Correspondence: Dr K. Brackley, Lecturer in Fetal Medicine, Birmingham Women's Hospital, Edgbaston, Birmingham B15 2TG, UK.
Objective To compare the maternal cerebral circulation in pre-eclampsia and normal pregnancy using an alternative method of Doppler waveform analysis called the Laplace transform analysis, which provides haemodynamic data additional to standard Doppler indices.
Design A prospective cross-sectional study.
Setting Department of Obstetrics and Gynaecology, Nottingham University Hospital.
Sample The study involved 17 women in the third trimester of a normal pregnancy, 11 with pregnancyinduced hypertension and 26 with pre-eclampsia.
Methods Doppler recordings were obtained from the internal and external carotid and middle cerebral arteries, with the measurements in hypertensive women being carried out before any treatment was given. The waveforms were then subjected to Laplace transform analysis which provides information on vessel wall stiffness and upstream and downstream flow conditions.
Main outcome measures The determination of the Laplace transform analysis parameters, including alpha, the natural frequency of oscillation and real pole, and pulsatility index.
Results Laplace transform analysis demonstrated a significant increase in vessel wall stiffness in all the arteries in hypertensive pregnancies, but this was more marked in pre-eclampsia. The data were also consistent with, but do not prove, increased downstream resistance in the middle cerebral artery in women with pre-eclampsia but not in those with pregnancy-induced hypertension.
Conclusions The Laplace transform analysis of Doppler waveforms yields important physiological information concerning the cerebral circulation in pre-eclampsia, not detected using conventional Doppler indices. The results suggest that both pre-eclampsia and pregnancy-induced hypertension are associated with increased cerebral arterial wall stiffness and that, in addition, there may be cerebral vasoconstriction in pre-eclampsia.
The systematic study of the cerebral vasculature in pre-eclampsia presents a number of practical and ethical problems. For this reason, Doppler ultrasound has some attractions, being a noninvasive technique which can be used sequentially. We have previously described the use of Laplace transform analysis of Doppler waveforms as a means of deriving additional haemodynamic information, distinguishing between vessel wall stiffness and upstream and downstream flow conditions1. This technique aims to analyse the changes in Doppler waveform shape that can be observed in altered circulatory conditions. We have recently reported a longitudinal study through normal pregnancy, using this technique to analyse a variety of maternal Doppler signals2.
There is a high incidence of neurological symptoms and signs in women with pre-eclampsia, even in those who do not progress to eclampsia. These include headaches and visual disturbance, both of which occur in up to 40% of women with pre-eclampsia, as well as hyper-reflexia and cortical blindness. The brains of women dying from eclampsia in the days before effective antihypertensive treatment showed evidence of haemorrhages, microinfarctions and cerebral oedema3 and one view is that eclampsia is a manifestation of hypertensive encephalopathy4. However, eclampsia can still occur in the presence of satisfactory blood pressure control or even in the apparent absence of hypertension5.
Using a variety of different imaging techniques to study the cerebral circulation, conflicting findings have been reported in women with eclampsia, including increased blood flow6, no change in blood flow7 and cerebral ischaemia associated with cerebral vasoconstriction8–11. It has been argued that over-distension of the cerebral arteries leads to extravasation of blood into the brain through damaged endothelium6. However, cerebral arterial constriction is also considered to be an important pathophysiological feature of the neurological manifestations of pre-eclampsia. Indeed it is possible that more than one mechanism is involved. We now describe for the first time the application of the Laplace transform analysis of Doppler waveforms to study the cerebral circulation in pre-eclampsia.
This study, which focused on hypertensive pregnancy, was performed over the same two year period as a prospective study of the identical haemodynamic variables throughout normal pregnancy2. It involved 26 women with pre-eclampsia, 11 with pregnancy-induced hypertension and 17 with a normal pregnancy, all of whom were in the third trimester. Pregnancy-induced hypertension was defined as a blood pressure ≥ 140/90 mmHg at > 24 weeks of gestation plus an increase from the first trimester of > 30 mmHg systolic and/or > 15 mmHg diastolic. The same blood pressure criteria were used to define pre-eclampsia, with the addition of ≥ 0.5 g proteinuria over 24 hours (or 3+ protein on dipstick if an emergency admission). All women had singleton pregnancies and gestation had been confirmed by second trimester detailed anomaly scan. Normal subjects were volunteers recruited using poster advertisements in the hospital or general practitioners' surgeries or via community midwives. Hypertensive women were recruited from antenatal wards or delivery suite. Written informed consent was obtained and the study was approved by the University Hospital Ethics Committee.
