Persson & Weldner, Deter et al, Larsen et al and
Jeanty (using Shepard’s weight formula). The values for the birth weight standard by Wilcox et al are
displayed as triangles. The middle four curves (Hadlock, Gallivan, Larsen and Persson) are closely
related.

35
Figure 4.2. Proportional growth curves for ultrasound-derived fetal growth
standards.
The ultrasound-derived standards published by Hadlock et al, Gallivan et al, Ott, Persson
& Weldner, Deter et al, Larsen et al and Jeanty (using Shepard’s weight formula) have
been transformed into ‘proportional’ growth curves, whereby the values for each gestation
represent the percentage of the predicted 280 day fetal weight.

36
Figure 4.3. Average proportional fetal growth curve.
The transformed proportional fetal growth curves of the ultrasound-derived
standards published by Hadlock et al, Gallivan et al, Ott, Persson & Weldner, Deter
et al, Larsen et al and Jeanty (using Shepard’s weight formula) have been averaged
arithmetically to yield an average curve
.

37
5. SCREENING STRATEGIES FOR ABNORMAL FETAL
GROWTH
5.1 Introduction
In spite of the widespread introduction of obstetric ultrasound, our
clinical ability to detect the small-for-dates fetus remains poor, with
only about 30% -50% of cases detected in the ante-natal period (Jones,
1986; Hepburn & Rosenberg, 1986) . We are also rather ineffective in
detecting fetal macrosomia, with sensitivities of about 50% (Sandmire,
1993; Pollack et al, 1992).
The question has been raised on several occasions of whether
antenatal detection of growth disturbances is going to significantly
affect neonatal prognosis . While there is no long-term follow-up data
on this issue, there is some evidence that those SGA infants that are
detected tend to have a better short-term outcome than the undetected
cases (DeCourcy-Wheeler, personal communication). Hence we
should persist in our efforts to improve the antenatal detection of the
potentially compromised fetus.
There are two basic methods in practice for the detection of fetal
growth anomalies: obstetric ultrasound and assessment of the fundal
height.
5.2 Fetal Ultrasonography
Obstetric ultrasound has been investigated as a screening technique
since the early 70's (Campbell, 1971).While it has proved successful in
the detection of congenital abnormalities (Chitty et al, 1991) and in
establishing gestational age, the detection of growth restriction and
growth acceleration have remained much more elusive goals. Fetal
macrosomia is a common cause of concern for obstetricians, and it is

38
common practice to refer cases to the ultrasound department for fetal
weight estimation. There is, however, mounting evidence that so far
the performance of ultrasound in this weight group is poor compared
with other categories (Sandmire,1993). Two ultrasonic methods are in
common use for the detection and assessment of fetal growth
abnormalities: serial and static measurements of fetal anatomy .
At least five randomised trials have been performed since 1984 to
assess the efficacy of antenatal ultrasound as a screening tool for
growth restriction or developmental anomalies. These were published
by the following authors:
1. Bakketeig LS and collegues (1984)
2. Waldenstrom U and collegues (1988)
3. Ewigman B and collegues (1990)
4. Ewigman B and collegues (1993)
5. Newnham JP and collegues (1993)
The results have been somewhat contradictory and inconclusive. A
significant reduction in the number of SGA infants, a modest increase
in the mean birth weight and a significant reduction in the induction
rate was demonstrated by Waldenstrom and colleagues, following
routine scanning at 12 weeks. This was attributed to a reduction in
smoking due to visualisation the baby. On the other hand, in a group
undergoing both Doppler and ultrasound imaging on up to 5
occasions, Newnham and colleagues noted a slight but significant
increase in the SGA frequency in the screened group. In the largest
randomised study to date (4) involving 15151 low-risk pregnancies ,
no significant differences in outcome were noted between the screened
and the routine management group. The latter, however, did undergo
ultrasound examination when clinically indicated, thus limiting the
scope of the inferences that can be made from this study.

39
Optimal strategy for the detection of growth restricted fetus continues
to be a controversial issue (Daniellan and colleagues,1994). The study
by Chang and colleagues (1993) suggests that the use of either growth
velocity or single fetal weight estimates is rather limited at detecting
the truly growth restricted fetus as defined by neonatal morphometric
indices; at a false positive rate of 10% only 20-40% of the growth
retarded fetuses were detected. Similar figures were reported by
Daniellan and colleagues (1993). Both of these studies used
morphometric indices as the definitive criteria for IUGR; the
limitations of these indices are discussed in chapter 9. The data
presented by Hedriana and Moore (1994) suggests that a single
ultrasound examination is nearly as good as multiple examinations in
predicting the birth weight, but they did not test the hypothesis that
growth velocity as assessed by multiple measurements is a better
predictor of poor outcome than fetal weight estimated from a single
measurement.
5.3 Fundal height assessment
5.3.1 Introduction
The earliest report on measuring the symphysial-fundal height (SFH)
was published in the German literature by Spiegelberg in 1891.
Rumboltz and McGoogan (1953) were the first to describe a
relationship between reduced growth of the uterine fundus and
'placental insufficiency'. Since then, many conflicting reports have
been published on screening for growth disturbances by the clinical
measurement of the symphysial-fundal height (SFH).
5.3.2 Precision and accuracy of SFH measurements.
The estimation of symphysis-fundus distance is subject to
considerable error. Bagger and colleagues (1985) reported an average

