3.2. Risultati del modello Results of the Model |
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3.2. Results of the Model |
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3.2.1. Physiological Situation |
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systolic peak of flow cc/min |
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end-diastole flow cc/min |
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mean flow cc/min |
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max pressure mmHg |
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min pressure mmHg |
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3.2.2. Pathological Situations |
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In figure 81, the obtained curves have been analyzed simulating generalized pathologies affecting low percentages (lower than 15%) of villi: qualitatively the variations compared to the physiological situation are quite little, difficult to be noticed with the modern diagnostic systems.
Increasing the pathological situation (pathology of 30% of the villi
of cotyledons), in the model, some changes appear (see figure 82):
1, lessening of the systolic peak of flow in the umbilical arteries
(about -3%),
2, lessening of the value of flow at end-diastole, more evident than
in aorta (about -35%),
3, lessening of the medium flow (about -10%),
4, accentuation of the slope down in the umbilical arteries.
Simulating pathologies that affect 60% or more of the villi, the model shows stronger changes compared to the physiological situation (see figure 83):
1, halving of the capacity at end-diastole in the umbilical arteries,
2, appearance of retrograde flows in aorta,
3, further lessening of the medium flow (about - 20%).
The diagrams show that the placenta, also without regulation systems,
can sustain light anomalous situations that are commonly found at the term
of gestation. In particular we noticed that the placenta, an extremely
primitive organ but however over-dimensioned, at least from the haemodynamic
point of view, compensates pathologies that affect up to 15-20% of the
villi.
Figure 85 allows to compare the results of the model.
An interesting aspect of the waves of flow in the umbilical arteries obtained from the simulation is maintenance of their shape: the pulsatility does not change appreciably, and only in case of important pathologies (affecting at least 35% of cotyledons) there is a sort of rounding towards the bottom of the diastolic arc.
The waves of pressure calculated by the model show an increment already with pathologies of 20-30% of vessels. Such changes affects the blood circulation: in a real situation, characterized by a system of regulation of the arterial pressure (still not introduced into our model), the cardiac capacity would decrease, with consequent remarkable worsening of the blood oxygenation. It is not yet possible to carry out clinical verifications on this particular effect, since the measurement of the arterial pressure of a fetus is strongly invasive.
Differently from the results obtained by the models previously developed, also in case of pathologic situation the waveforms of flow match with the velocimetries (supplied by dr Enrico Ferrazzi of the San Paolo hospital of Milan), as evidenced by the figures 87 and 88.
Comparing the first velocimetry (the placenta, dissected after the childbirth, had infarct of 5% of the tissue dedicated to the exchange of gases) with that physiological one there are not strong differences. The second one refers to a pathological situation more serious (infarct of 12% of the parenchyma), and the peak at end-diastole is almost not detectable.
The following tables 33, 34 and 35 summarize the data of the simulation.
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Generally adimensional indices are used by physicians (cf. 1.3.3).
The advantage is the possibility to quantify in simple way morphologic
data of the diagrams, obtaining values independent from the insonation
angle.
The diagrams of figures 89, 90
and 91, obtained by the model, show the how such indices
and other values of the curves of flow and pressure change with the level
of pathology.
The model, also under this aspect, supplies results matching with they
data in literature [34], even if on the physiological
values of such indices there is not a full agreement between the researchers.
Commonly the following limits are accepted [34]:
PI 0.65 to 2.8 (Reuwer)
RI 0.6 to 0.9 (Arbeille)
A/B 2.1 to 6.4 (Stuart).
Other authors think that the physiological situation is characterized
by a lower pulsatility index (PI < 2).
The values obtained with the simulation are summarized in table 36.
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In the model there is an increment of all the indices increasing of
the percentage of interrupted rami, as in the real case.
We carried out further calculations, changing the resistances of the
chorionic arteries or of the stem-villi only, in order to execute a comparison
with a previous simulation [45] that considered
this type of localized pathology, but the results are not significative.
The diagram of figure 92 allows to compare the variations
of the flow in the umbilical arteries due to a doubling of the mentioned
resistances. The differences are small. The increase of the resistances
of vessels of the chorionic plate cause greater variations respect to a
similar increase of the resistances in the stem-villi. Since the minimum
(flow at end-diastole) does not change, the index PI is almost unchanged.
The increase of 70% of the resistance of the terminal villi does not produce
meaningful variations.
Type of pathology | Syst. peak
cc/min |
var.
% |
end-diast.
cc/min |
mean flow
cc/min |
var
% |
PI |
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Still considering figure 85, the reduction of delay of the peak of systolic flow in the umbilical arteries versus its generation by the cardiac contraction is an element of interest. It is resulting by the model but still not confirmed. The diagram of figure 93 shows this result.
The phenomenon is not depending on the particular values assigned to
geometries of vessels, but it is due to the complex structure of the hydraulic
network, constituted by a long series of filter elements. We also tried
to determine which the importance of a variation of the diameters of the
vessels of the chorionic plate, since the values used in the model, obtained
from the literature [20][25],
could still not be confirmed by the analyses done on the placentas perfused
with formalin.
For this reason we carried out a simulation (Monte Carlo analysis)
introducing random variations of the resistances of the chorionic arteries
and the trunci, within a tolerance of 70%: the figure 94,
evidencing that the situation is substantially unchanged, confirms the
results of the model.
Therefore we think that it would be opportune to execute a clinical
verification of this phenomenon through a synchronization of a echo-Doppler
examination of the umbilical arteries with a fetal electrocardiogram
(FECG): the instrumentation generally available in a hospital should allow
to perform this examination in a non-invasive way.
In case the data on the shortening of the systolic delay was confirmed,
we would probably obtain an instrument more reliable than the adimensional
indices, finally able to perform early diagnoses. This type of analysis
is still independent from the angle of insonation Doppler, and is easy
to perform. Moreover the reduction of the systolic delay in function of
the level of pathology of the placental villi is appreciable also for low
percentages (see table 38).
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The developed model did not introduce any feedback circuits. In the
real situation the system fetus-placenta has several systems of regulation,
in particular:
1, The placental vessels change their geometry and resistances in function
of the partial pressures of gases;
2, The fetal nervous system is able to change the cardiac flow in function
of the arterial pressure;
3, It is proved that the blood viscosity is increased by placental
pathologies.
These elements, not completely known, can affect the pathological situation.
The increased blood viscosity and the regulation of the arterial pressure
cause a bigger change of the parameters.
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