Necessarily, only one Doppler recording could be made from each hypertensive woman before treatment was commenced. Further recordings were made at 12 weeks postpartum after all treatment had been stopped and blood pressure had returned to normal levels. Since these hypertensive women presented over a wide range of gestational age (Table 1), normal data were obtained from the prospective study of 17 healthy women2 using data from the four visits between 24 weeks of gestation and term and also from the 12 week postpartum visit.
Table 1. Parity numbers in the pre-eclampsia group.
We were interested in studying the Laplace transform analysis technique in a variety of maternal and fetal vessels. We report here Doppler signals that were obtained from maternal external carotid, internal carotid and middle cerebral arteries. Vessels were insonated only on the right side to minimise the duration of the study period in the hypertensive subjects. At least 15–20 waveforms were recorded from each vessel on to videotape for later analysis. The woman was in a semi-recumbent position throughout the study to avoid aorto-caval compression. Mean blood pressure was determined from the average of 10 minute interval measurements over the time of the Doppler study, using an automatic sphygmomanometer (Dinamap; Critikon Inc, Tampa, Florida, USA). Mean heart rate was obtained from analysis of the Doppler signals.
A Kontron Sigma 44 HVCD ultrasound scanner was used which operates at a power output of less than 100 mW/cm2 spatial peak temporal average in the imaging and Doppler modes. An annular array 7.5 MHz sector scanning probe with 8 MHz pulsed-wave Doppler was used to image and record signals from the internal carotid artery and external carotid artery, aided by colour flow imaging as we have described previously2. A 2 MHz pencil probe was used to obtain middle cerebral artery signals using the technique described by Aaslid et al.12. The pencil probe was placed above the zygomatic arch, between the lateral margin of the orbit and the ear, insonating through the thin ‘temporal window’. Pulsed-wave Doppler recorded signals from a depth of approximately 50 mm12.
The Doppler waveforms were analysed using a Dopstation computer (Scimed, Fishponds, Bristol, UK)2. Several optimal Doppler signals can be frozen on the computer screen for automatic analysis (a ‘screen-save’). The averaged waveform is generated from the maximum frequency envelopes and the standard Doppler indices are calculated. Fourier transform analysis of the averaged signal is performed and the harmonic frequency content is displayed by the computer as a plot of normalised amplitude against angular frequency (up to 40 radians/sec1). The equivalent Laplace transform is calculated using a curve-fitting technique. Laplace transform analysis is a mathematical method of Doppler waveform shape analysis which is based on an electrical model of the arterial circulation13,14. From the roots of the Laplace transform equation, the Laplace transform analysis parameters are determined and these include 1-2-13:
1Alpha, which in the theoretical model is inversely proportional to the upstream vessel radius, and therefore relates to upstream flow conditions. Alpha increases in the presence of increasing upstream resistance.
2Natural frequency of oscillation (ω0) which is theoretically proportional to the square root of Young's modulus (E) of elasticity of the vessel wall and is therefore concerned with vessel wall stiffness. Values rise with an increase in vessel wall stiffness.
3Real pole which is inversely proportional to the square of the distal vessel radius and therefore reflects downstream resistance. Increasing downstream resistance is associated with larger values of real pole.
Statistical analysis was performed using SPSSX-3 (Statistics package for the Social Sciences, SPSSX, USA). Data were aggregated from the multiple entries made for each vessel at each study visit using the mathematical mean. To allow direct comparison with the normal pregnancy data2, data from the hypertensive subjects were grouped into the same four-week gestation periods (24–27, 28–31, 32–35 and 36–39 weeks inclusive). Median and interquartile ranges were determined for the Laplace transform analysis parameters and pulsatility index from each vessel for each gestation group and at 12 weeks postpartum in normotensive, pregnancy-induced hypertension and pre-eclamptic subjects.
Median and interquartile ranges for women without hypertensive complications are shown as reference data in the form of line graphs in all the figures. Individual hypertensive women's data were plotted and superimposed onto these line graphs. In the interests of space only a limited number of figures are presented to illustrate the data.
The Mann-Whitney U test was used to make comparisons between the unpaired data in normal subjects and each hypertensive group within a four-week gestation period or at 12 weeks postpartum. The Wilcoxon matched-pairs signed-rank test was used when possible to assess differences in paired data for individual subjects, comparing readings in pregnancy to 12 weeks postpartum. Statistical significance was determined at P< 0.05. Coefficients of variation for the Laplace transform analysis variables and pulsatility index over short and long term have been previously reported (majority < 15%)2.