40
intra-observer variation of 1.5-2 cm and an inter-observer variation of
4 cm; these were not correlated with the actual SFH measurements.
Some observers were found to consistently overestimate or
underestimate .The accuracy of SFH measurements was checked by
comparing clinical measurements with those obtained by ultrasound
guided measurement; the differences between the former and the latter
ranged from -0.2 to +2.7 cm. Calvert (1982) found intra-observer and
inter-observer coefficients of variation of 4.6% and 6.4%, slightly
lower values than those published by Bagger's group. The limits of
agreement of the inter-observer variation were estimated in a study by
Bailey and colleagues (1989) to be -5.0 to +1.6 cm, corresponding to a
coefficient of variation of 4%. This study highlights what is probably
the major shortcoming of SFH measurents: that the error due to inter-
observer variation, even between experienced practitioners, is too
wide in relation to the standard deviations in the published reference
charts.
5.3.3 Fetal weight estimation by fundal height measurement.
Estimation of fetal weight by unaided clinical palpation was reported
by Loeffler (1967) to be accurate within 450g of the birth weight in
80% of cases; it is of interest that in this study the accuracy of the
individual observers improved with experience.
The first attempt to estimate fetal weight by measuring the fundal
height was reported by Johnson and colleagues (1954). This method
included correction factors for engagement of the fetal head and
obesity.The standard deviation of the reported errors was 353g, which
is slightly greater than ultrasound estimation using Campbell's formula
for abdominal circumference(Campbell & Wilkin,1975). More
recently, a Belgian study of an African population showed that SFH
was more closely related to fetal weight than gestation (De Muylder
and colleagues,1988).

41
5.3.4 Derivation of SFH standards.
In all the studies, women without 'sure' dates or an early dating
ultrasound scan were excluded. In six of the nine papers reviewed the
data was filtered by removing those cases whose birth weights were
outside arbitrary limits; depending on the degree of restriction, the
standard deviation of the SFH values thus obtained would be
narrower. The inclusion criteria are summarised in table 3. In all of the
above studies there appears to be some flattening of the SFH curve
near term. As pointed out by Westin, miscalculation of gestational age
may lead to serious error. In all the standards so far published,
gestation was reckoned on basis of menstrual dates, ultrasound dating
being used routinely to 'confirm' dates (Pearce),or reserved for those
cases whose last menstrual period was unknown (Calvert, Quaranta)
or otherwise excluding those cases without a known LMP (others).
Geirsson (1991) has convincingly argued that even when certain, LMP
dates are less reliable than those derived from ultrasound, with an
overall tendency to overestimate gestation. He pointed out that birth
weight standards in populations whose gestations are derived from
ultrasound dating show a much less marked 'terminal flattening' of the
reference curves at term. This has also been our experience (Wilcox et
al, 1993a). It is likely that SFH reference standards are also subject to
the same effect.
5.3.5 Ethnic variations in SFH standards.
Table 5.1 shows the differences in SFH standards by ethnic group.
For comparative purposes, the 40-week median value is given for each
group; the SD deviation is omitted because of the widely different
methodologies used. It thus appears that for European populations
there are only small differences among the published standards. Indian

42
populations, however, have lower term values of around 33 cm,
compared with 36 cm for Europeans. Grover and colleagues (1991)
published a reference standard derived from 200 low-risk Indian
women with birth weights within +/- 1 SD of the local standard.
Compared with European curves, their fundal height increments were
similar from 20 weeks until 32 weeks (1 cm/week); some slowing was
noted thereafter, resulting in term values that were 3 -4 cm lower.
Similar values were published by Mathai and colleagues (1987) in
South India. However, Depares and colleagues (1989),on comparing
European and Pakistani SFH values in Bradford (UK), could not
detect significant differences.This may be because of the small
samples in their study.Oguranti studied SFH in 581 unselected
Nigerian women; their values were also lower than European
standards pre-term, but reached similar values at term. These
differences in SFH standards among ethnic groups may arise from the
well-known differences in birth weights, but could also be due to other
factors such as maternal body build and prevalence of fetal pathology.
5.3.6 Clinical performance of SFH measurements.
The definitions of 'positive for SGA' by SFH measurements differ in
the literature. The populations tested also differ, some being high-risk,
hence artificially increasing the detection rate. In most cases at least
two or three consecutive readings have to be below the 10th centile.
Theoretically, increasing the number of abnormal measurements in
order to diagnose SGA should reduce the false positive rate. In a large
uncontrolled study of low risk, uncomplicated pregnancies Westin
(1977) in Sweden showed that SFH measurements were superior to
maternal weight gain, maternal girth measurements, and biochemical
analytes (uE3, HPL) for the detection of the SGA infant.The routine
introduction of reference SFH charts in the case notes of all their
patients was associated with a significantly steeper fall in the local

43
perinatal mortality rate compared with the overall Swedish statistics.
Pearce and Campbell (1987) compared serial SFH mesurements with a
single fetal abdominal circumference (FAC) obtained by ultrasound as
screening tests for SGA. No significant differences were noted
between the two, when specificities were set equal at 79%.
Interestingly, they found a peak sensitivity at 34 weeks, similar to
Quaranta's peak at 32 weeks. The only randomized controlled trial on
the clinical performance of SFH measurement versus clinical
palpation was reported by Lindhard and colleagues (1990), in a
population of 1639 women. No significant differences were found
between the two methods in terms of the detection rate of SGA,
number of interventions, additional diagnostic procedures or the
condition of the newborn.
Table 5.3 summarises the clinical performance of SFH measurements
in detecting SGA infants. Because fundal height standards and the
definitions of an abnormal SFH test vary, it is not possible to pool
results in order to arrive at average values.Persson and colleagues
(1986) summarise positive predictive values for various studies
including their own, which is the largest. They range from 13% to
79%; there is a tendency for larger studies to show lower PPV's. This
is consistent with the hypothesis that the larger the number of
observers, the greater is the effect of inter-observer variability and
hence the poorer the tests' performance.
5.4 Discussion
If , as one would expect, antenatal detection of IUGR improves
neonatal outcome, then an effective screening strategy for growth
disturbances is a major target in perinatal medicine. That randomised
studies have not been able to document a definite improvement in
outcome following routine ultrasound examinations may be due to a
number of factors. To some extent this is likely to reflect the limited

