Placentu(1991), 12, 289-298

Human Placental Lactogen the Normal Pregnancy

(hPL) Model for

J. CARLalb,d,M. CHRISTENSEN“ & 0. MATHIESEN” a Department of Oncology,h Danish Cancer Society, Department of Eqen’mental Clinical Oncology, “ Department of Clinical Chemisty, Aalborg Sygehus .!?yd,Hobroaej 18-22, 9000 Aalborg, DK-Denmark d To whom correspondenceshould be addressed Paper accepted4.3.1991

SUMMARY This study includes 75females with normalpregnancies, andpresents individual cases of longitudinal series of human placental lactogen (hPL). Samples for hPL levels are taken during the period from gestational week 26 and until labour. A modified Gompetiz equation is &jned, characterined as growth at a continuously decreasing exponential rate, which finally plateaus in gestational week 36. This modajied Gompertz equation adequatebjtted individual hPL series. The work describes that a final hPL forecastfor the normal pregnancy could be obtained in gestational week 30 using knowledge on maternal height and age, combined with a single hPL sample. The present model was applied in six pathological pregnancies with intrauterine growth retardation, and in all cases measured hPL levels were below the model estimate.

INTRODUCTION During human pregnancy growth of the fetus is closely related to the placenta (Gruenwald, 1974). Syncytiotrophoblasts in the placenta synthesize human placenta lactogen (hPL) early in pregnancy -hPL is related to the functional mass of the placenta-and has been used as a marker for fetal malnutrition and, consequently, intrauterine fetal growth retardation (Chard,l974). Screening of a population for deteriorated placenta function by means of a single hPL determination in each individual has led to ambiguous results on the clinical value of the hPL assay (Spellacy, 1979; Obiekwe and Chard, 1982; Kyank, 1985; Rosen, 1986). When a single hPL value is used, the pathological level has to be outside a normal range, which has 10 and 90 per cent percentiles of 5 mg/l and 10 mg/l respectively in gestation weeks 36-40 (Obiekwe and Chard, 1983). The predictive value of hPL for malnutrition has been improved by application of longitudinal hPL values (Spellacy, Buhi and Birk, 1975). An approach to model longitudinal series of hPL measurements, applying a statistical model has been described (Lundbye-Christensen, 1990). This model assumes a linear progression over 0143-4004/91/030289

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1991 RailEre Tindall L.td

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time of the logarithm of the hPL concentration from gestational week 26 up to 36. However, growth of the normal fetus has been demonstrated to follow Gompertz pattern analogous to the autonome growth of solid cancers (McCredie et al, 1965). The Gompertz pattern is characterized as an exponential growth pattern with a decreasing exponent. It has been the objective of this study to investigate a predictive model based on the Gompertz equation, normally used to describe the growth of solid cancers, to explain growth of the placenta and consequently the course of hPL in serum during normal pregnancy.

MATERIALS AND METHODS Patients One-hundred and eleven females, regularily menstruating during the past year, participated in the study. Gestational age was calculated from the first day in the last menstruation period. In each individual longitudinal series of hPL values were obtained weekly from gestational week 25 (GWzs) until labour. Blood-samples were obtained from an antecubital vein after 0.5 h rest without smoking. Serum was separated within 1 h and the sample was kept at 4°C until the analysis (Nrargaard-Pedersen and Gaede, 1973), which was performed no later than 3 days after sampling. Placenta and child weight were registered, together with a score, O-9, of the mother’s tobacco habits. Informed consent was given. Inclusion criteria were, mothers age between 16 and 35 years, uneventful pregnancy and birth of a normal healthy child, and a minimum of five hPL samples between GWzs and labour. Seventy-five of the participating females fulfilled these criteria. A subgroup of 44 females also had registration of changes in haemoglobin (Hgb) during the period GWz6-GW36. Longitudinal series of hPL in six cases of pathological conditions during pregnancy causing intra uterine growth retardation (IUGR) was included.

statistics A modified Gompertz growth equation (see Appendix) was applied to model the longitudinal series of hPL values in each individual. The modification assumes that hPL levels reach a plateau hPL,, at about gestational weeks 35-37 (Chard, 1974), in contrast to the Gompertz equation in which a plateau is reached only asymptotically. The growth equation [Gomp(GWi)] is a standardized equation (Table 1) dependent only on the GW. The scaling factor, hPL,,, that provided the least square deviation between the equation and the longitudinal hPL values, was estimated using equation 2 in the appendix. Relations between hPL,,> placenta weight, child weight and registered maternal parameters were tested using univariate and multivariate linear regression analysis.

