Study and Validation of a Model
of Fetoplacental Circulation
3.3. Conclusioni Results
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Il lavoro descritto ha lo scopo di portare alla definizione di un valido strumento diagnostico
in grado di rilevare, più tempestivamente di altre metodologie,
patologie fetali e placentari.
Tali variazioni possono essere simulate e valutate con l'ausilio di un
modello, per poi venire confrontate con i risultati di ecografie, abbastanza
precise e diffuse, anche se limitatamente alle sole arterie ombelicali e aorta.
L'obiettivo dello studio non si é limitato alla realizzazione
di un modello, ma si é avvalso di una vasta sperimentazione
che ha contribuito a verificare ipotesi di funzionamento della placenta
proponendo metodi di analisi e misurazione della caratteristiche vascolari.
La sperimentazione condotta presso l'ospedale S. Paolo
di Milano, sviluppata durante circa 50 sedute di prova, ha dato
modo di realizzare un metodo di indagine
preciso per verificare le caratteristiche della fluidodinamica della placenta.
Il circuito di perfusione realizzato ha permesso di attuare una perfusione
controllata della placenta, con parametri di portata di ingresso e di
uscita noti, impiegando sangue bovino come fluido di perfusione.
Le portate d'ingresso con cui sono state svolte le prove erano comprese
tra 100 e 220 cc/min. La pressione arteriosa rilevata è risultata variabile: da 49 mmHg a 187 mmHg per ogni
100cc/min, per una durata media di 15 minuti.
La principale difficoltà incontrata
nasce dal tentativo di alimentare le arterie ombelicali con portate
fisiologiche, poiché si generano pressioni molto elevate. Il
fenomeno è stato riscontrato da tutti gli altri ricercatori, i quali non hanno potuto
raggiungere i nostri valori di portata, neppure utilizzando soluzione fisiologica.
Si è anche evidenziata una notevole reattività della
placenta alla concentrazione di anidride carbonica.
Un ulteriore motivo di interesse si é incontrato nel trasudamento di siero verso l'esterno della placenta.
Il nostro circuito è stato quindi impiegato per una successiva
serie di esperimenti, usando una soluzione di formaldeide
e glutaraldeide. L'analisi
al microscopio delle placente così fissate ha confermato l'ottima
qualità della perfusione, ed ha reso finalmente possibile una misurazione
precisa dei calibri dei vasi in pressione.
Il dispositivo messo a punto si propone dunque come valido ausilio
per uno studio morfometrico della rete vascolare placentare,
a differenza degli studi precedenti nei quali i vasi sono sempre stati
fissati a riposo.
Le misure raccolte sulle placente così perfuse hanno costituito
parte dei dati sui quali é stato basato il modello.
Preliminarmente si è svolto un'ampia ricerca nella letteratura
medica per ottenere tutte le informazioni quantitative sulla morfologia
dei vasi, che confrontata con quanto ottenuto dalle nostre osservazioni,
ha permesso di definire le geometrie di ogni ordine di vaso. Infine si
é realizzata una tabella per il dimensionamento delle resistenze
e delle capacità idrauliche del modello del circolo feto-placentare.
Il modello, realizzato attraverso un circuito elettrico equivalente,
é stato impiegato per studiare la fluidodinamica della
circolazione feto-placentare nella situazione fisiologica e
in situazioni patologiche. I grafici ottenuti
sono esattamente coincidenti con le flussimetrie esistenti.
I grafici relativi alle situazioni patologiche offrono
argomenti di discussione: vengono evidenziati effetti e peculiarità delle modificazioni
dei flussi finora non indagati, offrendo prospettive
di sviluppo qualora questi venissero verificati sperimentalmente.
In particolare, all'aumentare del grado della patologia simulata, non
si è osservata la diminuzione di pulsatilità della portata
nelle arterie ombelicali erroneamente evidenziata da modelli precedenti.
Le variazioni nei parametri di portata
citati sono molto deboli (inferiori alla precisione degli strumenti oggi
in uso) in caso di situazioni patologiche lievi, e gli indici adimensionali PI, A/B e RI
non risultano adatti per la formulazione di diagnosi precoci.
Ci é inoltre parso di estremo interesse la rilevazione della
diminuzione, all'aggravarsi della patologia, del ritardo temporale tra
battito cardiaco e picco sistolico nelle arterie ombelicali. L'andamento
di tale ritardo è quasi lineare, ed assume valori apprezzabili
già con lieve occlusione del dei vasi. Il fenomeno ancora non
è stato osservato in ambito clinico, ma risulta facilmente controllabile
con i mezzi attuali, ed è indipendente dall'angolo di insonazione
e dalla misura del diametro del vaso.
La versatilità del programma
utilizzato ha suggerito inoltre sviluppi per analisi
di vario tipo: patologie più localizzate, patologie che alterano
la struttura istologica dei vasi cambiandone la costante elastica, situazioni
fisiologiche non a termine.