44
accuracy of ultrasound in estimating fetal size; in none of the studies
was fetal weight rather than the individual biometric parameters
plotted. Another factor is the threshold for clinical intervention. In
Newnham's study, the induction rates of the screened women did not
differ significantly from the regular group even though the former
were significantly more likely to be given the diagnosis of IUGR. This
suggests some reluctance on the part of the clinicians to act on the
basis of the ultrasound findings. Not to be discounted is the lack of an
appropriate standard for detecting deviations in growth velocity.
The concept that fetal growth could be monitored by such a simple
and inexpensive tool as a tape measure has generated wide
interest.The lack of agreement in the literature on the efficacy of SFH
measurements is not surprising, given the wide differences in
definitions and population sampling. The fact that the median 40-week
values for different ethnic groups reflect their differences in mean
birth weights provides additional support to the notion that SFH
measurements are an indicator of fetal size.
At least three studies compared traditional clinical palpation with SFH
measurements for the detection of SGA fetuses. Secher and colleagues
(1990) found no significant differences betweeen these two methods.
Similar results were obtained by Pschera and colleagues (1984), and
by Lindhard and colleagues (1990). This may be due to the clinicians’
longer experience with clinical palpation as opposed to the newer SFH
measurement, and hence the results may have been biased by this
factor.
There is no good evidence that introduction of routine SFH
measurements leads to a reduction in perinatal mortality rates. The
improved figures reported by Westin may well have been a chance
result, since this study was not properly controlled.
In view of the magnitude of the error due to inter-observer variability,
it is likely that SFH measurements are clinically more useful when

45
performed serially and frequently by the same observer using a
consistent technique.
There is some evidence to suggest that test performance for SFH may
be optimal around 32-34 weeks, and it is of interest that this coincides
with the period of peak performance for ultrasonic fetal weight
estimation of 32 to 36 weeks (Hedriana & Moore, 1994). If ultrasound
growth screening is to be performed as a one-stage routine, then this
gestational age interval offers the best hope for success. It could also
be possible to improve the accuracy of ultrasonic fetal weight estimate
by combining it with the SFH; this approach was described by Farmer
and colleagues (1992), who, in addition toultrasound data and the SFH
also included maternal characteristics such as height and parity. They
developed a trained neural network which, in the case of suspected
macrosomia, was significantly more accurate in estimating fetal
weight than either Hadlock’s or Shepard’s formula; its mean
percentage error was 4.7% with a standard deviation of 3.9%.
Accurate fetal weight estimation is the key to an effective screening
program for growth disturbances. This is an area that continues to
evolve, and improvements may be brought about by advanced
information processing techniques, using current clinical
measurements.

46
Table 5.1 Criteria for Population Selection of SFH Standards
Study Population selection criteria for
derivation of standard.
Quaranta Birth weight between 25th and 90th
centiles
Belizan Birth weight between 10th and 90th
centiles
Westin Mean birth weight +/- 1 SD
Calvert Birth weight between 10th and 90th
centiles
Pearce Birth weight between 10th and 90th
centiles
Grover Birth weight within mean +/- 1sd
Mathai Term delivery of live infant
Rosenberg Birth weight between 25th and 90th
centiles
Ogunranti All patients sure of their dates.
Persson Infant weight/length ratio between 10th
and 90th centile

47
Table 5.2 Ethnic variation in SFH standards.
Study Ethnic Group Sample size 40-week value
Quaranta European 138 36.5
Belizan Latin American 139 34.5
Westin European 428 36
Calvert European 381 36
Pearce European 699 37
Persson European 1350 36
Ogunranti Afro-caribbean 581 39.4
Grover Indian 200 33
Mathai Indian 250 33.8

48
Table 5.3 Clinical performance of SFH measurements.
Study Definition of abnormal result FP sens spec
Quaranta 2 cons or 3 isolated vals <10th cent 21 73 80
Belizan 1 single val <10th 21 86 90
Westin 1 single val<2cm below median or
3 cons static or decreasing vals 54 75 64
Lindhard As above 41 28 97
Calvert 1 single val<2cm below median or
3 cons static or decreasing vals 80 76 60
Pearce 1 single val below 10th centile 64 76 79
Grover 1 single val < 1sd below mean 16 81 94
Mathai 1 single val < 1sd below mean 23 78 88
Rosenberg 20% of measurements below
10th centile 21 62 85
Cnattingius 'catch-up and low' SFH growth NA 79 92
Persson outside 2sd's NA 27 88

49
6. PRINCIPLES OF THE CUSTOMISED GROWTH CHART.
6.1 Introduction
To produce an adjustable standard that takes into account the
physiological factors influencing fetal weight is a computational task
that is not easily performed by using tables and graphs. The logical
solution to this problem is computer software.
The principles of a computer-generated growth standard which carries
out this task were first published in the Lancet in 1992 by J.Gardosi,
Professor A.Chang and colleagues.Unlike previous attempts that relied
on fixed correction factors from tables applied to birth weight
standards, the calculations were performed by computer software and
growth charts could be displayed on screen and printed. Ultrasound-
derived fetal growth standards rather than birthweight standards were
used for generating growth curves, and corrections factors that
included maternal weight at booking, maternal height, parity, ethnic
group and fetal sex were scaled up or down depending on the
gestational age.
6.2 The prediction of normal growth potential
The initial obstetric database consisted of 4179 pregnancies with
ultrasound-confirmed dates. Multiple regression analysis showed that
in addition to gestation and sex, maternal weight at booking, height ,
ethnic group and parity were factors that significantly affected birth
weight. This was confirmed by analysis of variance.The multiple
regression analysis was repeated by Mr Mark Wilcox on a much larger
sample of 38114 cases, smoking being entered as an independent
variable.Continuous variables such as gestation, height and weight
were centered around their means so as to minimize computational