RESULTS The sensitivity for quantitation of hPL was 0.6 IU/l. The standard deviation (s.d.) of the actual hPL level was determined from linear regression on the observed coefficient of variation estimated as between-assay precision under routine conditions. The regression equation presents as follows: s.d. = 0.016 x C + 0.124 IU/l, Where C is the actual hPL level. Typical applications of the modified Gompertz equation to

Carl, Christensen, Mathiesen: hPL Moaklfir Normal Pregnancy

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Table 1. Standardized Gompertz function Gomp(GW) calculated at each gestational week (GW), from week 22 to week 40. The column titled ‘Forecast’ represents the calculated model for the case in the example in the appendix

GW

Gomp(GW)

Forecast

22 23 24 25 26 27 28 29 30 31 32 33 34 3.5

0.262 0.303 0.347 0.393 0.442 0.494 0.547 0.601 0.657 0.714 0.771 0.829 0.886 0.943

2.3 2.6 3.0 3.4 3.8 4.3 4.8 5.2 5.7 6.2 6.7 7.2 7.7 8.2

37 36 38 39 40

1.ooo 1.000 1.000 1.000 1.000

:::: 8.7 8.7 8.7

longitudinal hPL values is shown in Figure 1(a-g). Figure 1(a) shows two examples of normal pregnancies where measured hPL values are adequately fitted by the Gomp(GWJ equation. Variance around the model equals that of the assay. Figure l(b-g) are six cases of pathological pregnancies with IUGR as follows: Figure l(b) IUGR on ultrasound during the last two gestational weeks. Placenta infarcted. Child weight at birth in GWzs = 858 g. Figure l(c) Ultrasound-verified IUGR. Placenta infarcted. Child weight at birth in GW4,= 1375 g. Figure 1(d) Ultrasound biometrics normal. Placenta normal, but circumvallat type. Child weight at birth in GW# = 3140 g. Figure l(e) Ultrasound biometrics normal. Placenta previa, with vaginal bleeding in GWs+ Child weight as section in GWs6 = 2440 g. Figure l(f) IUGR on ultrasound. Missed abortion in GWT. Child birth weight at birth in GWa = 2850 g. Figure 1(g) Ultrasound biometrics normal. 220-V electric shock in GWs7. Child weight at birth in GW,t = 3340 g. Table 2 presents the results from the univariate regression and one-way variance analysis (ANOVA) on fetal parameters with the corresponding maternal parameters. Maternal height and age were related to the hPL,,,; hPL,, increased with decreasing maternal height. Placenta weight and newborn child weight, increased with maternal height. Only maternal age was significantly related to child weight, which increased with maternal age. A similar trend existed for placenta weight and hPL,,,. Change in Hgb was not significantly related to any of the fetal parameters. The data indicates a trend of increasing hPL,, with increasing Hgb. Relations between maternal tobacco-score and fetal parameters was not significant when tested by ANOVA, but a trend existed for decreasing child weight and increasing hPL,, with increasing tobacco consumption.

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Placenta (1991), Vol. 12 14r (b)

9 8I

13 12

: (e)

I I i IO 9

8 7 6 5 4. 3, 2-

I 0' 20

25

30

35

40

I I 45 20 Gestotionol

1

25 week

30

35

40

45

(JarI, Christensen, Mathiesen: hPL Model for Normal Pregnancy

20

25

30

35

Gestational

40

45

week

Figure I. The modified Gompertz model (solid line) model estimate for hPL based on a single mothers height and age, shown together with the corresponding longitudinal series of hPL levels in Error bars indicate two s.d. ofthe measured hPL level. Two typical examples ofnormal pregnancies (b-g) represent measured hPL levels in various pathological pregnancies with intra uterine growth their model estimates (see text).

hPL value and serum (circles). are given in (a). retardation and

Table2. The table shows significance level and sign of the regression coefficient (P-value) from univariate regression analysis of placenta, child weight and hPL,, on maternal reciprocal height, and change in Hgb during the period between gestational week 26 and gestational week 36. N is the number of females in each regression. Relations to tobacco-consumption was tested using ANOVA. The table shows P-values. Sign (+ or -) indicates the trend of calculated means for each tobacco-score.

