Problems in using linear ultrasound parameters for the determination of fetal weight

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26

Issel et al., Linear ultrasound parameters

j. Perinat. Med. Problems in using linear ultrasound parameters for the determination of 4(1976)26 fetal weight

E. P. Issel, P. Prenzlau, F. Laag

Frauenklinik des Bereiches Medizin (Charite) der Humboldt-Universität zu Berlin (Head Prof. Dr. med. habü. H. Bayer)

The birth weight is the most powerful predictive parameter for the prognosis of a newbom infant.

Therefore, the determination of the fetal weight in utero is of paramount interest for obstetrical deci- sions. We have studied this problem for several years and have published formulas and nomograms [5, 6]. These have been of acceptable accuracy for clinical use (if a time expenditure of 15 minutes is considered justifiable), however, would be desirable to improve the accuracy even more (Tab. I).

We intend to discuss the associated problems in this paper. We consider it important that the clin- ician understands which criteria are to be observed when evaluating acalculatedfetal weight and where the possible source of efrors are in such a numeri- cal value.

l Material and methods

For intrauterine fetal measurements we use the ultrasound apparatus "Vidoson" manufactured by SIEMENS (FRG). The apparatus provides a B-scan with rapid imaging. The penetration is to a depth of 15 cm. The symphysis is not being penetrated because the energy applied is too low.

Our experience with the calculation of the fetal weight is based on 1300 cases. However, a detailed analysis is available only for 621 cases (Tab. I).

The technique for obtaining fetal measurements with ultrasound has been described in detail in the literature [1,5,7].

A similar measuring technique. was described in 1974 by YLÖSTALO and JÄRVINEN [8, 9] who

Tab. I. The percentual error in calculating fetal weight.

Birth weight Relative eiror < 1 800 g 1 800-2500 g

in the calcu-

lated weight n % n %

< - 20%

-20 bis -10% 1

±10% 4 + 10 bis + 20% 1

> + 20%

17 72 66 74 17 14

6 ' 1.96.8 71.9 13.65.8

2501-3300 g n %

1229 215 508

3.89.2 68.6 15.92.5

3301 -4000 g n %

343 102 27

20.31.8 61.6 16.3

> 4000 g n %

25 24 1

166 75 3

Total n

1976 419 9314

% 12.23.1 67.4 15.02.3

Total 100 103 100.0 314 100.0 166 100.0 32 100 621 100.0

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27 used a de vice which stored the images. Since cor-

relations between the fetal measurements by ultra- sound and the real fetal weight are not linear, different formulas are needed for larger and smaller fetuses when using (äs in our method) a multiple linear regression equation.

The formulas developed by us for the conversion from fetal measurements into weight are the fol- lowing three which have proven their practical value:

I. For the estimation of fetuses of normal ränge:

462.7 X biparietal diameter (in cm) + 118.5 X sagittal thoracic diameter (in cm) + 251.9 X transverse thoracic diameter (in

cm)

+ 181.2 X length of the trunk (in füll cm) -8541

= fetal weight in g

The limitations for applying this formula are the following measurements:

— The biparietal diameter must be 8.0 cm or more.

— The length of the trunk must be 18 cm or more.

II. For very small fetuses we recommend:

Fetal weight in g = (biparietal diameter

3

+ sagittal thoracic diameter

3

) X 1.75;

limitations: the biparietal diameter must be smaller than 8.0 cm.

III. A good check method for most fetuses:

Fetal weight in g = 314.4 X (sagittal + trans- verse thoracic diameter in cm) - 2734.

2 The problems of calculating the fetal weight Because of the inter-felation between the different problem areas, we suggest the following classifi- cation of the possible sources of error:

2.1 biological variatipns 2.2 pathological variations

2.3 The definition of fetal measuring points 2.4 subjective errors of measurement 2.5 the mathematical regression procedure 2.1 Biological variations

Mathematically the fetus is an irregularly shaped body. With increasing growth, i.e. with an increase

in weight it grows in all three dimensions, however this growth is individually different according to the genetic factors in each dimension. As there are different somatic types in the adult, similar con- ditions are found in the newborn. The distribution and amount of fat vary greatly. In order to get a really exact weight determination, a detailed anal- ysis of the entire fetus wich an ultrasonic B-scan would be needed. The resulting planes should then have to be planimetrically measured in l cm inter- vals and added up.