50
problems. The details of the analysis have been published elsewhere
(Gardosi et al, 1994), and the coefficients are given in table 3.1. This
regression model allows us to estimate the fetal weight at 40 weeks for
any combination of maternal characteristics. In the prediction of
normal birthweight, the confounding effect of smoking is dealt with by
entering the non-smoking coefficient for all cases.The model can only
explain 31% of the variability of birth weight in the database, but this
is likely to be an underestimate, since up to 55% of records in
obstetric databases may have at least one error (Dombrowski, 1994);
the East Midlands Obstetric Database is not subject to rigorous quality
controls.
6.3 The generation of normal fetal growth curves
The method of generating growth curves relies on the working
hypothesis that, for normally grown fetuses, the morphology of the
growth curves is approximately the same irrespective of birth weight.
This means that if the mean curves from population subgroups are
described in terms of a polynomial function of gestation, division of
the polynomial coefficients by the 40-week weight will yield a new
function whose coefficients will not vary appreciably between
subgroups. Some indirect support for this postulate comes from the
work by Dunn (1989) and Thomson (1968).
In chapter 4 we reviewed the literature on ultrasound-derived fetal
weight growth curves and for each mean curve we derived a
'proportional' curve, by dividing the coefficients of the original by its
predicted 40 week weight . An average growth curve was produced by
taking the arithmetic mean of the respective coefficients; this function
will estimate the percentage of term weight for any gestation.
Multiplying this function by the predicted 40-week weight obtained
from the regression model will yield an individual 'ideal' antenatal
growth curve. The 10th and 90th centile reference curves are derived

51
from the standard error of the regression analysis, and are adjusted at
each gestation so that the ratio of the standard error to fetal weight
(coefficient of variation) remains constant at 11%.
Some paired examples of the charts are shown in figures 6.1 to 6.4.
Mrs Average (fig 6.1) is a European woman of average height and
weight (163 cm and 63.4 Kg) who has had a previous delivery of a
male infant weighing 2700 g at 37 weeks. The value within the square
(9) is the centile value of this weight for 37 weeks. The expected birth
weight at 40 weeks is just over 3800 grams. Figure 6.2 shows a
woman of the same parity and size but of Indo-Pakistani origins; the
term birth weight expectation is reduced to 3600 grams, but the
previous delivery is not classified as SGA (centile 19). The chart of a
large European lady with the same obstetric history is shown in figure
6.3; the previous birth weight is given a centile value of 4. In contrast,
a short and light lady with the same history would be given a centile
value of 24 (figure 6.4).
6.4 Other functions
The early versions of the customised growth charts also allowed the
entry of fundal height measurements by including a fundal-height y-
axis on the right side. This was calibrated to approximate the standard
published by Pearce and Campbell (1987).
An axis for the fetal abdominal circumference was also displayed,
based on the standard of Deter and colleagues (1982). Previous
deliveries and their birth weight centiles may be entered and displayed
on the same chart.
The x-axis displays gestation as exact weeks and also the calculated
corresponding dates.
The expected date of delivery, maternal height and weight, parity and
ethnic origin are displayed on the top left hand corner of the chart. In
the latest version of the chart, the maternal body mass index is

52
displayed if this falls below the 10th centile for our pregnant
population at booking, as this indicates the possibility of malnutrition
in the periconceptional period.
6.5 Clinical performance
The initial sample of 4179 deliveries contained 385 cases with a birth
weight below the 10th centile by unadjusted criteria (SGA). Of these,
only 278 were still below the 10th centile following adjustment for
maternal characteristics. Hence 107 (28%) would have been given a
false positive diagnosis of SGA by conventional standard. Adjustment
90 cases that would have been missed by conventional assessment.
Babies that by the conventional standard only were deemed SGA had
significantly fewer instances of low Apgar scores.
6.6 Discussion
It is apparent from the foregoing that this method of producing an
adjustable growth standard relies on many hypotheses on the
physiology of fetal growth. Yet these are necessary if a model is to be
developed. These may be summarised as follows:
1. The physiological variables affecting fetal weight at term are also
effective in the antenatal period in proportion to the fetal weight.
2. The intrinsic shape of the normal fetal growth curve is the same for
all subgroups, differing only by a scalar, or 'magnification' factor
proportional to the predicted term weight. This postulate will be
referred to as the ‘proportionality ‘ principle.
3. The average fetal growth curve entered in the program is close to
the true population average.