N

Maternal characteristic

75 7s 44 61

Age Hgb change Tobacco

l/Height

Placenta

Child weight

0.047 (-) 0.34 0.41 0.59

0.04 (-) 0.01 (+) 0.33 0.14 (-)

hpL, 0.0006 0.13 0.12 0.14

(+) (+) (+) (+)

Table 3 presents the final regression model from multivariate linear regression analysis. relates significantly to maternal height and age, increasing when the former The hPL,, decreases and the latter increases. Inserting maternal height and age in the equation of Table 3, an estimated value, EhPLmax, for hPL,,, was provided. Multivariate regression analysis on the subgroup of 44 females with registered changes in Hgb from GW26 to GW36 (Table 4), as a result of declining Hgb, in addition to significant showed a significant decrease in hPL,, relation to maternal reciprocal height and age. Figure 2(a) is the distribution of the mean error (see Appendix) of a longitudinal hPL series around the Gompertz model in the 75 females. The distribution of the model’s errors lies within the range O-l.3 IU/l, with a median value around the model of 0.7 IU/l. The Gompertz model calculated applying the equation in Table 3, provided the wide, flat distribution of mean error in Figure 2(b). Combining the calculated value Eh~~max with a single hPL value in GW30 as a weighted average, gave a distribution Figure 2(c), of mean errors closer to the original one in

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Placenta (1991), Vol. 12 Table3. Multivariable regression of maternal reciprocal height and age on hPL,,. Seventy-five females were included in the regression. The table shows final regression coefficients and significance level. s.d. is standard deviation on regression coefficients; P is the significance level of t-test on estimated coefficients. Final regression model: E t,pt_max= 4080/height(cm)

+ 0.13

x

ageeears)

- 20.3

where Et,PL_ is the regression estimate of hPL,, and age. Ninety-five per cent confidence limits for approximately constant, within the range 4-14 IU/l 3.7 IUA Thus the se. on Et,pLrnax is Variables Constant l/Height Age

Coefficient

s.d.

-20.3 4080.0 0.132

6.57 1016.8 0.06

given the maternal height E,,PL,,,~ were found to be of hPL,,,, with a value of = 1.85 IU/l. t-value

P

-3.09 4.01 2.29

0.0029 0.0001 0.029

Table 4. Linear multivariable regression of maternal reciprocal height, age and change in Hgb between GWa6 and GWse on hPL,,. Forty-four females were included in the regression. s.d. is standard deviation on regression coefficients; P is the significance level of t-test on estimated coefficients. Variables Constant l/Height Maternal age Change Hgb

Coefficient

s.d.

-30.7 5307.5 0.263 1.15

7.97 1188.4 0.078 0.55

t-value

P

-3.85 4.47 3.39 2.11

0.0004 0.0001 0.0016 0.042

Figure 2(a). Combining EhPLmax and two hPL values provided distribution of mean errors [Figure 2(d)].

little improvement

in the

DISCUSSION Applying the proposed model in this study, longitudinal hPL series was fitted within the hPL assay variation. The observed relation between maternal height and the maximal hPL level in the present study was predicted by the model outlined in the Appendix. The observed relation cannot account for the total variation in hPL,,. One reason for this is that the maternal vascular volume does increase during pregnancy. Even though erythropoiesis increases during pregnancy, it has been shown that the increase in vascular volume leads to a decrease in haemoglobin (Sagen et al, 1984). This observation was confirmed in the present study, where the inclusion of change in Hgb in the multivariate regression gave a better fit of model. Because change in Hgb was measured only in a limited number of females, this extended model has not been used further. Changes in excretion or production of hPL may be a reason for poor fit of the model. Cyclical changes have been reported in endogenous overnight creatinine clearance during the third trimester ofpregnancy (Paaby et al, 1988). In some of the 75 females, the longitudinal hPL series apparently underwent cyclical changes during pregnancy. In the present study, the number of data points were to few to allow for a more sophisticated modelling. Smoking has been demonstrated not to influence the size of placenta, but to cause lower