Such a method is very complex even with a built- in Computer and would be very difficult in the event of fetal movement. Therefore, currently the only practical approach is the determination of uni- dimensional measurements.

The fetal skull and trunk within certain limits may grow independent of each other. Therefore, meas- urements from both parts are needed for the cal- culation of weight. The use of the biparietal dia- meter alone (Fig. 1) which is the ultrasonograph- ically most accurately obtainable measurement yields weights after the 28 th week of gestation with a variance of äs much äs ± 1050 grams when 97% of all cases are inclüded.

As can be seen in the following figures (Figs. 3,4, 5, 7) the Variation of the fetal weight with the use of a trunk measurement are equally large.

This Variation between calculated and real weights is markedly reduced only when the sum of the thoracic diameters is used (± 850 grams, Fig. 6) and it is ± 730 grams with the use of our formula I without corrections. The biological variations are taken into consideration by calculations of the mean within the regression analysis. The latter allows the calculation of the fetal weight from longitudinal measurements only up to certain de- gree of accuracy even if several measurements are taken. Independent of the method of calculation, i.e. from the formula used, there remains a Variation which results from the variability of the fetal meas- urements and which cannot be eliminated.

2.2 Pathological variations

In contrast to the biological variations, whose fre-

quency distribution has a trend toward mean

value s, the pathological changes of body shape do

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28 5000 4000 3000

2000 1000

weight in g

7,0 .5 8,0 .5 ^.5 , ·

bip. D.

in cm

Fig. 1. The fetal bipaiietal skull diameter meäsured with ultrasound and the birthweight of infaiits delivered within three days of the measurement. Thelight hatched area contains 97% of the measürements. The solid line is the regression curve (y = 900 - 5200). The interrupted line runs exactly through the mean values for the virth weight for each biparietal diameter. The bold hatched areas indicate the deviation of the regression line from the true mean value äs it increases toward the margins. The point outside the light hatched area are observations of extreme deviations.

not confirm to this frequency distribution. The following examples may illustrate this:

I. Fetal dystrophy: The typical clinical appear- ance is the thin trunk of the newborn. The head is at most only minimally behind the normal growth, the thoracic measürements are markedly diminished (particularly in compari- son to the skull), while the length may be almost normal.

Those formulas in which the value of the biparietal diameter influences the result strong- ly calculate these fetuses much too heavy (e.g.

formula IV by HANSMANN et al. [2]). Formula in which the thoracic measürements weigh heavily or are used exclusively (Formula III) would calculate these fetuäes äs too light.

II. Hypertrophy of the fetus: The typical presen- tation is the fetus of the diabetic mother. Pro-

portions and errors in the calculations of the fetal weight are the reverse'of those with fetal dystrophy.

III. Multiple pregnancies: We have included mul- tiple pregnancies in the group of "pathologica!"

errors in calculation because conditions similar to those in dystrophy prevail. The skull is too large in comparison to the trunk measürements (including the length of the trunk). Hpwever, these relations were only observed with triplets.

In twins the body proportiöns are not chänged.

The determination of the weight in twins is more difficult only because of the frequently found positional anomalies. With triplets and other pregnancies it is üsually not possible to correctly correlate heads and trünks.

IV. Fetal malformations: With monstroüs malfor-

mätions and anencephaly one should not

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29 factor with which the biparietal diameter must be multiplied in order the arrive at the mean real birth weight

300

200

100

10

ff cm

biparietal diameter

Fig. 2. The biparietal diameter of the fetus and the factor with which it must be multiplied in order the arrive at the mean birth weight.

attempt to calculate the weight from these formulas.

However, even lesser malformations may result in changes in the calculated proportions if they are not recognized antenatally, e.g. micromelia.

2.3 The defmition of the fetal measuring points In order to make the method of the estimation of the weight generaUy applicable the fetal measuring points must be defined exactly and it must be possible to locate them in each case. This can be done according to two principles.