53
4. The distribution of fetal weights is approximately normal for all
gestations.
5. The variance of fetal weights is a constant fraction of the gestational
median , ie a constant coefficient of variation of 11% (derived from
term birth weights).
6. The selected variables of maternal weight, height, parity and ethnic
group have mainly a physiological rather than pathological
significance.
A major problem is to separate physiological from pathological effects
e.g. to what extent is a low maternal weight at booking due to
nutritional factors as opposed to constitutional factors.
In view of the known adverse effects of malnutrition in early
pregnancy on fetal growth, measures are needed to prevent the
application of unduly small adjustments for maternal weight in cases
where the low values are due to undernutrition at booking. While this
is an infrequent problem in western populations, this is not the case in
the developing world. To deal with this issue, the current version of
the customised growth chart calculates the body mass index (BMI) at
booking; if this is below the 10th centile the maternal weight at
booking is corrected so that the BMI is at the 10th centile. The
birthweight expectation is thus the one for a normally nourished
individual at the lower end of the normal range. A similar algorithm is
applied at the 90th centile of the BMI.
The rationale for making adjustments on the basis of parity is an issue
open to debate. The primigravid state, although 'natural', would be a
relatively infrequent finding in a female population of reproductive
age unaffected by contraceptive practices, as the statistics from a

54
century ago show. Goldenberg and colleagues (1989) stated that the
genetic potential for fetal growth in primigravidas and multigravidas is
identical and that the differences noted between these two groups are
attributable to growth-restricting factors operating in primigravidas.
Henced they advocated a parity-independent standard derived from a
population of mixed parity. On the other hand, Thomson and
colleagues (1968) argued in favour of adjusting for parity, believing
that the effect of parity is a physiological factor present in the fetal
environment.
The effects of smoking on birthweight are relatively large. An
alternative method to obtaining regression coefficients applicable to
the whole population would be to include non-smokers only. But this
process could theoretically lead to the selection of a genetically
'supra-normal' population, and thus adjustment factors that may not be
universally applicable.
More robust estimates of the coefficients for the different ethnic
groups would have required a much larger sample . We did not have
sufficient numbers of Far Eastern women to separate them from the
heterogenous 'others' grouping, and hence we do not have a reliable
coefficient for these.
In view of the known pathological effects of malnutrition on fetal
growth, measures are needed to prevent the application of unduly
small adjustments for maternal weight in cases where the low values
are due to undernutrition at booking. While this is an infrequent
problem in western populations, this is not the case in the developing
world.
In the current version of the customised growth program, a lower limit
is entered for the weight adjustment. If the maternal booking weight is
below this limit, the adjustment does not decrease; the birthweight
expectation is thus the one for a normally nourished individual at the
lower end of the normal range.

55
Large databases containing maternal characteristics, accurate antenatal
fetal weight estimates and birth weights would be needed to address
these issues.

56
Table 6.1 Multiple regression coefficients for the
prediction of normal growth potential .
CONSTANT 3409.853
STANDARD ERROR 389.032
ADJUSTED R SQUARE 0.31824
NUMBER OF CASES 38114
Coefficient
GESTATION (from 280 days)
Gest 1 20.667
Gest 2 -0.21289
Gest 3 -0.000167
SEX
Male - 116.871
Female -233.742
MATERNAL HEIGHT
(from 162 cm)
7.764
BOOKING WEIGHT
(from 64.3 kg)
Weight 1 8.676
Weight 2 -0.11740
Weight 3 0.000716
ETHNIC GROUP
European 31.670
Indian Sub-cont. -154.263
Afro-Caribbean -95.789
Other -33.446
PARITY
Para 0 4.898
Para 1 112.904
Para 2 153.458
Para 3 154.767
Para 4 154.690
SMOKING
Non-smoker 31.9160
Smokes 1-10 -120.602
11-20 -182.568
> 20 -214.112

57
7. METHODS OF GESTATIONAL AGE ESTIMATION
7.1 Introduction
An accurate assessment of gestation is crucial in the development of
fetal growth standards. It is also of importance in evaluating most of
the variables in current use for fetal monitoring and in the
management of post-term pregnancy.
Gestational age may be estimated ultrasonically by measuring fetal
parameters such as the crown-rump length (Robinson & Fleming,
1975) until 12 weeks and the biparietal diameter (Campbell &
Newman, 1971) until about 20 weeks gestation. Measurement of the
BPD in the mid-trimester has been shown to be 5% more accurate in
predicting the date of delivery than impeccable dates (Pearce and
Campbell,1983).
In practice, most ultrasound departments follow either the '10-day rule'
or the '7-day rule', whereby preference is given to menstrual dates if
these are within 7 or 10 days of the ultrasound estimate by the BPD.
Here we study the reliability of these methods by analysing the East
Midlands Obstetric Database.
7.2 Materials and Methods
The computerised obstetric records of three major maternity units in
the East Midlands (City and University Hospitals in Nottingham and
Derby City Hospital) date from 1986. So far more than 60000 cases
are available for analysis. A significant drawback is that the database
does not allow the reliable exclusion of induced labour. Multiple
pregnancies, stillbirths, congenitally abnormal babies, late bookers
(over 24 weeks), preterm deliveries (<37 weeks) and those with
unknown menstrual dates were excluded. A total of 31747 cases with
both menstrual and ultrasound data were retrieved for analysis.
Gestational age at delivery was calculated in days from 1. The

58
biparietal diameter according to the dating charts by Campbell (1971)
if over 13 weeks at booking, otherwise the crown-rump length was
used (Robinson & Fleming,1975) and 2. The last menstrual period.
The error in predicting the EDD was calculated in days for three
different dating methods: ultrasound data only, the 7-day rule and the
10-day rule as follows:
Error (days) = estimated gestational age at delivery - 280
These were expressed as signed and as absolute values. Statistical
analyses were performed with the 'SPSS for Windows' statistical
package.
7.3 Results
Table 7.1 shows the means, standard deviations and skewness of the
errors for each method. The distribution of the error is weakly but
significantly skewed to the left. Analysis of the signed errors suggests
that ultrasound on its own and the 7-day rule tend to underestimate the
EDD, whereas the 10-day rule overestimates it. Because of the
significant skewness of the data, the differences between the methods
were evaluated non-parametrically using Wilcoxon Matched -Pairs-
Signed-Ranks Test; the results are shown in table 7.2 . The mean and
the standard deviation of the absolute error using ultrasound alone is
slightly smaller than the other methods. Dating by ultrasound only is
significantly more accurate in predicting the EDD than either the 7-
day or 10-day rules.
7.4 Discussion
The length of gestation has traditionally been calculated from the first
day of the last menstrual period using Naegele's rule -i.e., by adding 7
days and 9 months to the date of the last menstrual period. Although
this formula has been attributed to Franz Karl Naegele (1778-1851), it
was first proposed by professor Herman Boerhaave (1709) at the