,‘arl, Christensen, Mathiesen: hPL Modelfor Normal Prepamy 0.25

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2.6

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2. (a) Distribution of mean error of measured hPL levels around best least square fit of modified Gompertz model in 75 longitudinal hPL series. (b) Distribution of mean error of measured hPL levels around modified Gompertz model calculated using height and weight to obtain a regression estimate for hPL,,. There are 75 cases in the distribution. (c) As in (b), but hPL, has been calculated using a weighted average between the regression estimate of hPL, and a single measured hPL level at gestational week 30. There are 61 cases in the distribution. (d) As in (c) using two measured hPL levels instead of one. Fifty-three cases are shown in the distribution.

hPL levels and child weight (Spira et al, 1977). The present study demonstrated similar trends for size of placenta and child weight, but the tobacco-score was not a significant factor in the final regression model. Investigations that lead to more accurate corrections for the increased vascular volume or half-life of hPL would be interesting. In the presented cases of pathological pregnancies with IUGR, measured hPL levels were lower than those of the corresponding models, which are not fitted to measured values but calculated using age and height of the mother and a single hPL value only. This held true, even in the case where the sample included in the model calculations was pathological.

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Placenta (I 991), Vol. 12

However, a consecutive study now needs to be conducted in order to evaluate the clinical potential of this model approach. The concept proposed in this study might be useful in connection with other pregnancy screening assays, such as AFP screening for neural tube defects. In conclusion, a model to forecast hPL levels during normal pregnancy was constructed by applying a modified Gompertz equation. The model was shown to adequately fit a longitudinal series of hPL values. Individual hPL forecast was constructed from a modified Gompertz equation scaled by a factor based on a weighted average of a single hPL value and an estimated Er+Lrnax for the maximal hPL level reached duringthe pregnancy. In pathological pregnancies measured hPL values were below the corresponding model estimates.

REFERENCES Chard, T. (1974) The hormonal assessment of foetal and placental function. Clinics in Obstetrics and G.ynaecology, 1, 85-102 Gruenwald, P. (1974) Placental insufficiency-a questionable concept. Archives ofDisease in Childhood, 49,915916. Kyank, H. R. (1985) HPL as indicator of intrauterine malnutrition.~oumal ofPerinatalMedicine, 13, 100-101. Lundbye-Christensen, S. (1990) A multivariate growth curve model for pregnancy. Biometrics, (in press). McCredie, J. A., Inch, W. R., Kruuv, J. &Watson, T. A. (1965) The rate oftumor growth in animals. Growth, 29, 331-347. Nergaard-Pedersen, B. & Gaede, P. (1973) Immunoelectrophoretical quantitation of human placental Lactogen Journal of Immunology, 2, 129-13 1. hormone. Scandinavian Obiekwe, B. C. & Chard, T. (1983) A comparative study of the clinical use of four placental proteins in the third trimester.3oumal ofPerinatalMedi&ze, 11, 121-121. Obiekwe, B. C. & Chard, T. (1982) What do placental function tests predict? European Journal of Obstetrics, Gynecology and Reproductive Biology, 14,69-73. Paaby, P.. Nielsen, A., Meller-Petersen, J. & Rafn, K. (1988) Cyclical changes in endogenous overnight cream&e clearance during the third trimester of pregnancy. Acra Medica Scandinaka, 223,459-468. Rosen. S. W. (1986) New olacental nroteins: chemistrv uhvsioloev and clinical use. Placenta. 7.575-594. Sage&N., N&en, ‘S. T., ‘Kim, H. ‘C., Berg+, P. & Keller, 6. (1984) ‘Maternal hemoglobin concentration is closely related to birth weight in normal pregnancies. Acta Obstetricia et Gynecologica Scandinavica, 63,245-248. Spellacy, W. N. (1979) The use of human placental lactogen in the antepartum monitoring ofpregnancy. Clinics in Obstetrics and Gynaecology, 6, 245-258. Spellacy, W. N, Buhi, W. C. & Birk S. A. (1975) The effectiveness of human placental lactogen measurements as an adjunct in decreasing perinatal deaths. AmericanJournal of Obstetrics and Gynaecology, 121,835-844. Spira, A., Philippe, E., Spira, N., Dreyfuss, J. & Schwartz, D. (1977) Smoking during pregnancy and placental pathology. Biomedikse Express, 27,266-269.