I. The largest or sinailest measurement from a larger region of the body is chosen.

II. The exact location on the body is determined on which a measurement is always taken.

Both methods have disadvantages. For instance, a largest measurement can be markedly erroneous

because of the so called "salami effect". A small- est measurement may change its topographical location during fetal growth. The exact definition of a genuine skeletal measuring point äs it is used in anthropometry, is not possible with the current technology of ultrasonography. Therefore, meas- urements are always obtained from a relatively large area of the body.

In praxis the two principles are combined: The

measurement of the biparietal skull diameter occurs

at the location of the largest measurement with

penetrating median echo. The thorax is measured

in its largest dimension during simultaneous appear-

ance of the basis of the heart and orientation from

the vertebral column. As can be seen in Fig. 5, the

choice of the smaller of the two thoracic diameters

does not improve accuracy. The length of the trunk

äs measured from the top of the shoulder to the

end of the coccyx can be measured much less

accurately than the measurement of skull and ehest.

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30

Issel et ah, Linear ultrasound parameters

birth weight in g

5000 · 4000 - 3000 - 2000 - 1000 -

5 6 7 8 9 10 11 12 13 transversal

thoracic diameter (cm)

Fig. 3. Fetal transverse thoracic diameter and birth weight. In the light hatched area 97% of the measurements are fouiid.

The outlying points are observed single values.

However, since it is the only measurement of the third dimension of the fetal body it is a value and improves the accuracy of the result.

Other measurements are less easily obtained. Thus, the fronto-occipital diameter of the skull has not been useful to us because the flexion of the head cannot be corrected for. The measurement of the circumferences do not add the accuracy of the result because there are also only linear measurements. HELLMANN et al [3] utilized the skull circumference and HOLLÄNDER [4] uses the ab- dominal circumference in their formulas.

The fetal extremities do not enter at all into these measurements; they are included in the biological and pathological variations.

2.4 The subjective errors of measurement

These are inherent in the measurement and can be avoided in part. The "salami effect", measurement

at incorrect points and inexperience of the examiner can be largely avoided. The examiner should allow himself sufficient time for the measurements and should obtain several measurements if the fetus is positioned unfavorably by repositioning the patient äs well äs the transducer. Considerable difficulties may occur with the measurements in oligohydramnios because the fetal thorax is poorly separated from the placenta or the uterine wall.

Devices with a high resolution may be able to eliminate this problem. Fetal parts which have entered into the lower pelvis are not accessible for

observation with the SIEMENS apparatüs.

2.5 Mathematical regression analysis

All mathematical regression analyses are base upon a calculation of the mean. From the individual measurements the formula is calculated where the sum of the squares of the variations are the lowest.

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Issel et al., Linear ultrasound paiameters 31

birth weigth in 9

5000 - 4000 * 3000 - 2000 · 1000 -

5 6 7 6 9 1 0 1 1 1 2 1 3 sagittol

thoracic diometer(cm)

Fig. 4. Sagittal thoracic diameter and birth weight.

Such a formula is valid only for the area in which a sufficient number of cases were available for its calculation. Clinical cases observed later which are outside of the measuring ränge may be subjected to large errors when using such a formula. Such extrapolations are only permissible if it has been shown that the mathematical model is valid. Three mathematical problems are of importance:

I. The conventional regression equation considers only the absolute difference of the Variation. It is much more important for the clinician to consider the relative difference. An error of 500 grams with a fetal weight of 4000 grams is clinically irrelevant but not if the fetal weight is 1500 grams. This problem can be overcome mathematically but this adds to the complexity of the calculation.

II. The methods of calculation are based on the assumption that the deviation of the calculated from the real weights are a chance deviation from a mean value. This yields excellent results for the normal fetus in the intermediate weight classes.

However, it is more' important for a clinician to have reliable calculations for the fetuses in the marginal weight classes and for those with in- trauterine growth retardation.

To our knowledge no method exists to overcome this problem. Therefore we have used the mean value of formulas I and III in cases where thoracic measurements and biparietal diameters are marked- ly different in their percentiles.

III. The linear model of regression equations is

sufficiently accurate only for portions thereof (i.e.

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32 birthwögth in g

5000- 4000- 3000- 2000- 1000 -

5 6 7 8 9 10 11 M 13 minimol

thoracit diometo (cm

Fig. 5. The lesser of two thoracic diameters and birth weight.

on the whole it is inadequate). Therefore, we have developed for the calculation of the weight of the very small fetus, a simple quasilinear formula II which also fulfills the condition of a zero intercept.