59
University of Leyden (Speert, 1958). The formula implies a mean
duration of pregnancy of 274 days from the LMP, which is at variance
with the observed value of 280 days (Doring,1962). If the dates were
not 'reliable', gestation was estimated by clinical palpation. There is
mounting evidence that even among women with 'reliable' menstrual
dates, considerable error may arise in the calculation of gestation. This
is because the onset of ovulation within the menstrual cycle is
relatively erratic, particularly in younger women (Geirsson,1991), and
may also vary from cycle to cycle. We have studied the error of
menstrual dates using the BPD-derived gestation as the reference
standard, in a database of 31561 cases (Gardosi & Mongelli, 1993).
For 21.5% of pregnancies ultrasound scan dates were outside plus or
minus 7 days from the dates based on menstrual dates. Furthermore,
the distribution of the error associated with menstrual dates was
significantly skewed, such that the 95% confidence interval for
gestational age derived from menstrual history was -27 to +9 days.
In our unit the ultrasound department calculates the EDD at booking
by using the 10-day rule if reliable menstrual dates are available,
otherwise the BPD or the FL is employed. About 6% of all cases are
induced for post-maturity on this basis, but these cannot be identified
reliably from the computerised records. Therefore one would expect
that this iatrogenic interference on the normal duration of pregnancy
would bias the statistics in favour of the 10-day rule. However, in spite
of this bias, we found that dating by ultrasound alone appears the best
method for predicting the EDD; bearing in mind the direction of the
bias, it is likely that the advantage of using ultrasound only may be
greater than what our figures indicate.
It has been suggested that the use of the BPD alone in estimating
gestational age is flawed, in that the larger babies would be assigned a
longer gestation than the smaller babies (Henriksen & Wilcox, 1994).
Persson and colleagues (1978) did find a relationship between birth

60
weight centiles and the size of the BPD in early pregnancy, but the
difference between the small (<10th centile) and large (>90th centile)
babies amounted to only about 1.5 mm at 18 weeks. This difference is
equivalent to less than one day's variation in gestational age by
Campbell's dating standard. We recently investigated this issue using a
database of 19 singleton pregnancies precisely dated from in-vitro
fertilisation or artificial insemination. No significant correlation was
found between the BPD centiles at the booking ultrasound
examination and the birthweight centiles (Gardosi et al, 1994).
In this study we assumed that the modal length of normal pregnancy of
280 days is equally applicable for all population subgroups. Only a
limited number of studies have been published on this issue, all of
them using menstrual dates. They report trivial differences in duration
of pregnancy between social classes or ethnic groups (Butler &
Bonham, 1963; Henderson, 1967). There is also some evidence that
BPD standards do not vary appreciably between ethnic groups (Vialet
et al, 1988; Simmons et al, 1985), and thus this should not be an
important source of bias.
Our findings do not support the use of the 7-day or 10-day rule in the
assignment of gestational age when valid ultrasound measurements are
available. Although the error associated with their use may not matter
in clinical practice (Mongelli & Gardosi, 1994), these methods are
best avoided in defining normal standards in pregnancy.

61
Table 7.1 Descriptive statistics for the errors resulting from each
dating method.Values expressed in days (N = 31747).
Variable Mean SD Skew S.E.
Skew
Min Max
Signed Errors
Ultrasound
only
-0.72 8.50 -0.12 0.01 -20 28
7-day rule -0.20 8.65 -0.15 0.01 -27 28
10-day rule 0.18 8.79 -0.16 0.01 -30 30
Absolute Errors
Ultrasound
only
6.91 5.00 0.69 0.01 0 28
7-day rule 7.02 5.06 0.70 0.01 0 28
10-day rule 7.15 5.12 0.73 0.01 0 30

62
Table 7.2 Significance of differences in absolute errors between
dating methods. Wilcoxon Matched -Pairs Signed Ranks Test.
Pairs: A Vs B Mean
Rank
A>B A<B Ties
A=B
Z-value 2-tailed P
value
Ultrasound only
Vs 7-day rule
8443.96
8782.91
8251 8989 14507 -7.1 <0.00005
Ultrasound only
Vs 10-day rule
9493.64
10137.31
9231 10438 12078 -11.4 <0.00005
10-day rule
Vs 7-day rule
1265.5
1140.34
1449 980 29318 -10.4 <0.00005

63
8. FORWARD PROJECTION OF FETAL WEIGHT ESTIMATE
The proportionality principle applied to dynamic fetal weight
estimation.
8.1 Introduction.
Fetal weight estimation from ultrasound parameters or other methods
is almost invariably made from static measurements. In practice,
delivery often does not occur until days or weeks after the ultrasound
examination, and the weight estimation is not corrected for this time
interval. This problem was appreciated by Spinnato and colleagues
(1988) who published a series of dynamic weight estimation formulae
to allow forward projection of the fetal weight estimate to the
expected date of delivery.
Here we present an alternative method that, in addition to forward
weight projection, should also allow for backward fetal weight
interpolation from the birth weight.
8.2 Subjects and Methods.
In order to compare our method with Spinnato’s method, we selected
only those cases who delivered within 35 days of the last ultrasound
examination. Two hundred forty two cases were available for analysis;
these were liveborn infants, inclusive of adverse outcomes and
congenital malformations. The forward projection equation was
derived from the principle that the shape of the fetal growth curve is
similar for all cases irrespective of the birth weight. It is in fact a form
of proportional extrapolation, which we will refer to as the ‘prop-ex’
method. Hadlock’s growth formula was selected because: 1. The
weight estimation formulae considered were also developed by
Hadlock and colleagues and 2. This growth formula is close to the
average of previously published growth formulae (Gardosi et al,
1994). If Hadlock is the growth function, EFW the ultrasound fetal