APPENDIX The growth of fetal wet weight was demonstrated by McCredie et al (1965) to agree with a Gompertzian pattern, characterized as an exponential growth pattern with a decreasing exponent. Mathematically it presents as W = W,” exp (A”(1 - exp (-P*GW))

(I)

where Wis weight of the fetus (g), GW is time since conception (weeks). The parameterA determines the asymptotic value for W, i.e. the birth weight of the fetus (Wbirb = W,* exp (A)). The parameter /I determines how fast the growth rate is declining. Equation (1) is assumed to be adequate for the growth of the placenta, with the modification that growth of placenta levels off around gestational week 36 (GW&. M(GW) M(GW)

= MO* exp (A”(1 - exp (-p*GW))

GWc36

= M(GWx)

GW>36

(2)

297

C,krl, Christensen, Mathiesen: hPL Mode/for Normal Pregnancy

where M(GW) is the weight of placenta at gestational time GW, M, is the weight at time zero (conception). The numeric values ofA is set to 10 and forp to 0.07 weeks-‘. The production of hPL is assumed to be proportional with placenta weight, i.e. the mean production (K) of hPL/cell/day is assumed to be constant. The amount of hPL synthesized is released and distributed in the vascular volume V,. hPL in the vascular volume is removed according to first-order kinetics with a half-life ,u of lo-20 min. The following balance equation for the hPL level C(t) at a given time tin the vascular compartment exists.

2dC(t)/dt = PM(t)/V,

- In (2)

x

C(t)/p.

(3)

The hPL serum level changes slowly, within weeks, so C(t)/p is much larger than dC(t)/dt, and equation (3) is approximately zero or C(t) -- K*M(t)/(V, X In (2)/p)

(4)

This equation shows that the hPL serum level is proportional to the weight of placenta-is a necessary condition for use of the hPL level as function of placenta and, consequently, fetus weight. Equation (4) shows that the hPL level should correlate to the reciprocal value of the intravascular volume. In equation (3) we have the unknown parameter M,; this is the reason for introducing the standardized Gompertz function, Gomp(GW) given as = M(GW)/M(36)

Gomp(GW) This function

is tabulated x

C(GW) = hPL,,,

(9

in Table

1. The model for the hPL level in serum then becomes

Gomp(GW)

GWa36

C(GW) = hPL,,,

(6)

GW>36

where hPL maxis the maximal hPL level occurring at the level off in GWs,. The only unknown parameter in this equation is hPL,,. Equation (6) is linear in hPL,,, and the least squares fit of equation (6) to a longitudinal hPL series is provided by the following equation hPL,,,

=

Mean error =

1

hPLi/Gomp(GWJ/N (7)

i

a

(C(GW,)

- hPLi)2/N

where hPLi is the hPL level measured at gestational week GWi. Nis the total number of hPL values in the longitudinal series. Mean error is the mean distance of measured hPL levels to the model fit. Example The following example illustrates how the model can be used in clinical practice. the standardized Gompertz equation are taken from Table 1. A 24-year-old female in her 27th gestational week (GW27) has a routine sample hPL determination. The sample shows a hPL serum level of 4.7 IU/l. Her height What will the hPL forecast for an uncomplicated pernancy look like? The final model in Table 3 is used to provide an estimated hPL,, using height and age: Ehpimax = 4080/167 The corresponding C(GW&

- 0.132”24

- 20.3 = 7.2 II-J/l.

hPL level for GWz7 is calculated

= EhPLmav x Gomp(GW2,)

= 7.2*0.494

as

= 3.61 IU/l

Values for drawn for is 167 cm. regression

Placenta (1991), Vol. 12

298

Standard error on E hPL,_was 1.85 IU/l, thus standard error on C(GW27) is 1.85 X 0.494 = 0.91 II-J/l, which is used as a weighting factor for C(GWz7). The median value of the distribution in Figure 2(a), 0.7 IU/l, is taken as a weighting factor of the measured sample, and the forecast is updated as follows: Weighted Average = Wl x 3.61 + W2 x 4.7 = 4.3 mIU/l Wl = (o.7)2/((o.7)2 + (0.91)2 = 0.37 W2 = (0.91)2/((0.7)2 + (0.91)2 = 0.63. The updated value for hPL,,, hPL,,,

= 4.3/0.494

The updated

then is

= 8.7 IU/l

forecast is tabulated

for each gestational

week in Table 1.