The demographic details of the subjects are shown in Table 2. Overall mean blood pressure was significantly higher and heart rate significantly lower in the preeclamptic and pregnancy-induced hypertension groups compared with normal pregnancy.
Table 2. Demographic details of the women in the study. Mean blood pressure and heart rate for the pre-eclampsia and pregnancy-induced hypertension groups were the average over the period of the Doppler study. The mean values for the normotensive women were the average of the mean values for each visit between 24 weeks of gestation to term. Values are given as n or mean (SD). IUGR = intrauterine growth retardation.
Normal pregnancy (n= 17)
Pre-eclampsia (n= 26)
Pregnancy-induced hypertension (n= 11)
Gestation at delivery (weeks)
IUGR < 10th centile
Systolic blood pressure (mmHg)
Diastolic blood pressure (mmHg)
Maternal heart rate (bpm)
As found in our previous longitudinal study of normal women2, there were some missing Doppler data due to an inability to record satisfactory signals from the middle cerebral artery in some pre-eclamptic women (n= 4) within the time available.
The shape of the Doppler waveforms from all three vessels was often changed in pre-eclampsia with an increase in the height of the second systolic peak compared with normotensive pregnancy (Fig. 1). Waveform outline changes in pregnancy-induced hypertension were less apparent.
Upstream resistance (alpha) did not differ between hypertensive and normotensive women in any of the vessels studied. For example, median and interquartile ranges for alpha in women with pre-eclampsia at 32–35 weeks of gestation compared with normal pregnancy were: external carotid 2.42 (2.07–2.58) vs 2.30 (2.07–2.18); internal carotid 2.25 (1.81–2.55) vs 2.09 (1.91–2.23); middle cerebral 1.97 (1.75–2.37) vs 1.79 (1.45–1.94), respectively.
Vessel wall stiffness (ω0) was significantly increased in all three vessels, both in women with pre-eclampsia and those with pregnancy-induced hypertension, compared with findings in normal pregnancy (Figs. 2 and 3). The differences were substantial and in the case of the middle cerebral artery nearly all the readings in both hypertensive groups were above the normal range (P= 0.0013 in pre-eclampsia at 32–35 weeks; P= 0.007 in pregnancy-induced hypertension at 36–39 weeks). Median and interquartile ranges for ω0 in pre-eclampsia at 32–35 weeks of gestation compared with normal pregnancy were as follows: external carotid 25.7 (24.9–34.3) vs 22.5 (20.2–26.3); internal carotid 29.7 (27.7–35.7) vs 23.2 (19.1–26.2); middle cerebral 33.5 (31.9–35.8) vs 23.1 (20.2–24.8), respectively.
Real pole (reflecting downstream resistance) tended to be increased (P= 0.08 at 32–35 weeks) in the middle cerebral artery of womén with pre-eclampsia (Fig. 4), but not in those with pregnancy-induced hypertension (data not shown). Real pole was unchanged in the internal carotid (Fig. 4) and external carotid arteries in pre-eclampsia and pregnancy-induced hypertension compared with normal pregnancy. The median and interquartile ranges for real pole in pre-eclampsia at 32–35 weeks of gestation compared with normal pregnancy were: external carotid 4.85 (4.31–5.44) vs 4.81 (4.25–5.81); internal carotid 5.01 (4.33–5.92) vs 5.03 (4.13–5.97); middle cerebral 5.59 (4.40–6.50) vs 4.26 (3.90–5.01), respectively.
When data from 17 primiparous subjects with pre-eclampsia between 28 and 39 weeks were compared with data (n= 18) from the seven primiparous women in normal pregnancy, by combining the individual four-week study periods between 28 and 39 weeks, real pole was significantly increased in the middle cerebral artery (P= 0.0025).
The pulsatility index was significantly reduced in pre-eclampsia (external carotid P<0.01, internal carotid P<0.05, middle cerebral P<0.05) and pregnancy-induced hypertension compared with normal pregnancy in all three vessels. Illustrative data for the middle cerebral artery in pre-eclampsia are shown in Fig. 5. Median and interquartile ranges for pulsatility index in pre-eclampsia at 32–35 weeks of gestation compared with normal pregnancy were as follows: external carotid 2.22 (2.00–2.63) vs 2.85 (2.38–3.20); internal carotid 0.92 (0.72–0.99) vs 0.97 (0.85–1.12); middle cerebral 0.77 (0.68–0.86) vs 0.90 (0.83–0.95), respectively.