With linear formulas suitable for normal sized fetuses negative weights are arrived at from bi- parietal diamters below 6.0 cm. This is also un- preventable if a square polynomial formula is used äs in the work of HANSMANN and co-workers [2].

One of their formulas has the following appearance 71 X biparietal diameter (in mm) + 31.27 X transverse thoracic diameter

(in mm)

+ 0.0553 X biparietal diameter

2

- 0.0901 X transverse thoracic diameter

2

-6173

= fetal weight in grams

Polynomials of higher order are not suitable be- cause the accuracy decreases with the number of elements and the curves are irrelevant outside of the fitted Segments.

The correlation of the thoracic diameter with weight höwever, is almost linear (Figs. 3, 4, 5,6);

therefore, our formula III is applicable almost for the entire ränge of fetal weights.

On the other hand, the biparietal diameter (Fig. 1) and the length of the trunk (Fig. 7) in their inter- mediate values deviate märkedly from linearity.

This is particularly unfavorable for the biparietal

diameter because it üsüally enters with the highest

value into the multidimensional regression calcul-

ations (Formula I, and Formula IV of HANSMANN

et al. [2]). In order to deinonstrate that the rela-

tions do not correspond to a known mathematical

model, we have depicted in Fig. 2 the factors with

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33 birth weigth in 9

5000 ' 4000 - 3000 2000 1000

10 15 16 17 16 19 20 ZI 22 23 24 sagifctol + transversal thoracic diameter(cni)

Fig. 6. Sum of the sagittal and tiansveise thoracic diameter and birth weight.

which the biparietal diameters of our cases would have to be multiplied in Order tp have äs a result the mean weight of this gröüp. The left portion of the curve resembles a parablast while the right- sided portion is almost linear; the portions are connected by a markedly curved segment.

3 Discussion and conclusions

Under the current technical conditions we are forced to find a regression cürve from a few well and reliably obtainable fetal longitudinal meas- ures. The introduction of planimetry technology into B-scan ultrasonography with additionally improved resolution would be a cpnsiäerable pro- gress in this respect.

Thus far the four measurements recommended by us which contain values from head and trank in all

three dimensions appear to be best suited for such a regression equation. Since three trunk measure- ments and only one skull measurements are clini- cally useful, weights can be determined even in dystrophic fetuses.

The marginal groups in our linear multiple re- gression equation (Formula I) are less accurately calculated than fetuses of intermediate weight.

Therefore, we recommend the following empiri- cally obtained corrections:

If the calculated fetal weight is

above 4000 grams: - 200 grams

above 4400 grams: - 400 grams

below 2600 grams: + 100 grams

below 2000 grams: + 200 grams

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34 birlh weigth in g

5000 - 4000 - 9000 - 2000 ·

. \

1000

15 16 17 18 19 20 21 22 23 2t 25 iengthoHhe trunk (cm)

Fig. 7. Trunk length and birth weight. The bold hatched area contains 97% of the measurements. The light hatched area combines the former for demonstration purposes. The interrupted line runs through the true mean values for each week of gestation.

Complex mathematical models have the disad- vantage that weight estimations cannot be done without the use of a Computer. It is unlikely that this can be accomplished for most ultrasound facilities in the near future.

The best formulas published so far barely have reached a degree of accuracy that they can be re- commend for use. On the basis of occasional mis-

calculations of the fetal weight, we think that more attempts should be made to improve the accuracy of the calculation of fetal weight. We intend to attempt this initially with empirical means and to publish the new results. So far we wefe not able to do this because of the low number of cases in the marginal groups.

Summaiy

We have developed three formulas for the calculation of fetal weight by means of ultrasound which have proved clinically useful (Formula I for normal size fetuses, Formula II for very small fetuses, and Formula III äs a control).

From 621 controlled calculations of the fetal weight and the general experience from our ultrasound clinic (over 20,000 examinations) we discuss the inherent problems.

We used the Vidoson apparatus manufactured by Siemens (West Germany) which is a rapid imaging B*scan.