64
weight estimation, u is the gestational age at ultrasound examination
and d is the gestational age at delivery, the following relationship
applies:
EFWu : EFWd = Hadlock(u) : Hadlock(d)
Therefore:
Projected fetal weight at delivery:
EFWd = EFWu * Hadlock(d)/ Hadlock(u)
Likewise, Spinnato’s equivalent dynamic weight equation for the
Hadlock weight formulae is:
Log (EFWd) = 1.0009 * log (EFWu ) +0.0043(d -u)
Both techniques were applied to our sample. Prediction errors were
calculated both as signed and as absolute percentage errors of the birth
weight (BWT) as follows:
Percentage error = 100* (EFWd -BWT)/BWT
Trends in the error in relationship to birth weight were examined using
Spearman’s rank correlation coefficient. Differences between the two
methods were tested by Wilcoxon’s matched pairs signed-ranks test.
8.3 Results
The signed and absolute percentage errors for the two methods are
shown in Table 8.1. Table 8.2 displays the statistical significance of
the differences between these two methods.
The errors from using Spinnato’s method were not significantly
correlated with true weight ( R = -0.0880, P>0.05), whereas with our

65
method there was a weak but statistically significant inverse
correlation with the true weight (R= -0.23, P<0.0005). This correlation
was not significant if birth weights below 3200g were excluded.
For both techniques, there was no significant correlation between
either the signed or absolute errors and the lag-time interval.
8.4 Discussion
These statistics show that the proportional extrapolation method we
describe for birth weight prediction from remote ultrasonographic
examination is significantly better than Spinnato’s technique in our
population. This may be because the latter uses the lag-time difference
between ultrasound examination and delivery, without considering the
actual values of the gestational ages of these events.
The random errors described in Spinnato’s original paper are slightly
lower than when his method was applied to our population (11 vs 12
%), with a tendency towards underestimation as opposed to
overestimation in our sample.
Two other advantages of the prop-ex technique are that: 1. It is
applicable to any fetal weight estimation technique, whereas
Spinnato’s method requires different equations for different weight
estimating formulae. 2. It can be modified to allow for retrospective
fetal weight estimation from the birth weight by interpolation as
follows:
IFWu = BWT* Hadlock(u)/ Hadlock(d)
where IFWu is the interpolated fetal weight. This formula, however,
cannot be validated without an independent, highly accurate method of
fetal weight estimation such as NMR.
The results of these studies validate the concept of incorporating a
lapse-time factor in equations to predict the birth weight from remote

66
ultrasonographic data. As the errors are not correlated with the lag-
time interval, both methods are accurate throughout the range of time
intervals measured. It is likely that accuracy will be lost in cases
affected by growth disturbances, and this is reflected in the negative
correlation between the signed errors and the birth weight, which is
lost for birth weights over 3200 grams.
These findings also support the ‘proportionality’principle - a key
aspect of the customised growth chart program- which is the
assumption that fetal growth in normal populations is essentially the
same, once growth is expressed in terms independent of the actual
birth weight.

67
Table 8.1.Signed and absolute percentage errors for
projected fetal weight estimation.
Formula Systematic Error (%) Random Error (%)
Prop-ex 6.01 11.0
Spinnato 8.56 12.0
Mean Absolute Error (%) Standard Deviation (%)
Prop-ex 9.9 7.7
Spinnato 11.8 8.9
Table 8.2. Non-parametric comparison of the errors generated using
the two methods on the same population. Wilcoxon Matched-Pairs
Signed-Ranks Test.
Differences in Ranks Mean Rank No Cases
- Ranks (Spinnato < Prop-ex) 172.70 51
+ Ranks (Spinnato > Prop-ex) 130.75 225
Ties (Spinnato = Prop-ex) 1
Total = 277
Z = -7.7646 2-Tailed P-value <0 .00005

68
9. SELECTION OF ULTRASONIC WEIGHT FORMULA
9.1 Introduction
The performance of ultrasound fetal weight estimation formulae may
have important implications for growth standards and antenatal
screening. In choosing the best formula, two main selection criteria
need to be satisfied:
(a) Minimal overall error.
(b) Minimal bias in the error in relation to fetal weight.
The first condition is self-evident. The significance of minimising
error trends in relation to fetal size has been somewhat underestimated
in the literature. If a particular formula has a strong tendency to
overestimate the small and underestimate the large fetus, both the
weight standard and screening performance may be adversely affected.
One may argue that fetal growth standards should be weight formula-
specific.If this was the case, then centres where a particular formula is
either not in use or is not suitable will not be able to use the standard.
In this study we examine the effect of different weight estimation
formulae on apparent growth kinetics, and their clinical performance
in our population is evaluated .
9.2 Patients and Methods
Persson and colleagues (1986) have shown that the average fetal
weight curve derived from the means of the ultrasound parameters for
each gestation is very similar to that derived from the means of the
individual weights. Hence, to illustrate the effect of different weight
formulae on growth curves, we studied the means published by Chitty
and Altman (1993) for individual ultrasound parameters. These were
input for the following weight estimation formulae:
- Hadlock (BPD, AC, FL)