Eighteen of the women with pre-eclampsia returned at 12 weeks postpartum for a follow up study, together with 15 of those women without hypertensive complications: blood pressures were 119 (15)/73 (7) mmHg and 112 (2)/67 (7) mmHg, respectively. Postpartum values for the Laplace transform analysis parameters in the normal and pre-eclampsia groups from the internal carotid and middle cerebral arteries are shown in Tables 3 and 4 respectively. Data for normal women at 36–39 weeks of gestation and for the whole pre-eclampsia group are presented for comparison. We have previously reported2 that vessel wall stiffness (ω0) is significantly lower in normal pregnancy compared with postpartum in the internal carotid (P < 0.05) and middle cerebral (P < 0.001) arteries. In addition, real pole significantly decreases postnatally in the external and internal carotid arteries (P < 0.005) in normal pregnancy.
Table 3. Laplace transform analysis (LTA) indices from the internal carotid artery in normal pregnancy (36 to 39 weeks of gestation), preeclampsia and at 12 weeks postpartum. Twelve weeks postpartum, there were no significant differences between values in the normal pregnancy and pre-eclampsia groups. Values are given as median (interquartile range).
‡Twelve weeks postpartum values significantly decreased Compared with values in pregnancy when pre-eclamptic (P < 0.05).
36–39 weeks (n= 14)
12 weeks postpartum (n= 15)
Pre-eclampsia (n= 26)
12 weeks postpartum (n= 18)
Table 4. Laplace transform analysis (LTA) indices from the middle cerebral artery in normal pregnancy (36 to 39 weeks of gestation), preeclampsia and at 12 weeks postpartum. No significant differences were found between pregnant and postpartum values in the pre-eclamptic group. Twelve weeks postpartum, there were no significant differences between values in the normal pregnancy and pre-eclamptic groups. Values are given as median (interquartile range).
In the current study, in women with pre-eclampsia real pole was significantly decreased postnatally in the internal carotid artery (P < 0.05)(Table 3). The decrease in the middle cerebral artery did not reach significance (Table 4). By 12 weeks postpartum, there was no significant difference between the previously hypertensive and normal pregnant groups in any of the Laplace transform analysis parameters or pulsatility index for any of the vessels. The increased values of ω0 in pre-eclampsia did not change postnatally and were therefore at the same level as found in nonpregnant individuals, in whom systemic blood pressure is much lower.
There have been few systematic studies of cerebral blood flow in pre-eclampsia. All have used transcranial Doppler ultrasound but the blood velocity waveforms have been analysed by various angle-independent ratios of systolic to diastolic velocity. This approach is inherently limited in physiological interpretation for a number of reasons1. For example, heart rate can be a confounding factor with the ratios exhibiting an inverse correlation to heart rate. Substantial changes in blood velocity may not be reflected in the conventional indices if the ratio remains unchanged. Furthermore, pharmacological agents which are unlikely to share a similar action on cerebral vessels can produce the same change in ratio. Thus, infusion of the potent vasoconstrictor angiotensin II leads to a fall in pulsatility index in the common carotid artery of nonpregnant women15, the internal and external carotid arteries of women in the first trimester13 and the middle cerebral artery of women at 28 weeks of gestation16. However, magnesium sulphate, which may act as a cerebral vasodilator and which is certainly not a vasoconstrictor, also reduces pulsatility index in the middle cerebral artery17. This clearly illustrates the problems of ascribing physiological meaning to the conventional indices as it is not clear which factors are involved in producing a change in pulsatility index. Indeed, in two studies where a normotensive control group has been used for comparison, systolic blood velocity was found to increase in the middle cerebral artery in women with pre-eclampsia and this was interpreted as evidence of vasospasm18,19.
Laplace transform analysis overcomes these methodological difficulties. The technique aims to quantify the overall Doppler waveform shape by analysing the frequency content of the signal and is, therefore, independent of heart rate. The different parameters obtained from this analysis (alpha, the natural frequency of oscillation and real pole) each provide separate haemodynamic information concerning the upstream, local and downstream factors which affect blood flow at the point of insonation within an artery1,2,13. We have used this approach for the first time in women with pre-eclampsia. The women have been followed up after delivery to ensure that the hypertension and proteinuria resolved, confirming the diagnosis of a pregnancy-induced condition.