We have learned from many years of studying means pf calculating fetal weight that a regression equation from linear fetal measurements can be used: namely the biparietal skull diameter, the sagittal and the transverse thoracic diameter and the length of the trunk (Tab. I).

For fetuses in the intermediate weight langes a multiple

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Issel et al., Linear ultrasound paiameters 35 linear regression equation is sufficient. For largei and

smaller fetuses empirical corrections aie recommended.

For very small fetuses a quasilinear equation is needed.

The problems which in the calculation of the fetal weight can be classified äs follows:

1. Biological Variations. They are caused by the variations in the body structure of the newborn. The variations (between the calculated and the real weight) have an approximate normal distribution. This is taken into account in the regression analysis by the calculation of the mean. These biological variations cannot be eliminated by mathematical procedures.

2. Pathological Variations. They originate from the altered relations of the linear measurements to the weight by changes in the body proportions in comparison to the normal fetus. The characteristic examples are: fetal dystrophy; diabetic fetopathy; triplets and other multiple pregnancies (twine do not have altered proportions); and fetal malformations.

3. The definition of fetal measuring points. Our current ultrasound technology is not advanced enough for the use of anthropometric measuring points in the fetus.

For practical useonehas to be satisfied with identifying a prominent area of the fetal body äs accurately äs possible. While the length of the trunk can be deter-

mined less accurately than the two thoracic diameters, it is of value because it is the only longitudinal measurement. Introduction of more but less exact measurements into the calculation of fetal weight detracts from the accuracy.

4. Subjective measuring errors originate from the process of measuring. They have no cause in the fetal body and can be avoided to a large degree by the experienced examiner, e.g. the so called "salami effect".

5. The mathematical regression procedure. The regression curve correlating the thoracic measures and the weight (Figs. 3, 4) are almost linear while the mean values of the bipaiietal diameter (Fig. 1) and the trunk length (Fig. 7) deviate more from their regression line. There- fore, the linear multiple regression model is only condi- tionally suitable.

The use of polynomials does not add significantly.

If an intrauterine growth retardation is suspected it is recommended to additionally use Formula III in addition to Formulas I or II. In these cases the low sum of the thoracic diameters (Fig. 6) may corroborate the suspicion for dystrophy. The search for an adequate mathematical model should be continued because this would allow extrapolations in the ränge of very small and very large fetuses.

Keywords: Estimation of fetal weight, obstetrisc, problems of measurement, regression, ultrasonics.

Zusammenfassung

Die Problematik der Verwendung linearer Ultraschallmeß- größen zur Bestimmung des fetalen Gewichtes

Zur Berechnung des fetalen Gewichtes mittels der Ultra- schalltechnik haben wir 3 Formeln entwickelt, die sich klinisch bewährt haben (Formel I for normalgroße Feten, Formel II für sehr kleine Feten und Formel III zur Kon- trolle).

An Hand der Auswertung von 621 kontrollierten Berech- nungen des fetalen Gewichtes und den allgemeinen Erfah- rungen aus unserer Ultraschallsprechstunde (über 20 000 Untersuchungen) wird die Problematik der Berechnungs- methodik erörtert. Verwendet zu den Untersuchungen würde das Gerät "Vidoson" der Firma Siemens (BRD), ein B-scan mit schnellen Bildaufbau.

Unsere langjährigen Untersuchungen auf dem Gebiet der Berechnung des fetalen Gewichtes haben ergeben, daß man sich auf eine Regressionsrechnung aus linearen fetalen Maßen stützen kann: den bipaiietalen Schädeldurchmesser, den sagittalen und den transversalen Thoraxdurchmesser sowie die Trunkuslänge (Tab. I). Für Feten mit mittlerer Gewichtslage reicht die multiple lineare Regressionsrech- nung aus. Für größere und kleinere Feten werden empi- risch gewonnene Korrekturen empfohlen. Für sehr kleine Feten benötigt man jedoch einen quasi linearen Ansatz.

