Study and Validation
of a Model of Fetoplacental Circulation

Direct and invasive experiments over the fetus are not proposable. Speaking about indirect measurements, the Doppler velocimetry allows to describe the blood flow characteristics of the fetal side and of the maternal side of the placenta, but measurements are affected by heavy tolerances and the reliability of the results is depending by the competence of the operator.

The target of this work was the analysis of the fetoplacental circulation through a model that can be applied to modern systems of clinical analysis, in order to perform reliable but not invasive medical examinations able to early detect some pathologies of the pregnancy.
This study was supported by the design and the realisation of perfusion techniques (using bovine blood and formaldehyde) that allowed the verification of the hypothesis preliminarily introduced into the theoretical model.

The experimentation executed at S. Paolo hospital, Milan, has been developed over 61 placentas during about 50 sessions. This allowed to study and verify the characteristics of the placental fluidodynamics. Soon after the child-birth, the placenta was connected to a perfusion set, able to simulate the physiological perfusion condition at the 38th week of gestation. An oxygenator maintained the concentration of oxygen and carbon dioxide of the blood at physiological level. The circuit allowed to perform controlled perfusions, with known parameters about input and output flow.

Fig. 1: Diagram of the perfusion circuit

The experiments averaged a correct perfusion of the placental vessels with bovine blood during about 15 minutes, generally showing a first period of stability of the measured data.
The efficiency of the perfusion has been tested using a fluorescent coloring agent and dissecting a placenta under UV light at the end of the experiment.
The input flows of the tests ranged 100 to 220 cc/min. The measured arterial pressure was variable from test to test, with an average of 99 mmHg/100cc/min. The venous pressure was close to the physiological value: 13 to 20 mmHg.

During the beginning of our experimentation the main difficulty we faced derived from the attempt to supply the umbilical arteries with a flow close to the physiological one, because of the pressure generated by a condition of general constriction of the placental vessels just after the drawing.
This phenomenon had already been observed by all the other researchers who attended to placental in vitro perfusion: they could not reach our flow values, not even using alkaline solution instead of blood. The placenta showed also a strong reactivity to the carbon dioxide concentration: a value lower than the physiological one in the fetal side produces a sudden constriction, that breaks off the perfusion within less than 5 minutes from the beginning.
Also the concentration of carbon-dioxide in the maternal side can produce important effects, so the experimentation cannot proceed correctly if the placenta floats in normal water, not added with carbon-dioxide.

Blood flow cc/min | 213 |  | Blood: |
Seepage % | 12.7 |  | Ht % | 31.5
Tot. Leakage % | 31.9 |  | P CO2 | 15.2
Arterial Pressure mmHg | 104 |  | P O2 | 13.4
Venous Pressure mmHg | 14 |  |  |

Table 1: Data on perfusion of placenta nr. 8.

A kind of seepage of serum is an additional reason of interest. It is evidenced by the progressive haematocrit increasing showed by the perfused blood: this element has been used to compute separately the percentage of leakage and of seepage. This phenomenon confirms that a placenta is also a "dialyzer" for its perfusion fluids.

Total Leakage: DV = V2 - V1
Leakage of corpuscular part: DVc = Ht2 * V2 - Ht1 * V1
Real leakage: DVb = 2 * DVc / (Ht1 + Ht2)
seepage: DVt = DV-DVb

Our perfusion circuit has been used also to perform a further set of tests, using a solution with formaldehyde and glutaraldehyde instead of blood. This type of 'fixing' perfusion has been extended averaging 23 minutes, with a flow ranging 100 to 250 cc/min, measuring an arterial pressure always lower than 120 mmHg.

The analysis, performed with the microscope, of the placentas that have been fixed in this way confirmed the quality of the perfusion, and finally the accurate measurement of the gauge of placental in-pressure vessels was possible. The obtained data, regarding the first orders of vessels, don't match the data of the medical literature. In particular the latter group of figures is burdened with deficiency errors.

Fig.2: Stem villus (ramus IV), not perfused placenta.

Fig.3: Stem villus (ramus IV). perfused placenta.