The most obvious and consistent change in Laplace transform analysis parameters in women with pre-eclampsia and pregnancy-induced hypertension is the higher values for the natural frequency of oscillation or ω0. This variable is proportional to the square root of Young's elastic modulus in the theoretical model of the Laplace transform analysis and therefore is related to local vessel wall stiffness1,2,13,14. The increase in ω0 in women with hypertension suggests increased vessel wall stiffness in all the arteries under investigation. The increase tended to be greater in women with pre-eclampsia compared with pregnancy-induced hypertension. In normal pregnancy we have previously reported a decrease in ω0 within the carotid and middle cerebral arteries from early in pregnancy followed by an increase postpartum2. Interestingly, the higher ω0 values found in pre-eclampsia and pregnancy-induced hypertension are similar to the levels seen in nonpregnant women where blood pressure is much lower2,13. However, we are unable to determine whether this lack of change in vessel wall stiffness postpartum indicates a primary or secondary phenomenon as we do not have prospective data for the hypertensive women. A lack of relaxatory capacity in pre-eclampsia has been demonstrated recently in myometrial resistance vessels, which supports our hypothesis (albeit from another vascular bed) about a general stiffness of the vasculature in this condition20.
We also found a trend to increased real pole, compatible with higher downstream resistance, but only in the middle cerebral artery and only in women with pre-eclampsia. This suggests that a difference exists between pre-eclampsia and pregnancy-induced hypertension. Both appear to be associated with an increase in the vessel wall stiffness of cerebral arteries—albeit with greater changes in pre-eclampsia—but only in the women with pre-eclampsia was the hypothesis of cerebral vasoconstriction potentially supported, as reflected by increased resistance downstream in the middle cerebral artery. It is acknowledged that this interpretation remains unproven and further work is required in larger numbers of women.
We found a decrease rather than an increase in pulsatility index in pre-eclampsia and pregnancy-induced hypertension compared with normal pregnancy, which appears to contradict the conventional interpretation of lower pulsatility index values signifying reduced downstream resistance. Heart rate was significantly lower in hypertensive women which would not explain these results, pulsatility index being inversely correlated to heart rate. Altered upstream factors such as reduced myocardial contractility or proximal stenoses may be responsible for the lower pulsatility index values21,22. It is postulated that an increase in mean blood flow velocity occurs due to the increased second systolic peak in the Doppler waveforms, which by increasing the denominator of the ratio, leads to a decrease in pulsatility index. The velocities are higher within stiffer vessels which are able to propagate the waveform more efficiently than an elastic, less rigid vessel as less energy is absorbed by the vessel wall. The inadequacies of the standard Doppler indices in certain clinical situations are therefore illustrated in our study. In smaller numbers of women Qureshi et al.23 and Ohno et al.24 have also detected lower pulsatility index values in the middle cerebral artery in pre-eclampsia and eclampsia compared with normal pregnancy in association with normal or increased mean blood flow velocities.
Our findings are consistent with previous Laplace transform analysis data from the internal and external carotid arteries during angiotensin II infusions in human pregnancy13. The natural frequency of oscillation (ω0) increased as blood pressure rose, consistent with the increased vessel wall tone which would be expected with infusion of this potent vasoconstrictor. Comparable changes in the Doppler waveform outlines also occurred. Our findings are also in keeping with current views on increased vascular tone in pre-eclampsia resulting from widespread endothelial injury.
These observations support the view that pre-eclampsia is accompanied by an increase in cerebral vascular stiffness in addition to vasoconstriction involving the smaller cerebral vessels. If this were to be of sufficient severity then it is plausible that resulting cerebral ischaemia would result in the neurological manifestations of pre-eclampsia and eclampsia. These findings also provide the basis for developing and testing hypotheses concerning the possible mechanism of action of magnesium sulphate in the prevention of eclamptic convulsions. We reported that nimodipine, a drug with cerebral vasodilating properties, appeared to reverse the course of a moribund woman with eclampsia9. Subsequently we demonstrated that magnesium sulphate potentially reverses carotid vasoconstriction caused by endothelin-1, angiotensin II and neuropeptide-Y in the rat25. We and others have proposed that magnesium sulphate may reverse or prevent cerebral vasoconstriction in pre-eclampsia/eclampsia, but so far the only data relating to the effects of magnesium sulphate on the cerebral circulation in the human have been obtained using conventional Doppler indices (see above17). The application of Laplace transform analysis offers the opportunity to test this hypothesis in a more rigorous manner.
This study was funded by the Sir Jules Thorn Charitable Trust.