Die Probleme, die bei der Berechnung des fetalen Gewich- tes auftreten, können wir wie folgt einteilen:

1. Die biologischen Schwankungen. Sie beruhen auf dem unterschiedlichen Körperbau der Neugeborenen. Die durch sie bedingten Streuungen (der berechneten zu den realen Gewichten) sind etwa normal verteilt. Das wird durch die Mittelwertsberechnung bei den Regres-

sionsanalysen berücksichtigt. Diese biologischen Schwankungen lassen sich durch kein mathematisches Rechenverfahren beseitigen.

2. Die pathologisch bedingten Schwankungen. Sie entstehen durch die veränderten Relationen der linearen Meßwerte zum Gewicht durch Veränderungen der Körperproportionen gegenüber den normalen Feten.

Die charakteristischen Beispiele sind: die fetale Dystro- phie, die Fetopathia diabetica, Drillinge und weitere Mehilinge (Gemini haben keine veränderten Propor- tionen) und fetale Mißbildungen.

3. Die Definition der fetalen Meßstellen. Unsere derzeitige Ultraschalltechnik ist noch nicht soweit, daß sie uns in die Lage versetzt, anthropometrische Meßpunkte beim Feten anvisieren zu können. Man muß sich für die Praxis auf brauchbare Kompromisse einigen, die eine markante fetale Körperregion möglichst genau eingren- zen. Die Trunkuslänge läßt sich zwar weniger genau als die beiden Thoraxdurchmesser ermitteln, als einziger Parameter der Längenausdehnung ist sie jedoch von Wert. Das Einfügen weiterer, nicht mehr so genau zu er- hebender fetaler Maße in die Formeln zur Berechnung des fetalen Gewichtes, wirkt sich nachteilig auf die Genauigkeit aus.

4. Die subjektiven Meßfehler entstehen durch den Meß- vorgang. Sie sind nicht im fetalen Körper begründet und lassen sich vom erfahrenen Untersucher meist ver- meiden, wie z. B. der sog. "Salamie-Effekt".

5. Das mathematische Regressionsverfahren. Die Regres- sionskurve zwischen den Thoraxmaßen und dem Ge- wicht (Fig. 3 und 4) hat nahezu einen geraden Verlauf, während die Mittelwerte beim biparietalen Durchmesser

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36

(Fig. 1) und bei der Trunkuslänge (Fig. 7) stärker von der Regressionsgeraden abweichen. Insgesamt ist das lineare multiple Regressionsmodell daher nur bedingt geeignet. Auch der Einsatz von Polynomen bringt keinen Gewinn.

Beim Verdacht auf intrauterine Retardierung empfiehlt es sich zu einer der Formeln I oder II noch die Formel III

zur Berechnung heranzuziehen, da dann die geringe Summe der Thoraxdurchmesser (Fig.^f 6) den Verdacht einer Dystrophie bekräftigen kann. Die Suche nach einem ad- äquaten mathematischen Modell sollte fortgesetzt werden, da dieses Extrapolationen in Bereiche seltener Fälle von sehr großen und sehr kleinen Fetus erlaubt.

Schlüsselwörter: Geburtshilfe, Gewichtsberechnung des Fetus, Probleme der Meßtechnik, Regressionsrechnung, Ultra- schall.

Resume

Problemes de Futilisation de mesures lineaires par ultra- sons pour Fevaluation du poids du foetus

Pour determiner le poids du foetus a l'aide de la technique x par ultra-sons nous avons mis au point 3 formules dont les resultats cliniques ont ete convaincants (Formule I pour le foetus de taille normale, Formule II pour le foetus tres petit et Formule III pour le contröle).

Nous appuyant sur l'evaluation de 621 mesures controlees du poids foetal et les experiences generales de nos consul- tations totalisant plus de 20 000 examens par ultra-sons, nous nous sommes proposes d'exposer les divers aspects et difficultes de la methode de calcul. Precisons ici que nous avons utüise pour nos examens Fappareil «Vidoson» de la Firme Siemens (RFA), un B-scan avec structuration rapide de Fimage.

Nos longues annees d'etudes sur Fevaluation du poids foetal nous ont montre qu'il est possible de s'appuyer sur un calcul de regression a partir de mesures foetales lineaires:

le diametre cränien biparietal, le diametre thoracique sagittal et transversal ainsi que la longueur du tronc (Tab. I). Pour le foetus de poids moyen, le calcul regressif lin^eaire multiple suffit. Pour les foetus plus grands et plus petits que la moyenne, il est recommande de com- pleter par des corrections empiriques acquises. Et pour les foetus tres petits on a besoin d'une disposition quasi lineaire.