3.3. Results 
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The aim and the achievement of this work have been to
aid the outlining of a valid diagnostic tool, capable to detect fetal and
placental pathologies, more immediately then other already applied techniques.
In fact these pathologies cause variations of some parameters in comparison
to the physiologic situation. Such variations can be simulated and evaluated
using a model, to be then compared with the results of blood flow velocity
waveforms, that are accurate enough and already practised in the medical
field, even if useful only to analyse umbilical vessels and aorta.
The goal of the study was not simply limited to the development of
a model, but it took advantage of a prior huge experimentation that contributed
to verify the hypothesis of placental working, suggesting methods of analysis
and measurement of the vascular characteristics, up to now performed only
in extremely partial way.
The first part is introductory, it is aimed to introduce the elemental
concepts on placental physiology and morphology to engineers. In the second
part of this work the experimentation executed at S. Paolo hospital, Milan,
is described. It has been developed during about 50 sessions, and it permitted
to develop and setup a reliable and accurate method of research. This allowed
to study and verify the characteristics of the human placenta fluidodynamics.
Soon after the childbirth and the drawing 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 concentrations
of oxygen and carbon dioxide of the blood at physiological level.
The circuit realized in this way allowed to perform a controlled perfusion,
with known parameters about input and output flow. The perfusion fluid
was bovine blood, with physical characteristics similar to the fetal blood
ones, instead of alkaline solution, as done by other researchers.
The experiments, performed in this way, averaged a correct perfusion
of the placental vessels during about 15 minutes, generally showing a first
period of stability of the measured data.
The input flows of the tests ranged 100 to 220 cc/min (the physiological
value is about 300 cc/min). The measured arterial pressure was quite variable
from test to test: from 49 mmHg to 187 mmHg per 100cc/min, with an average
of 99 mmHg/100cc/min. The venous pressure was close to the physiological
value: 15 to 20 mmHg.
During the experimentation the main difficulty we met with comes from
the attempt to supply the umbilical arteries with a flow close to the physiological
one, because a very high pressure is generated for a condition of general
constriction of the placental vessels. This phenomenon has 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. Moreover, as it is not possible to simulate
the situation of the intervillous space, increasing the input flow (and
the arterial pressure too) a sudden settling of the capillaries was obtained,
breaking off the test.
The placenta showed also a strong reactivity to the carbon dioxide
concentration: a value lower than the physiological one (40 mmHg) cause
a quick constriction, that breaks off the perfusion within less than 5
minutes from the beginning.
A kind of transudation of serum is an additional reason of interest.
It is proved by the progressive haematocrite increasing showed by the perfused
blood. This phenomenon confirms that a placenta is also a "dialyzer" for
its perfusion fluids.
Our perfusion circuit has been utilised also to perform a successive
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 placentae that have been fixed in this way, confirmed the very high
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.
These miscorrelations are essentially due to the adopted methods of measurement.
So, the developed device can be a valid support for a morphometric
and anatomic study of the placental vascular net, unlike the previous studies,
where the vessels have almost always been fixed and analysed at rest, that
is a not-physiological situation.
The obtained values are part of the data that have been used to design
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
of the hydraulic capacitances of the model of fetoplacental circulation.
The model, realised using an equivalent electric circuit, 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 extremely interesting, because the match exactly the actual
Doppler velocimetry waveforms: they are in favour of the choices that have
been made to develop the mathematical model. So, the model revealed itself
to be useful about a physical interpretation of the Doppler waves and about
the various types of empirical pulsatility index used in the medical field.
The flow diagrams obtained simulating pathological situations give
remarkable discussion points. There is a strong likeness between the result
of the model and the collected medical data (variations of the typical
data regarding waveforms and adimensional index). Moreover some effects
and peculiarities of the flow modifications are emphasized. 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 the previous models. On the contrary the waveform persists nearly
unchanged, and the decrease of the instant flow at the end of the diastole
(minimal value) happens more quickly than the corresponding decrease of
the mean flow, as in the clinical data. The variations on the mentioned
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 index PI, A/B and RI are not able to express well-timed
prenatal 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.
Moreover 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 sizeable 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.
The model shows a substantial correspondence with the vascular structure
of the fetoplacental cardiocirculatory system. It allows not only to make
comparisons with already known results and methods, but it gives way to
bring an original contribution suggesting more accurate and suitable diagnosis
methods.
The flexibility and the powerful computational skills of the program
used for the analysis of the electrical net suggest important possible
developments for various types of investigation: more localised pathologies,
pathologies altering the histological structure of the vessels (if able
to change their elastic constant), physiological situations not at term.
The introduction of the tuning system for the cardiac flow versus the
arterial pressure is an interesting investigation, that may offer valuable
results. To remove the hypothesis of fixed flow does not involve any difficulty
for the modification of the equivalent electric net, and it allows to introduce
an optimisation work in order to obtain results closer to the real situation.
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Last updated: October 1, 2003