69
- Hadlock (AC, FL)
- Warsof (BPD, AC)
- Shepard (BPD, AC)
- Campbell (AC)
- Modified Persson (BPD, AC, FL)
Persson's original formula used the abdominal diameter (AD); this was
modified by converting the AD into AC as follows:
log10 EFW (grams) =
0.972* log10 BPD + log10 (AC/3.1416) +0.367*log10 FL -2.646
The calculations were performed by computer software, and the
different growth curves for each formula displayed graphically using
Cricket Graph software.
In order to determine the best formula for the population in our study,
we selected those cases that delivered within 14 days of an ultrasound
examination. A sample of 129 cases was retrieved, from a total of 171
cases that had been seen one year before the completion of the growth
study. A correction for the interval growth between time of ultrasound
examination and delivery was made by projecting forward the
estimated fetal weight using Hadlock's fetal growth formula as
follows:
Predicted weight =
EFW * H(gestation at delivery)/H(gestation at scan)
where EFW is the ultrasound-estimated fetal weight and H is
Hadlock's fetal growth function as described in chapters 4 and 8.
Using the weight formulae listed above, the signed percentage error
for each case was computed thus:
Percentage error = (Predicted weight - Birth weight)/ Birth weight

70
A positive value indicates overestimation whereas a negative value
indicates underestimation of true fetal weight. The weight formulae
were then corrected for systematic error by multiplying them by a
correction factor as follows:
Correction factor = 1/(1 + systematic error)
where the systematic error is expressed in fractional terms.
Statistical analyses were performed with the SPSS for Windows
statistical package. The means, standard deviations, 95% confidence
limits and the distributions of the errors were computed. The trends
between error and true weight were expressed in terms of Pearson's
moment correlation coefficients.
9.3 Results
Figure 9.1 shows the fetal growth curves obtained for Chitty and
Altman's data using different fetal weight estimation formulae .
For our population, the mean and standard deviations of the errors for
each formula and the correlation of the error with the observed weight
are displayed in table 9.1. Table 9.2 shows the errors at the extremes
of birth weight. All the formulae tested on our population tend to
overestimate true weight, and this applies also to the extremes of fetal
weight (except for Campbell's and Persson's formulae for
weights>4000g). The errors were recalculated after applying the
correction factor for systematic error and the results are shown in
table 9.3.
9.4 Discussion
For any given population, it is apparent from Figure 9.1 that from
about 36 weeks onwards the type of fetal weight formula can have a
marked effect on the apparent fetal growth kinetics, particularly at
term. Hence it is important to select the weight formula that is most

71
suitable for the operator and the population under study. This could
explain some of the variability in the fetal growth kinetics exhibited by
previously published standards, which also appears greatest after 36
weeks.
In our sample all of the formulae studied tended to overestimate the
true fetal weight. The error associated with the use of Hadlock's
formula for BPD, AC and FL was not correlated with the true weight,
whereas all of the other formulae produced errors that were
significantly correlated. Robson and colleagues (1993) also found a
trend to overestimate true fetal weight. They noted a significant
correlation of the error with birth weight for all the formulae they
tested, but these did not include the Hadlock formula included in our
study. This systematic overestimation may arise from differences in
ethnicity between North American and British populations, or in
techniques and equipment. After applying the correction factor for
overestimation, Hadlock's formula for the BPD, AC and FL showed
the smallest SD of the error, and this was the formula selected for our
study. If the BPD could not be measured because of suboptimal
visualisation, the formula used was Hadlock's for the AC and FL. The
modified weight formulae were then applied retrospectively to this
sample and prospectively to the remaining half of the population.
Our approach to selecting weight formulae and correcting for them
makes the assumption that the errors observed at term are similar to
those obtained in the preterm period. To verify this would require a
substantial number of infants born preterm who had had an ultrasound
examination. Another solution is to use echo-planar NMR for accurate
weight estimation in the preterm period and to compare this with the
ultrasonic weight estimates; but this is not as yet an economic
proposition.

72
Table 9.1 Errors of ultrasonic weight formulae in relation to birth
weight for cases delivering within 14 days of examination (N =129).
Formula
Systematic
Error (%)
SD
of Error Skew
Correlation
(R) with
birth weight
P-value
of R
Persson * 0.43 10.79 0.11 -0.2145 0.015
Campbell 0.89 11.85 0.06 -0.4226 0.000
Hadlock
(AC, FL) 3.23 11.52 0.2 -0.1246 0.159
Warsof
(BPD,AC) 3.78 11.76 0.08 -0.2299 0.009
Hadlock
(BPD,AC,FL) 5.32 1.21 .17 -0.1230 0.165
Shepard
(BPD,AC) 9.24 12.31 0.09 -0.2442 0.005
* original formula using the AD modified to include the AC as follows:
log EFW = 0.972* log BPD + log (AC/3.1416) +0.367*log FL 2.646

73
Table 9.2 Error of ultrasonic weight formulae at the extremes of birth
weight (all cases).
Formula
Birthweight
> 4000g (N = 37)
Mean Error (SD)
Birthweight
< 2500g (N = 17)
Mean Error (SD)
Persson -1.3 (10.36) 7.2 (12.5)
Campbell -3.2 (10.86) 14.0 (16.3)
Hadlock
(AC, FL) 0.9 (10.8) 6.4 (13.8)
Warsof 2.7 (11.8) 11.2 (12.2)
Hadlock
(BPD,AC,FL) 3.4 (10.4) 8.3 (13.2)
Shepard 7.9 (12.3) 17.4 (12.8)

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