Les problemes soulev6s par le calcul du poids foetal peu- vent s'enoncer comme suit:

1. Les oscillations biologiques dües a la difference de con- stitution des nouveaux-n6s. Les ecarts qui en sont la consequence (entre les poids evalues et reels) se repartis- sent a peu pres normalement. II en est tenu compte par le calcul de la moyenne dans les analyses regressives.

Ces oscillations biologiques resistent a toutes les me- thodes de calcul mathematique.

2. Les oscillations d'origine pathologique causees par les relations modifiees des mesures lineaires au poids, con- secutives aux changements des proportions du corps

par rapport au foetus normal. Les exemples caract- eristiques en sont: la dystrpphie foetale, la fetopathia diabetica, les triples et autres multiples (les gemini ne montrent pas de modification dans les proportions) et les malformations foetales.

3. La definition des points de mesure dans le foetus. notre actuelle technique par ultra-sons n'est pas encore suffis^

amiiient developpee pour nous permettre de viser a des pointsde mesure anthropometriques chez le foetus. II faüt s'entendre pour la pratique sur des compromis utilisables delimitant avec une precision optimale une region marquante du corps foetal. La longueur du tronc ne peut certes etre mesuree avec la meme precision que les deux diametres thoraciques, mais eile n'en repre- sente pas moins le seul parametre de Fextension longitudinäle. L'addition d'autres mesures foetales moins precises dans les formules de calcul du poids foetal nuisent a Fexactitude des resultats.

4. Les eneurs de mesure subjectives resultent du procede applique et non du foetus; ün exäminateur experimente peut les eviter pour la plupart comme il en est, par exemple, pour ledit «effet Salami».

5. La methode de regression mathematique. La courbe de regression entre les mesures du thöräx et le poids (Fig. 3 et 4) est presque drpite tandis que les moyennes pour le diametre biparietal (Fig. 1) et pour la longueur du tronc (Fig. 7) s'ecartent davantage des degres de regression. Au total le modele de regression multiple lineaire ne convient donc qu'a certaines conditions. Le recours a des polynomes n'est pas d'un plus grand secours.

En cas de suspicion d'un retardement intra-uterin, il est recommande d'appliquer Fune des formules I ou II plus la formule III, la somme reduite des diametres du thorax (Fig. 6) poüvant alors confirmer Feventualite d'une dystrophie. II serait bon de poursuivre les recherches en vued'un modele mathematique adequat,celui-cipermettant des extrapolations dans les spheres des cas rares de foetus tres grands et tres petits.

Mots-cles; Calcul de regression, evaluation par ultra-sons du poids du foetus, obstetrique, problemes de la technique de mesure.

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37

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[5] ISSEL, E. P., P. PRENZLAU: Eine neue Methode zur Berechnung des fetalen Gewichtes mittels Ultraschall- B-Bild-Technik. Zbl. Gynäk. 96 (1974) 417

[6J ISSEL, E. P., P. PRENZLAU: Zur Berechnung des Ge- burtsgewichtes kleiner Fetus mit dem Ultraschallver- fahren (B-scan). Zbl. Gynäk. 96 (1974) 722

[7J PRENZLAU, P., E. P. ISSEL: Die praktische Bedeu- tung der Messung der Schulter-Steiß-Länge beim Fetus mittels Ultraschall. Zbl. Gynäk. 95 (1973) 1421 [8J YLÖSTALO, P.: Measurement of fetal body dimen-

dions by the ultrasound B-scan method. Ann. Chir.

Gynaec. Fenn. 63 (1974) 20

[9] YLÖSTALO, P., P. A. JÄRVINEN: Estimate of fetal weight from the ultrasonic measurement of the biparietal diameter and the body dimensions in normal pregnancies and pre-eclampsia. Ann. Chir. Gynaec.

Fenn. 63 (1974) 24

Received July 30, 1975. Accepted October 25, 1975.

Dr. med. E. P. Issel Universitäts-Frauenklinik Tucholskystr. 2

DDR-104 Berlin