The obtained values are part of the data that have been used to develop the model.
Preliminarily an extensive search for the required quantitative information about the morphology of the vessels has been held. The comparison of these data with the obtained ones allowed to define the size of each order of vessels. Finally we elaborated a table to determine the resistances and the hydraulic capacitances of the model of fetoplacental circulation.
The model was realized through an equivalent electric circuit with variable current generators, resistances and capacitances. We have to highlight that simplified models, using only a few R-C cells, do not reflect the placental characteristics: even if such models can show valid results at normal conditions, they cannot reproduce the pathological conditions, evidencing that they do not represent the placental circulation in proper way.

Fig. 4: Diagram of our model.

Our model was firstly applied to study the fluidodynamics of the fetoplacental circulation in the physiological situation, then in pathological situations, associated to infarction of vessels in rising percentage. The obtained graphs, relating to the flow in umbilical arteries and in fetal aorta, in physiological condition, are interesting, because they match exactly the Doppler velocimetry waveforms. So the model revealed itself to be useful to understand the Doppler waves and the various types of empirical pulsatility index used in the medical field.

Fig. 5: Arterial blood flow resulting from the model, physiological status.
Green: Aorta, Red: Umbilical artery.

peak of systolic flow cc/min | 651
end-dyastolic flow cc/min | 116
mean flow cc/min | 291
max. pressure mmHg | 63.3
min. pressure mmHg | 49.6

Table 2: Values related to the arterial umbilical flow resulting from the model.

There is a strong similarity between the result of the model and the collected medical data (variations of the typical data regarding waveforms and adimensional indexes). Moreover some effects and peculiarities of the flow modifications can be better analyzed. They have not yet been investigated enough: they can give prospects of development if experimentally verified.
In particular, increasing the degree of simulated pathology, the model doesn't show a decrease of pulsatility in the umbilical arteries, as wrongly showed by previous models. On the contrary the waveform persists nearly unchanged, and the decrease of the flow at the end of the diastole (minimal value) happens more quickly than the corresponding decrease of the mean flow, according to the clinical data. The variations on the flow parameters are quite weak (lower than the accuracy of the currently used instruments) in case of slight pathological situations (15% of infarction), and the adimensional indexes PI, A/B and RI are not able to express well-timed diagnosis, as their significant shifting from the physiological-considered values happens only in case of pathologies reaching 30, 40% of the placental vessels.
They produce a decrease of the mean flow greater than 10%, corresponding to pathologies that are already effective and compromising the functionality of the placenta.

Fig. 6: The blood flow in umbilical artery increasing the ratio of infarctuation.

Pathology % | PI | A/B | RI
0 | 1.86 | 5.66 | 0.823
14.28 | 1.90 | 5.91 | 0.831
28.56 | 1.99 | 6.34 | 0.842
57.16 | 2.26 | 8.32 | 0.880
71.44 | 2.68 | 11.96 | 0.916
85.72 | 3.89 | -- | 1.002

Table 3: PI, A/B, RI versus ratio of infarctuation resulting from the model.

From the model we noticed an interesting decrease of time delay between heart beat and systolic peak in the umbilical arteries when the pathology worsens.
The course of this delay is quasi-linear. It assumes sizable values (-7%) already with 15% of occluded vessels, thus even before similar variations in the characteristics of the Doppler flow waveforms occur. This phenomenon has not yet been observed in the medical field, but it can be checked by the current instrumentation set, and it is independent by the insonation angle and by the vessel gauge.

Fig. 7: Time delay between heart beat and systolic peak in the umbilical arteries when the pathology worsens, according to our model.

Possible developments of the model will allow various types of analysis: more localized pathologies, pathologies altering the histological structure of the vessels (if able to change their elastic constant), physiological situations not at full term.

The introduction of the tuning system for the cardiac flow versus the arterial pressure is an interesting investigation, that may offer valuable results: the fetal heart tries to compensate too high pressure decreasing the blood flow.
Removing the hypothesis of fixed flow used in our model does not involve any difficulty for the modification of the equivalent electric net, and allows to introduce an optimization work able to give better results. In this way the resulting flow diagrams should be more sensitive to the level of infarction, thus closer to the clinical data.

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Last updated: November 2, 2002.